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II.  Carnap and Pseudoproblems

Auch wir haben "Bedürfnisse des Gemüts" in der Philosophie, aber die gehen auf Klarheit der Begriffe, Sauberkeit der Methoden, Verantwortlichkeit der Thesen, Leistung durch Zusammenarbeit, in die das Individuum sich einordnet.
          Rudolf Carnap, Die logische Aufbau der Welt, 1928; epigraph in A Parting of the
          Ways: Carnap, Cassirer and Heidegger
, Michael Friedman, 2000

We too, have "emotional needs" in philosophy, but they are filled by clarity of concepts, precision of methods, responsible theses, achievement through cooperation in which each individual plays his part.
          Rudolf Carnap, The Logical Structure of the World, translated by Rolf A. George, 1967

1.  What Carnap Wants to Do to Heidegger and Others   
2.  What Words and Sentences Mean   
3.  How to Reason One's Way to Meanings
  
4.  Metaphysical Words Without Meanings  
5.  Carnap Confronts Heidegger  

1.  What Carnap Wants to Do to Heidegger and Others 

1.1  At roughly the same time as Martin Heidegger was writing Sein und Zeit, Rudolf Carnap was writing Die logische Aufbau der Welt.  A few years later, in an article called "Überwindung der Metaphysik durch Logische Analyse der Sprache"(Erkenntnis II, 1932),Carnap used some passages from Heidegger's Was ist Metaphysik? as an example of the use by some philosophers of what he called metaphysical pseudo-statements.  The article was translated into English by Arthur Pap with the title. "The Elimination of Metaphysics Through Logical Analysis of Language" (in Logical Positivism (1959), edited by Alfred Ayer).  The passages by Heidegger quoted by Carnap read in the translation by Pap:

What is to be investigated is being only and -- nothing else; being alone and nothing further -- nothing; solely being, and beyond being -- nothingWhat about this Nothing?  . . .  Does the Nothing exist only because the Not, i.e. the Negation, exists?  Or is it the other way around?  Does Negation and the Not exist only because the Nothing exists?  . . . We assert : the Nothing is prior to the Not and the Negation.  . . .  Where do we seek the Nothing?  How do we find the Nothing?  . . .  We know the Nothing  . . .  Anxiety reveals the Nothing.  . . .  That for which and because of which we were anxious, was 'really' -- nothing.  Indeed : the Nothing itself -- as such -- was present.  . . .  What about this Nothing?  . . .  The Nothing itself nothings.

Carnap proposes to show that forming such alleged pseudo-statements becomes possible because of a logical defect of language. 

1.2.  In the translation of Was ist Metaphysik? by David Farrell Krell which appears in Martin Heidegger, Basic Writings (1977), the passages quoted by Carnap read as follows :

What should be examined are beings only, and besides that -- nothing; beings alone, and further -- nothing; solely beings, and beyond that -- nothing.  What about this nothing?  . . .  Is the nothing given only because the "not", i.e., negation, is given?  Or is it the other way around?  Are negation and the "not" given only because the nothing is given?  . . .  We assert that the nothing is more original than the "not" and negation.  . . .  Where shall we seek the nothing?  Where will we find the nothing?  . . .  we do know the nothing  . . .  Anxiety reveals the nothing.  . . .  that in the face of which and for which we were anxious was "really" -- nothing.  Indeed: the nothing itself -- as such -- was there.  . . .  How is it with the nothing?  . . .  The nothing itself nihilates.

In the original German, from Wegmarken (1978, 2nd edition; 1st was 1967), the passages are :

Erforscht werden soll nur das Seiende und sonst -- nichts; das Seiende allein und weiter -- nichts; das Seiende einzig and darüber hinaus -- nichts.  Wie steht es um dieses Nichts?  . . .  Gibt es das Nichts nur, weil es das Nicht, d. h. die Verneinung gibt?  Oder liegt es umgekehrt?  Gibt es die Verneinung und das Nicht nur, weil es das Nichts gibt?  . . .  Wir behaupten das Nichts ist unsprünglicher als das Nicht und die Verneinung.  . . .  wir kennen das Nichts  . . .  Die Angst offenbart das Nichts  . . . wovor and worum wir uns ängsteten, war "eigentlich" -- nichts.  In der Tat: das Nichts selbst -- als solches -- war da.  . . .  Wie steht es um das Nichts?  . . .  Das Nichts selbst nichtet.

1.3.  In German, "nothing" is das Nichts (noun) or nichts (adverb), and das Nicht (noun), translated by Krell as "the 'not' " correlates with nicht, "not" (adverbs).  Heidegger indicates that he is using das Nicht as a synonym for Verneinung, "negation", "saying no to", or (to coin a word) "not-ing" (not "noting", from note, but "not-ing", from not), and presumably not as a synonym for Vernichtung, which can be translated by "annihilation", "destruction", "extermination", etc., depending (as usual) on context.  Not-ing is saying or thinking "not", as in "Heidegger is not here" or "Heidegger was not all there", or symbolically as in the logical formula ~(~p) = p, i.e., negation of negation of a proposition p gets us back to the proposition p we started with.  It will give some idea of one of the difficulties which arise in connection with terms of this sort can be seen by contrastinh how negation of negation (double negation) works in formal logic versus how it works in everyday English. The statement p = "He cannot do nothing" will, according to common usage, usually be taken to mean the same as q = "He cannot not do something", so let's try setting set p = q, where "=" translates as "has the same meaning as" (this assumes we have in mind some meaning for "meaning").  (Actually, "He can't do nothing" often is taken to mean something more like "He must do something", in which there has been a shift from the modal "can" to the modal "must", but I will ignore this complication).  Suppose now we try to construct English versions of the double negations of p and of q by extending the use and interpretation of the negation sign ~ as follows.  Let's imagine moving the negation sign ~ from left to right through q, and whenever we get to a "not" in the English substitution for q, we erase the "not", and then stop using the sign ~ for that pass.  Then for ~q, we get "He can not do something", by erasing the first "not" in "He cannot not do something".  Applying the same rule again to ~q, we get ~(~q) = "He can do something".  On the other, doing this for p, we get for ~p "He can do nothing", and for ~(~p) we get -- well, we get "He can do hing", and "hing" is not an English word.   Something has gone wrong.  Several possible moves occur to me which might remedy this situation, but let this serve as a wake-up call to investigate how dealing with negations and nothings can lead to curious results.  For example, we might argue that "hing" in English doesn't mean anything, so it means nothing.  But aside from this being a possibly irritating little joke, if we did this we would get ~(~p) = "He can do nothing", so ~(~p) = ~p,  To make matters even more complicated, in some contexts and some dialects in English, "He can't do nothing" is customarily taken to mean "He cannot do anything".  Also, the use of double negatives is different in different languages.  In Spanish, for example, the double negative in "Él no puede hacer nada" translates as "He cannot do anything" in the sense of "He cannot act", not as the more literal "He cannot do nothing" in the sense of "He can (ought to, must) act". 

1.4.  I note that in the English language, besides being used as an adverb or an (apparent) noun, the term  "nothing" can also be classified as a pronoun, where it may be taken to stand for "no thing", as in one interpretation of "the dead feel nothing".  Here we don't intend to say that the dead feel (or feel something), nor do we intend to name an entity or a nonentity that the dead feel.  We may take it that here "nothing" is used as a noun-like word in place of a noun, i.e. as a pronoun, and that the sentence "the dead feel nothing" means the same as the sentence "the dead do not feel".  However, "nothing" might also be taken in some contexts as a noun or name for, "no thing", where "no thing" is taken to mean "something other than a thing", the term "thing" having been previous been restricted to refer to physical objects (defined in some way) or to phenomena of some specified kind.  I note in passing that "nothing" is sometimes used misleadingly to refer to the number (or numeral) zero, but while this involves another story  Also "nothing" may be used as an adjective, as in "that nothing statement", where "nothing" means something like "worthless".  Or the term "nothing" may be used to mean "something that doesn't exist", as in "the primeval nothing", which might be used when talking about a creation ex nihilo, which means -- well, it means a creation out of nothing.

1.5.  It appears to be easier in English translations than it is in the original German to wonder if Heidegger is involved with a pun on the term "nothing", viz., merging "nothing"  with "no-thing", i.e. "no thing", and with "not a thing", and also with what I have called not-ing, negation.  From this standpoint, it appears that Heidegger might be interpreted as saying something like this:  Being (Sein mit Temporalität) (or Is-ingness as I have called it) is different from being and beings (Seiende, Seiendes, Seienden, etc.), since Being is in no way an instance of the things or beings or kind of being we experience in our everyday lives as or by way of Dasein (maybe in the manner of Heidegger, we should coin "by way of Daseiende", i.e., "being-in-the-world-ing").  It is likely too naive to suggest that Heidegger is saying that the things (whatever they are) of our everyday lives are perceivable and conceivable by humans, perhaps in some Kantian manner, but Being, like Kant's noumenon, cannot be perceived or conceived in such a manner, and must be disclosed or open up to us in some other way to or because of our Dasein, our daily being, our being-here-and-there.  That would be rather a commonplace claim, theologically speaking.  Or is he perhaps elevating the negation maneuvers present in languages and logics into a device for annihilating Being and Time as they have been presented by metaphysicians up to his time, and getting at a new Being and Time (or an ancient Greek original Being and Time) to replace older and (he hopes) obsolete Beings and Times?  

1.6.  On the other hand, so far as Heidegger having been affected by formal logic (or any other kind of logic) in his use of das Nicht or die Verneinung, Vincent Vycinas says in Earth and Gods, referring to what Heidegger says in Was ist Metaphysik? :

Heidegger thinks Being.  Being cannot be thought logically.  In its primary phase logic was a thinking interpretation of the experience of Being; but from the time of Aristotle, logic degenerated into an instrument which is no longer related to Being, but "binds itself to the calculation of beings only and exclusively serves them alone."  Heidegger transcends logic in the traditional sense, because he thinks Being and not of beings.

1.7.  The battle is joined.  According to the interpretation of Vycinas, Heidegger says that thinking Being is not done rationally, if one considers that what is rational must involve use of some kind of logic of the sorts that have descended from that described in Aristotle's Organon.  And in fact, in What is Metaphysics? (as translated by Krell), Heidegger says : 

Are we allowed to tamper with the rule of "logic"?  Isn't intellect the taskmaster in this question of the nothing?  Only with its help can we at all define the nothing and pose it as a problem -- which, it is true, only devours itself.  For the nothing is the negation of the totality of beings; it is nonbeing pure and simple.  . . .  Is the nothing given only because the "not," i.e., negation, is given ?  Or is it the other way around?  Are negation and the "not" given only because the nothing is given?  . . .  We assert that the nothing is more original than the "not" and negation.

Heidegger seems here to be proposing that people would never have able to negate in languages if there weren't a referent, or at least a sense, which can be attached to the word or concept of das Nichts, "the Nothing", or "Nothingness".

1.8.  Talking about Being cannot be done without using language, says Heidegger.  If talking is defined to be use of language, this is OK, since it is tautologous.  But according to Heidegger (and mystics) language -- at least ordinary (daseinische?) language -- gets in the way of disclosure of Being (Is-ingness), though Heidegger has argued that the language of certain poets (especially German poets) can provide a path to thinking Being.  On the other hand, Vycinas has a footnote in which he advises against saying in English "thinking of Being", or the like, to indicate what Heidegger is driving at, since Heidegger doesn't have some kind of subject-object relationship in mind.  It seems rather that what Heidegger wants is a unio mystica, a kind of communion with a non-deistic and non-theological but God-like Being.


2.  What Words and Sentences Mean

2.1.  In the light (or darkness) of this discussion of Heidegger's use of nothing, I turn now to a consideration of Carnap's arguments against the propriety of Heidegger's use of language when he does metaphysics.  Carnap says, in Pap's translation:  "A language consists of a vocabulary and a syntax, i.e. a set of words which have meanings and rules of sentence formation."  Sentences, or statements, are sequences of words.  What are words, and what are meanings of words?  Carnap says:

The researches of applied logic or the theory of knowledge, which aim at clarifying the cognitive content of scientific statements and thereby the meanings of the terms that occur in the statements, by means of logical analysis, lead to a positive result and to a negative result.  The positive result is worked out in the domain of empirical science; the various concepts of the various branches of science are clarified; their formal-logical and epistemological connections are made explicit.  In the domain of metaphysics, including all philosophy of value and normative theory, logical analysis yields the negative result that the alleged statements are entirely meaningless." 

In the original German, this passage reads as follows:

Die Untersuchungen der "angewandten Logik" oder "Erkenntnistheorie", die sich die Aufgabe stellen, durch Logische Analyse der Erkenntnisgehalt der wissenschaftlichen Sätze und damit die Bedeutung der in den Sätzen auftretenden Wörter ("Begriffe") klarzustellen, führen zu einem positiven and zu einem negativen Ergebnis.  Das positive Ergebnis wird auf dem Gebiet der Empirischen Wissenschaft erarbeitet; die einzelnen Begriffe der verschiedenen Wissenschaftszweige werden geklärt; ihr formal-logischer and erkenntnistheoretischer Zusammenhang wird aufgewiesen.  Aus dem Gebiet der Metaphysik (einschliesslich aller Wertphilosophie und Normwissenschaft) führt die logische Analyse zu dem negativen Ergebnis, dass die vorgeblichen Sätze dieses Gebietes gänzlich sinnlos sind.

2.2.  In this passage Pap translates "der in den Sätzen auftretenden Wörter ("Begriffe")" as "the terms which occur in the statements", thus rendering "Wörter" ("Begriffe") by "terms".  (It is notably awkward to say that Pap translated the words Wörter ("Begriffe") by the word "terms", or by the term "terms".)  Elsewhere, Pap translates "Wörter" by "words".  I conjecture that by using "terms" instead of "words (concepts)", Pap might have intended to capture Carnap's easy identification of words with concepts.  This identification might be taken to be a weakness, insofar as relations of words to concepts have been for a long time much debated not only by philosophers, but by linguists, psychologists, cognitive scientists, literary theorists, and others.  At the beginning of his Aufbau, Carnap makes a similar kind of identification.  Having defined object as "anything about which a statement can be made", he without comment uses the term "concept" where one would expect him to use the term "object" which he has just defined.  On this point, Alan W. Richardson says in his book Carnap's Construction of the World (1998) (following Michael Friedman, Richardson translates the word konstruieren as "to constitute" rather than following Rolf A. George who used "to construct" in his translation of the Aufbau)

It may seem that Carnap is sloppily moving back and forth between the view that objects are constituted and the view that concepts are constituted in these passages.  In a sense, he is doing just that, but he will soon argue that it is a matter of indifference just how one expresses this point: "Fundamentally it isn't at all a matter of the different views, rather only of two different interpretative modes of speech."  What matters for Carnap is not the domain of constitution, but constitution itself.  His primary goal is to demarcate the philosophical difference between what he calls constitution and both realistic and idealistic conceptions of concept formation or object construction.  The important difference is that constitution is a purely logical relation.

2.3.  In this regard, in his article "Carnap's Aufbau Reconsidered" (1987), Michael Friedman argues that a fundamental aim of Carnap's was to point the way to a construction "of all concepts of science through purely structural definite descriptions."  Friedman observes that the method which Carnap has in mind for this elimination is that of implicit definition.  This is a technique made familiar to mathematicians by David Hilbert in his Grundlagen der Geometrie, first edition 1899.  It is explained as follows by Paul Bernays in his article "Hilbert's significance for the philosophy of mathematics" (1922) :

Reliance on spatial representation is completely avoided here, not only in the proofs but also in the axioms and the concepts. The words "point," "line," "plane" serve only as names for three different sorts of objects, about which nothing else is assumed directly except that the objects of each sort constitute a fixed determinate system. Any further characterization is carried out only through the axioms. In the same way, expressions [such as] "the point A lies on the line a" or "the point A lies between B and C" will not be associated with the usual intuitive meanings; rather these expressions will designate only certain, at worst indeterminate, relations, which are implicitly characterized only through the axioms in which these expressions occur.  [Author's Footnote: One speaks in this sense of implicit definition.]

According to this conception, the axioms are in no way judgments that can be said to be true or false; they have a sense only in the context of the whole axiom system. And even the axiom system as a whole does not constitute the statement of a truth; rather, the logical structure of axiomatic geometry in Hilbert's sense -- analogously to that of abstract group theory -- is a purely hypothetical one. If there are anywhere in reality three systems of objects, as well as determinate relations between these objects, such that the axioms of geometry hold of them (this means that by an appropriate assignment of names to the objects and relations, the axioms turn into true statements), then all theorems of geometry hold of these objects and relationships as well. Thus the axiom system itself does not express something factual; rather, it presents only a possible form of a system of connections that must be investigated mathematically according to its internal properties.  Accordingly, the axiomatic treatment of geometry consists in separating the purely mathematical part of knowledge from geometry, considered as a science of spatial figures, and investigating it on its own in isolation.  The spatial relationships are, as it were, projected into the sphere of the mathematical-abstract in which the structure of their connections appears as an object of pure mathematical, thought.  This structure is subjected to a mode of investigation that concentrates only on the logical relations and is indifferent to the question of the factual truth, that is, the question whether the geometrical connections determined by the axioms are found in reality (or even in our spatial intuition).

This sort of interpretation of the axiomatic method presented in Hilbert's "Foundations of Geometry" offered the particular advantage of not being restricted to geometry but of being directly applicable to other disciplines.  From the beginning, Hilbert envisaged the point of view of the uniformity of the axiomatic method in its application to the most diverse domains, and guided by this viewpoint, he tried to bring this method to bear as widely as possible. In particular, he succeeded in grounding axiomatically the kinetic theory of gases as well as the elementary theory of radiation in a rigorous way.

2.4.  I infer, provisionally, that we may take it that if Carnap's program could be carried out, then it would make no logical difference whether the instances of variables (objects, elements of domains) in his purely logical statements of relations are interpreted as words, considered as consisting of sequences of sounds or signs (symbols, characters, hand gestures, etc.), or as concepts which these sequences represent or trigger in minds or brains. Nor will it make any difference what the ontological status of such concepts may be, such as, for example, Platonic ideals or Kantian constructions or Husserlian phenomena or sense data or neural states.  However, for scientific purposes, the words used would have to be in some way traceable to or derivable from (human) experiences. This, I take it, is an important feature of Carnap's claim in his Erkenntnis article to have found a method of eliminating metaphysics.  From this point of view, one might think of the first phrase of the title, "Überwindung der Metaphysik", as being translated by "Overcoming of Metaphysics" rather than "Elimination of Metaphysics".  Thus one can speculate that Carnap's program, if it could be carried out, might provide a method for dealing rationally (logically) with metaphysical views as well as physical or phenomenological views, although what Carnap comes to call meaningless words would occur in metaphysical statements; roughly speaking, these would be words or terms (especially nouns) which could not be traceable to, or derivable from, certain basic sentences based on intersubjective human experiences, i.e. experiences which are potentially open to all (unimpaired) humans.  However, there are certain parts of traditional metaphysics which would be eliminated according to Carnap's scheme, namely those statements which are syntactically ill-formed, as discussed below.

2.6.  Hilbert's technique has been forcefully criticized in various ways, for example by Gottlob Frege.  In the Hilbert procedure, such terms (or logical variables) as "point" and "line" are called undefined terms.  These terms are said to be implicitly defined by axioms, axioms being statements of some sort of pure logic which prescribe the rules for manipulating these terms in the particular system (or model) at hand, such as euclidean geometry (using real numbers), or one of the non-euclidean geometries, or arithmetic.  In this regard, when I taught geometry of various kinds, I used to tell students that one can say that if we interpret points as, say, astronomical objects, and lines as (straight) light beams, then we can try applying Hilbert's axioms to stars, planets, comets, meteors, etc., and to (non-relativistic) beams of light.  However, I told them that, while this may be rather charming to think about, they won't get very far in the study of geometry unless they interpret (or visualize or intuit) points as little bitty marks (maybe even 0-dimensional), and (straight) lines as edges of tables (maybe infinite in length, or at least always extendable), or as some abstractions or idealizations corresponding to such interpretations (perhaps, as one says, interpretations in one's mind, as contrasted with what we see, feel, etc.)   If it is fair to say that something along these lines is what Frege meant by defining such terms as "point" and "line" before they are used in axioms, then I suppose I am agreeing with Frege in his criticism of Hilbert's proposal for founding geometry and other scientific enterprises.  Still, it was very pleasant to be able to avoid getting into frustrating discussions about what points and lines really (or ideally) are by asking students to simply ignore such philosophical problems for purposes of doing geometry in the way mathematicians do, and just to be sure that they only use the terms in the way prescribed by the axioms and subsequent theorems, using valid maneuvers of (standard, Aristotelian) logic, so far as they could detect such valid maneuvers without much study of formal logic (but with some study of such logic).  

2.7.  In my experience, most mathematicians other than some working in foundations of mathematics make a philosophically crude distinction between implicit and explicit definitions.  A term is taken as implicitly defined if it appears in a set of axioms, and if no statements about what the term signifies are taken explicitly into account in deriving theorems from these axioms.  However, it is clear enough that in practice, one cannot avoid taking some kind of significations of the term into account if the term has agreed on significations in ordinary language.  Mathematicians often speak of such significations has having intuitive meaning, without trying to explain what they mean by intuition.  A term is said to be explicitly defined if it is satisfactorily introduced by statements which only depend on previously defined terms in some logically and grammatically satisfactory or acceptable way .

2.8.  It appears that in his Aufbau, Carnap aimed to lay down a scheme for making scientific statements depend only on their logical form, in some way independent of what the names of objects -- the names of objects -- which occurred as instances or substitutions in these statements were interpreted, so long as in some way the objects were traceable to or were founded on (human) objective or empirical experiences, of the sort that can be shared among (unimpaired) humans .  For example, objects could be interpreted as physical entities in some objective or intersubjective way, or as concepts of some kind derived from intersubjective experiences, or as words with sharable meanings, or as being derivable from some basic physical or mental entities of this sort, to which words refer.  I note that this leaves open the possibility that one might apply Carnap's proposed scheme for intersubjective experiences to subjective or presumably private experiences, which would seem to let his system, if successful, be applicable to metaphysical and/or theological experiences or concepts.  However, passing this by for the time being, and confining ourselves (hopefully) to intersubjective experiences or concepts, it appears that at least for purposes of communication, words must be used, so to find allowable words, i.e. words with (sharable) meanings, it will be desirable to distinguish words with meanings from meaningless words.

2.9.  It seems that Carnap has, without mentioning it, restricted himself to words (terms) which appear in written form.  He makes no mention of the kind of distinctions one makes between spoken words and written words, between speech acts and written acts (or writing as result of acts), nor does he speak about the use of facial expressions and body movements, or different stresses on some particular sounds in spoken language conveying different meanings, and whatever else goes with spoken language.  Nor does he take into account here, in connection with written words, uses of punctuation or other written symbols as conveying or affecting meanings of words.  Nothing is said about meanings which can be conveyed or triggered by symbols or activities other than words, e.g., graphs, private or public images or pictures, sign languages for the deaf, blinking lights, private or public moving objects, etc.  In short, it appears that Carnap has in mind construction (or constitution, as some say) of a language, a method of recording and communicating, with units of meaning of a special kind.  What kind of units of meaning?

2.10.  Carnap starts with units he calls Wörter, i.e. words, and he proceeds by showing how he proposes one should go about finding a meaning for the word "stone".  The quotes here may be taken to indicate that "stone" should be interpreted orthographically, and that we should suspend questions of meaning, so far as possible, and concentrate on the string of symbols, which here are five letters in a certain alphabet.  This is somewhat what one does when looking the term up in a dictionary.  I do not intend to use a dictionary to find an authoritative meaning for the string "stone", but I will trust a competent lexicographer to have recorded some ordinary or technical or colloquial or metaphorical or obsolete usages he or she has found.  As far as I can see, and as I will talk about later, to find a meaning for a word by Carnap's method, I have to start with some notion of how the word has been applied.  In a certain unabridged Merriam-Webster dictionary published in the year 2000, a version of which I have loaded into my computer, the word "stone", taken as a noun (and not a verb or adjective or adverb, which I also could do) is defined as follows :

1 : a concretion of earthy or mineral matter of igneous, sedimentary, or metamorphic origin: a (1) : such a concretion of indeterminate size or shape : BOULDER, PEBBLE *stones rolling down the hill* *gathering stones on the beach* (2) : the substance of this concretion : ROCK *the mountain is solid stone* *trees turned to stone in the petrified forest* b : such a concretion mined, quarried, or shaped in a definite form or size or for a specified function: as (1) : a building block *demolish the structure a stone at a time* (2) : a paving block : COBBLESTONE *building barricades of the very stones of the streets* (3) : a precious stone : GEM (4) : a mineral matter used for a particular ornamental or commercial purpose *ornaments made of the rarer stones * banded slate, rose quartz, steatite American Guide Series: New Jersey* (5) : a pillar or block of stone set as a monument or sign; especially : GRAVESTONE *the burying ground, where you can find the stones of veterans of the Revolution J.P.Marquand* (6) : a rounded missile fired from an arm or a sling *six stones for his sling* (7) : a shaped piece of rock used in a feat of strength (as curling) (8) : MILLSTONE (9) : GRINDSTONE (10) : WHETSTONE (11) : a stand or table with a smooth flat top on which to impose or set type called also surface (12) : a surface upon which a drawing, text, or design to be lithographed is drawn or transferred (13) : a watch jewel
2 : something resembling a small stone or pebble in shape, composition, or hardness: as a (1) : CALCULUS 1a (2) : a hard natural growth (as an otolith) found in an animal b : TESTIS c : HAILSTONE d (1) : the hard central portion of a drupaceous fruit (as a peach) (2) : a hard stonelike seed (as of a date)
3 plural usually stone : any of various units of weight ranging from 4 to 26 pounds: as a : an official British unit equal to 14 pounds b : a British unit for meat equal to 8 pounds called also Smithfield stone
4 : any of the colors common in stone or weathered rock see DEEP STONE, HONEY 6, LIGHT STONE, STONE GRAY
5 : CHINA STONE, CORNISH STONE
6 : a small crystalline contamination in glass comprising unmelted batch material or a particle of the melting vessel
7 : a playing piece used in backgammon

2.11.  The capitalized terms in the above definition give computer links to other terms in the dictionary.  I ask now, in what way can the first criterion given by Carnap for the meaning of a word be interpreted as applying to some part of this dictionary definition?  The criterion appears not to be applicable at all as it stands, since in order for a meaning of a word to be arrived at, one must first have imbedded the word in what Carnap calls an elementary sentence (Elementarsatz).  In the present case, the elementary sentence given by Carnap translates as "x is a stone".  I will now entertain for a moment the conjecture that one might be able to determine a meaning for a word without embedding it in a sentence (statement, proposition), and thus avoid starting off with a dictionary definition.  One way might be to use verbal association, i.e. by seeing what other words or phrases or sentences occur to a person when a given word is presented to this person.  Although this recalls the word association tests used by psychoanalysts, I don't intend such associations to be interpreted as subconsciously generated or to be generated as quickly as possible -- any kind of unassisted generation will do, whatever any particular psychological or physiological theory may say about how the generation occurs.  In such an exercise, one will not be determining a meaning of the sort one may find from a dictionary definition (unless, perhaps, one is engaging in lexicography).  Still, there is a kind of relationship between a word and what is associated with this word by a person in this way.

2.12.  So here goes, with me as the person associating with the word stone:  hard, pebble, throw, hit, hurt, watch out, gravel, driveway, gullets of some birds, minerals, collecting . . . . .  I will stop here.  A moment ago, the word stone triggered in me certain responses.  I will now repeat the exercise for stone:  hard, minerals, stalactite, amazonite, stone cold dead in the market, rolling stones, punishment by stoning . . . . .  I have generated a different list, although a couple of terms occur in both lists.  These lists are peculiar to me at this place and time, and if another person performs a similar maneuver (especially without having seen my results above recently), the chances are very good that quite different lists will be generated.  It is amusing for me to speculate that the terms minerals and collecting in the first list, and the name amazonite in the second list, were generated by me because at one time I was an avid mineral collector.  The occurrence of stalactite in the second list might have been triggered because I was wondering for an instant whether or not a stalactite qualifies as a stone or not, a question I would be tempted to answer by looking at the dictionary definition of "stone" I gave, and comparing it with the definition of "stalactite" in that dictionary.  I wouldn't be overly trustful of the result, though, since a look into some geological treatises might reveal to me that certain experts have had an attitude different from the one the lexicographers who compiled that dictionary had.  My dictionary defines "stalactite" as a deposit of calcium carbonate resembling an icicle.  Here is a definition of "stalactite" from a glossary of geological terms found on the Internet: "A mineral deposit (speleothem) which hangs downwards from a roof or wall of a cave."  A "speleothem" is defined as:  "A deposit formed in caves when calcium carbonate (CaCO3) or some other mineral precipitates from drips or thin films of water."  Now the dictionary definition of "stone" I gave above has as a primary meaning for this term:  "a concretion of earthy or mineral matter of igneous, sedimentary, or metamorphic origin."  (The geological glossary does not give a definition of "stone", which suggests that the geologist(s) who compiled it didn't regard "stone" as a technical term used by geologists).  So, given that "precipitation" is a kind of "sedimentation", and given that we trust the dictionary and glossary I used, we may conclude that a stalactite is a stone, or that "stalactite" is a name for a kind of stone.  However, I can imagine a person saying "I don't care what your dictionaries and glossaries say, I don't call a stalactite a kind of stone."  What do I do then?  (I will drop this line of thought.)

2.13.  To get back to finding meanings by word association, the term stalactite may have occurred to me in connection with the word "stone" because I was moved to think of some names of minerals, and the pronunciation of the term "stalactite" sounded (within me, somehow) like the name of a mineral.  In fact, immediately after I listed stalactite, the question flashed in me of how legitimate it was to think of a stalactite as a stone, so I next recalled what I was (and still am) sure is the name of a mineral, viz. "amazonite".  I will refrain from further analysis of my lists, and ask myself whether or not this technique has yielded some kind of meaning (to me, at least) of the term "stone".  My answer is, yes, something about the meaning of this word, for me, has been revealed to me.  However, this technique will not do for the sort of thing Carnap evidently has in mind.  Why not?  For one thing, such lists are not time invariant, even for one and the same person.  For another, they are not person invariant, and will vary from person to person.  I take it that the kind of meaning for a term that Carnap has in mind must be both time and person invariant, something objective or at least intersubjective.  Now to start finding a meaning for "stone" using Carnap's procedure, I am asked by him to imbed the word in the elementary sentence "x is a stone", and then to consider replacements for x until I find a sentence which tells me how to empirically or phenomenologically verify that some object or phenomenon I want to characterize is in fact a stone.  There are a lot of possible substitutions for x, so, as I will discuss below, it seems desirable to restrict myself just to a limited number of them.  Here I want to point out that my decision to start with a dictionary definition of stone rather than some other way was in part motivated by a desire to get some idea of how the word "stone" has been used by lots of people, in line with what Carnap's desire to have a shared or shareable meaning for the word.

2.14.  For a while now there has been bubbling in my mind a consciousness that what I've been doing is the sort of thing Ludwig Wittgenstein did, so I got hold of a copy of G. E. M. Anscombe's translation of Wittgenstein's Philosophische Untersuchungen, his Philosophical Investigations (1945-1949).  I was taken aback to find that what I've been doing is rather startlingly similar to what Wittgenstein does there in the first several pages.  I hadn't looked into the Philosophical Investigations for many years, but aside from what I may have remembered from that work by direct contact a long time ago, as the years went by I must surely have been indirectly affected by what's there, in view of the widespread influence that work has had among philosophers and some others.  In any case, I got to speculating about the fact that I was led to my comments about language by trying to understand what Carnap meant by the meaning of a word in his article published in 1932, and I recalled that in a footnote of this article, he refers the reader for fuller explanations to his own work, Der logische Aufbau der Welt (edition of 1928), and also to Wittgenstein's Tractatus Logische-Philosophicus (1922).   Now, Wittgenstein says in his preface (1945) to the Philosophical Investigations that he has "been forced to recognize grave mistakes in what he wrote" in the Tractatus.  So it appears that in reading Carnap's article, I was affected indirectly by Wittgenstein's Tractatus of 1922 (which I also hadn't looked at in quite a few years) by way of certain of Carnap's views in 1932 about his construction of a special kind of clarified languages, which he says he based to some degree on Wittgenstein's Tractatus of 1922; and it appears that my response to Carnap's views (in the year 2005) has been affected, again probably mainly indirectly, by Wittgenstein's later views of 1945 about his own Tractatus of 1922, although  I expect I was also affected by my own experiences with languages over a period of nearly 80 years.

2.15.  I return now to the question of how Carnap proposes, in the article under consideration, to assign a meaning to a word.  In his article on the elimination of metaphysics, Carnap says, in the translation by Arthur Pap :

What stipulation concerning a word must be made in order for it to be significant.  . . .  First, the syntax of the word must be fixed, i.e. the mode of its occurring in the simplest sentence form in which it is capable of occurring; we call this sentence form its elementary sentence.  The elementary form for the word "stone" e.g. is "x is a stone"; in sentences of this form some designation from the category of things occupies the place of "x," e.g. "this diamond," "this apple."  Secondly, for an elementary sentence S containing the word an answer must be given to the following question, which can be formulated in various ways :
    (1.)  What sentences is S deducible from, and what sentences are deducible from S?
    (2.)  Under what conditions is S supposed to be true, and under what conditions false?
    (3.)  How is S to be verified?
    (4.)  What is the meaning of S?

Carnap regards these formulations as in some way saying the same thing in different terms, with phraseology peculiar to different fields of study.  I will return to this point, but first I will examine what he has said so far.  In the original German, this passage reads :

Welche Festsetzung müssen in bezug auf ein Wort getroffen sein, damit es eine Bedeutung hat?     . . .  Erstens muss die Syntax des Wortes festliegen, d. h. die Art seines Auftretens in der einfachsten Satzform, in der es vorkommen kann; wir nennen diese Satzform seinen Elementarsatz.  Die elementare Satzform dieser Form steht an Stelle von "x" irgendeine Bezeichnung aus der Kategorie der Dinge, z. B. "dieser Diamant", "dieser Apfel".  Zweitens muss für den Elementarsatz S des betreffenden Wortes die Antwort auf folgende Frage gegeben sein, die wie in vershiedener Weise formulieren können :
    1.  Aus was für Sätzen ist S ableitbar, and welche Sätze sind aus S ableitbar?
    2.  Unter welchen Bedingungen soll S wahr, unter welchen falsch sein?
    3.  Wie ist S zu verifizieren?
    4.  Welchen Sinn hat S?

2.16.  Carnap says that to specify the meaning of a word, one must first form an elementary sentence in which the word occurs.  He does not give in this article a characterization of the term "elementary sentence", but instead gives an example of how one may proceed.  He says that "x is a stone" is an elementary sentence for the word (or concept, or thing) "stone".  In "x is a stone", the "x" may be replaced by "some designation from the category of things".  This last is the translation by Pap.  The original German is "irgendeine Bezeichnung aus der Kategorie der Dinge".  Pap translates Bezeichnung with "designation".  However, alternative translations are "name" or "term".  With this in mind, one can interpret Carnap's statement as equivalent to saying that one can replace "x" by the name of, or term for, or concept of, some thing, or, it appears, one can replace "x" by the thing itself, if one is comfortable with speaking about things in themselves, independent of perceptions or conceptions.  No criteria for a sentence being elementary are given, and one might provisionally conclude that it is a matter of grammar, e.g. the "x" should be the subject in a sentence, and the "stone" (in his example) should be a predicate.  Or, using a symbolic notation, we are considering a sentence function (propositional function) of the form S(x), where S = "stone" (or just S = stone, if we are thinking of some sort of physical object, rather than a name for that object), and the x comes from some domain (as mathematicians frequently call it), in this case the domain of "Dinge", i.e. things, or objects, or names for things or objects.  From this point

2.17.  Carnap says that once one has an elementary sentence function S(x) of this sort, we can ask for an answer to a question which can be formulated in four different ways, as listed above.  Of these, he says that the first version is the correct one; the second version uses the phraseology of logic; the third uses that of epistemology; and the fourth uses what he calls "philosophy", by which he indicates he intends phenomenology (without further qualification).  The first version speaks of what is deducible from and (so to speak) deducible to an elementary sentence S, resulting from a suitable substitution for x in S(x).  By deducible to, I intend to speak of that which S can be deduced from, which I take it must be other sentences, be they elementary or not.   I take it that when Carnap uses the word "word" (Wort) here, he doesn't mean an orthographic word, one which, when written as a sequence of characters of the English language, such as letters, numerals and hyphens, is provided with blank spaces on each end, and has no blank spaces in the sequence of characters.  For example, such strings of characters as "look up" or "think tank" can be referred to by the word "word".   They are treated as such in sufficiently detailed dictionaries.  This suggests thinking of a word as a lexical item, i.e. an orthographic word or a sequence of orthographic words which can appear as a definiendum (something to be defined) in, say, an unabridged dictionary of the English language, together with a definiens or some number of definientia (statements giving the meaning(s) of the word).  This may be too broad for present purposes, since we may want to exclude grammatical terms (sometime called function terms), such as "the" or "of" which, it seems, cannot be given dictionary definitions of the sort nouns, verbs, adjectives and adverbs can, and which present special difficulties in translating to and from one natural language to another.  In this connection I note that if I were working in some other language, say Chinese for example, I would have to talk about words differently.  This is obvious enough with regard to written Chinese, but even English and German have different ways of forming words, which show up when translating from one of these languages to the other.

2.18.  It appears at first sight that Carnap was not thinking about relations of dictionary definitions to his notion of word meanings, since he starts not with a word by itself, but with a word imbedded in a propositional function.  As an example, he gives "x is a stone", where for purposes of testing, x may be replaced by other words such as, he says, "this diamond" and "this apple", yielding the propositions "this diamond is a stone" and "this apple is a stone".  He thus appears to be restricting values of x to a domain of nouns or names, and moreover, I suspect, to names of specific physical objects given ostensively.  That is, he uses "this diamond", and not "diamond", which would yield "diamond is a stone". This last could be taken to refer to all possible diamonds, or some sort of metaphysical essence of diamond, whereas "this stone" suggests someone pointing to a specific object, and indeed a single specific object.  

2.19.  The first criterion Carnap gives for determining the meaning of the word "stone" by using a proposition like "this diamond is a stone" or "this apple is a stone" is to see what propositions can such a proposition be derived (deduced) from, and what propositions can be derived from such a proposition.  Proceeding further, Carnap says that for many words, and for the overwhelming majority of scientific words, their meanings can be specified by "reduction to other words", and he gives this process two names, constitution and definition.  In the original, he speaks of "Zurückführung auf andere Wörter ("Konstitution", Definition)".  Here "Zurückführung auf" can be translated more literally as "leading back to", although another possibility, in some contexts, is "affiliation with" or "association with".  The reason Konstitution appears in quotes in evidently because this term is used by Carnap in a special sense, to refer to a basic method which he has put forward in his Aufbau.  To give an example of this process, Carnap does not use his previous example, "x is a stone", but rather "the thing x is an arthropod" (not "x is arthropod" nor "this thing is an arthropod", but let this pass).  He claims that "the thing x is an arthropod" can be deduced from, he says, "premises of the form "x is an animal", "x has segmented body", "x has jointed legs", and that conversely each of these sentences is deducible from the former sentence.  It appears then that in the latter case, where we deduce the meaning of the word "arthropod" by seeing what sentences can be deduced from the sentence "the thing x is an arthropod", we are, in effect, getting a lexical meaning for arthropod, albeit we are formulating our results in complete sentences of subject-predicate form.  Let's compare the definition Carnap gives with the definition from an abridged version of the unabridged dictionary I used previously :

arthropod :
any of a phylum (Arthropoda) of invertebrate animals (as insects, arachnids, and crustaceans) that have a segmented body and jointed appendages, a usually chitinous exoskeleton molted at intervals, and a dorsal anterior brain connected to a ventral chain of ganglia.

The words (terms) "animal", "segmented body" and "jointed legs (appendages)" appear in both Carnap's and the dictionary definitions.  However, the question arises, has Carnap left out of his definition some necessary terms or their equivalent, viz. "exoskeleton" and a characterization of the animal's nervous system?  To answer this question, I presume one would have to consult biological taxonomies.  This, I feel confident, would lead to problems involved different taxonomies given by different biologists (or one biologist at different times), and deciding which ones (if any) are most authoritative.  I won't follow this path, but instead give, for comparison, the definition of "arthropod" given in the unabridged version of this dictionary :

arthropod : 
a phylum consisting of articulate invertebrate animals with jointed limbs, the body divided into metameric segments, the brain dorsal to the alimentary canal and connected with a ventral chain of ganglia, and the body generally covered with a chitinous shell that is molted at intervals and including the crustaceans, insects, and spiders and related forms as well as several less prominent groups (as the millepedes and onychophores), often the trilobites, and sometimes the tongue worms, sea spiders, and water bears

Note the use of the word "often" and "sometimes" in this definition. 

2.20.  I note that Carnap speaks of "premises of the form" so-and-so being deduced from "x is an arthropod", which suggests that he was being careful not to claim that he was going to give a complete definition, but just a sample of the sort of statements one can deduce.  This brings me to the second part of the first criterion Carnap gives for determining the meaning of a word, viz. deducing "x is an arthropod" from a set of statements.  Does Carnap intend that we verify we have a complete set of statements for this purpose?  How does one do this?  In the case of "arthropod", we could use the criteria in the definitions given by lexicographers in some dictionary, and trust that the lexicographers have arrived at these definitions by consulting some authoritative sources (presumably biologists or works written by them).  There is still a question of whether or not one manages to interprets these definitions correctly, and whether or not the lexicographers interpreted their sources correctly.  This may be a captious objection, since it is well known that humans sometimes make (corrigible) mistakes.  However, there are other problems, such as the facts that there is more than one authoritative taxonomy and that taxonomies change in time.

2.21.  Moreover, and more to my point, when Carnap chose "the thing x is an arthropod" as an example, he chose a word, "arthropod" which has been explicitly defined as a technical term in a specific branch of science some of whose practitioners are especially known for their exhaustive classifications of living creatures.  What if Carnap had chosen, say, "x is a centrifugal force" or "the thing x is a physical object" or "x is a physical law"?  In fact, what if Carnap had chosen his own first example, "x is a stone"?  It appears that for one of the meanings of "stone", one (or one's lexicographers) should consult geological glossaries or texts (or geologists).  I may be wrong, but I have the impression that "stone" is not a technical term for geologists in the way "arthropod" is for biologists.  I did find a definition of "stone" in one geological glossary on the Internet : "a small piece of rock; may or may not refer to ornamental material".  The term "rock" is defined in this glossary as: "An indefinite mixture of naturally occurring substances, mainly minerals.  Its composition may vary in containment of minerals and organic substances, and are never exact."  Hmmm. . . . . .

2.22.  Suppose for a moment or two that we compare the process which Carnap has been recommending for finding a meaning of a word with using a computer in which there has been stored a program for an unabridged dictionary of the English language.  Having started the program running, a human (e.g. you or me) may use the computer's keyboard to enter the string "stone" in the appropriate place shown on the computer's monitor, and then press the key labeled "Enter" (or the equivalent).  The computer takes over, as it were.  The program and its electrical means of execution will cause a jump within the computer's memory, after which a different string of letters appears on the computer monitor, which, when interpreted by the human, constitutes a definition of the word "stone".  Here the word  "stone" is to be interpreted (by me and hopefully you) in a way that is different from interpretation of the string "stone".  The string "stone", as far as pressing keys of the the computer keyboard is concerned, is a sequence of letters, or a sequence of pressures by human fingers on various keys of the keyboard.  This sequence appears as a string on the computer's monitor, and when the "Enter" key is pressed, this string is transformed into a sequence of electrical impulses in the computer, and after various electrical activities within the computer, the computer generates a different string which appears on the monitor, and may be interpreted by a human.  The human may then be said to have found a definition (or meaning) for the word "stone".  This is what I did when I gave a definition of "stone" earlier. What the human does when looking up a definition of a word in a dictionary in the form of a printed book is an analogous process.  The steps of the process are implemented in a different way involving various motions and other physiological and/or psychological processes in the human, rather than the sort of processes which occur within a computer.  Another analogous process occurs when one human asks another human such a question as "What is a definition of the word "stone" (or maybe "What is the definition of the word "stone", as if there were one and only one such definition), and the second person responds (orally) with a definition.  My point is not to compare a computer program and its execution with any psychophysical processes going on within humans, as if to show that people have something analogous to computer programs located somewhere in their nervous systems.  My point is rather this :  In all three cases, the human starts with words, and the human ends with words.  The human has not escaped from language.

2.23.  Using as an example the sentence "the thing x is an arthropod" in which the word "arthropod" has been imbedded, Carnap has indicated that one can deduce certain sentences from this sentence, and that the sentence can be deduced from the sentences which one has deduced from the sentence.  The deduced set of sentences should, he indicates, be necessary and sufficient for the purpose of giving a (or the?) meaning of the word "arthropod".  That is, there should be enough deduced sentences to unambiguous identify when a creature is an arthropod, but there shouldn't be any more sentences than is sufficient to identify the creature as an arthropod.  However, as it stands, it appears from what I said above that Carnap has not yet escaped from language, from words and sentences and made connection with any living creatures.  He is very aware of this situation, and he says:

By means of these stipulations about deducibility  . . .  of the elementary sentence about "arthropod" the meaning of the word "arthropod" is fixed.  In this way every word of the language is reduced to other words and finally to the words which occur in the so-called "observation sentences" or "protocol sentences".  It is through this reduction that the word acquires its meaning.

Thus it appears that we don't get a meaning for the word "arthropod" simply by deducing sentences from one another, unless in the process of deduction we arrive at one or more terminal sentences which somehow allows us to escape from language, from words and sentences, and to move from language to living creatures, or perhaps to some more inclusive non-linguistic things.

2.24.  In order to effect such an escape to what is sometimes called "the real world" (meant not to include mere verbiage, as people like to say in this connection), Carnap has introduced what he calls observation or protocol sentences.  Thus, for example, in order to get a meaning for the word "arthropod", those sentences successively deduced from the elementary sentence "the thing x is an arthropod" must terminate in one or more protocol sentences.  Let's agree for simplicity that if the result of such repeated deductions is more than one protocol sentence, these sentences can be reduced (e.g. by conjunction and/or disjunction) to just one protocol sentence.  From what Carnap has said so far, it appears that one can start with the protocol sentence, and reverse the deduction process to move back to the elementary sentence "the thing x is an arthropod", and then to the word "arthropod".  That is, one can move logically from the meaning of the word "arthropod", given by a protocol sentence, to the word arthropod.  I will postpone a discussion of this contention until I have examined some remarks Carnap makes about protocol sentences in the article under consideration.

2.25.  On the other hand, Carnap says that

For our purposes we may ignore entirely the question concerning the content and form of the primary sentences (protocol sentences) which has not yet been definitely settled.  In the theory of knowledge it is customary to say that the primary sentences refer to "the given"; but there is no unaminity on the question what it is that is given.  At times the position is taken that sentences about the given speak of the simplest qualities of sense and feeling (e.g., "warm," "blue," "joy," and so forth); others incline to the view that basic sentences refer to total experiences and similarities between them; a still different view has it that even the basic sentences speak of things.

This was published in 1932, but the choices it offers for protocol sentences could have been extracted from a work about sensation and perception written by a psychologist in 2005.  In any case, Carnap claims that whatever the protocol sentences turn out to be like (assuming, presumably, that their content and form can be established at all),

it is certain that a sequence of words has a meaning only if its relations of deducibility to the protocol sentences are fixed  . . .  and similarly, that a word is significant only if the sentences in which it may occur are reducible to protocol sentences.  Since the meaning of of a word is determined by its criterion of application (in other words: by the relations of deducibility entered into by its elementary sentence-form, by its truth conditions, by the method of its verification), the stipulation of the criterion takes away one's freedom to decide what one wishes to "mean" by the word.  If the word is to receive an exact meaning, nothing less than the criterion of application must be given; but one cannot, on the other hand, give more than the criterion of application, for the latter is a sufficient determination of meaning.  The meaning is implicitly contained in the criterion; all that remains to be done is to make the meaning explicit.

I will try to make some deductions from these proposals of Carnap below, in an effort to to see what they mean using Carnap's conception of mean (as I take him to mean mean).   I will use Carnap's example, or rather Pap's translations of them to get to some protocol sentences from some elementary sentences Carnap gives, though I will not try to get back from the protocol sentences to the original sentences, on the grounds that such maneuvering is not relevant to Carnap's attack on metaphysics.


3.  How to Reason One's Way to Meanings

3.1.  It appears, then, that according to Carnap, to find the (exact) meaning of a word, we must proceed according to rules of logic.  I take it that just looking up the word in a dictionary, or many dictionaries (including ones which translate words (and phrases) from one language to another), does not qualify as a logical way to find the meaning of a word, since a person does not (presumably) use rules of inference to get from a word to other words or sentences in the dictionaries, but rather some other sort of process.  So in order to facilitate use of rules of logic, Carnap recommends that the first step in finding a meaning for a word should be to embed it in what he calls an elementary sentence.  An example that Carnap gives for this process is "x is a stone", where "stone" is a word whose meaning is to be found.  What is a word here?  Presumably it is just a string of letters in some alphabet (or a sound of a certain kind), since we have not yet assigned a meaning to what you see (or hear).  Strictly speaking, this example is a sentence (or propositional) function rather than a sentence, according to common usages.  According to Carnap's procedure, we are to deduce from "x is a stone" other sentence functions. Carnap gives no examples of such deduced functions for this example (as he does for his other example, "x is an arthropod").  I will deduce these:  "x is a concretion of mineral matter",  which is part of a definition of "stone" given in a dictionary I haveThus I have looked something up in a dictionary after all.  But then how did Carnap get from "x is an arthropod" to such functions as "x is an animal", "x has a segmented body", and "x has jointed legs"?  He may have obtained them from his memory, but at some stage in his life, somehow the words "animal", "segmented body", and "jointed legs" must have become associated for him with the word "arthropod".  However, I wonder if in fact he peeked in a dictionary (of German words) or a suitable biology book, or asked a biologist he knew, for suitable terms to associate with "arthropod" in order to form (or as he says, deduce) sentencel functions which would in fact lead to a meaning of "arthropod" within a protocolic function.

3.2.  In any case, proceeding from my function "x is a concretion of mineral matter", I seem now to have to look for (somehow) meanings of "mineral"  and of "concretion", so I form I form "x is a mineral" and "x is a concretion".  Using the same dictionary, I deduce from "x is a mineral" the function "x is a solid homogeneous crystalline chemical element or compound that results from the inorganic processes of nature", and from "x is a concretion" the function "x is something concreted".  In the latter case, from "x is concreted", I deduce "x is something formed into a solid mass".  For the sake of argument, I will take this last function to be protocolic.  (I have formed an adjective from "protocol" to avoid having to use protocol sentence function to replace Carnap's protocol sentence, in view of the common use of the term sentence as a value of a sentence function.)  But what about the function I deduced from "x is a mineral", i.e. "x is a solid homogeneous crystalline chemical element or compound that results from the inorganic processes of nature"?  Is it protocolic?  It looks like I have to consult a mineralogist or works of mineralogists to find out whether one can empirically verify, or find the truth condition, for a value of this function, say for example, the value "this stalactite is a stone".  I did this, and I find (rather to my surprise) that stalactites are regarded by some such experts as crystalline.  So far, so good.  Is this stalactite solid?  Well, I don't have a stalactite at hand, so "this stalactite" in our function will have to be regarded as a (specific) stalactite that I have in mind.  Let's suppose that this stalactite I have in mind is solid, where solid is suitably interpreted to apply to what I have in mind.  Well, is this stalactite homogeneous?  Well, maybe the one I have in mind is, but I gather from what I read that, in fact, stalactites are non-homogeneous.  So if I move from my imaginary stalactite to a physically present stalactite, I will probably find upon empirical investigation that it is not homogeneous.  If all of this is correct, and if I take ""x is a solid homogeneous crystalline chemical element or compound that results from the inorganic processes of nature" to be protocolic, then I will be able to conclude that the stalactite I test is not a stone, since it is not a mineral.  So under these conditions, I will have found that a stalactite is not a stone, i.e., the sentence "this stalactite is a stone" is false.  On the other hand, suppose that in "x is a solid homogeneous crystalline chemical element or compound that results from the inorganic processes of nature", I put x = this diamond (that I have in mind, and which I have named "this diamond"), and that I find (or I take someone's word) that the resulting protocol sentence is or can be found to be true (or can be verified).  Then I conclude that "this diamond is a stone" is true.  And, if I understand Carnap correctly, I have found an (exact) meaning for the word "stone":  A stone is a solid homogeneous crystalline chemical element or compound that results from the inorganic processes of nature.  But in common usage, are all stones crystalline?  I will leave this where it is for now.

3.3.  I note that for sentence functions, it is customary to specify a domain from which choices of words or phrases can be made to substitute for x in the examples, to get sentences, which are values or in the ranges (or images) of this sentence function. "This diamond is a stone" is a value of the function "x is a stone".  Now, what is the domain from which I chose the word "diamond"?  Or did I not choose the word "diamond" from some domain of words, but rather a physical (or phenomenological) object from a domain of such objects, a shiny object which I name "this diamond".  How would I know that what chose is in fact a diamond?  Unless I just take someone's word for it, it looks like I will have to find a meaning for "diamond", which according to Carnap will involve me in making deductions from "x is a diamond" until I arrive at a protocol sentence which will allow me to conclude, after some sort of physical or phenomenological testing, that "this diamond is a diamond".  

3.4.  We might expect some light to be shed on the sort of questions I'm asking here by two further examples Carnap gives.  For the first, he asks us to suppose a person invents a new word "teavy" ("babig" in the German) and someone else asks this person what this word means.  Carnap doesn't provide here any deductive chains linking sentence functions, but instead simply indicates that if the the person provides no empirical "criterion of application", but still insists the word has a meaning, and that some things are "teavy" and some are not, then all we can conclude is that the person associates "some kind of images and feelings with the word."  This is said by Carnap to be a psychological fact, presumably in order to distinguish this fact from other sorts of facts.  These other sorts of facts are presumably empirically verifiable in some sense of empirical, and moreover, judging from the way Carnap describes this example, the empirical tests can be understood and applied by anyone who is competent enough and wishes to do so.  This, I take it, is a form of what is commonly called radical empiricism by philosophers.  We do not seem to get from this example any further explanation of methods of deducing a meaning for a word by reasoning from elementary sentence functions to protocol sentence functions, or conversely, or how one might reverse this process.  All we know is that a person who introduces a new word, but provides no way to get protocol statements acceptable to another person, has not provided a meaning for the word.   Carnap concludes :

If no criterion of application for the word is stipulated, then nothing is asserted by the sentences in which it occurs, they are but pseudo-statements.

3.5.  Carnap's other example involving a new word is "toovy" ("bebig" in the German), a word which is given a meaning.  Here someone is assumed to have  invented the word "toovy", and that we (other people) somehow how find out that the person uses the word just like we use the word "quadrangular", for which we are assumed to have a meaning, and that the word is used by the inventor in no other observable way.  That is, as far as we are concerned we take "toovy" to be a synonym for "quadrangular", and, it appears, an exact synonym, with the same denotations and connotations , or senses and references as the invented word.  Then we are to suppose that the inventor claims that he or she did not intend for the word to mean the same as "quadrangular", but that the situation is that quadrangularity is only the visible manifestation of toovyness, and toovyness happens not to be observable.  Carnap says :

We would reply that after the criterion of application has been fixed, the synonymy of "toovy" and "quadrangular" is likewise fixed, and that we are no further at liberty to "intend" this or that by the word.

I note that the "criterion of application" presumably has been fixed by us, and that we (excluding the inventor) are stuck with a meaning of "toovy" which makes it completely interchangeable with "quadrangular", and, I take it, therefore superfluous, except possibly to indicate to us that the inventor has some private meaning for the word which we cannot access, no matter how hard we may try.  Again, in the treatment of this example, nothing further has been added about methods of deducing meanings.  

3.6.  It is striking that in the examples which Carnap used when he sketched his method for deducing meanings by inferring protocol sentences from elementary sentences, he used nouns "stone" and "arthropod", nouns (or names) of a special kind which are commonly agreed by speakers of English (starting in early childhood) to refer to something, i.e. to some thing, where "thing" means some observable object, or perhaps some consistently invoked phenomenon.  I wonders how one is to obtain a meaning for the word "freedom" deductively, starting with the elementary sentence function as "x is a freedom", or (even more puzzling) "x is freedom" (without the indefinite article "a").  I leave aside for the time being questions arising from the fact that some languages do not use a copulative or linking "is" in a sentence corresponding to one in English of the form "x is a [noun]" (at least for many nouns), so that for example the Russian corresponding to English "this stalactite is a stone" can be stated in Russian so that its word-by-word translation into English would be "this stalactite stone".  As a matter of fact, people learning English as adults often make statements like "this stalactite stone", and are understood by native speakers of English to mean "this stalactite is a stone".   If such a learner of English just said "stalactite stone", a native speaker of English would most likely take this to mean "this stalactite is a stone" provided the learner was actively pointing to stalactite or a representation of one, but perhaps in the absence of an observable stalactite (or picture of one, or even a mention of the word "stalactite") would take it to mean "stalactite is stone", meaning "all stalactites are stones".  Such considerations as these point to some difficulties which can arise in connection with forming and interpreting sentence functions, and forming and interpreting their values, i.e. sentences obtained from the functions by substitution for a variable.

3.7.  Moreover, in his examples involving invented words, Carnap doesn't use noun-like words, but ones which are customarily classified grammatically as adjectives.  What does one do with an elementary sentence of the form "x is free" to deduce a meaning for "free"?  One might take it that "x is free" is equivalent to "x has freedom", or "x participates in freedom", or "x is able to exercise a freedom".  But then it looks like one would be faced with some sort of set theoretical concept, along the lines of "x is in F" where F = set of all freedoms, and with problems involving universals, of the sort suggested by comparing "x is a freedom" (which can be regarded a set-theoretic) with "x is freedom".  The formulation "x is freedom" seems to beg for a reification of "freedom", as existing in some idealized or abstracted way, or at any rate for a concept of naming some more or less well-defined collectivity along with ways to use the name.  And then there are the other traditional part of speech, pronouns, verbs, adverbs, conjunctions, prepositions, and interjections; and there are other signs or symbols or ways of writing which seem to have some sort of meaning.  In written speech, there are punctuation marks, italics, boldface, change of fonts or sizes of characters, mathematical and special scientific notations, notations for formal logics, smiley face symbols and so-called emoticons, etc., etc.  In spoken language, there are changes of pitch and loudness, facial and other body expressions or movements, use of simulated or genuine foreign or regional accents and so on.  How do we assign meanings which take into account all this?  Perhaps, for purposes of doing science, Carnap had in mind requiring that in dealing with such a statement function as "x is a [word]", one should only substitute for [word] words of a certain type or class, which one would presumably have to specify more or less comprehensively (and comprehensibly).  Similarly, one might specify what words, corresponding to what kind of things, can be put for x.  Perhaps one would have to vary what can be substituted for x (the domain of x) depending what word has been substituted for [word] in a statement function, for the purposes of doing science (whatever "doing science" means).  For example, in "x is a stone", one might confine oneself to substituting for x what one takes as physical objects (however these are to be identified), or to sense data of certain kinds, or Husserlian phenomena characterized in some way.  On the other hand, for "x is an electron" or "x is a law of nature", one might want to restrict oneself to different sorts of substitutions for x (or at least, in the case of "electron", extend some former specification for a "physical object").


4.  Metaphysical Words Without Meanings

4.1.  Carnap proceeds again with examples.  He asks us first to consider the term (Terminus, not Wort) "principle" (Prinzip).  He says we are to understand this term in the sense of "principle of being, not principle of knowledge or axiom".  Thus it appears that he is asking us to consider the term (or word, in the extended sense I discussed earlier) "principle of being", rather than just the term (or word) "principle".  However this may be, he observes that "various metaphysicians offer an answer to the question [of] which is the (highest) "principle of the world" (or of "things," of "existence", of "being"), e.g. water, number, form, motion, life, the spirit, the idea, the unconscious, activity, the good, and so forth.  (Trivia question: which philosophers was Carnap thinking about here?)  He then says that in order to find out what these metaphysicians mean by such terms, we should (actually, he says that we must) ask the metaphysician "under what conditions a statement of the form "x is the principle of y" would be true and under what conditions it would be false.  (So here we have a sentence function of two variables; however, Carnap has been using such functions tacitly earlier, e.g. when he used as examples the two sentences "x is a stone" and "x is an arthropod".)  Carnap claims that when a metaphysician is asked "for the criteria of application or for the definition of the word 'principle' as the metaphysician uses the word in such phrases as 'principle of being', that the metaphysician replies approximately as follows:  'x is the principle of y' is to mean 'y arises out of x,' 'the being of y rests on the being of x,' 'y exists by virtue of x' and so forth."  (In German, , these alleged replies read  "y geht aus x hervor", "das Sein von y beruht auf dem Sein von x", "y besteht durch x").  Carnap proclaims that "these words are ambiguous and vague", and that the metaphysician doesn't use these words as they are sometimes used to indicate "empirically observable" relations.  "The expression 'arising from' ", Carnap says, "is not to mean here a relation of temporal and causal sequence, which is what the word ordinarily means." 

4.2  Thus Carnap appears to be lodging a double complaint against metaphysicians.  First, metaphysicians use sentences which don't provide an empirical way to understand or verify what they mean, which, in view of what he has said earlier, presumably means that one can't deduce protocol sentences from sentences which are instances of such sentence functions as "y arises out of x" (as metaphysicians use "arises out of", at least sometimes).  Second, metaphysicians don't always use ordinary meanings of words, which leads to words being deprived of their ordinary meanings, although, he says, "From an earlier period of significant use, it [the word] is still associatively connected with various mental images; these get associated with new mental images and feelings in the new context of meaning."  However, Carnap makes it clear that such new mental images and feelings do not furnish a new meaning for a word, since there is no way to connect the word with something that can be sensed and perceived by Carnap and anyone else who can carry out what is indicated by protocol sentences derived from such an offending sentence asserted by a metaphysician.  This seems not to take into account any procedure which might be proposed by a metaphysician (or theologian, or mystic) by means of which a person can successfully (at least sometimes) produce mental images and feelings which sufficiently resemble what the metaphysician intends to convey, and can be regarded as communicating a meaning from the metaphysician to the other person.  This is presumably because, in Carnap's view, a meaning of a word must not only be to some degree communicable, more or less faithfully, but the word must also point to a way to associate the word with something (or, some thing) which is external to both the metaphysician and other people.  Otherwise, I suppose, one can, in the spirit of what Carnap has said, conclude that the word, in colloquial English, is "all in one's mind", i.e. only imaginary or not real, where "imaginary" and "real" are used here in some ordinary senses.  Or, to use Carnap's way of speaking, one can say the word has no meaning (Bedeutung, akin to deuten auf, "point to" -- which suggests that a meaningless word, according to Carnap, doesn't point to anything, or at least to anything worthwhile).

4.3.  Carnap next discusses usages of the word "God".  Carnap speaks, in the manner of Auguste Comte and his positive philosophy, of an historical evolution of usages from the mythological to the metaphysical to the theological,  although he notes that these stages of usage overlap temporally.  He regards mythological uses of the word "god" (or the equivalent in languages other than English) as having a "clear meaning", since he takes such usages to denote physical beings, beings which can manifest themselves either as human-like or by means of things or processes which are empirically verifiable.  He asserts that metaphysical usages of the word "God" refer to "something beyond experience".  In such usages, he says, not even the first requirement of finding a meaning for the word "God" is met, namely forming an elementary sentence [function] of the form "x is a God" (Pap translates "x ist ein Gott" by "x is a God", although in English usage, such mythological beings would require "x is a god" to prevent problems arising about monotheism versus polytheism, or about what constitutes a religion as opposed to a mythology.)  Carnap says of the function "x is a God" (or "x is God", perhaps) that a metaphysician "rejects this form entirely without substituting another, or if he accepts it he neglects to indicate the syntactical category of the variable x".  To explain what he means by "syntactical category", he says:  "Categories are, for example, material things, relations between things, numbers, etc."  Using a different terminology, it appears that Carnap is saying that metaphysicians do not specify an admissible domain for the sentence function "x is a god", a domain of sort which Carnap has in mind, consisting of such things as things (physical objects), or relations between things, or such (mysterious) entities as numbers

4.4  Thus Carnap is saying, using his special formulation based on logic, that  metaphysicians use the word "god" (or "God") and then ignore or resist or don't see the necessity of using the word in sentences from which one can deduce protocol sentences which connect "God" to the sort of things -- well, to the sort of things Carnap wants the metaphysicians to connect them to.  These presumably could be things which can be perceived in the manner humans interact with physical objects, without prejudice as to whether or not humans are seeing the objects in themselves, or seeing some sort of phenomenal representations of the objects, or both.  In short, metaphysicians refuse to be scientists.  As far as theologians are concerned, Carnap says that "several theologians have a clearly empirical (in our terminology, "mythological") concept of God", and that "in this case there are no pseudo-statements", i.e. no statements using "God" without having in mind a meaning for the word.  However, according to Carnap, this makes their statements "subject to the judgment of empirical science".  Carnap doesn't say so explicitly, but I suspect that when he said this, he had in mind that that their statements would then turn out to be unverifiable, or perhaps just false.  Other theologians, says Carnap, make statements using the term "God" which are "clearly metaphysical", i.e. which are meaningless, which assert nothing, which are mere pseudo-statements.  He also points to some theologians who alternate between the metaphysical and the empirical, and to some whose statements can't be classified as one or the other, but seem to be both at once, which Carnap seems to take as illegitimate.  (Note:  With Heidegger in mind, I note that when Carnap says pseudo-statements "assert nothing" (besagen nichts), he must mean that they "do not assert something", and not that they "assert nothing", i.e. affirm the existence of that which doesn't exist.  Presumably this would require "besagen Nichts", as in Heidegger's notorious question in Was ist Metaphysik?, which is among those Carnap is about to complain about :    Wie steht es um das Nichts?, translated by Krell as "How is it with the nothing?")

4.5.  Next, we are to consider these two sentences (as contrasted with words) : 

(1) Caesar is and
(2) Caesar is a prime number

These are offered as statements which are meaningless, and therefore pseudo-statements, not because they contain meaningless words, but because, although the words in the statement are meaningful, "the words are put together in such a way that nevertheless no meaning results".  The first of these, "Caesar is and" is said to violates a rule of grammar, since "the rules of syntax require that the third position be occupied, not by a conjunction, but by a predicate, hence by a noun (with article) or by an adjective."  I take it that Carnap was referring specifically to grammar of the German language, but his rule can also be applied to grammar of the English language, if not to all languages.  Carnap doesn't offer an explanation of how one arrives at the assumed meanings of the terms "Caesar", "is", and "and".  Let's take it that the word "Caesar" functions as a noun, bypassing any difficulties as may arise in connecting the string of letters or the sound of "Caesar" with the string or sounds "the author of Bellum gallicum", and the bountiful difficulties in pinning down relations between sense and reference, name and description, denotation and connotation, etc., etc..  And let's ignore the fact that Carnap's recommended procedure for assigning meanings to words has so far been applied only to nouns and adjectives, although he assumes here that the conjunction "and" and the contentious verb "is" have been or at least can be assigned meanings.  In any case, most speakers of English would, I think, agree that "Caesar is and" is a meaningless statement, for whatever reasons.

4.6.  So let's consider "Caesar is a prime number".  This statement is syntactically permissible, since, Carnap says, it is formed in the same way as "Caesar is a general", which we are expected to agree is a meaningful statement.  Carnap asserts, however, the "Caesar is a prime number" is meaningless since " 'prime number' is a predicate of numbers; it can be neither affirmed nor denied of a person."  That is, a predicate, or rather a predicate function, must have a specified domain.  In this instead, we can set Pr = "prime number", and consider the function Pr(x).  We may specify that the x may be replaced only by a certain entity which we call a number, or rather by a name of a number, a numeral.  Suppose that we agree on some grounds or the other that "Caesar" is the name of a person, and that the name of a person cannot be the name of a number, or that we simply agree that Caesar is a person, and a person is not a number.  Then when we substitute "Caesar" for x in Pr(x), we will be violating a rule which we have set forth that the domain of Pr(x) can only consist of names of numbers, then we are entitled (it seems) to declare that Pr(Caesar) is meaningless.  By analogy with the process that Carnap has used to assign a meaning to a word, we might expect that the reason "Caesar is a prime number" is meaningless is that no (syntactically properly formed) statement which is empirically verifiable or falsifiable can be deduced from it, according to rules of logic.  However, it appears that the reason is rather that we have illegitimately evaluated the predicate function "x is a prime number" at an entity which is not in the domain of this function.  Thus according to Carnap, we can conclude that a word is meaningless if we can show that there is no way to deduce a protocol sentence from an elementary sentence containing that word, and we can conclude that a statement which is composed only of meaningful words is meaningless, it is a pseudo-statement,  if we can show that we have evaluated a statement function at something not in the domain of that function which Carnap (or someone else) has specified.  Carnap in this article evidently has this in mind when he rejects "Caesar is a prime number" simply by saying " 'x is a prime number' is false if and only if x is divisible by a number different from a and from 1; evidently it is illicit to put here 'Caesar' for 'x' ".   (Note:  I observe that in English the term "prime number" is formed of two orthographic words, while in German the term is a single orthographical word, 'Primzahl'.  This suggests a possible problem about whether or not in specifying a domain for a statement function one has to be careful about separate meanings of distinct orthographic words in a phrase made up of more than one orthographic, but taken as a single lexical word.)

4.7.  Carnap concludes this section of his article with a description of how logicians seek to construct a logical syntax for language which would allow us to talk or write without making pseudo-statements, presumably to be used along with a logical technique for avoiding the use of meaningless words :

The fact that natural languages allow the formation of meaningless sequences of words without violating the rules of grammar, indicates that grammatical syntax is, from a logical point of view, inadequate.  If grammatical syntax differentiated not only the word-categories of nouns, adjectives, verbs, conjunctions etc., but within each of these categories made the further distinctions that are logically indispensable, then no pseudo-statements could be formed.  If, e.g., nouns were grammatically subdivided into several kinds of words, according as they designated properties of physical objects, of numbers etc., then the words "general" and "prime number" would belong to grammatically different word-categories  . . . . .  In a correctly constructed language, therefore, all nonsensical sequences of words would be just as linguistically correct as (1) [i.e., "Caesar is and"].  Considerations of grammar would already eliminate them as it were automatically; i.e. in order to avoid nonsense, it would be unnecessary to pay attention to the meanings of the individual words over and above their syntactical type (their "syntactical category," e.g. thing, property of things, relation between things, number, property of numbers, relation between numbers, and so forth).  It follows that if our thesis that the statements of metaphysics are pseudo-statements is justifiable, then metaphysics could not even be expressed in a logically constructed language.  This is the great philosophical importance of the task, which at present occupies the logicians of building a logical syntax.

This is a succinct statement of Carnap's recipe for adhering to David Hume's exhortation in An Enquiry Concerning Human Understanding :

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

And it also a statement of a proposed way to construct a language in which such sophistry and illusion would automatically be eliminated from discourse constructed in such a language rather than in a natural language (Carnap discusses this distinction later in the article).  As such, Carnap's program is often classified as neo-Kantian, in that if it were successful, it would provide a tool for dealing with problems and theories of the natural sciences (and perhaps science in general, whatever that is) while avoiding the kind of metaphysics Kant found objectionable.


5.  Carnap Confronts Heidegger  

5.1.  At last we get to Carnap's example of metaphysical pseudo-statements, chosen from Heidegger's Was ist Metaphysik.  For convenience, I will repeat here the passages to be criticized as given in the translation by Arthur Pap :

What is to be investigated is being only and -- nothing else; being alone and nothing further -- nothing; solely being, and beyond being -- nothingWhat about this Nothing?  . . .  Does the Nothing exist only because the Not, i.e. the Negation, exists?  Or is it the other way around?  Does Negation and the Not exist only because the Nothing exists?  . . . We assert : the Nothing is prior to the Not and the Negation.  . . .  Where do we seek the Nothing?  How do we find the Nothing?  . . .  We know the Nothing  . . .  Anxiety reveals the Nothing.  . . .  That for which and because of which we were anxious, was 'really' -- nothing.  Indeed : the Nothing itself -- as such -- was present.  . . .  What about this Nothing?  . . .  The Nothing itself nothings.

5.2.  Carnap doesn't deal with these passages directly, but rather by comparing the sort of statements made here by Heidegger with some sample sentences.  First, he considers what he takes to be two meaningful sentences of ordinary language, the question  "What is outside?", and an answer to the question, "Rain is outside".  He then offers a "Transition from Sense to Nonsense in Ordinary Language" by substituting the word "Nothing" for the word "Rain" in "Rain is outside", to get the sentence "Nothing is outside".  This last sentence is then replaced with what Carnap calls a "logically correct" sentence, "There is nothing (does not exist anything) which is outside".  I note that if the elaboration in parentheses in this last sentence is at all optional, then the logically correct sentence is just "There is nothing which is outside."  This last formulation seems to raise the same problem as the allegedly nonsensical sentence "Nothing is outside".  What is this problem?  It appears to be that the sentence "Nothing is outside" may lead one to conclude that there is in fact something outside, which may lead one to conclude that the word "Nothing" is some sort of object, be it physical or phenomenal.  The fact is, though, in ordinary English, most people will not understand the sentence this way, at least when they aren't discussing philosophical matters.  They will also take the sentence "There is nothing which is outside" not to assert the existence of a "nothing", i.e. interpret the "is" as asserting some sort of physical or phenomenal existence of an object.  Most people, under most circumstances (not including those involving certain philosophical usages) will take the sentence "Nothing is outside", especially as an answer to "What is outside?, to signify a version of Carnap's logically correct sentence, viz. "There does not exist anything which is outside", or something semantically equivalent to this.  (I forego an elaboration of what I mean by semantical equivalence, other than to say that what I mean when I say that two sentences are semantically equivalent is that the two sentences have the same meaning, or at least near enough to the same meaning in the context(s) in which they are used.  Besides leading me into the labyrinth of theories of meaning, this would lead me into discussing the virtues, or maybe even the necessity, of circular definitions and circular reasoning, under some conditions.)  So far, one might interpret Carnap's discussion as an analysis of a certain kind of joke, or pun.  Thus in an attempt at humor, someone (especially a child) might point out that because "Rain is outside" and "Nothing is outside" sound or look to be the same sort of assertions, then "Nothing" is the same sort of object as "Rain", or that "Nothing" is a name for the same sort of object that "Rain" is the name is.

5.3.  Carnap goes further, however, by translating the sentences into a symbolic language.  He does this to start with by setting "What is outside?" = Ou(?), and "Rain is outside" = Ou(r).  Thus the word "outside" has become a predicate, and from this a sentence function is constructed, symbolized here by Ou(?) rather than, say, Ou(x).  (The use of "?" rather than "x" to denote the place where candidates from a specified domain can be substituted to form sentences which can be used to deduce verifiable or falsifiable sentences is meant to suggest that we are expected to put something in place of the symbol "?", i.e., we are expected to answer a question.  I am aware that I might fruitfully expostulate here about what a predicate is, but I will assume that some more or less satisfactory meaning has been attached to or predicated of  the term "predicate".)  Having constructed Ou(?), then Carnap evaluates this function at r = "Rain", to get "Rain is outside".  I note that "Rain is outside" is Pap's translation of the German "Draussen ist Regen", which if translated from left to right, is "Outside is rain", an English sentence which would lead a native speaker of English to conclude that the sentence was formed by a person who was not a native speaker of Engllish.  But, as a matter of fact, Pap's version, "Rain is outside" would likely lead to the same conclusion.  The answer most often given by a native speaker of English to the question "What is outside?" would be "It's raining outside".  In fact, a native speaker of English might have trouble understanding that the question "What is outside?" was meant to elicit an answer concerning rain, i.e. the speaker might not realize in many contexts that "rain" was meant by the questioner to be in the domain of Ou(?).  To indicate that the questioner meant "rain" to be in the domain of Ou(?), the question might have been put in the form "What's that sound outside?", or perhaps "What's that, outside?" where the comma indicates a kind of pause and emphasis which would be interpreted as asking what that sound is, provided both the person questioned and the questioner were hearing a sound.  Such are the vagaries of ordinary language, as language is used ordinarily.

5.4.  In any case, after forming Ou(?) and Ou(r), Carnap turns to a different evaluation of Ou(?).  He evaluates at "nothing" = no, geting Ou(no) which symbolizes, according to Pap's translation, "Nothing is outside".  Confusion is somewhat confounded here, since in the original German, this symbol for this sentence is dr(Ni), and the German for the sentence symbolized is "Draussen ist nichts".  Thus we get tangled up with the fact that "Draussen" is capitalized not because it is a German noun, but because it is the first word in the German sentence; in fact, as used here, "draussen" appears to be classifiable as either an adverb or an adjective.  There is a further capitalization problem insofar as in the English translation, "Nothing" is capitalized because it is the first word in a sentence, which may suggest, once more, that Nothing is something.  Furthermore, in the German sentence, "nichts" is not capitalized, which suggests that whatever part of speech is meant (probably not a noun, but a pronoun), it is not the noun das Nichts = "nothingness", or the noun das Nicht = "the Not" = negation.  To further muddy the waters, I note that in the German symbol for the sentence "Draussen ist nichts", Carnap (or a typesetter) has put "Ni" with a capital "N" for uncapitalized "nichts".

5.5.  Now we come to the cruncher in this example.  Carnap offers as a logically correct form of the German sentence  "Draussen ist nichts" the sentence "Es gibt nicht (existiere nicht, ist nicht vorhanden) etwas, das draussen ist."  He also offers as a symbol for this sentence ~(Ex)(dr(x)).  In my experience as a mathematician, I have found that this symbol is commonly translated, at least into spoken English, by something close to (or the same as) "There does not exist an x such that d r of x".  However, one also hears such versions as "There isn't any x such that d r x" or the like, relying on the "is" to be interpreted in the sense of "exist".  I will take it that correspondingly the phrase es gibt nicht etwas in German can be translated either as "there doesn't exist" or "there isn't anything",depending on such matters as emphasis, stylistic preferences, habit, or just plain chance.  Thus in English, I will take it that suitable translations of "Es gibt nicht etwas, das draussen ist" are "There isn't anything which is outside" and "There doesn't exist something which is outside".  A close equivalent in English to these is the statement "There is nothing outside".  However, "There exists nothing, which is outside" (with a comma, as in the German) or "Nothing exists outside" as translations of "Es existiere nicht etwas, das draussen ist" might well lead one to point out, perhaps mischievously, that these English sentences can be interpreted, as asserting the existence of that which does not exist.  In any case, Pap translates Carnap's sentence by "There is nothing (does not exist anything) which is outside".  Thus Pap avoids translating the phrase ist nicht vorhanden used by Carnap.  This is perhaps just as well, since Heidegger uses the word "vorhanden" in a special sense, and contrasts it with the unusual word "zuhanden".  In such contexts, "vorhanden" is often translated by "present-at-hand" and "zuhanden" by "ready-to-hand".  Speaking vaguely, what Heidegger wants to do, it seems, is to make a distinction between theoretical and practical objects, or between theory and practice, or between "thinking about" (e.g., about "phenomena") and "working with" (e.g., using tools).  Presumably Carnap had no such distinctions in mind, but just wanted "Es ist nicht vorhanden etwas, das draussen ist" to convey approximately the sense in English of "There is not something present outside" or (as used before) "There is nothing outside".

5.6.  In the formula ~(Ex)(dr(x)), the symbol Ex is called an existential quantifier.  From what I have said earlier, one may consider that this notation is deficient insofar as it doesn't include any indication that Carnap seems always to have a domain in mind from which an existent or subsistent or entity or object can be chosen, a domain which is limited in some way, and doesn't consist of just anything.  What sort of existents might one want to include in a domain for dr = draussen, or to revert to English, Ou = outside?  Clearly, Carnap intends rain to be included.  What else?   Flowers, visitors, cars, stars, chocolate bars -- things of this sort seem all right.  What about Ou(Plato) = "Plato is outside"?  Well, it depends.  If Plato is taken as the name of the family dog, it's OK, but if it's taken as the name of the well-known ancient Greek philosopher, then while at one time the answer "Plato is outside" to "What is outside?" might have been reasonable (true or false), but a couple of thousand years later and more, it would have to be taken as a joke, or as involving some sort of metaphorical use of the term "Plato", e.g. an interpretation of something Plato wrote which is about to be entered into a discussion by the person who made this answer.  I rather doubt that Carnap considered this sort of allowable substitution for x in Ou(x).  Even more, how about putting "The Platonic Idea of Truth is outside" for x in Ou(x).  If so, from ~(Ex)(Ou(x)) could be translated into ordinary English as "There is no Platonic Idea of Truth which is outside".   The truth or falsity of this would, it seems, depend on an interpretation of the term "outside".  It does seem to me, though, that it would be stretching this term, or would be a feeble metaphorical use of the term, to suppose that "outside" would be intended to signify something like "outside the physical universe", or perhaps "outside the bounds of good sense".  In any case, for all I can tell from what Carnap has said, "There is no Platonic Idea of Truth which is outside" is a logically correct statement, provided Carnap didn't have in mind a restricted domain for Ou(x).

5.7.  In any case, it appears that this sort of thing is more than Carnap wanted to address here, and that he was just telling us that "Draussen ist nichts" or "Nothing is outside" shouldn't mislead us into thinking that "nichts" = "etwas", or "nothing" = "something" because the grammatical form of these statements is the same as "Draussen ist Regen" or "Rain is outside" (leaving aside the awkwardness of the English version).  After this example, Carnap turns to the question, "Wie steht es um diesen Regen?", translated by Pap as "What about this rain?".  Carnap elaborates on this statement or offers as synonymous with it the statements "was tut der Regen?" and "was lässt sich über diesen Regen sonst noch aussagen?", translated by Pap as "what does the rain do" and "what else can be said about this rain".  (It appears that in context, "what is the rain doing" would be a more appropriate translation for the first of these.)  Carnap gives two answers to this question (or these questions, regarded as saying the same thing):  "Wir kennen den Regen" and "Der Regen regnet", translated by Pap as "We know the rain" and "The rain rains".  Here again, it seems more appropriate here, or at least more colloquial, to translate the first of these by "We know it is raining" or "We recognize that it's raining".  As to the "The rain rains", one might offer as an alternative something like "The rain is falling", since "The rain rains" sounds quite jocular in English, and/or somewhat dejected.  In any case, this is beside Carnap's point.

5.8. Carnap now comes to the crux of his complaint about Heidegger's allegedly illogical use of language.  He sets out to compare the answers he gave to "What about this rain?" to some grammatically analogous answers to the question notoriously posed by Heidegger in his Was ist Metaphysik?:  "Wie steht es um dieses Nichts?", translated by Pap as "What about this Nothing?"  (I note here that Carnap answers "Was ist draussen?" with "Draussen ist nichts" with "nichts" uncapitalized, but answers "Wie steht es um dieser Nichts?" with "Nichts" capitalized.  In the light of what I've said earlier about "nicht", "nichts", "das Nicht" and "das Nichts", this is questionable, this is suspicious -- see below.)  Carnap offers three answers to Heidegger's question "What about this Nothing?", derived from what Heidegger wrote.  The first is symbolized by k(Ni), with Ni = Nichts, and three instances of k are given, translated by Pap with "We seek the Nothing", "We find the Nothing" and "We know the Nothing".  The second answer quoted is "Das Nichts nichtet", and the third is a truncated quotation, "Es gibt das Nichts nur, weil . . ."  These are symbolized by ni(Ni) and ex(Ni).  Now as to logically correct forms for these answers, which according to what Carnap indicates would be symbolized by ~(Ex)(k(Ni)) and so on, Carnap says "None of these forms can even be constructed".  They are what Carnap calls pseudo-statements (Scheinsätze).

5.9.  Why can't these answers be transformed into logically correct statements?  Of the first answer (with three instances), Carnap says that Heidegger's error is simply that the word "nichts" in, for example, "Wir suchen das Nichts" = "We seek the Nothing" has been applied as if it were the name of an object (Gegenstandsname).  (In Carnap's explanation, he uses "nichts" although in the sentence at hand he uses "Nichts".)  Carnap declares that in ordinary language this word ("nichts" and/or "Nichts") is not used as the name of an object, but to indicate that one should understand that one is to interpret or translate the sentence into a negative existential statement of the sort symbolized by ~(Ex)(f(x)), with an appropriate substitution for "f" (presumably along with a suitable domain).  So here Carnap is making a statement about ordinary language, and about a certain relation of it to a purified or rectified language which is logically sound (unlike, one gathers, ordinary language in general), and whose soundness can be best guaranteed by moving back and forth between appropriate symbols for (interpreted) words and the words themselves.  So what happens if we try this with "We seek the Nothing"?  Using Pap's notation, we can symbolized "We seek the nothing" with K(no) where "no" = "nothing" and (for example) "K" = "we are seekers of" or the equivalent.  ("K" = "we seek" doesn't seem to work.)  We are already stopped here before we try to use an existential quantifier because, I would say, according to Carnap's view, the word "nothing" cannot be legitimately be put into the domain of this "K", or into the domain of any other choice for "K".  It seems that this is because domains are here assumed to contain only nouns or names of objects (phenomenal or physical), and "nothing" is not really a noun, or should not be taken as the name of an object.  Aside from my emphasis on the use of domains for statement functions, this seems to be equivalent to what Carnap has said about this example.

5.10.  Carnap's second answer to "What about this Nothing?", taken from Heidegger's Was ist Metaphysik? is "Das Nichts nichtet" which Pap translates as "The Nothing nothings" (my first impulse is to translate it by "The Nothing negates").  Of this sentence, Carnap says that the word "nichtet" (or its infinitive, "nichten") is a meaningless word, and furthermore it is not meaningless because it is a meaningful word "deprived of its meaning through its metaphorical use in metaphysics", but because here "a new word is introduced which never had a meaning to begin with."  I suppose we can take Carnap's word for the newness of "nichten".  However, there is a German word "nichte" as in Der Regen machte all seine Chancen zu nichte which can be translated as "The rain made his chances come to nothing", i.e. "The rain ruined his chances" (note the use of "nothing" in the first of these translations into English).  There is also a word "vernichten" which, depending on context, can be translated as "destroy", "ruin", "defeat", "wipe out", "annihilate", "kill", "exterminate", etc.  (Also, "die Nichte" means "the niece", but this seems to be irrelevant here.) 

5.11.  In any case, Carnap's assertion that "nichten" never had a meaning to begin with seems, in the present context, to have to be based on the fact that there is no way to logically deduce a protocol sentence from an elementary sentence containing the word "nichtet" (or "nichten", or some other inflected form).  In the article I am analyzing, Carnap only gives examples of elementary sentences of the form "x is a T", corresponding to a sentence function symbolized by T(x), where T is derived from a name or noun.  Suppose we try "x nichtet" as a suitable elementary sentence.  To see what this might involve, let's look first at Carnap's example of an elementary sentence, "x is a stone".  Let's try taking in place of "x is a stone" the sentence "x stones", where "stones" is a new word I have introduced, an inflection the verb "to stone", where "to stone" has been given a new meaning (or definition) taken to signify something like "is being a stone" or perhaps "to engage in an activity of existing as or becoming a stone", under the assumption that the noun "stone" has already been given a logically satisfactory meaning by application of Carnap's procedure.  Let's choose the interpretation "x is being a stone" for "x stones", since this seems to say much the same thing as "x is a stone", except that " x is being a stone" introduces time in a way that "x is a stone" doesn't (or doesn't have to).  What sort of symbol should we use for "x stones"?  If we try s(x), where "s" = "stones", and we try translating back into English in the way we did with nouns, we get  "x is a stones", and we seem not to be forming a valid sentence according to ordinary English usages.  Let's try s(x) where "s" stands for "to stone", the infinitive form of the verb "to stone" furnished with my new meaning.  Then to get a meaning for "to stone" as I have defined the term using the process described by Carnap, it seems we must reason our way to a protocolic sentence function of the form "to stone is to x" for which the domain is to consist of words designating acts or actions or occurrences or perhaps temporal processes, which is to say, by verbs.  Another possibility would be to work with participles instead of verbs, e.g. using "x is stoning" in place of "x stones".  Then we would look for protocolic sentence functions of the form "stoning is x", where x would be replaced by participles.  For the infinitive form "to stone is to x" we might get a protocol sentence like "to stone is to retain such-and-such kinds of structure for some length of time as shown by such-and-such empirical tests or such-and-such phenomena", whereas using participles, we could say the same in the form "stoning is retaining such-and-such kinds of structure for some length of time as shown by such-and-such empirical tests or such-and-such phenomena", and these say the same.

5.12.  When I examined Carnap's method for deriving a meaning for "stone" from "x is a stone", I started with a dictionary definition, a lexical meaning for "stone", although I indicated that one could also start by consulting a geologist or the like.  Here, we can't start quite that way, because as far as I know, the word "stone" never appears in dictionaries as a verb with the sense I have designated (although it appears as a verb in a number of other senses).  This suggests that in this situation I should try to create, and to communicate in the form of comprehensible statements, some empirical way to find out whether or not an activity is engaged in the activity of being a stone. At this point, one might want to consider whether or not anyone else besides me will use my criteria for verifying whether or not "stoning" is going on in my sense, but that would be part of another story, so I leave it aside.  

5.13.  I will now try applying my procedure described above to n(x), where "n" = "nothings", by examining the function "to nothing is to x".  Despite the fact that Heidegger seems to have been trying to introduce a meaning for "nothing" ("nichten") as a verb, and that such a meaning isn't found in standard dictionaries, I will to start with try looking up synonyms for the word "annihilate", which occurred to me when I considered trying to assigned a meaning for "nothing" as a verb.  That is, I will first set out to deduce a protocol sentence by using "to nothing is to annihilate".  When I try my previous trick of using lexical meanings to help me, I find "to destroy utterly" as a synonym for "to annihilate".  Actually what I find is:  "to destroy utterly (matter cannot be annihilated)".   This suggests to me that what Heidegger was after in making a verb "to nothing" ("zu nichten") was to somehow introduce a name for an activity which does annihilate matter, or to put it in somewhat more in the style of Heidegger, he wanted to talk about annihilation of Being, where Being is a term meant to cover all that can't help trying to continue to exist.  Nevertheless, when one considers, say, death of humans, or death of an ancient city, or even death of two physical particles when they interact and become one different particle, one may suspect that what can't help trying to exist nevertheless can get annihilated.  Moreover, in the case of human deaths, one might want to talk about a human being utterly destroyed as a human being, or about the soul or mind of a human being utterly and irrecoverably destroyed.  It seems that Heidegger was trying to give a name to what can't help trying to utterly destroy what exists, and also to what this whatever-it-is does, by naming that which can't help trying to utterly destroy what exists "the Nothing" (das Nichts), and name what the Nothing does by inventing a verb "to nothing" (zu nichten).. 

5.14.  The nonstandard German verb nichten used by Heidegger looks or sounds like it is related to the standard verb vernichten.  Similarly, I will introduce a nonstandard English word nihilate suggested by the standard English word annihilate.  I then translate Heidegger's das Nichts nichtet as "the Nothing nihilates" rather than "the Nothing nothings", as Pap did.  Admittedly, this annihilates the assonance of the German version, but on the other hand we get in English a better looking and sounding present participle, nihilating, rather than the over-assonant nothinging we would normally get when we try to use to nothing as a verb.  To use a terminology that descends from writings of Gustav Frege, it seems to me to be easier to suspect that the sentence "the Nothing nihilates" has a sense than to suspect that the sentence "the Nothing nothings" does, and to be more moved to look for referents for the word "Nothing" and to entertain the idea of a process of nihilating.  A person might even try to deduce a Carnapian protocol sentence from "the Nothing nihilates", so that "the Nothing nihilates" will turn out not to be a pseudo-statement after all.  Well, whether "the Nothing nihilates" is nonsense or not is the sort of question Heidegger asked.  One way to avoid thinking about possible answers to such a question is that is impossible or meaningless to state such a question in a logically correct way, and therefore useless to look for empirical or phenomenological ways to detect whether or not there is a kind of obverse or opposite of Being, where Being is taken to comprise all that which is what it is, and, so to speak, which keeps on is-ing unless it is opposed or acted on by something other than Being, which we could call Nothing or Nothingness, and of which we could sensibly say that when Nothing acts on or interacts with Being, then the Nothing nihilates.  Many people believe and have believed that such a question has been or can be answered, and who guide and behave themselves accordingly, and who may produce statements intended to communicate that answer and which they take to have some kind of empirical or phenomenological foundation open to use by all who want to apply them.  Of course, I am thinking about the age-old disparities between certain religious and metaphysical beliefs as contrasted with age-old scientific and physical beliefs, disparities which can be and have been described in innumerable ways, in terms of innumerable -isms and -logies.  And I am suggesting that Carnap is mainly on one side of this battle-ground, and Heidegger is on the other side.  Alas, I myself seem to be somewhere in the middle of the battle-ground, not knowing for sure which side I'm on -- perhaps I'm on both sides, and people on both sides will find me disloyal.

5.15.  There is still one more of Heidegger's locutions that Carnap wants to characterize as being logically incorrect, a part of a sentence which Pap translates as "The Nothing exists only . . . because . . . "  Besides making mistake of using the word "Nothing" as a noun, says Carnap, there is a contradiction, " for even if it were admissible to introduce "nothing" as a name or description of an entity, still the existence of this entity would be denied in its very definition, whereas [this] sentence goes on to affirm its existence."  Thus it appears that Carnap has in mind a definition (Definition) of "nothing" (or "the Nothing") as a noun, but evidently wants to argue that it can't be shown to have a logically correct meaning (Bedeutung).  I suppose we can take this to be a distinction of the sort Frege recommended, and say that Carnap here thinks that the word "the Nothing" has a sense, but doesn't have a reference (a connotation but no denotation, an intension but no extension).  This ties in with what I said in the previous sentence.  I tried to make some sense out of the word "the Nothing", but I tried to leave open the question of whether or not the word refers in some empirical or phenomenological way, and also to hint that whether or not it is taken to refer may depend on who is making the test.  There may not exist a conclusive answer to this question which is accessible by all people, or otherwise put, there may not be an objective answer, and answers must remain subjective, although this need not mean solipsistic, since there will be (and, of course, there are and have been) numerous people who agree to one answer, and numerous people who agree to another, and still other people who agree to still another answer, and so on.  And there will be numerous people (such as myself) who simply haven't picked any one answer to agree to, and may even suspect that they will never find a definite answer (logically correct or not) to which they will agree.  These points of view could be described in terms of countless -isms and -logies and religious faiths and scientific theories, and indeed have been and continue to be described in such terms.  However, I will not attempt this here.

5.16.  Carnap goes on to offer some arguments against some defenses of what metaphysicians do.  Some of the anticipated defenses he undertakes to refute are related to comments I have made above, which while not intended to defend what metaphysicians do, my comments were intended to question what Carnap says metaphysicians do, and therefore my comments might be construed as or lead to such defenses.  In any case, Carnap suggests first that Heidegger may have had in mind a meaning for the word "nothing" which was "entirely different from the customary one", an eventuality I have spoken of above.  Here Carnap refers to Heidegger's statements in Was ist Metaphysik? (which he doesn't quote) to the effect that "anxiety [Angst] reveals the Nothing, that the Nothing is present as such in anxiety".  From this, Carnap concludes that "here the word 'nothing' seems to refer to a certain emotional constitution, possibly of a religious sort, or something or other that underlies such emotions", and he says that if this were the case, then there would be no logical errors in the words of Heidegger that Carnap quoted from Was ist Metaphysik?.  Thus Carnap assumes here a familiar sort of distinction between emotive and cognitive statements, between statements which describe some sort of feelings one has not arrived at by reasoning but in some other way, and statements which are arrived at by reasoning in some logically correct way.  Carnap rejects this defense of metaphysics by pointing to the first sentence in the quotation that he cited from Heidegger.  This sentence reads in Pap's translation, "What is to be investigated is being only and -- nothing else' being alone and further -- nothing, solely being, and beyond being, nothing."  In the original, the sentence reads, "Erforscht werden soll das Seiende nur und sonst - nichts; das Seiende allein und weiter nichts; das Seiende einzig und darüber hinaus -- nichts.  If we take it that Heidegger intends Seiende to refer to all and everything which exists in some empirical or phenomenal way, then one reasonable inference is that Heidegger has announced that he will be talking about what exists or subsists or reveals itself in some way other than empirical or phenomenal (the latter perhaps in some Husserlian sense).  And indeed, as Carnap notes, Heidegger goes on to assert that Angst (anxiety, fear, dread) reveals das Nichts.  Heidegger does say that Angst reveals nichts, but that it reveals das Nichts.  After the sentence of Heidegger's I just quoted, Heidegger's next sentence is the famous or infamous sentence "Was gibt es um dieses Nichts", "What is it about this Nothing".   That is, Heidegger has given the name das Nichts, "the Nothing, to that which he claims Angst reveals to people in a way different than the way Being is revealed to people.  Carnap, on the other hand, infers from Heidegger's statement that Heidegger has announced that he will talk only about all and everything that exists and about nothing beyond that, and that the word nichts here  "has the usual meaning of a logical particle that serves for the formulation of a negative existential statement".  So Carnap evidently concludes that Heidegger has announced that he will only talk about what exists, and that therefore Heidegger has announced that he will not be talking about what does not exist, and that yet Heidegger goes on to do just that, in answer to the question "Was gibt es um dieses Nichts".  It seems to me that Carnap has made here a reasonable inference from these statements by Heidegger, provided that he has interpreted the word "Seiende" differently from Heidegger.  Moreover, it seems to me that the statements in question in isolation can be interpreted in either of the two ways I have indicated, and the two interpretations will both be logically correct.  As usual, the sense and reference of statements (if any) will depend on context, and it is all too easy to get different and possibly contradictory interpretations of statements by not taking into consideration sufficiently broad or detailed contexts in which the statements were (or are) made.

5.17.  Carnap says that any doubts about whether or not he (or you) may have misunderstood Heidegger "gets completely dissolved" when we consider something further that Heidegger has said about the use of logic:

Question and answer in regard to the Nothing are equally absurd in themselves  . . .  The fundamental rule of thinking commonly appealed to, the law of prohibited contradiction, general 'logic' destroys this question.  . . .  If thus the power of the understanding in the field of questions concerning Nothing and Being is broken, then the fate of the sovereignty of 'logic' within philosophy is thereby decided as wee.  The very idea of 'logic' dissolves in the whirl of a more basic questioning.

In the German, the first sentence of this quotation is "Frage und Antwort im Hinblick auf das Nichts sind gleicherweise in sich widdersinnig", another possible translation of which is "Question and answer with regard to the Nothing are likewise paradoxical in themselves".  The context of this quotation isn't given by Carnap, and I don't know what the "likewise" may have referred back to; the same may be said about the translation "equally" of "gleicherweise" that Pap used.  In any case, Carnap asks "will sober science condone the whirl of counter-logical questioning?" Carnap takes as an answer to this Heidegger's statement that "The alleged sobriety and superiority of science becomes ridiculous if it does not take the Nothing seriously."  (I note that "sober" and "sobriety" here are Pap's translations of nüchterne and Nüchternheit, which could also be translated by "matter-of-fact" or even "pragmatic", along with corresponding nouns.)  Carnap concludes:  "Thus we find here a good confirmation of our thesis; a metaphysician himself here states that his questions and answers are irreconcilable with logic and the scientific way of thinking."

5.18.  What comes to my mind now is that Heidegger may have been thinking of the sort of thing I described in the paragraph before last, concerning how Carnap seems to have interpreted the statements of Heidegger that Carnap was criticizing.  I said that Carnap's interpretation seemed valid in one context, but I described another conflicting interpretation which could be made in a different context.  Along these lines, if one were to want to be charitable to Heidegger, one could take what Heidegger intended the statements quoted in the paragraph to say was something like this:  We shouldn't give up asking and answering questions about "the Nothing" because some interpretations of some questions and answers about "the Nothing" involve violations of the logical "law of non-contradiction".   That is, one could take Heidegger to have recommended, none too clearly, that the authority which many ascribe to so-called positive science (Wissenschaft), and to traditional laws of logic shouldn't, by itself, make us give up asking and trying to answer the sort of questions asked by metaphysicians, or at least by some metaphysicians, such as certain ancient Greeks.  But Carnap speaks against such a justification for doing metaphysics.  He does so not, he says, because he is rejecting metaphysics as "mere speculation" or "fairy tales" or "superstition".  These, he says, may not conflict with logic, although they may conflict with experience.  For metaphysical statements, says Carnap, are "meaningless sequences of words".  Carnap makes a similar objection to defenders of doing metaphysics who argue that human beings or any other "finite beings" are limited in such a way that it is impossible for them to find answers to metaphysical questions, but that such questions are nevertheless meaningful, but which a being with higher or perfect knowledge could answer.  Carnap again argues on the basis of meaninglessness and says that "if the meaning of a word cannot be specified, or if the sequence of words does not accord with the rules of syntax, then one has not even asked a question.  . . .  Where there is no question, not even an omniscient being can give an answer."  To a defender of metaphysics who says that a higher being might have the power to communicate "new knowledge" (presumably not by way of answers to meaningless questions, but in some other way, such as by what religious people call revelation), Carnap replies that if they communicate something to people but the people don't or perhaps can't know how to verify what has been communicated, then "no information has been communicated to us, but merely verbal sounds devoid of meaning though possibly associated with images."  Presumably here "to verify" refers to being able to test in some way by empirical means which can be employed by any competent person, and whose results will be agreed on by all such persons, or at least some significant numbers of them, and at least for some significant period of time.  Carnap says that "what we do not know for certain, we may come to know with greater certainty through the assistance of other beings; but what is unintelligible, meaningless for us, cannot become meaningful through someone else's assistance, however vast his knowledge might be.  Therefore no god and no devil can give us metaphysical knowledge." 

5.19.  It seems, however, that some metaphysical statements which are meaningless according according to Carnap's criteria might be revealed by a higher being to be empirically meaningful and objectively or intersubjectively shareable, according to criteria which aren't empirically based in the sense that Carnap understands the term "empirical.  Historically, numerous people have made claims along these lines, and in some cases groups of people have acted according to such a basis, at least sometimes with results which appear to me to be open even to empirical verification of the sort Carnap has in mind, at least so far as externally observable behavior of the people are concerned, even though there might be non-communicable meanings of their statements might not open to empirical verification in the sense of Carnap, since Carnap requires meanings to be communicable.  It strikes me that Carnap is describing a program he has undertaken for restricting ordinary languages and constructing artificial (and restrictive) languages useful for some purposes, and it strikes me that one may well agree with him that confining oneself to linguistic uses and rules of the sort he proposes in his Logische Aufbau der Sprache will affect how one interprets what a class of people he calls metaphysicians have said and continue to say.  The same may be said for his work after he wrote his 1932 article on how to cure oneself of metaphysics.  But as I have tried to adumbrate in my discussions above, there are numerous openings (or gaps) which can arouse doubts about whether applying his particular recommendations will enable people to eliminate or overcome doing what Carnap calls metaphysics, even in such austere fields of work as the natural sciences and mathematics.  Of course, one can handily use some of his work to criticize metaphysicians, and even to ridicule them, but on the face of it, if a person doesn't think metaphysicians in general aren't saying anything of scientific interest, or are talking a lot of nonsense, it would be more comfortable for the person just to stay away from metaphysics (and maybe from metaphysicians), so far as the person can, than for the person to spend a lot of time and effort making sure that the syntax and semantics and theory of meaning of the languages he or she uses, at least where reasoning is involved, obeys a complicated set of rules, to be tested by translating ordinary languages into symbolic ones.  However, there are people who think that metaphysical language of the sort Carnap criticizes is not only meaningless, but also pernicious.  And there are people who find regard metaphysical language of this sort to be close for comfort to certain kinds of theological or religious language.

5.20.  There is more to Carnap's article.  There is a section rather peremptorily entitled "Meaninglessness of all Metaphysics".  Here Carnap remarks that "perhaps the majority of the logical mistakes that are committed when pseudo-statements are made, are based on the logical faults infecting the use of the word 'to be' [sein]", and corresponding words in other languages.  He speaks about the ambiguity of this word and its inflections in ordinary usage, and the way he talks, it seems that he would like to eliminate all ambiguity of words in his articificial languages.  He speaks about "type confusion", involving predicates of different types, as illustrated by his example "Caesar is a prime number".  Here it appears that he has in mind that predicates should be regarded as functions which have differing admissible domains.  Then Carnap makes this rather startling claim :

Having found that many metaphysical statements are meaningless, we confront the question whether there is not perhaps a core of meaningful statements in metaphysics which would remain after elimination of all the meaningless ones.  . . .  But actually the situation is that meaningful metaphysical statements are impossible.  This follows from the task which metaphysics sets itself; to discover and formulate a kind of knowledge which is not accessible to empirical science.

So Carnap makes himself clear.  Any kind of knowledge which is not accessible to empirical knowledge is, he says, meaningless.  He goes on to discuss how what Wittgenstein called "tautologies", stated to be roughly the same as Immanuel Kant's "analytic judgments" are not factual statements but only serve to transform factual statements.  These and their negations are or include the rules of logic, and are said to true or false simply because of their form.  They are to be included among the meaningful statements.  The only other kind of meaningful statements are said to belong to the domain of empirical science.  Than, says Carnap,

Since metaphysics does not want to assert analytic propositions, nor to fall within the domain of empirical science, it is compelled to employ words for which no criteria of application are specified and which are therefore devoid of sense, or else to combine meaningful words in such a way that neither an analytic (or contradictory) statement nor an empirical statement is produced.

What freedom!  How liberating!  How much of the work of philosophers and theologians and other speculators of that sort is swept aside!  If a person has been attracted to a study of traditional philosophies, how much easier it has become.  But wait.  Carnap asks

But what, then is left over for philosophy, if all statements whatever that assert something are of an empirical nature and belong to factual science?  What remains is not statements, nor a thoery, nor a system, but only a method; the method of logical analysis.

So if you're a university study with a penchant for philosophizing, be sure to become proficient enough in mathematics or some empirical science, as well as in logic, so you will have something to do -- that is, something to do that's meaningful.

5.21.  Finally, Carnap talks about metaphysics as "expression of an attitude toward life", and classifies it as an inferior kind of art.  It seems that what artists do is also meaningless in Carnap's sense, but nevertheless the arts furnish adequate means for expressing one's attitude toward life, whereas metaphysics doesn't.  Lyrical poets, for example, are said not to be conveying meanings in their poems, but only expressing attitudes.  Carnaps observes that perhaps music is the purist means of expression of attitudes toward life

because it is entirely free from any reference to objects.  The harmonious feeling or attitude, which the metaphysician tries to express in a monistic system, is more clearly expressed in the music of Mozart.  And when a metaphysician gives verbal expression to his dualistic-heroic attitude towards life in a dualistic system, is it not perhaps because he lacks the ability of a Beethoven to express this attitude in an adequate medium?  Metaphysicians are musicians without musical ability.

There's an old saying used to indicate that someone isn't just fooling around, but is saying something that is -- well, saying something meaningful or valid:  "He (or she) isn't just whistling Dixie!".  This refers of course to an old song dear to Southerners in the USA, prominent as a battle song in that Lost Cause known as the Civil War, or the War Between the States, or the Great Rebellion, or the War of Northern Aggression, or the American Iliad.  It appears that Carnap thinks metaphysicians are just whistling Dixie, although dreadfully out of tune.