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PART V

PHILOSOPHY AND SYNTAX

A. ON THE FORM OF THE SENTENCESBELONGING O THE LOGIC OF SCIENCE

$ 72, Pnrr,osopnv RrprecrD By rHE Locrcor Scrrwce

The questions dealt with in any theoretical field-and similarlythe corresponding sentences and assertions-can be roughlydivided into object-questions nd ogical questions, This differentia-tion has no claim to exactitude; it only serves as a preliminary tothe following non-formal and inexact discussion.) By object-questions are to be understood those that have to do with theobjects of the domain under consideration, such as inquiries re-garding heir properties and relations. The logical questions, onthe other hand, do not refer directly to the objects, but to sen-tences, erms, theories, and so on, which themselves efer to theobjects. (Logical questions may be concerned either with themeaning and'content-of he sentences, erms, etc,, or only with theform of these; of this we shall say more later.) In a certain sense,of course, ogical questions are also object-questions, ince heyrefer to certain objects-namely, to terms, sentences, nd so on-that is to say, o objects of logic. When, however, we are alking ofa nonJogical, proper object-domain, he differentiation between

object-questions and logical questions s quite clear. For instance,in the domain of zoology, he object-questions are concerned withthe properties of animals, the relations of animal s to one anotherand o other objects, etc.; the logical questions, n the other hand,are concerned with the sentences of zoology and the logical con-nections between them, the logical character of the definitionsoccurring in that science, he logical character of the theories andhypotheses which may be, or have actually been, advanced, andso on,

According to traditional usage, he name'philosophy' serves

as a collective designation for inquiries of very different kinds,

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278 PART V. PHILOSOPHY AND SYNTAX

, Object-questions s well as logical questions are to be foundamongst hese nquiries. The object-questions re in part con-cerned with supposititious bjects which are not to be found in theobject-domains f the sciences for instance, he thing-in-itself,the absolute, he transcendental, he objective dea, he ultimatecause f the world, non-being, and such hings as values, absolutenorms, the categorical mperative, and so on); this is especially

the case n that branch of philosophy usually known as meta-physics. On the other hand, the object-questions orf philosophyare also concerned with things which likewise occ6r in the em- ,pirical sciences (such as mankind, society, language, histoqy,economics, ature, space and time, causality, tc.); this is especlJally the case n those branches hat are called natural philosophy,the philosophy of history, the philosophy of language, nd so on.The logical questions ccur principally n logic (including appliedlogic), and also n the so-called heory of knowledge or epistemo-logy), where they are, however, for the most part, entangled withpsychological questions. The problems

of the so-called philo-sophical foundations of the various sciences such as physics,biology, psychology, and history) include both object-questionsuna tirgicat questions. /

$72. nHtlosoptlYREPLAC:liDtYTIIIiL(x;I(loI ; s(:tliNcli 271)

questions nd psychologiclrl ncs. Vcry oltc:lr ltcr rrrtnttl ; t t iottt l ' lrquestion oe s ot make t clearwhcthcr t i s r r tcr r t l t : t lt s : t t syr ' l t ' r-logicalor a logical otre,an d lr this way l groilt lcltlol'coltlttsittttarises.] he remailring uestions, ha t s, n ordirl:rrycrttt i t tolrgy,questions f logic, of the heory of knowlcdgc or cpistt:rt tokrgy),fnatural philosophy, f the philosophy f history, ctc:. , rc sotllt :-times designated y those who regard netaphysics s unscicntific

as questions f scientific philosophy. As usually ormtrlated, hcscquestions are in part logical questions, but in part also object-questions which refer o the objects of the special ciences. Fhilo-sophical uestions, owever, according o the view of philosophers,are supposed o examine such objects as are also nvestigated ythe special sciences rom quite a different standpoint, namely,fro;:n he purely philosophical one. As opposed o this, we shallhere maintain hat all these emaining philosophical uestions relogical questions. Even the supposititious object-questions relogical questions n a misleading guise. The supposed peculiarlyphilosophical point of view from which the objects of science reto be investigated proves o be illusory, ust as, previously, hesupposed eculiarly philosophical ealm of ol.rjects roper o meta-physics. isappeared nder analysis. Apart from thc questions ofthe individual sciences, nly the questions f the logical rnalysis fscience, f its sentences' erms, conccPts, heorics, ctc', ill'c eft asgenuine cientific uestions. We shall call this ctlnrplcx l'

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z8o PART V. PHILOSOPHY AND SYNTAX

consideration hat th e word 'philosophy' is already heavilyburdened, and ha t it is argely applied particularly n the Germanlanguage) o speculative metaphysical discussions. he designation' theory of knowledge' or 'epistemology') s a more neutral one,bu t even his appears ot to be quite unobjectionable, ince t mis-leadingly suggests resemblance etween he problems of ourlogic of scibnce nd the problems of traditional epistemology; he

latter, however, are always permeated by pseudo-concepts andpseudo-questions, nd frequently in such a way/that their dis-entanglement s impossible.

The view that, as soon as clainrs to scientific qualificationFatemade, all that remains of philosophy s the logic of science, annotbe established ere and will not be assumed n h'hat follows. Inthis part of the book we propose o examine he character of thesentences f the logic of science, nd to show thatlthey are syn-tactical sentences. For anyone who shares withXs the anti-metaphysical tandpoint t will thereby be shown that all philo-sophical problems which have any meaning belong o syntax. Thefollowing investigations oncerning he logic of ecience s syntaxare not, however, dependent upon an adheience o this view:those who do not subscribe o it can ormulate our results simplyas a statement hat the problems of that part of philosophy whichis neither metaphysical or concerned with values and norms aresyntactical.

Anti-metaphyiical views have often been put forward in the past,especially y Hume and the Positivists. he more exact hesis hatphilosophy an be nothing other han a logical analysis f scientificconcepts nd sentences in other words, what we shall call he ogicof science) s represented n particular by Wittgenstein and theVienna Circle,

and has been both established n detail and in-vestigated n all its consequences y them; see Schlick Metaphysikf,fWendel, fPositioisrnusl; Frank fKausalgesetzl; Hahn lWiss.Weltau.ff.l; Neurath fWiss. Weltauff.], fWegeh Carnap fMeta-physihl; further bibliographical eferences re given by NeurathfWiss. Weltauff.] and n Erhenntnis, , 315 f. Neurath s definitelyopposed o the continued use of the expressions philosophy','scientificphilosophy', natural philosophy , theory of knowledge',etc,

The term logicof science' ill be understood y us n a very widesense, amely, as meaning he domain of all the questions hich areusually designated s pure and applied ogic, as he logicalanalysisof the special sciences r of scjence as a whole, as epistemology, as

$72. nurlosopuy RErLAcEDBy rHE Locrc oF scIENcE z8r

problems of foundations, and the like (i n so far as these questionsare free from metaphysics and from all reference to norms, values,transcendentals, etc.). To give a concrete illustration we assign thefollowing investigations (with very few exceptions) to the logic ofscience the works of Russell, Hilbert, Brouwer, and their pupils, theworks of the Warsaw logicians, of the Harvard logicians, of Reichen-bach's Circle, of the Vienna Circie centring around S,chlick, themajority of the works cited in the bibliography of this book (andothers by the same authors), the articles in the journals Erkenntnisand Philosophy of Scimce, the books in the collections " Schriftenzur wissenschaftlichen Weltauffassung " (edited by Schlick andFrank), "Einheitswissenschaft" (edited by Neurath), and finallythe works mentioned in the following bibliographies: Erkenntnis,r, 315 ff. (general), 335 ff. (Polish logicians); rr, r5r ff. (foundationsof mathematics), r89 f. (causality and probability); v, r85 ff.(!eneral), r95 fr . (American authors), r99 ff. (Polish authors), 4o 9 ff.(general).

$ Zg. THn Locrc oF ScIENcE S THE SvNrexOF THE LEUCUECN OF SCIENCE

In what follows we ghall er(amine he nature of the questions ofthe logic of science n the wide senee, ncluding, as already ndi-cate( the eo-called hilosophical roblems concerning hc founda-tions of the ind.ividtral sciences, nd we shall show that thesequestions re questions f syntax. In order to do this, it must firstbe shown that the o bject-questions which occur in the logic ofscience for exaglrle, questions oncerning numbers, hings, timeand space, h#elations between he psychical and the physical,etc.) are only pseudo-object-questisls-i.s. questions which, be -cause f a misleading ormulation, appear o refer o objects whileactually hey refer to.sentences, erms, heories, and th e like-andare, accordingly, in reality, logical questions. And secondly, itmust be shown that all logical questions are capable of formalpresentation, nd can, consequently, e formulated as syntacticalquestions. According to the usual view, all logical investigationcomprises wo parts: a formal inquiry which is concerned onlywith the order and syntactical kind of the linguistic expressions,and an inquiry of a material character, which has o do not merelywith the formal design but, over and above hat, with questions ofmeaning and sense. Thus the general opinion is that the formalproblems constitute, at the most, only a small section of the domain

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282 PART v. PHILosoPHY AND sYNTAx

of logical problems. As opposed to this, our discussion of generalsyntax has already shown that the formal method, if carried farenough, embraces all logical problems, even the so-called pro-blems of content or sense (in so far as these are genuinely logicaland not psychological in character). Accordingly, when we saythat the logic of science is nothing more than the syntax of thelanguage of science, we do

not mean to suggest that only a certainnumber of the problems of what has hitherto bepn called the logicof science (as they appear, for example, in the'works previouslymentioned) should be regarded as true problems of the legic ofscience. The view we intend to advance here is rather that "all

problems of the current logic of science,",

.ooo{, they areexactly formulated, are seen to be syntactical problems.

ItwasWittgensteinwho firstexhibited the close connection bcg#eenthe logic of science or "philosophy", as he calls t) and syntax. Inparticular, he made clear the formal nature of logic and emphasizedthe fact that the rules and proofs of syntax should have no referenceto the meaning of symbols (lTractatusl, pp. Sz, 56, and 164),

Further, he has shown that the so-called sentences of metaphysicsand ofethics are pseudo-sentences. According to him philosophy is"critique of language" (op. cit. p, 6z), its business is "the logicalclarification of ideas" (p, Z6), of the sentences and concepts ofscience (natural science), that is, in our terminology, the logic ofscience. Wittgenstein's view is represented, and has been further,developed, by the Vienna Circle, and in this part of the book I owea great deal to his ideas. If I am right, the position here maintainedis in general agreement with his, but goes beyond it in certain im-portant rcspects, In what follows my view will sometimes be con-trasted with his, but this is done only for the sake of greater clarity,and our agreement on important fundamental questions must nottherefore be overlooked.

There are two points especially on which the view here presenteddiffers from that of Wittgenstein, and specifically from his negativetheses, The first of these heses op. cit, p.78) states: ( Propositionscannot represent he logical form: this mirrors itself in the proposi-tions. That which mirrors itself in language, language cannot repre-sent. That which expresses tsef in language, we cannot express bylanguage.. . . If two propositions contradict one another, this isshown by their structure; similarly, if one follows from another, etc.What can be shown cannotbe said.. . , It would be as senseless oascribe a formal property to a proposition as to deny it the formalproperty." In other words: There are no sentences about the formsof sentences thereis no expressiblesyntax. In oppositionto thisview,our construction of syntax has shown that it can be correctly formu-lated and that syntactical sentences do exist. It is just as possible to

$73. rocrc oF scrENcE THE syNTAx oF LANcUAGE F scIENcE 283

construct sentences about the forms of linguistic expressions, andtherefore about sentences, as it is to construct sentences about thegeometrical forms of geometrical structures, In the first place, hereare the analytic sentences of pure syntax, which can be applied to thcforms and relations of form of linguistic expressions (analogous tothe analytic sentences of arithmetical geometry, which can be ap-plied to the relations of form of the abstract geornetrical structures);and in the second place, the synthetic physical sentences of de-scriptive syntax, which are concerned with the forms of the linguisticexpressions as physical structures (analogous to the synthetic em-pirical sentences of physical geometry, see $ z5). Thus syntax isexactly fonnulable in the samc way as geometry is.

Wittgenstein's second negative thesis states that the logic ofscience (" philosophy ") cannot be formulated. (For him, this tlresisiloes not coincide with the first, since he does not consider the logicof science and syntax to be identical; see below.) " Philosophy is nota theory, but an activity. A philosophical work consists essentiallyof elucidatione. The result of philosophy is not a number of 'philo-sophical propositions,' but to make propositions clear" (p. Z6).Consistently Wittgenstein applies this view to his own work. also;at the end he says: " My propositions are elucidatory in this way: he

who understands me finally recognizes them as senseless, when hehas climbed out through them, on them, over them. (He must, so tospeal, throw away the ladder, after he has climbed up on it.) Hemust surmount these propositions; then he sees the world rightly.Whereof one cannot speak, thereof one must be silent" (p. t88).According to this, the investigations of the logic of science containno sentences, but merely more or less vague explanations which thereader must subse.quently recognize as pseudo-sentences andabandon. Such a1L{nterpretation of the logic of science is certainlyvery unsatisfactftL lRamsey first raised objections .to Wittgen-stein's conception of philosophy as nonsense, but important non-sense ([Fozndationsf, p, 263), and then Neurath, in particular,(lSoziol. Phys.l, pp. 39S f . and fPsychol.f , p. zg) definitely rejected it. ]When in what follows it is shown that the logic of science is syntax,it is at the same time shown that the logic of science can be formu-lated, and formulated not in senseless, f practically indispensable,pseudo-sentences, but in perfectly correct sentences. The difrerenceof opinion here indicated is not merely theoretical; it has an im-portant influence on the practical form of philosophical investiga-tions. Wittgenstein considers that the only difference between thesentences of the speculative metaphysician and those of his own andother researches nto the logic of science is that the sentences of thelogic of science-which he calls philosophical elucidations-in spiteof their theoretical lack of sense, exert, practically, an importantpsychololical influence upon the philosophical investigator, whichthe properly metaphysical sentences do not, or, at least, not in thessme way. Thus there is only a difference of degree, and that a very

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284 PART V. PHILOSOPHY AND SYNTAX

vague one. The fact that Wittgenstein does not believe in the possi-bility of the exact formulaiion of the sentences of the logic of sciencehas as its consequence that he does not demand any ocientificexactitude in his own formulations, and that he draws no sharp lineof demarcation between the formulations of the logic of science an d

those of metaphysics. In the following discuseion we shall Bee hattranslatability into the formal mode of speech-that i0, into syn-tactical sentences-is the criterion which separates he propcr sen-tences of the logic of science rom the other philosophical ecntences-w e may call thbm metaphysical. In somc of hic forynulrtiona,Wittgenstein has clearly overstepped thie b

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?;86 PART V. PHILOSOPHY AND SYNTAX

Babylon it does not matter whether 61 is true or false' Further'

tt"i6,

is only a pseudo-object-sentence s clear from the circum-

stance^that d,"""

be translated into the following sentence of

(descriptive) .yrrt"*t "In yesterday's ecture either"the word; B"bylorr' or an exPression ynonymous with the word ' Babylon'

occurred (62).Accordingly, we distinguish three ki'nilsof sentences: ,

we have already shown. Even if the syntax-language S, is a sub_Ianguage of S, it is, of course, both possible and necessary o dis-tinguish between a sentence 6r, of S, (which may also belong toSr), and a syntactical entence r, concerning 61 , which belongs oS, and therefore also o 51. For simplicity's sake, we will formulatethe criterion of the material mode of speech or the simplest sen_tential form only (and further, for the sake of.brevity and clarity,we will formulate it for a symbolic Bentence) see $ 64). Let 6, be'P (a)\; 61 is called quasi-syntactrcaln respect f ,a', if there exists

naterial mode f specch. Q' is called a syntactical redicate orre_lated o the quasi-syntactical redicate p'1 and , is called a syn_tbctical sentence orrelated o the quasi-syntactical entence gr .In the translation ftom the matcrial to the formal mode of ,prrri,6, is tratulated into 6s.

in 6, of the word 'Babylon' is parallel o that property which is

$ 74. rseuoo-oBJEcr-sENTENcES 287

r, Obiect-sentences

Examples: " 5 isa prime number"l" Babylon was a bigtown t' ; " liong ar emammalg"'

z. Pseudo-obiect'ssnlen6ss = quasi-

syntactical sentences

Material mode ofsPeech

Exarriples: " Five isnot a thing, but anumber "; " BabYlonwas treated of inyesterday's lecture."

(" Five is a number-word " is an examPlebelonging to the au-tonymous mode ofspeech.)

3, Syntacticalsentences r

Fonnal *oil|ofsPeech

Examples "' Five'is not a thing-word,bu t a number-word";" the word 'Babylon'occurred in Yes-

terday'slecture"l

t r t4 . -A ' is a con-tradictory sentence. "

J

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28 8 PART V. PHILOSOPHY AND SYNTAX

asserted n 6, of the town of Babylon ; for if, and only if, ycntcrtluy'u

lecture was concerned with a ccrtairt object, tlitl t tlcsigrrrtl ot t ol '

that object occur in the lecturc. I 'hc cri tcrion of thc rrtrttcrirtl ttorlc

of speech s likewise fulfilled ftlr thc sclltclr(r(1 , ol'tlrc exrtttt;rle

concerning 'f ivc ' ; for i l t , antl only if , t l rc 1tt 'opclty exlttctrltt 'tl

in 6r-that of bcing not a thing ll t t t t t t t t t l t tbcl ' l rekrl tgn rt l ' tol l lcobject (for i nstance, tu tltc nt trttltcr (ivc) tftrcs ltc )1rlopclty cx -pressed n 6r-thnt of bcirrg not rr t l r i rrg-wortl l rr t t t r t t r t r t t l rct-

word--belong trr a clcsigrri t t iot t f tlritr oll.icct ir r tlre cxutltPlqJB)the word 'five').

$ ZS. SttN'lr tru

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290

84, The sentnceo 61 and 9shave the same mcaning.

qa , 1 on d 91 hrvo r dif 'lorent meanin! but thcy ttl,r(tont(orl r lorcr ibo) ho rlmo fnct ,

rza. This letter es about t]l'eson of Mr . Miller.

r3a. Th e exPression le che-va l de M' designates or: means)the horse of M.

r4a, Th e expression'un 616-phant bleu' means a blue ele-phant.

PART V. PHILOSOPHY AND SYNTAX

6a. The expressions merle' | 6!' 'Merle' and 'blackbird'and 'blackbird' have the same I are L-synonymous'meaning or: mean he same; or :have the same ntmional object).'*7r.-;-et."ingstar'and'-nii#^'

I z o' .'Evening star 'an d

in ,iu, ;hurr"u ifi"r"nt.n""rring, | ' morni"g ,tt": -ut-l T::::I"-

itlt they dt tignate the same object' I onyrnous' but P-synonymous'

[Wiih .".p""t to a symbofi-c-(!=)anguage,'f".3b"::.:tJt1"J::

S6. 61 and 6s are L'equi'nollcnt.'

oD . 9r rn d 61 ar c no t L'oqulpollcnt but P-oquiPollcnt.

lWit l r lmpcct t( t 0 iymlnl ic langurgo:-80' ' 1 r 91 lr rnelyt ic '

, )Al g, = er ' in no t an; lyt ic but l ' 'v l l id ,]

roa. 'lhc scntcnccr of ar i th ' I loD' 'Ihe rontoncoa f orith'

rnct ic state (orl exprcss) certain I mcticarecomporedof numcrical

properties oi ttu*L"te and,cer- | expreosions andonc- or mony-

iain rclations between numbers' I termed numerical predicateeI combined in such and euch a waY'

t7 a, Aparticular sentenceof i - rrD'A particular sentence f

ph;il; ririrt itt" "o"ditionof a I nhrsics consists of a descriptive

Ipi,l.i p"i", at a given time. |-ntiai""t". and s1-111;11nnoralco-ordinates as arguments.

The following examples 12a' 13at and t4a appear at first to be of

the same hind as ta and 4a' Actually, however, they demonsuate

o"tti""i"tiv clearly the danger of error which is involved inthe use

bf the material mode of sPeech.tzb. In this letter a sentence

Fr (!IJ occurs in which [1 is the

description 'the son of Mr 'Miller'.

136. There is an equiPollentexpressional translation from theFrench into the English lan'euaee nwhich'the horse of M'is

;he;orrelate of'le cheval de M "4D. (Analogous to r3D.)

$75. seNrnncEs ABour MEANTNG 29r

I-et us assume that Mr. Miller has no son; even in this case thesentence 12 a may still be true ; the letter will then merely be tellinga lie. Now, from the true sentence tza, according to the ordinarylogical rules of inference, a false sentence can be derived. In orderto make the derivation more exact, we will use a symbolism in placeof the word-language. Instead of 'this letter' we will write , b'; in-stead of 'b is about a' we will write 'F I (b , a) ; and instead of . the sonof a' we will write 'Son'a' (descriptional in R.ussell's symbolism,se e $ l8c) . Hence for tza wil l be wri t ten: 'FI(b, Son'Mil ler) '(Gt), According to a well-known theorem of logistics (see myQletstih), $ 7 c: L 7.z), f.rom a sentence Fr (Urg) in which a descrip-ttorl occurs as argument, a sentence is derivable which asserts thatthere exists something which has the descriptional property.

TAccordingly, from 6, would be derivable '( f x) (Son(x,Miller))'VGJ; or,'in words: " a son of Mr. Miller exists . This, however, isa

false eentence. Similarly the possibly false sentence " There is ahorse of M " ia derivable from r3 a, and the false sentence " there isa blue elephant" from r4a, On the othcr hand, by t he usual rulesno fulsc acntences can be derived from the sentences z 6, r 3 6, andr4D of the formal rnode of spcech. These examples ghow that theure of the motcriol mndc of specch leads to contrndictions if themotlrotlr of irrtblenco which nre correct fol: other Bentenccg arethoughtleauly scd alro in txrnncr: t iorr it h it . [I t cnnnot bc main-tr incd t :hat hc formulat i rrns za t I3 a, nnd r4a arc rrcorrect , r thatth o ur e f he moteriul nrtxk: of apecch eads nccesusrily o contra-dictiona; for, ufter all, tho word-langrrrrgc s not borrnd by thc rulesof logietir:e, If, thcreforc, onc wiuhcs to admit thc material modc bfepeech, ne must apply to it a uystern of tules which is not only morecomplicated han that of logistics but is also more complicated thanthat which gove-gns he rest of the sentences of the word-language.]

rySorue senten&s contain a relation of meaning which is to some

extent concealed. Vith sentences of this kind it is not obvious, atfirst sight, that they belong to rhe material mode of speech. Themost mportant exarnples of this are the sentences which use theso-ealled ndirect or oblique mode of speech that is to say, sen-tences which say something about a spokerg thought, or writtensentence, ut razhich o so not by a $I:atement f the original word-in g bu t instead y rneano f a 'that', 'whether'', or other'w..,'sentence, r o.[ a subordinate sentence sithout a connective word,or of an nfinitive with 'to'). In the foliowing examples rS a andr6a, the formulations r5D and 166 show that the sentences nwhich he indirect mode of speech occurs are of the sarne kind asthe examples previously d,iscussed, nd hence also belong to thematerial mode of speech.

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292 PA.RT V. PHILOSOPHY AND SYNTAX

L Material mode of sPeech Il. Formal modeof speech

r. Sentences n in-direct speech

rSa, Charles said(wrote, thought) Peterwas coming tomorrow

(or; that Peter wascoming tomorrow).

t6 a. Charles saidwhere Peter is.

z. Sentmces aboutmeaning

r 5 6. Charles saida sentence whichmeans that Peter is

coming tomorrow.

r6 D. Charles saida sentence whichstates where Peter e.

r 5 c. Charles saidthe sentence Peter iscomingtomorrow'(or:

a sentencs of whichthis s a conbequence),16 c. Charles said

a sentence of ttrgform'Pcter is -' #which a spatial deeig-nation takes he placeof tho dash.

The use of the indircct mode of epeech e admittedly ehort andconvenient; lut it containe he same dangers s he other sentencesof thc materinl mode. For instance, entence 5d, as contrastedwith scnterrce 5c, gives he false mpression hat it is concernedwith lteter, while in reality t is only concerned with Charles airdwith the word'Peter'. When the direct mode of speech s used,this danger does not occur. For instance, he sentence: Charlessays'Peter s coming omorrow"'does not belong o the materialmode of speech: t is a sentence of descriptive syntax. The directmode of speech s the ordinary form used n the wordJanguage orthe forinal syntactical mode. (On the construction of the syn-tactical designation of an expression with the help of invertedcommas, ee $ 4r.)

The examples so far given suffice to show that, with certain

formulations in the material mode of speech, here is the danger ofobscurity or of contradictions. t is true that in such simple casesas hese he danger s easy o avoid. But in less obvious cases fessentially he same kind, especially n philosophy, he applicationof the material mode of speech has ime and again ed to incon-sistencies nd confusions.

$ 26. UNrvnnsel WonosWe will call a predicate of which every full sentence s an ana-

lytic sentence a uniztercal redicate, or, if it is a word in the word-language, a universal word. [For every genus of predicates a uni-

$ 76, uNlvrnsAl woR.Ds 293

Eaarnples of uniztersal words ,thing', ,object ,

,property','relation , t fact , 'condition', process , , event , action , ,rp"ti"l

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29 4 PART V, PHILOSOPHY .d},IDSYNTAX \vpoint ' , 'spatial relation' , space' (system of spatial pnints con-nected by spatial elations), temporal poirlt', 'tcmporal rclalion','time' (system of temporal points conneCtccl ry tr:rrrporal clir-t ions) ; 'number ' , in teger ' ( in I ancl X) , ' rea l nt r rnbcr ' ' i i r surr t tcsystems), function' , 'aggregate' or 'class '); 'cxprconior.r ' ir r nlanguage f pure syntax); and many othcrs.

We all use such universal ords n

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296 PART V. PHTLOSOPHY ND SYNTAX

a universal word are held by Wittgenstein) be nonsense, becausehe does not consider the correct formulatiod of syntactical sentencestobepossible.

\ , t.The use of unioersal wor^ in questions'in connection wiih one of

th e w... interrogatives ( 'what ' , 'who' , 'where ' , 'which ' , etc .)is akin to their use in universal and e4istential sentences. Herealso, in tra:rslation. into a symbolic lan{uage,

the universal worddetermines the choice of the kind of variable. A yes-or-no ques-tion demands either the afirmation or the denial of a certain sen-lence 6r, that is to say, the assertion of either 6, or - 6r.

lExample: The question "Is the table round?,' requires us toassert n answer ei ther: "the table is round" or:,,the table is notround."l As contrasted with this, a w.,, question demande nreference to a certain eentential function the ossertion of a cloaedfull sentence (or sentcntial framcwork). In a eymbolic quertion,the genua of the argumcnts requeatcd ie determined !y the kind ofthe argument variables. In the word-languages $lfs genus is in-dicated by means either of a specific w... interro=g\ive (such as'who' , 'where ' , 'when') or of an unspecif ic w... interrogative(such as what', 'which') with an auxiliary universal word. Hencehere also the universal word is, so to speak, an index to a variable.

Examples: r, Suppose I want to ask someone to make an assertionof the form " Charles was - in Berlin ", where a time-deteminationof which I am ignorant but which I rvish to learn from the assertionis to take the place of the dash. Now the question must indicate bysome means that the missing expression is to be a time-determina-tion. If symbols are used this can be effected by giving a sententialfunction in which in the place of the argument a variable , !,, whichis established as a temporal variable, occurs. [To symbolize thequestion, the variable whose argument is requested must be boundby means of a question-operator, e.g. ( ? ) (Charles was in Berlin) ,.1In the word-language the kind of argument requested is made knowneither by means of the specific question-word'when' (,,When wasCharles in Berlin ? ) or by means of the universal word , time' or'temporal point' attached to an unspecific question-word (,,Atwhat time was Charles in Berlin ? ).

z. I wish to ask someone to make me an assertion of the form" Charles is - of Peter", where a relation-word is to take the placeof the dash ( ' father ' , ' f r iend' , ' teacher ' , or the l ike) . Th e symbolicformulation of this question,. by means of the relational variable . R' ,

is : '( ? R) (R (Charles, Peter))'. Its formulation in the word-languageby means of the addition of the universal word , relation' to anunspecific question-word is : " What relation is there betweenCharles and Peter ?

$ 77. uNrrnset. woRDs N MATERTALoDEoF spEEcH 2g7

5ZZ. UNrvrnser, Wonps rN rHE Mnrnnrel,Mooe oF SpEEcH

In the first use of the universal word, which we have up to nowbeen discussing, t appears as an auxiliary symbol determining thegenus of another expression; t was found that, if in place of this

other expression a symbol ndicating its own genus was ntroduced,then the universal word could be dispensed with. As opposedto this, in t he second use the uniztersal word appears as an inde-pmdent e*pression, hich in the simplesl form occupies he placeofthe predicate n the sentence n question. Sentences fthis kindbelong to the material mode of speech; or a universal word is hereI quesi-syntactical redicate; he correlated syntactical predicateis that which designates he appertaining expressional genus.

lExanplc:'numbr' is a universal word because t belongs ana-lytically o all the objects of a genue of objects, namely, hat of thenu6bers the correlated syntactical predicate s

'numerical ex-pression' or 'number-word'), since his applies o all expressionswhich designate number. The sentence Five is a number " is aquasi-syntactical entence fthe material mode ofspeech; a corre-lated syntactical sentence s " ' Five' is a number-word ". ]

S entenc s witli unioer s alutords

(Material mode of speech)17 a. The moon is a thing ; five

is not a thing, but a nurnber.

Syntactical sentences

(Formal mode of speech)176. 'Moon' is a thing-word

(thing-name) I 'five' is not athing-word, but a number-word.

In t7a, as contrasted with sentences ike "the thing moon.,.","the number f ive. , ." , the universal words ' thing ' and'number ' ar eindependent.

18a. Apropertyisnot athing. I r8D. An adject ive property-I word) is no t a thing-word.

That the formulation r8a is open to objection is shown by thefollowing consideration. r8a violates the ordinary rule of types.This comes out particularly clearly when an attempt is made tbformulate it symbolically, either by means of '(F)(Prop(f")c -Thing(F)) ' or by means of ' (rc) Prop(r)c -Thing(x)) ' ; in thefirs t case, 'Thing(F) ' , and in the second case 'Prop(r) ' , is incon-

sistent with the rule of types. Therefore, if r8 a is admitted as asentence (it makes no difference whether true or false), by the usualsyntax of logistics Russell's antinomy can be constructed. If this isto be avoided, special complicated syntactical rules are necessary.