2528419 Ludwig Witt Gen Stein Tractatus LogicoPhilosophicus

8/3/2019 2528419 Ludwig Witt Gen Stein Tractatus LogicoPhilosophicus

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TRACTATUS

LOGICO- PHILOSOPHICUS


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TRAC TATUS LOGICO- PHILOSOPHICUSLudwig Wittgenstein

Tiznslated by C. K Ogden Introduction by Bertrand Russell,F.R.S. Introduction rothe New Edition by Bryan Vescio

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Introduction Copyright @ zoo3 by Barnes & Noble Books First Published rgzz Thisedition published by Barnes & Noble Publishing, Inc. All rights reserved. No part of this book may be used or reproduced in any manner whatsoeverwithout writtenpermission of the Publisher. Cover Design by Pronto Design, Inc. aoo3 Barnes &Noble Publishing, Inc. ISBN o-76o7-52gb-4 Printed and bound in the United Statesof America rgb79ro864z


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CONTENTS

EDITORS'NOTES INTRODUCTION TO THE NEW EDITION

IX

XI

INTRODUCTION

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TRACTATUS LOGICO- PHILOSOPHICUS

SUGGESTEDREADING

r59


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Ded,icated Tb tlw Menury of My Frimd Daaid H. Pinsmt

Motto: . . . und alles,was rnan weiss,nicht blossrauschm und,brausm gehdrthat, kisst sich in drei Wortm sagm. Kdnrvarncrn.


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IN rmdering Mr wittgmstein' s TractatusLogico-philnsophicus aaailabre th,e fur English readers, somathat unusuar courcehasbeen ad,opted printof ing the miginalsidt @ sidz with the transrntion. Sucha mpthodof presmtation seemed dcsirablc bo

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c. K. o.r922 Fm the re&sons statedaboue,thisBarnesr Nobleed,ition maintains thed,ual-languageformat themiginal. of


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Luowrc wittgenstein is widery regarded as the most important philosopher of thetwentieth century, and the Tractatui LogicoPhilosophicu.s the only book-length work of philosophy he is pub_ lished in his lifetime. Together, these two facts conveysome idea of the power this work has exerted over the minds of other philosophers and over the disciprine itself, In the book, wittgenstein claims no lesst

han to have solved all the problems of philosophy, and for a work with such a short page count, it is astonishing inits ambition. It managesto offer a radical new theory of logic, along the way addressingsuch problems as the foundations ofmathematics, sorip sism,the nature of ethics and art, and even free will. Ail these topics are confronted in an intricately structured seriesof numbered statements that are notoriously accompanied by little argument, but that are neverthelesscommanding in their declamatory tone and even beautiful in their gnomic brilliance. By the end of this trearise on logic, the book takes a striking turn toward the mystical, and. this shift indicates the somewhat conflicted attitude toward philosophy that lies at its core. Ludwig wittgenstein's life was marked by thesame pervasive sense of conflict that characterizeshis work. He was born in r 889 into the family of a wealthy viennese industrialist bur gave the bulk of his

inheritance away. was bothJewish He and t o-mosexual in a dme and place that acceptedneither. The youngest of


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eight gifted children who grew up in an exceptionally cultured household, Wittgenstein at first seemed to lack the talents of his older siblings, particularly in music. He wassent to study engineering, and eventually went to Manchesteq England, to study aeronautics. During this time he became interested in the theory of mathematics and began reading the works of Gottlob Frege and Bertrand Russell,

who had independently been trytng to prove that mathematicsis a branch of logic.He decided to share his own ideas on the subject with Frege, who suggestedthathe go to Cambridge to study with Russell.At Cambridge, Russell quickly became convinced of Wittgenstein's genius and encouraged him to develop his own theory oflogic, which Wittgenstein began to do in Norway until World War I broke out. AnAustrian patriot, Wittgenstein enlisted on the opposite side of the war from Russell'sEngland, and it is both incredible and appropriate that he was able to complete tlre Tractatus, his theory of logic, during active combat duty. It was published in rgzr. After a brief stint as a rural schoolteacher, Wittgenstein returned to Cambridge and eventually received an appointment as professor. He becamelegendary for his eccentric behavior and lectures,but in these lecturesWittgenstein developed an entirely new approach to philosophy that departed sharply from

his work in the Tiactatus. This approach culminated in the posthu(rgg3), the other mous publication of his Philnsophical Inuestigations major work on which hisreputation now rests. But he found academic life to be incompatible with his work, and he resigned from Cambridge in r.947, only eight yearsafter he wasappointed to G.E. Moore's chair.He died of prostatecancerin rg5r. The TradatuJwaswritten in three distinct stages,each of which produced one of the book's m{or contributions to phllosophy. In rgr3-r4, Wittgenstein worked in a remote village in Norway to develop his theory of logic. This theory is formulated explicitly in response to Russell's"Theory of T1pes,"arguing that a properly conceived symbolism makes the latter superfluous. During the first months of the war, in which Wittgenstein sawno combat, he developed his Picture Theory of Propositions, which heldthat proposi-


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tions represent statesof affairs in the world becausetheir parts mirror objectsand relations in the world itself. On this theory it is a common form or structure that propositions share with the facts they represent, and it is this form orstructure that logic caPtures. After 1916, when Wittgenstein began to experience combat firsthand, he became suicidal, as he frequently did throughout his life, and he turned to religion for consolation. This conversion is largely responsible for the mysticism that fills the final pagesof the Tractatru, which holds that science and language must remain silent on the ultimate truths about the world, including those of metaphysics, ethics, and aesthetics. It is remarkable thatthese apparently distinct ideas are blended and what unites them is whole in the Tractatus, into a seamless Wittgenstein's central distinction between saylng a

nd showing. According to Wittgenstein, language can only describe facts about the world, not the logical stnrcture that it shareswith thosefacts.For to describethe latterwould be to describethe very limits of the world, and that can only bedone from an unattainable position outside the world. The logical structure that undergirds our language - and thus, for Wittgenstein,that definesour world - cannot be described at all; rather, it can only be "shown," and it is shown everywherein language that is used properly. Mysticism, which Wittgenstein defines as"feeling the world as a limited whole," is a kind of knowing beyond prepositional knowledge, a sensethat even though the limits of the world cannot be said orthought, those limits nonetheless exist. But this leavesphilosophy, whose goal is precisely to describe those limits, in a peculiar position. Wittgenstein considers all the problems of philosophy to stem from an attempt to saywhat ethics, and aesthetcan only be shown.All positions in metaphysics, ics, asstatementsabout

the limits of possibility in the world, are fundamentally in error. Once this becomes apparent, Wittgenstein thinks, all the problems of philosophy are solvedin the sensethat is they are all dissolved.Yet the Tractatus concerned to preserve some sort of role for philosophy to play. Most often, philosophy is said to clari& or elucidate ordinary language. On the other hand,


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Wittgenstein famously concludes by admitting that his own "elucidations" are "nonsensical,"forming a ladder to be aba/rdoned as soon as one has climbed up it. Here, the proper philosophical perspectiveappears to be identified with the mystical itself. This ambi. guity captures what has struck so many readers as the curiously divided nature of the Tractatus, beginnings in the precision of its mathematical logic and its conclusion in the vagueness the mystiof cal. It suggeststhat Wittgenstein himself had a divided attitude toward philosophy. In a historical sense,the most important contributlon of the Tractatus was to ensure the dominance of the analytic tnadition in the discipline of philosophy in the English-speakingworld. At the end of the eighteenth century Immanuel Kant had establishedphilosophy as a separatediscipline by grving it a distinct cultural role. While o

ther disciplines gathered knowledge abour particular phenomena in the world, Kant thought that only philosophers gathered knowledge about the conditions for thepossibility of knowledge itself. But around the turn of the century Frege and Russellbegan to focus on narrower problems of meaning and logic. In the TractatusWittgenstein elelates the latter problems to the status of Kant's conditions ofpossibility of knowledge, holding that even more fundamental than Kant's epistemological questions about how the mind connects with the world are questions about meaning, about how language connects with the world. After the publication ofthe Tiactatusand before his return to Cambridge, Wittgenstein was invited to join the discussionsof a group of philosophers that included Moritz Schlick and Rudolf Carnap. This group later became known as the 'Vienna Circle," and their ideas, heavily influenced by the Tractatus, became known as logical positivism. Wittgenstein's book wasthe link between this group and the earlier efforts of Frege

and Russell, and particularly after Carnap and other expatriates arrived to teach in the United States,this school of philosophy came to dominate the professiofon both sides of the Atlantic. This shift has come to be known as the "linguistic turn" in philosophy. To this day, the "analpis of meaning,"


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and not Kantian epistemology,continues to be the prevalent mode of professionalphilosophy in the English-speakingworld. Few philosophers embraced the Tractatr-rs with unqualified enthusiasm, however. Although he wrote a growing introductionthat helped get the book published, Bertrand Russellfound the book's mysticismdistasteful and alwaysconsid,eredit an unnecessaryappendagero wittgenstein's phi

losophy of logic. other philosophers, including members of the Vienna circle, voiced similar concernswith the book's mysticalturn. But the most penetrating andsevere criticisms of the book were wittgenstein's own. when his Philosophical Investigations were published after his death, the preface he had written eight yearsearlier made it clear that he had come to regard his earlier work as largelymistaken. The book begins, in fact, with a powerful critique of the picture Theory of Meaning. Quoting a much earlier version of the theory in Augus_ tine's confessions, wittgenstein shows that this theory can at best account for a small subset of meaning in language, and certainly cannot be called the essenceof language. From this idea, he derives the view that language consists of multiple ,,language_ games," of which there is no essentialtype. This view also becomes a critique of the "logical atomism" of the Tractatus, implying that the meanings of wo

rds and sentences, given by their usesin lan_ guage-games "forms of rife," depend on their rerations to other or language-games rather than on one-to-one correspondencewith the world. This critique moved wittgensrein from the atomism of theTractatus the direction of the holism about meaning espoused in by Willard VanOrman euine and later Donald Davidson. But in spite of the fact that philosophers often make sharp distinctions betweenan "earlier" and a "later" wittgenstei.,,so-e of his concerns remain constant. In particulaq Wittgenstein,s metaphilo_ sophical views embody the continuities, as well as the divergences betweenhis earlier and later work. Both Ihe Tractatusand the Inuatu gationscan be read asstarting from the sameproblem: the way ordinary life and experience constantly thwartour efforts to comprehend them systematically philosophy. Both in works are


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designed to put philosophy in its place, in the Tiadett$ so that language can beleft on its own to "show" the logical structure it shares so with ttre world, and in the Investigations that language can simply the get on with its ordinary b

usiness.The main difference betr,veen the more playful irony of the somber mysticism of the former and latter may be this view which aPpearsin section 5.454r ofthe Tiottatus: "Men have alwayshad a presentiment that there must be a realm inwhich the answers to questions are symmetrically combined - a priori - to forma self-contained system'" Despite his reservations about the power of philosophy, in the TraetatuwittBenstein seemsanxious to preservettris intuition, while inthe Investigati.ansheappearscontent to abandon it. In other words, at the heartof wittgenstein's thought, early and late, is a deep dissatisfaction with philosophy in general. This made wittgenstein a Permanent revolutionary in his discipline throughout his careet and it explains much about his life and work, especially his abandonment of philos ophy after finishing t}re Tiactahs, his subsequentreturn, and his res. ignation when he was seemingty at the height of his career.

This love-haterelationship with his discipline and his calling is entirely in keeping with a personality as fraught with conflict and selidoubt as wittgenstein's was.It is preciselythis element of his thought that has been hardest for professional philosophers to come to terms with, but it is also probably this element that has given his work cultural significance beyond the discipline in which it was created. wittgenstein's life and work has been the subject of novels, plays, and television dramas, and his work has had substantial influence in disciplines outside philosophy like literary studies. Much of this is becauseof his praise for the resourcesof ordinary language at the expense of the Pretensionsof philosophy, an idea that was born in the Tia{tatusbut remained intact in laterworkslike the Investigatioru' is The Tiadahu,as its appropriately imposing title suggests, awork of can only be fu$ understood in the contechnical philosophy, and it text of the very technical problems that obsessedFrege and Russell. But, parti

cularly in its astonishing final sections,it is also that rare work that transcendsits disciplinary boundaries to speak to a wider


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audience of non-specialists,and this is undoubtedly because Wittgenstein, an outsider in so many areasof his life, adopted an outsider's stancetoward philosophyas well. Upon first encountering him at meetings of the Vienna Circle, Rudolf Carnap remarked that Wittgenstein approached philosophical problems asan artist,rather than asa scientistlike the other members of the circle. Even asmany havebeen eclipsedin Wittgenstein'sown of the ideasin the Tiactaf,ru thought and within his discipline, its power asa work of art endures. Bry* Vescio teachesin the Department of Humanistic Studies at the University of Wisconsin-Green Bay.

XVII


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whether or not LogicuPhilosophirzs, Mn WITTcENSTEIN's Tiactatus it should proveto give the ultimate truth on the matters with which by it deals,certainly deserves, its breadth and scopeand profundity, to be considered an important event inthe philosophical world. Starting from the principles of Symbolism and the relations which between words and things in any language, it applies are necessary t

he result of this inquiry to various departments of traditional philosophy, showing in each casehow traditional philosophy and traditional solutions arise out of ignorance of the principles of Symbolism and out of misuse of language. The logical structure of propositions and the nature of logical to inference are firstdealt with. Thence we passsuccessively Theory of Knowledge, Principles of Phpics, Ethics, and finally the Mystical (dn^s Mystisclw). In order to understand MrWittgenstein's book, it is necessary to realize what is the problem with which he is concerned. In the part of his theory which deals with Symbolism he is concerned with the conditions which would have to be fulfrlled by a logically perfectlanguage. There are various problems as regards language. First, there is the problem what actually occurs in our minds when we use language with the intentionof meaning something by iq this problem belongs to psychology.Secondly, there i

s the problem as to what is the relation subsistingbetween thoughts,


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words, or sentences,and that which they refer to or mean; this problem belongs to epistemology.Thirdly, there is the problem of using sentencesso as to convey truth rather that falsehood; this belongs to the special sciencedealing with thesubject-matterof the sentencesin question. Fourthly, there is the question: whatrelation must one fact (such as a sentence) have to another in order to be capa

blz being a symbol for that other? This last is a of logical question, and is rhe one with which Mr Wittgenstein is concerned. He is concerned with the conditions for accurate Symbolisrr', i.e. for Symbolism in which a sentence "means" something quite definite. In practice, language is alwaysmore or less vague, so thatwhat we assertis never quite precise. Thus, logic has two problems to deal within regard to Symbolism:(r) the conditions for senserather than nonsensein combination of symbols;(z) the conditions for uniquenessof meaning or reference in symbolsor combinati.ons of q.rnbols. A logically perfect language has rules of syntax which prevent nonsense,and has single symbolswhich alwayshave a definite andunique meaning. Mr Wittgenstein is concerned with the conditions for a logically perfect language not that any language is logically perfect, or that we believe ourselvescapable, here and now, of constructing a logically perfect language,

but that the whole function of language is to have meaning, and it only fulfilsthis function in proportion as it approaches to the ideal language which we postulate. The essentialbusinessof language is to assertor deny facts. Given the syntax of a language, the meaning of a sentenceis determinate as soon as the meaning of the component words is known. In order that a certain sentence should asserta certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact.This is perhaps the most fundamental thesis of Mr Wittgenstein's theory. That which has to be in common between the sentence and the fact cannot, so he contends, be itself in turn saidin language. It can, in his phraseology,only be shutn,not said, for whatever we may saywill still need to have the samestmcture.


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The first requisite of an ideal language would be that there should be one namefor everysimple,and never the samename for two different simples.A name is a simple symbol in the sensethat it has no parts which are themselves symbols. In a logically perfect language nothing that is not simple will have a simple symbol.The symbol for the whole will be a "complex," containing the symbols for the par

ts. In speaking of a "complex" we are' as will appear later, sinning against therules of philosophical grammar, but this is unavoidable at the outset. "Most propositions and questions that have been written about philosophical matters arenot false but We senseless. cannot, therefore, answerquestionsof this kind at all, Most but only statetheir senselessness. questionsand propositions of the philosopher result from the fact that we do not understand the logic of our language. They are of the same kind as the question whether the Good is more or lessidentical than the Beautiful" (+.oog).What is complex in the world is a fact. Factswhich are not compounded of other facts are what Mr Wittgenstein calls Sachanhalte,whereasa fact which may consist of two or more facts is called as thus, for example, "Socratesis wise" is a Sachuerhalt, a Thtsache: "Socratesis wise and Plato is his pupil" is well as a Tatsache,whereas not a Thtsachebut a Sachasrhalt. H

e compares linguistic expression to projection in geometry. A geometrical figuremay be projected in many ways:each of these wayscorresponds to a different language, but the projective prop erties of the original figure remain unchanged whichever of these ways may be adopted. These projective properties correspond to that which in his theory the proposition and the fact must have in common, if theproposition is to assertthe fact. ln certain elementarywaysthis is, of course,obvious. It is impossible, for example, to make a statement about ttvo men (assuming for the moment that the men may be treated as simples),without employing two names, and if you are going to assert a relation that the sentencein which between the two men it will be necessary you make the assertion shall establish a relation between the two names. If we say "Plato loves Socrates,"the word "loves"which


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occurs between the word "Plato" and the word "socrates" establishes a certain relation between these fwo words, and it is owing to this fact that our sentence is able to asserta relation between the person's name by the words "Plato" and "Socrates.""We must nol say,the complex sign 'a R D'says'a standsin a certain relation .Rto D';but we must say,that ' a' standsin a certain relation to ,b' says t

hat aRd'g.r4gz). Mr wittgenstein begins his theory of Symbolism with the statement (a.r): *We make to ourselves pictures of facts."Apicture, he says,is a modelof the reality, and to the objects in the reality correspond the elementsof thepicture: the picture itself is a fact. The fact that things have a certain relation to each other is represented by the fact that in the picture its elements have a certain relation to one another. "In the picture and the pictured there must be something identical in order that the one can be a picture of the other atall. what the picture must have in common with reality in order to be able ro represent it after its manner - rightly or falsely- is its form of representation"(z.r6r, 2.ril. We speak of a logical picture of a reality when we wish to implyonly so much resemblanceas is essentialto its being a picture in any sense,thatis to say,when we wish to imply no more than identity of logical form. The logi

cal picrure of a fact, he says,is a Gedanke. picture can correspond or not correspond with the A fact and be accordingly true or false, but in both casesit shares the logical form with the fact. The sense in which he speaks of pictures is illustrated by his statement: "The gramophone record, the musical thought, the score, the wavesof sound, all stand to one another in that pictorial internal relation which holds between language and the world. To all of them the logical structure is common. (Like the two youths, their rwo horsesand their lilies in the story.Theyare all in a certain senseone)" (4.or4). The possibilityof a proposition representing a fact restsupon rhe fact that in it objects are represented by signs. The socalled logical "constants" are not represented by signs, but are themselves present in the proposition as in the fact. The proposition and the


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fact must exhibit the same logical "manifold," and this cannot be itself represented since it has to be in common between the fact and the picture. Mr Wittgenstein maintains that everything Properly philosophical belongs to what can only beshown, to what is in common between a fact and its logical picture. It resultsfrom this view that nothing correct can be said in philosophy. Every philosophic

al proposition is bad grammar, and the best that we can hope to achieveby philosophical discussionis to lead people to see that philosophical discussion is a mistake. "Philosophy is 'philosophy' must not one of the natural sciences.(The word mean something which standsabove or below, but not beside the The object of philosophy is the logical clarifrcanatural sciences.) tion of thoughts. Philosophyis not a theory but an activity.A of philosophical work consistsessentially elucidations. The result 'philosophical propositions,' is not a number of of philosophy but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, with this opaque and blurred" (4.r r r and 4.r rz). In accordance principle the things that have to be saidin leading the reader to understand Mr Wittgenstein'stheory are all of them things which that theory itself condemns as meaningless.With this proviso we will en

deavour to conveythe picture of the world which seemsto underlie his system. Theworld consistsof facts: facts cannot strictly speaking be defined, but we can explain what we mean by saylng that facts are what make propositions true, or false.Factsmay contain parts which are facts or may contain no such parts; for example: "Socrateswas waswise,"and of a wiseAthenian," consists the two facts,"Socrates "Socrateswasan Athenian." A fact which has no parts that are facts is calledby Mr Wittgenstein a Sachanhalt.T}:risis the same thing that he calls an atomicfact. An atomic fact, although it contains no parts that are facts, neverthelessdoes contain parts. If we may regard "Socratesis wise" as an atomic fact we perceive that it contains the constituents "Socrates"and "wise." If an atomic factis analysedas fully as possibly (theoretical, not practical possibility is

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or meant) the constituents finally reached may be called "sitrnples'o .,objects." is not contended by wittgenstein that we can actually It isolate the simple orhave empirical knowledge of it. It is a logical necessitydemanded by theory like an electron. His ground for maintaining that there must be simples is that every comPlex preassumedthat the complexity a supposes fact.It is not necessarily o

f facts is finite; even if every fact consisted of an infinite number of atomicfacts and if every atomic fact consisted of an infinite number of objects therewould still be objects and atomic facts (4.ZZrr ). The assertionthat there is acertain complex reducesto the assertion that its constituents are related in a certain way, on which is the asserti of a fact thus if we give a name to the complex the name only has meaning in virtue of the truth of a certain proposition, namely the proposition assertingthe relatednessof the constituents of the complex. Thus the naming of complexes presupposes propositions, while propositions Presupposesthe naming of simples. In this way the naming of simples is shown to be what is logically first in logic. The world is fully described if all atomic facts ane known, together with the fact that these are all of them. The world is notalso describedby merely naming all the objecs in iq it is necessary to know the

atomic facts of which these objects are constituents. Given this total of atomic facts, every true proposition, however complex, can theoretically be inferred.A proposition (true or false) asserting an atomic fact is called an atomic proposition' All atomic propositions are logically independent of each other' No atomic proposition implies any other or is inconsistent with any other. Thus the whole businessof logical inference is concerned with propositions which are not atomic. Such propositions may be called molecular' Wittgenstein's theory of molecular propositions turns upon his theory of the construction of truth-functions' Atruth-function of a proposition pis a proposition containing p and such that its truth or falsehood depends only upon the truth Lr falsehood,of p, and similarly a truth-function of severalproposi-


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tions p, Q,r. . . is one containing P, Q,r. . . and such that its truth or falsehood depends only upon the truth or falsehood of p, Q,r. . . It might seem at first sight as though there were other functions of propositions besidestmth-functions; such, for example, would be "A believesP)' for in general A will believe some true propositions and some false ones: unless he is an exceptionally gifted

individual, we cannot infer that p is true from the fact that he believes it orthat p is false from the fact that he does not believe it. Other apparent exceptions would be such as "p is a very complex propo sition" or "p is a propositionabout Socrates."Mr Wittgenstein maintains, however, for reasons which will appear presently, that such exceptions are only apparent, and that every function ofa proposition is really a truth-function. It follows that if we can define truth-functions generally, we can obtain a general definition of all propositions interms of the original set of atomic propositions. This Wittgenstein proceeds todo. Vol. It has been shown by Dr Sheffer (Trans. Am. Math. Soc., XIV.pp. 48r-488) that all truth-functions of a given set of propo. sitions can be constructed out of either of the two functions "notp or not-q" or "not-p and. not-q."Wittgenstein makes use of the latter, assuminga knowledge of Dr Sheffer'swork. The manne

r in which other truth-functions are constructed out of "not-pand not1' Jseasytosee. "Not-p and not-p" is equivalent to "not-p," hence we obtain a definition of negation in terms of our primitive function: hence we can define "p or qi' since this is the negation of "not-p and not-4," i.e. of our primitive function. The development of other truth-functions out of "not-p" and"p or q'is given in detail at the beginning of Principia Mathematica.Tl:is gives all that is wanted when the propositions which are arguments to our truth-function are given by enumeration. Wittgenstein, however, by avery interesting analysis succeeds extending the processto in general propositions, i..e. caseswhere the propositions which toare arguments to our truth-function are not given by enumeration but are givenas all those satisfing some condition. For example, letl be a propositional function (i.e. a function whose


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valuesare propositions), such as "x is human" then the various values of p forma set of propositions. We may extend the idea "not-pand not-1' so as to apply tosimultaneous denial of all the propositions which are values of /r. In this waywe arrive at the proposition which is ordinarily represented in mathematical logic by the words "/x is false for all values of x." The negation of this is woul

d be the proposition "there is at least one tr for which /x true" which is representedby "( E.x).fxl'If we had startedwith notarrived at the proposition "/x istrue /x instead of;[x we should have lor all values of /' which is represented by "(x).rfx." Wittgenstein's method of dealing with general propositions [i'a' "(x)'f'' and " (1 x) .fx"'l differs from previous methods by the fact that the generality comesonly in specifing the set of propositions concerned' and when thishas been done the building up of truth-functions proceeds exactly as it would inthe caseof a finite number of enumerated arguments P, 4, r - - Mr Wittgenstein's explanation of his q'rnbolism at !ht1n-oi{: is (6 not quite fully given in thetext. The symbol he usesis lP, ' N )l' The following is the explanation of this symbol: lsands for all atomic propositions' for any set of propositions' { standsfr (f ) sands fg the negation of all the propositions making uP f' The whole sym

bol lp, ,F (6-)l means whatever can be obtained by taking any selection of atomic propositions' negating them all, then taking any selection of the set of proposit

ions now indefiobtained, together with any of the originals and so on the gennitely. This is, he says,the general truth-function and also less eral form of proposition. What is meant is somewhat to describe a complicated than it sounds. Thesymbol is intended all process by the help of which, given the atomic propositions' others can be manufactured' The processdepends uPon: (a) Sheffer's proof that all truth-functions can be obtained out of simultaneous negati on, i.e' out of "not-p and not'(';

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(D) Mr Wittgenstein's theory of the derivation of general propositions from conjunctions and diqjuncrions; (c) The assertion that a proposition can only occur in another proposition as argument to a truth-function. Given these three foundations, it foilows that all propositions which are not atomic can be derived fromsuch as are, by a uniform process'and it is this processwhich is indicated by Mr

wittgenstein's symbol. From this uniform method of construction we arrive at anamazing simplification of the theory of inference, as well as a defi_ nition ofthe sort of propositions that belong to logic. The method of generation which hasjust been described, enablesWittgenstein to say that all propositions can be constructed in the above manner from atomic propositions, and in this way the totality of propositions is defined. (The apparent exceptions which r. _.r_ tionedabove are dealt with in a manner which we shall consider later.) wittgenstein isenabled.to assert that propositions are all that follows from the totarity of atomic propositions (together with the fact that it is the totality of them); that a proposition is alwaysa truth-function of atomic propositions; and that if pfollows from q the meaning of p is contained in the meaning of from which of 4, course it results that nothing can be deduced from an atomic proposition. All the

propositions of logic, he maintains, are tau_ tologies, such, for example, as,,por not p.', The fact that nothing can be deduced from an atomic proposi_ tion has interesting applications,for example, to causality. th.re cannot, in wittgenstein's logic, be any such thing as a causarnexus. "The events of the future," hesays,"cannotbe inferred from those of the present. superstition is the belief in the causalnexus.,,That the s'n will rise to-morrow is a hlpothesis. we do notin fact know whether it will rise, since there is no compulsion according to which one thing must happen because another happens. f .etus now take up another subject _ that of names.In Wittgenstein's theoretical logical language, names areonly given to simples. We do not give two names to one thing, or one name to two

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INTRODUCTION

things. There is no way whatever, according to him, by which we can describe thetotality of things that can be named, in other words, the totality of what there is in the world. In order to be able to do this we should have to know of someproperty which must belong to every thing by a logical necessity'It has been sought to find such a properry in self-identity, but the conception of identity is

subjected by wittgenstein to a destructive criticism from which the there seemsno escape.The definition of identity by means of identity of indiscernibles is rejected, becausethe identity of indiscernibles aPpearsto be not a logically necessaryprinciple' Accordis a ing to this principle x is identical with I if everyProperty of r possible for two property of y, but it would, after all, be logically fact tfti"gt to have exactly the same properties' If this does not in world'not a loghappen that is an accidentalcharacteristicof the the icaily n.cersarycharacteristic, and accidental characteri$ticsof of logic. world must, of coufse, not be admitted into the structure conMr Wittgenstein accordingly banishesidentity and adopts the ventionthatdifferentlettersaretomeandifferentthings.Inpracortice, identity is needed as between a name and a description as between two descriptions' It is needed for such propositions "The "socratesis the philosopher w

ho drank the hemlock"' or of identity it even prime is the next number after L"For such uses is easyto provide on Wittgenstein's system' The rejection of identity removes one method of speaking of method the totality of things, and it willbe found that any other that may be suggestedis equally fallacious: so, at least' Wittgenstein "object" contends and, I think, rightly' This amounts to sayingthat It folis a pseudoconcept. To say"r is an object" is to saynothing' "there are lows from this that we cannot make such statements as "there are an infinitemore than three objects in the world," or in number of objects in the world"' Objects can only be mentioned are connexion with some clefinite property' We can say "there morethanthreeobjectswhicharehuman,''or..therearemore thanthreeobjectswhicharered,''forint}reseStatement.$theword of logic' the object can be replacedby a variable in the language

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INTRODUCTION

variable being one which satisfiesin the first casethe function .,x is human"; in the second.the function .,r is red.,' But when we attempt to say"there are more than three objects," this substitution of the variable for the word "object" becomes impossible, and the proposition is therefore seen to be meaningless. we here touch one instance of wittgenstein's fundamentar thesis, thar it is impossib

le to sayanything abour the world as a whole. and that whatever can be said hasto be about bounded portions of the world. This view may have been originally suggest.A ly rro,u_ tion, and if so, that is much in its favour, for a good notation has a subtlery and suggestiveness which at times make it seem almosr like a live teacher. Notational irregurarities are often the first sign of philosophicalerrors, and a perfect notation would be a substitute for thought. But althoughnotation may have firsr suggested to Mr wittgenstein the limitation of logic tothings .ithi' tt* world as opposed to the world as a whole, yet the view, once sug_ gested, is seen to have much else to recommend it. whether it is ultimatelytrue I do not, for my part, profess to know. In this Introduction I am concernedto expound it, not to pronounce upon it. According to this view we could onry saythings about the world as a whole if we could get outside the world, if, thati

s to say, it ceased to be for us the whole world. our world may be bounded for some superior being who can survey it from above, but for us, however finite it may be, it cannot have a boundary since it has nothing outside it. Wittgenstein uses,asan analogy,the field of vision. Our field of vision does not, for us, havea visual boundaryjust because there is nothing outside it, and in like manner our rogical world has no logical boundary becauseour logic knows of nothing out_side it' These considerations lead him to a somewhat curious discussionof Solipsism.Logic, he says, fills the world. The bound_ aries of the world are also itsboundaries. In logic, therefore, we cannot say,there is this and this in the world, but not that, for to sayso would apparently presuppose that we exclude certain possi_ bilities, and this cannot be the case,since it would require that logic should go beyond the boundaries of the world if i, could ".XXIX


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INTRODUCTION

contemplate these boundaries from the other side also.what we cannot think we cannot think, therefore we also cannot saywhat we cannot think. givesthe key to Solipsism.What Solipsism intends This, he says, is quite correct, but this cannotbe said, it can only be shown' That the world is zz' world appears in the fact that the boundaries of language (the onty language I understand) indicate the bou

ndaries of myworld. The metaphysicalsubject does not belong to the world but isa boundary of the world. We must take up next the question of molecular propositions which are at first sight not truth-functions, of the propositions that theycontain, such, for example, as "A believesp"' wittgenstein introduces this subject in the statement of his posiHe don, namely, that all molecular functions aretruth-functions' occur says(5.54): "In the general propositional form, propositions in a proposition only as basesof truth-operations." At first sight, he in go.* on to explain, it seems as if a proposition could also occur as if the lrh..*"yr, e.g."Abelieves p." Here it seemssuperficially'But it is A' proposition pstood in a sort of relation to the object 'A thinks P,' 'A says are of the form'A believes that p,' p' clear that 'p says and here we have no co-ordination ofa fact and an P'; of ob.lect,tut a co-o.dination of facts by means of a co-ordin

ation their objecs" (b.5+z)' What Mr Wittgenstein sayshere is said so short$ that its point is not likely to be clear to those who have not in mind the controheis versieswith which he is concerned' The theory with wtrich truth disagreeingwill be found in my articles on the nature of of and Proceed,ings the Arisand lalseho od in Phitosophical Essays the r totelian Society,9o6-7' The problem at issue is the problem of what logical form of belief, i.e' what is the schema representing applies not occurs when a man believes.Of course, the problem only to belief, but also to a host of other mental phenomena considerwhich may be called propositional attitudes: doubting' ing,desiring,etc.Inallthesecasesitseemsnaturaltoexpressthe 'Adesires p"' etc'' which phienomenon in the form "A doubts F,"

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INTRODUCTION

makes it appear as though we were dealing with a relation between a person and aproposition. This cannot, of course, be the ultimate analysis,since persons arefictions and so are propo_ sitions, except in the sensein which they are factson their own account. A proposition, considered as a fact on its own account. may be a set of words which a man saysover to himself, or a com_ plex image, or tr

ain of imagespassingthrough his mind, or a set of incipient bodily movements.Itmay be any one of innumerable different things. The proposition as a fact on itsown account. for example the actual set of words the man pronounces to himserf,is not relevant to logic. what is relevant to logic is that common element among all these facts, which enables him, as we say,to meanthe fact which the proposirion asserts. psychology, To of course, more is relevant; for a symbol does notmean what it ry.ryn_ bolizes in virtue of a logical relation alone, but in virtue also of a psychological relation of intention, or association,or what-not. The psychological part of meaning, however, does not concern the logician. what does concern him in this problem of belief is the logical schema.It is clear that,when a person berievesa proposition, the person, considered as a metaphysical subject, does not have to be assumedin ord,er to explain what is happen_ ing' wha

t has to be explained is the relarion between the set or words which is the proposition considered as a fact on its own account' and the "objective" fact whichmakes the proposition true or false. This reduces urtimatery to the question ofthe meaning of propositions, that is to say,the meaning of proposi_ tions is theonly non-psychological porrion of the proUt._ involved in the analysisof belief. This problem is simply one of a relation of two facts, namely, the relation between the series of words used by the believer and the fact which makes these words true or false. The series of words is a factjust as much as what makes it true or false is a fact. The relation between these two facts is not unanalysable,since the meaning of a proposition results from the meaning of its constituent words. The meaning of the seriesof words which is a proposition is a function ofthe

xxxt


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INTRODUCTION

meanings of the separatewords. Accordingly, the proposition as a whole does notreally enter into what has to be explained in explaining the meaning of a proposition' It would perhaps help to suggest the point of view which I am trying to indicate, to say that in the caseswe have been considering the proposition occursas a fact, not as a proposition. Such a statement, however, must not be taken t

oo literally. The real point is that in believing, desiring, etc., what is logically fundamental is the relation of a as proposition considered a fact, to the fact which makes it true or false. and that this relation of rwo facts is reducible to a relation of their constituents. Thus the proposition does not occur at all in the same sensein which it occurs in a truth-function' There are some respects' in which, as it seems to me' Mr wittgenstein's theory standsin need of greater technical develop-.ni. This applies in particular to his theory of number (6'oz ff') which,asitstands,isonlycapableofdealingwithfinitenumbers' be No logic can be considered adequate until it has been shown to there is capable of dealingwith transfinite numbers' I do not think for anything in Mr Wittgenstein's systemto make it impossible him to fill this lacuna. More interesting than such questions of comparative detail is Mr Wittgenstein's attitude towards the mystical.

His attitude uPon this grows naturally out of his doctrine in pure logic, according to which the logical proposition is a picture (true or false) of the fact' and has in common with the fact a certain structure. It is this comthe mon structure which makes it capable of being a picture of it is a fact, but the structurecannot itself be put into words' since Everystmcture o/words, aswell as of thefacts to which they refer' very idea of the expresthing, therefore, which is involved in the in of siveness language must remain incapable of being expressed language, and is, therefore, inexpressible in a perfectly precise sense.This inexpressible contains, according to Mr Wittgenstein' the whole of logic and philosophy. The right method of teaching would be to confine oneself to propositions ofphilosophy, he says, leavthe sci.nces, stated with all possible clearnessand exactness'

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INTRODUCTION

ing philosophical assertionsto the learner, and proving to him, whenever he madethem, that they are meaningless.It is true that the fate of Socrares might befall a man who atrempted this method of teaching, but we are not to be deterred bythat feaa if it is the only right method. It is not this thar causes some hesitation in accepting Mr Wittgenstein's position, in spite of the very power_ ful a

rguments which he brings to its support. What causes hesita_ tion is the fact that, after all, Mr Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the scep tical reader that possibly there may be some loophole through a hierarchy of languages,or by some other exit. The whole subjectof ethics, for example, is placed by Mr Wittgenstein in the mystical, inexpressible region. Nevertheless he is capable of conveying his ethical opinions. His defencewould be that what he calls the mys tical can be shown, although it cannotbe said. It may be that this defence is adequate,but, for my part,I confessthatit leavesme with a certain senseof intellectual discomfort. There is one purelylogical problem in regard to which these difficulties are peculiarly acute. I mean the problem of generality. In the theory of generality it is necessary consider to all proposi_ tions of the formy'where/xis a given propositional functiln.

This belongs to the part of logic which can be expressed, according to Mr Wittgenstein's system. But the totality of possible ..rul,r., of x which might seem to be involved in the totality of propositions of the form.;fu is not admitted byMr Wittgenstein among the things that can be spoken of, for this is no other than the totatity of things in the world, and thus involvesthe attempt to conceivethe world as a whole; "the feeling of the world as a bounded whole is the mysti

_ cal"; hence the totality of the valuesof x is mystical (6.+S). This is expresslyargued when Mr wittgenstein denies that we can make propositions as to how many things there are in the world, as for example, that there are more than three.These difficulties suggesrto my mind some such possibility as this: that everylanguage has, as Mr Wittgenstein says,u ,*.rrrr. concerning which, in thelanguage,nothing can be said, but that

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INTRODUCTION

there may be another language dealing with the structure of the first language,and having itself a new sfucture, and that to this hierarchy of languages theremay be no limit' Mr Wittgenstein would of course reply that his whole theory isapplicable unchanged to the totality of such languages.The only retort would beto deny that there is any such totality. The totalities concernin$ which Mr witt

genstein holds that it is impossible to speak logically are nevertheless thoughtby him to exist, and are the subject-matter of his mysticism. The totatity resulting from our hierarchy would be not merely logically inexpressible,but a fiction, a mere delusion' and in this way the supposed sphere of the mystical would be abolished' it Such an hlpothesis is very diffrcult, and I can see objections to which at the moment I do not know how to answer'Yet I do not see how any easier hypothesis can escapefrom Mr wittgenstein's conclusions. Even if this very difficult hypothesisshould prove tenable' it would leaveuntouched a very large partof Mr wittgenstein's theory though possiblynot the part upon which he himself would wish of As to lay most stress. one with a long experience of the difficulties I of logic and of the deceptiveness theories which seem irrefutable' merely on find myself unable to be sure of the rightness of a theory to the ground that

I cannot seeany point on which it is wrong' But alnypoint obvihave constructed atheory of logic which is not at ously wrong is to have achieved a work of extraordinary difficulty and importance. This merit, in my opinion, belongs to Mr Wittgencan stein'sbook, and makes it one which no serious philosopher afford to neglect' Bnnrner.Io Russrlr-. May rgzz.

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T-RACTATUS LOGICO- PHILOSOPHICUS


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VOR WORT

Dlrsns buch wird vielleicht nur der verstehen,der die Gedanken, die darin ausgedruckt sind - oder doch ihnliche Gedanken schon selbst einmal gedacht hat. - Es ist also kein Lehrbuch. sein Zweck wdre erreicht, wenn es Einem, der es mit verstiindnis liest Vergnugen bereitete. Das Buch behandelt die philosophischen Probleme und zeigtwie ich glaube - dassdie Fragestellung dieser Probleme auf dem Missv

erstindnis der Logik unserer Sprache beruht' Man k6nnte sich den ganzen Sinn desBuches etwa in die Worte fassen:Was nicht riberhaupt sagen lisst, ldsst sich klar sagen;und wovon man reden kann, daruber muss man schweigen' Das Buch will also dem Denken eine Grenze ziehen' oder vielmehr - nicht dem Denken, sondern dem Ausdmck der Gedanwir ken: Denn um dem Denken eine Grenze zu ziehen, mfissten (wirmfrsstenalso denbeide seiten dieser Grenze denken k6nnen ken k6nnen, wassich nicht denken lisst)' k6nDie Grenze wird also nur in der Sprache gezogen werden sein' nen und wasjenseits der Grenze liegt, wird einfach Unsinn Philosophen Wieweitmeine Bestrebungenmit denen anderer will zusammenfallen, ich nicht beurteilen'Ja,wasich hier geschrieauf habe macht im Einzelnen uberhaupt nicht den Anspruch ben es mir Neuheit; und darum gebe ich auch keine Quellen an' weil vor mir schonein gleichgiltig ist, ob das was ich gedacht habe, anderer gedachr hat.


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PREFACE

Tnrs book will perhaps only be understood by those who have themselvesalready thought the thoughts which are expressedin it - or similar thoughts. It is therefore not a text-book. Ia object would be attained if there were one person who read it with understanding and to whom it afforded pleasure. The book dealswith theproblems of philosophy and shows,as I believe,that the method of formulating th

eseproblems restson the misunderstanding of the logic of our language. Its wholemeaning could be summed up somewhat as follows: What can be said at all can besaid clearly;and whereof one cannot speakthereof one must be silent. The book will, therefore, draw a limit to thinking, or rather not to thinking, but to the expressionof thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be ableto think what cannot be thought), The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense. Howfar my efforts agree with those of other philosophers I will not decide. Indeedwhat I have here written makes no claim to novelty in points of detail; and therefore I give no sources,becauseit is indifferent to me whether what I have thought has already been thought before me by another.


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ABHANDLUNG

Nur das will ich erwihnen, dassich den grossartigenWerken Fregesund den Arbeitenmeines Freundes Herrn Bertrand Russell einen grossenTeil derAnregung zu meinenGedanken schulde' wenn diese Arbeit einen wert hat, so besteht er in Zweierlei.

Erstens darin, dassin ihr Gedanken ausgedruckt sind, und dieser wert wird umso grosser sein,je besserdie Gedanken ausgedrirckt sind. Je mehr der Nagel auf den Kopf getroffen ist. Hier bin ich mir bewusst,weir hinter dem M6glichen zurttckgeblieben zu sein. Einfach darum, weil meine Kraft zur Bewdltigung der Aufgabe zu gering ist. - Mogen andere kommen und es bessermachen' Dagegen scheint mir die wahrheit der hier mitgeteilten Gedanken unantastbar und defrnitiv. Ich bin also der Meinung, die Pro' bleme im Wesentlichen endgtrltig gelost zu haben' Und wenn ich mich hierin nicht irre, so besteht nun der Wert dieserArbeit zweitens darin,dasssie zeigt,wie wenig damit getan ist, dassdieseProbleme gelostsind.

L. W.Wim, rgt9.


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I will only mention that to the great works of Frege and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts. If this work has a value it consistsin two things. First that in it thoughs are expressed,and this value will be the greater the better the thoughs are expressed.Themore the nail has been hit on the head. - Here I am conscious that I have falle

n far short of the possible. Simply because my powers are insufftcient to cope with the task. - Muy others come and do it better. On the other hand the huth o/the thoughts communicated here seemsto me unassailableand definitive. I am, therefore, of the been finally solved. opinion that the problems have in essentials not mistaken in this, then the value of this work secAnd if I am ondly consistsinthe fact that it showshow little has been done when these problems have been solved.


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lr l.l

1.lr

r.r2 r'r3t.2 r,2 l

Die Welt ist alles,wasder Fall ist. Die Welt ist die Gesamtheit der Thtsachen,nicht der Dinge. Die Welt ist durch die Thtsachenbestimmt und dadurch, dasses alleTatsachen sind. Denn, die Gesamtheit der Tatsachenbestimmt, wasder Fall ist undauch, wasalles nicht der Fall ist' Die Thtsachenim logischenRaum sind die Welt'Die Welt zerfiillt in Tatsachen. Eines kann der Fall sein oder nicht der Fall sein und alles tibrige gleich bleiben. Was der Fall ist, die Tatsache,ist dasBestehenvon Sachverhalten.

2

2.oDerSachverhaltisteineVerbindungvonGegenstiinden. (Sachen,Dingen.) 2.orrEsistdemDingwesentlich,derBestandteileinesSachverhaltes sein zu konnen.

,DieDecimalzahlenalsNummerndereinzelnenSitzedeutendaslogische meiner Darsrtellungliegt, Gewicht der Sitze an, den Nachdruck, der auf ihnen in No' n; die Sitze n'mr' Die Sitzen. r, n.2, n'3, etc., sind Bemerkungen zum Sitze n.m2, etc. Bemerkungen zum SatzeNo' n'm; und so weiter'


41/196

lr 1,1

The world is everything that is the case. The world is the totality of facts, not of things. The world is determined by the facts, and by these being allthefacs. For the totality of facts determines both what is the case.and also all that is not the case. The facts in logical spaceare the world. The world divides intofacts. Any one can either be the caseor not be the case,and everything elseremai

n the same. What is the case,the fact, is the existence of atomic facts. An atomic fact is a combination of objects (entities, things). to It is essential a thing that it can be a constituent part of an atomic fact.

1.1I

r.rz r'r 3 r.2 r . 2r 22.Ol

z.or r

' The decimal figures as numbers importance propositions

of the seperate propositions on proposition

indicate

the logical

of the propositions, the emphasis laid upon them in my exposition. The n.r, n.2,n.g, etc., are comments No. z; the proposiNo. n.m; and so on.

ttons n,mt , n.rnz, etc,, are comments on the proposition


42/196

LOGISCH-

PI{ILOSOPHISCHE

ABHANDLUNG

2.or p

In der Logik ist nichts zufillig: Wenn dasDing im Sachverhalt vorkommen kann, somuss die M6glichkeit des im Sachverhaltes Ding bereits priijudiziert sein' Es erschienegleichsamals Zufall, wenn dem Ding, das s.or2r allein fur sich bestehenk6nnte, nachtriglich eine Sachlage passenwurde' Wenn die Dinge in Sachverhaltenvorkommen k6nnen, so mussdies schon in ihnen liegen' (Etwas Logisches kann nichtnur-moglich sein' Die Logik handelt von jeder Moglichkeit und alle Moglichkeiten sind ihre Thtsachen.) Wie wir uns riiumliche Gegenstiinde uberhaupt nichtaus serhalb des Raumes, zeitliche nicht ausserhalbder Zeit denken konnen, so k6nnen wir uns keinen Gegenstand ausserhalbder Moglichkeit seiner Verbindung mit anderendenken. Wenn ich mir den Gegenstand im Verbande des Sachverhaltsdenkenkann,sokannichihnnichtausserhalb der Moglichkeit diesesVerbandes denken' Das Ding ist sel

bstindig, insofern es in allen mogliz.or2z chen Sachlagenvorkommen kann, aber diese Form der Selbstindigkeit ist eine Form des Zusammenhangs mit dem Sachverhalt,eine Form der Unselbstindigkeit' (Es ist unmoglich, dassWorte in zwei verschiedenenWeisen auftreten, allein und im Satz.) kenne, so kenne ich auch Wenn ich denGegenstand 2.or2Z sdmtlicheMoglichkeitenseinesVorkommensinSachverhalten. in derNatur des Gegen$ede solche Miglichkeit muss standesliegen') Es kann nicht nachtriglich eine neue M6glichkeit gefunden werden. Um einen Gegenstandzu kennen, mussich zwar nicht ?.or 23 r seine externen - aber ich mussalle seineinternen Eigenschaften kennen.


43/196


In logic nothing is accidental:if a thing canoccur in an aromic fact the possibility of that atomic fact must arready be prejudged in the thing. 2.or2r It would, so to speak,appear as an accident,when to a thing that could exist alone on its own account, subse_ quently a state of affairs could be made to fit. If thingscan occur in atomic facts, this possibility must already lie in them. (A logica

l entity cannor be merely possible.Logic treats of every possibility,and all possibilities are its facts.) Just as we cannot think of spatial objects at all apart from space,or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things. If I can think of an object in the context of an atomic fact, I cannot think of it apart fromthe possibilitl this of context.

2.or2

2.or22

The thing is independent, in so far as it can occur in all possiblc circumstance

s, but this form of independence is a form of connexion with the atomic fact, aform of dependence. (It is impossible for words ro occur in two different ways,alone and in the proposition.) If I know an object, then I also know all the possibili_ ties of its occurrence in atomic facts. (Every such possibility must liein the nature of the object.) A new possibilitycannot subsequently found. be

z.or21

g.or sBr

In order to know an object, I must know not its exter_ nal but all its internalqualities.


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LOGISCH.

PHILOSOPHISCHE

ABHANDLUI

2.or24

Sind alle Gegenstinde gegeben, so sind damit auch alle moglichen Sachverhaltegegeben. moglicher 2 . o r3 Jedes Ding ist, gleichsam, in einem Raume mir leer denken, Sachverhalte. Diesen Raum kann ich nicht aber das Ding ohne den Raum. Der rdumliche Gegenstand muss im unendlichen 2.or3r Raume liegen. (Der Raumpunkt ist eine Argumentstelle') Der Fleck im Gesichtsfeld muss zwar niclrt rot sein, aber eine Farbe muss er haben: er hat sozusagenden Farbenraum um sich. Der Ton muss eine Hohe haben, der Gegenstand des Tastsinneseine Hirte usw. Die Gegenstinde enthalten die Moglichkeitaller Sach2.or4 lagen. Vorkommens in Sachverhalten' Die M6glichkeit seines 2.or4L ist die Form des Gegenstandes. Der Gegenstandist einfach.2.O2 sich in eine Aussage r 2.O20 Jede Aussageuber Komplexe lisst tiber deren Bestandteile und in diejenigen Sitze zerlegen, welche die Komplexe vollstandig be

schreiben' derWelt' Darum Die Gegenstinde bilden die Substanz 2.O2r sein' konnensie nicht zusammengesetzt H?itte clie Welt keine Substtfrz, so wrirde, ob ein Sau 2.O2Ll Sinn hat, davon abhdngen, ob ein anderer Satzwahr ist'2.O2r2

Es wire dann unm6glich, ein Bild derWelt (wahr oder falsch) zu entwerfen. Es istoffenbar, dassauch eine von der wirklichen noch 2.O22 - mit so verschieden gedachte Welt Etwas eine Form der wirklichen gemein haben muss' Diese festeForm besteht eben aus den Gegenstinden' 2.o23 Die Substanzder Weltkann nureine Form und keine 2.o23L materiellen Eigenschaften bestimmen' Denn diese werden erst durch die Sitze dargestellt - erst durch die Konfiguration der GegenstAndegebildet' Beildufrg gesprochen: Die Gegenstiinde sind farblos' 2.0232


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If all objects are given, then thereby are all possible atomic facts also glven.z.org Everything is, as it were, in a spaceof possibleatomic facts. I can thinkof this space as empty, but not of the thing without rhe space. 2.or3r A spatial object must lie in infinite space. (A point in spaceis a place for an argument.) A speck in a visual field need not be red, but it must have a colour; it has,

so to speak,a colour spaceround it. A tone must have a pitch, the object of thesenseof touch a hardness,etc, 2.ot4 Objectsconrain the possibilityof all sraresaffairs. of The possibiliryof its occurrence in atomic facts is the form of theobject. 2.O2 The object is simple. 2.O20r Every statement about complexes can beanalysedinto a statement about their constituent parts, and into those propositions which completely describe the complexes. 2 . O 2t Objects form the subsranceof the world. Therefore they cannot be compound. z.oz r r If the world had no substance, then whether a proposi_ tion had sensewould depend on whether anotherpropo_ sition was true. 2.o2r2 It would then be impossible to form a picture ofthe world (true or false). 2'.u.22 It is crear that however different from the real one an imagined world may be, it must have something _ a form - in common with the real world. 2.029 This fixed form consists the objects. of 2.o2gr The sub

stanceof the world can only d.etermine a form and not any material properties. For these are first presented by the propositions _ first formed by the .orrfig.rration of the objects. 2.o.222 Roughly speaking:objectsare colourless. 2'or4r

2.or24


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LOGISCH-

PHILOSOPHISCHE

ABHANDLUNG

Zwei Gegenstinde von der gleichen logischen Form sind - abgesehenvon ihren exter

nen EigenSchaftenvon einander nur dadurch unterschieden.dasssie verschiedensind.Entweder ein Ding hat Eigenschaften,die kein andez.o21gr res hat, dann kann manes ohneweiteres durch eine Beschreibung aus den anderen herausheben, und daraufhinweisen; oder aber, es gibt mehrere Dinge, die ihre simtlichen Eigenschaftengemeinsamhaben, dann ist es uberhaupt unmoglich auf einesvon ihnen zu zeigen. Denn, ist das Ding durch nichts hervorgehoben, so kann ich es nicht hervorheben.denn sonstist es eben hervorgehoben. Die Substanzist das,wasunabhingig von dem wasder 2.024 Fall ist, besteht. Sie ist Form und Inhalt. 2.o2b Raum, Zeit und Farbe(Firbigkeit) sind Formen der 2.o2br Gegenstande. Nur wenn es Gegenstinde gibt, kann es eine feste 2.026 Form der Welt geben. Das Feste,das Bestehende und der Gegenstand sind 2.o27Eins. 2.o27r 2.o272 2.oZ 2.ogr z.og2 2.oZZ 2.024 Der Gegenstand ist das Feste, B

estehende; die Konfiguration ist das Wechselnde, Unbestdndige. Die Konfigurationverhalt. Im Sachverhalt hangen die Gegenstinde ineinander, wie die Glieder einer Kette. Im Sachverhalt verhalten sich die Gegenstinde in bestimmter Art und Weise zueinander. halt zusammenhingen, Die Art und Weise, wie die Gegensliinde im Sachverist die Struktur des Saclrverhaltes. Die Form ist die Moglichkeit der Struktur. Die Struktur der Tatsache besteht aus den Strukturen der Sachverhalte. derGegenstinde bildet den Sach-

2.o2gy


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LOGICO-PHILOSOPHICUS

Two objects of the same logical form are _ apart from their external properties- only differentiated from one another in that they are different. z.o2g7r Either a thing has properties which no other has, and then one can distinguish it str

aight awayfrom the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them. For if a thing is not distinguishedby anything, I cannot distinguish it - for orherwiseit wourdbe distinguished.

2.ozgg

2.o24 2.ozb 2.o2bt

Substance is what exists independently case.

of what is the

It is form and content. Space, time and colour (colouredness) are forms of

z.oz6 2.0222.o2Zr 2.0272 2.o3

objects. Only if there are objects can there be a fixed form of the world. The fixed, the existent and the object are one.The object is the fixed, the existent: the configuration is the changing, the variable. The configuration fact. of the objects forms the atomic

In the atomic fact objects hang one in another, like the

members of a chain. In the atomic fact the objects are combined in a defi_ niteway. 2.o92 The way in which objects hang together in the aromic fact is the structure of the atomic fact. 2.o33 The form is the possibilityof rhe srructure. 2.034 The structure of the fact consistsof the structures of the atomic facts. 2.ogL


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2.o4 2.o5 z.o6

Die Gesamtheit der bestehenden Sachverhalte ist die Welt. Die Gesamtheit der bestehenden Sachverhalte bestimmt auch, welche Sachverhalte nicht bestehen' Das Bestehen und Nichtbestehen von Sachverhalten

ist die Wirklichkeit. (Das Bestehen von Sachverhalten nennen wir auch eine positive, das Nichtbestehen eine negative Thtsache') Die Sachverhaltesind von einander unabhiingig' z.o6r Aus dem Bestehen oder Nichtbestehen eines Sachverz.o6z haltes kann nicht auf das Bestehen oder Nichtbestehen werden. eines anderen geschlossen Die gesamteWirklichkeit ist die Welt. 2.o63 Wir machen uns Bilder der Thtsachen. 2,r Das Bildstellt die Sachlageim logischen Raume, das 2,l r Bestehen und Nichtbestehen von Sachverhaltenvor'2.r2 2 . r3 2.r3r

Das Bild ist ein Modetl der Wirklichkeit. Den Gegenstinden entsprechen im Bildedie Elemente des Bildes. Die Elemente des Bildes vertreten im Bild die Gegen-

stinde. Das Bild besteht darin, dasssich seine Elemente in 2.r4 bestimmter Art und Weise zu einander verhalten' Das Bild ist eine Thtsache. 2.L+L Dasssich die Elemente des Bildes in bestitnmter Art 2-rb und Weise zu einander verhalten stellt vor, dass sich die Sachenso zu einanderverhalten. Dieser Zusammenhangder Elemente des Bildes heisse seine Struktur und ihre Moglichkeit seine Form der Abbildung. 2.rSrDieFormderAbbildungistdieMoglichkeit,dasssich die Dinge so zu einanderverhalten, wie die Elemente des Bildes2.IsrrDasBildistsomitderWirklichkeitverknirpfgesreicht bis zu ihr.


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2-o4

The totality of existent atomic facts is the world.

2.ob z.o6

z.o6r z.o'z

The totality of existent atomic facts also determines which atomic facts do notexist. The existenceand non-existenceof atomic facts is the reality. (The existence of atomic facts we also call a positive fact, their non-existence a negativefact.) Atomic factsare independent of one another. From the existence or non-existence of an atomic fact we cannot infer the existenceor non-existenceof another.

The total reality is the world. We make to ourselvespictures of facts. The picture presents the facts in logical space,the exiss. r r tence and non-existence of

atomic facts. The picture is a model of reality. 2.r2 To the objeca correspondin the picture the elements 2.rg of the picture. The elements of the picture stand, in the picture, for 2.r3r the objects. The picture consistsin the fact thatits elements are 2.r4 combined with one another in a definite way. The picture is a fact. 2.r4L That the elements of the picture are combined with z.rb one another in a definite way, represents that the things are so combined with one another. This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture. The form of representation is the possibility that the 2.rbr things are combined with one another as are the elements of the picture. Thus the picture islinked with reality; it reachesup s.rbr I to it. 2.o63 p.r


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ABHANDLUNG

2.r512 2.r5r2r

Es ist wie ein Masstaban die Wirklichkeit angelegt' Nur die iussersten Punkte de

r Teilstriche berfihren den zu messendenGegenstand. Nach dieser Auffassung gehort also zum Bilde auch 2.r5r3 noch die abbildende Beziehung, die es zum Bild macht' 2 . L 5 1 4 Die abbildende Beziehungbesteht aus den Zuordnungen der Elementedes Bildes und der Sachen' Diese Zuordnungen sind gleichsamdie Fuhler der Bil2.r5r5 delmente. mit denen das Bild die Wirklichkeit berirhrt' Die Thtsachemuss umBitd zu sein, etwasmit dem Abge2.r6 bildeten gemeinsamhaben. In Bild und Abgebildetem muss etwasidentisch sein' 2.r6r damit das eine uberhaupt ein Bild des anderen sein 2-r7 kann. Was das Bild mit der Wirklichkeit gemein haben muss' um sieauf seine Art und Weise- richtig oder falsch abbilden zu k6nnen, ist seine Formder Abbildung' Das Bild kann jede Wirklichkeit abbilden, deren Form 2.r7 es hat. Das riiumliche Bild alles Riumliche, das farbige alles Farbige, etc. Seine Form der Abbildung aber, kann das Bild nicht 2.r72 abbilden; es weist sie auf' (se

in Das Bild stellt sein Objekt von ausserhalb dar 2-t73 darum stellt Standpunktist seine Form der Darstellung), das Bild sein Objekt richtig oder falsch dar' Das Bild kann sich aber nicht ausserhalbselner Form 2.r74 der Darstellung stellen. Wasjedes Bild, welcher Form immer, mit der Wirklich2.r8 - richtig oder keit gemein haben muss,um sie tiberhaupt ist' falsch - abbilden zu konnen, ist die logische Form' das die Form der Wirklichkeit. Ist die Form der Abbildung die logische Form' so heisst z.r8r das Bild das logische Bild.


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2.rbr2 2. rbr2r z. r b r 3 z.rbr4 z.rbrb s.16 z.16r

2.r7

2.r7r

2.t-72 z.L7g

2.174 z.r8

s.r8r

It is like a scaleapplied to reality. Only the outermost points of the dividinglines touch the object to be measured. According to this view the representing relation which makesit a picture, also belongs to the picture. The representing r

elation consistsof the coordinations of the elements of the picture and the things. Thesecoordinations are asitwere the feelersof its elements with which the picture touches reality. In order to be a picture a fact must have something in common with what it pictures. In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all. What the picture must have in common with reality in order to be able to represent itafter its manner - rightly or falsely- is its form of representation. The picture can represent every reality whose form it has. The spatial picture, everythingspatial, the coloured, everythingcoloured, etc. The picture, however,cannot representits form of rep resentation:it showsit forth. The picture representsits object from without (its standpoint is its form of representation), therefore thepicture represents its object rightly or falsely. But the picture cannot place itself ouside of its form of representation. What every picture, of whatever form

, must have in common with reality in order to be able to represent it at all -rightly or falsely- is the logical form, that is, the form of reality. If the form of representationis the logical form, then the picture is called a logical picture.


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zr82 2.r92.2

(Dagegenist z' B' nicht JedesBild ist auch ein logisches' jedes Bild ein riiumliches.) Das logische Bild kann die Welt abbilden' Das Bild hat mit dem Abgebildet

en die logische Form

derAbbildung gemein. 2.2c1DasBildbildetdieWirklichkeitab,indemeseine M6glichkeitdesBestehensundNichtbestehensvonSachverhalten darstellt. Das Bild stellt eine mogliche Sachlageim logischen 2.2ci2 Raume dar' 2.203DasBildentheltdieMoglichkeitderSachlage,diees darstellt. 2.2LDasBildstimmtmitderWirklichkeitiibeneinoder nicht; es ist richtig oder unrichtig, wahr oder falsch' Das Bild stellt dar, was esdarstellt, unabhingig von 2.22 seiner Wahr- oder Falschheit, durch die Form derAbbildung. Was das Bild darstellt, ist sein Sinn' 2.22r InderUbereinstimmungoderNichttrberein+timmung 2.222 seinesSinnesmitderWirklichkeit,bestehtseineWahrheitoder Falschheit. 2.22SUmzuerkennen,obdasBildwahroderfalschist,mtissen wir es mitder Wirklichkeitvergleichen' Aus dem Bild altein ist nicht zu erkennen' ob es w

ahr 2.224 oder falsch ist. Ein a priori wahresBild gibt es nicht' 2.22b Das logische Bild der Tatsachenist der Gedanke' 3 konnen uns ,,Ein Sachverhaltist denkbar" heissl Wir l.oot ein Bildvon ihm machen' Die Gesamtheit der wahren Gedanken sind ein Bild 3.or derWelt. Der Gedanke enthalt die Moglichkeit der Sachlagedie 3.o2 er denkt. Was denkbar ist, ist auch moglich' Wir k6nnen nichts Unlogischesdenken' weil wir sonst 3.03 unlogisch denken miissten.

r8


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OPHICUS

2.182 2.rg 2.2 z.zor

Every picture is alsoa logical picture. (On the other hand, for example, not every picture is spatial.) The logical picture can depict the world. The picture has the logical form of representation in common with what it pictures. The pictur

e depictsreality by representinga possibility of the existence and non-existenceof atomic facts.

The picture represents a possible state of affairs in logical space. The picturecontains the possibility of the state of 2.203 affairs which it represents. Thepicture agreeswith reality or noq it is right or 2.2r wrong, true or false. Thepicture representswhat it represents,independ2.22 ently of its truth or falsehood, through the form of representation. What the picture representsis its sense.2.22r In the agreement or disagreementof its sensewith 2.222 reality, its truthor falsity consists. 2.202 In order to discoverwhether the picture is true or false we must compare it with reality. It cannot be discovered from the picture alone 2.224 whether it is true or false. There is no picture which is a priori tr

ue. 2.22b The logical picture of the facts is the thought. 3 "An atomic f,actisthinkable" - means:we can imagine it. 3.ool 2.222 3.or Z.o2 3.og The totality oftrue thoughts is a picture of the world. The thought contains the possibility of the state of affairs which it thinks. What is thinkable is also possible. We cannot think anything unlogical, for otherwise we should have to think unlogically.

l9


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Man sagteeinmal, dassGott alles schaffenkonne, nur nichts, was den logischen Gesetzenzuwider wiire. - Wir konnten ndmlich von einer ,,unlogischen"Welt nicht sagen, wie sie aussihe. Etwas,,der Logik widersprechendes" der Sprache in Z.oZz darstellen, kann man ebensowenig,wie in der Geometrie eine den Gesetzendes Raumes widersprechende Figur durch ihre Koordinaten darstellen: oder die Koordinaten ein

es Punktesangeben,welcher nicht existiert. Wohl k6nnen wir einen Sachverhaltriiumlich darstelB.o3zr len, welcher den Gesetzender Physik, aber keinen, der den Gesetzender Geometrie zuwiderliefe. Ein a priori richtiger Gedankewire ein solcher,dessen Z.o4 Moglichkeit seine Wahrheit bedingte. Nur so konnten wir a priori wissen,dassein Gedanke 3.ob wahr ist, wenn aus dem Gedanken selbst(ohne Vergleichsobjekt) seine Wahrheit zu erkennen ware. g.r Im Satz driickt sich der Gedanke sinnlich wahrnehmbar aus. Wir beniitzen das sinnlich wahrnehmbare Zeichen 3.rr (Laut- oder Schriftzeichenetc.) des Satzes Projektion als der moglichen Sachlage. Die Projektionsmethode ist das Denken des SatzSinnes. Das Zeichen, durch welcheswir den Gedanken aus3.r2 drucken, nenne ich das Satzzeichen.Und der Satz ist dasSatzzeichen seiner projektiven Beziehungzur Welt. in Zum Satzgehort alles,waszurProjektion gehort; aber 3.r3 nicht das Projizierte. Also die Moglichkeit des Pr

ojizierten,aber nicht dieses selbst. Im Satz ist also sein Sinn noch nicht enthalten, wohl aber die Moglichkeit ihn auszudrfrcken. (,,Der Inhalt des Satzes"heisst der Inhalt des sinnvollen Satzes.) 3.ogr


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g.o31

It used to be said that God could create everything, except what was contrary tothe laws of logic. The tnrth is, we could not sa) of an "unlogical" world how it would look. To present in language anything which "contradicts logic" is as im

possible as in geometry to present by its coordinates a figure which contradictsthe laws of space; or to give the co-ordinates of a point which does not exist.We could present spatially an atomic fact which contradicted the laws of physics,but not one which contradicted the laws of geometry An a priori true thought would be one whose possibility guaranteed is truth. We could only know a priori that a thought is true if its truth was to be recognized from the thought itself(without an object of comparison). In the proposition the thought is expressedperceptibly through the senses. We use the sensibly perceptible sign (sound or written sign, etc.) of the proposition as a projection of the possible state of affairs. The method of projection is the thinking of the sense of the proposition.The sign through which we expressthe thought I call the propositional sign. Andthe proposition is the propo. sitional sign in its projective relation to the wo

rld. To the proposition belongs everything which belongs to the projection; butnot what is projected. Therefore the possibility of what is projected but not this itself. In the proposition, therefore, its senseis not yet contained, but thepossibility of expressing it. ("The content of the proposition" means the content of the significant proposition.)

g.og2

3.o3z r

g.o4 3.ob

B.r 3.r r

Z.r2

3.rB


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g.r4

ImsatzistdieFormseinesSinnesenthalten'abernicht Inhalt. dessen Das Satzzeichenbesteht darin, dass sich seine Elemente. die Worter, in ihm auf bestimmte Art undWeise zu einander verhalten, Das Satzzeichenist eine Thtsache' Der Satzist kein

Wortergemisch' - (Wie das musikalischeThema kein Gemischvon Tonen')

3.141

Der Satzist artikuliert. Nur Tatsachenkonnen einen Sinn ausdrucken'eine 2.142 Klassevon Namen kann es nicht' Dassdas Satzzeicheneine Tatsacheist' wird durch die2.143 gewohnliche Ausdrucksform der Schrift oder des Druckes verschleiert. Dennim gedruckten Satz z' B' sieht das Satzzeichen nicht wesentlich verschieden ausvom Wort' (So war es m6glich, dassFrege den Satz einen zusammengesetzten Namennannte' ) wenn wir es Sehr klar wird dasWesen des Satzzeichens' g.L4Zr uns, statt aus Schriftzeichen, aus riumlichen Gegenstinden (erwaTischen, Stuhlen, Buchern) zusammengesetzt denken. Die gegenseitige riumliche Lage dieser Dinge druckt au

s' dann den Sinn des Satzes der Nicht ,,Daskomplexe Zeichen ,aRb' sagt' dassa ing.L4Z2 BeziehungR zu b steht", sondern: Dass"a" in einer gewissen Beziehungzu ,,b" steht, sagt,dassaRb' Sachlagenkann man beschreiben'nicht benennen' 2:44 (Namen gleichen Punkten, Sitze Pfeilen' sie haben 2.2 Sinn.) Im Satze kann der Gedanke so ausgedrfickt sein' dass Satzzeiden Gegensrjinden des Gedankens Elemente des chens entsPrechen' und Diese Elemente nenne ich 'einfache Zeichen" den Satz,,vollstiindig analysiert"'

B.zor


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3.r4

In the proposition the form of its senseis contained, but not its content. The propositional sign consistsin the fact that its elements, the words, are combinedin it in a definite way. The propositional sign is afact. The proposition is no

t a mixture of words (just as the musical theme is not a mixture of tones). Theproposition is articulate. Only factscan expressa sense, classof namescannot. aThat the propositional sign is a fact is concealedby the ordinary form of expression,written or printed. (For in the printed proposition, for example, the signof a proposition does not appear essentiallydifferent from a word. Thus it waspossiblefor Frege to call the proposition a compounded name.) The essential natureof the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs. The mutualspatial position of these things then expressesthe senseof the proposition. 'a"The complex sign ' aRb'says stands We must not say, in relation R to b"'; but we must say," That'a' standsin a certain relation to'b' says that aRil'. Statesofaffiairscan be described but not named. (Names resemble points; propositions re

semble arrows, they have sense.) In propositions thoughts can be so expressedthat to the objects of the thoughts correspond the elements of the propositional sign. These elements I call "simple signs" and the proposition "completely analysed".

Z.r4r

Z.r4z Z.r4Z

g.t4gr

g.r4g2

9.144

9.2

3.2or

23


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g'2o2DieimsatzeangewandteneinfachenZeichenheissen Namen. Der Name bedeutet den Gegenstand'Der Gegenstand g.zog Zeichen wie ,,A"') ist seine Bedeutung. (,,A" istdasselbe Der Konfiguration der einfachen Zeichen irn SatzzeiZ,2r chen entspricht die Konfiguration der Gegenstande in der Sachlage. Der Name vertritt im Satzden Gegenstand' g.22 g,rrtDieGegenstindekannichnurnennen'Zeichenvertreten sie. Ich

kann nur von ihnen sprechen,sie aussprechen kann ich nicht. Ein Satz kann nur sagen' wie ein Ding ist, nicht was es ist' S.2SDieForderungderM6glichkeitdereinfachenZeichen ist die Forderung der Bestimmtheit des Sinnes' welchervom Komplexhandelt' stehtin interner Der Satz, 2.24 Beziehungzumsatze,dervondessenBestandteilhandelt. Der Komplex kann nur durch seine Beschreibung gegeben sein, und diese wird sdmmen oder nicht stimmen. Der Satz,in welchem von einem Komplex die Rede ist, wird, wenn dieser nicht existiert

2528419 Ludwig Witt Gen Stein Tractatus LogicoPhilosophicus

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Transcript of 2528419 Ludwig Witt Gen Stein Tractatus LogicoPhilosophicus