KRITERION Nr. 17 (2003), pp. 1-6 Contentless Syntax, Ineffable Semantics, and Transcendental Ontology. Reflections on Wittgenstein s Tractatus Arkadiusz Chrudzimski Universities of Zielona Góra, Poland and Salzburg, Austria Abstract Wittgenstein s Tractatus [6] contains some very striking theses. We read, e.g., that in a sense we could not be wrong in logic, and that the whole subject matter of the theory of modalities could be reconstructed on the ground of the insights in the mechanism of the linguistic reference. Yet in the light of the last sentences of Tractatus the whole semantics turns out to be principally ineffable. In our paper we will try to clarify these matters. We show how these theses could be made plausible in the context of the transcendental method of Wittgenstein s Tractatus. 1 Syntax does not represent One of the most influential ideas of Wittgenstein s Tractatus is that the logical constants do not represent anything. Logical constants combine sentences truth-functionally, so that if we are to construct a model for a language L, we only need to assign the semantical values to the atomic formulas of L. The semantic values of the molecular formulas will be generated automatically, according to the well known functions that could be represented as truth-value tables. (5, 5.101) For the conjunction p q we obtain the following table: I should like to thank the Austrian Foundation for the Promotion of Scientific Research (FWF) for the financial support. p T F q T T F F F F For the disjunction p q the table looks like this: p T F q T T T F T F And for the material implication p q we have: p T F q T T T F F T Accordingly, we can say that the logical forms of composition, represented by,, and, for that matter, also by the one-place conjunctive, do not represent. They need no separate semantical correlates over and above the semantical correlates of the flanking sentences. Consequently, if we want to formulate a semantical truth-definition à la Tarski [5], we only need truth-makers for atomic formulas. All that is well known. Note, however, that nearly the same procedure could be applied to the under-atomic logical forms. Consider the simplest syntactical structure F a. Its semantical value depends exclusively on the question, whether or not the semantical value correlated with the name a belongs to the set which is the semantical value of the predicate F. We can thus construct the analogical (possibly infinite) table for the predicationform: a x y z... F F F F... {x} T F F... {y} F T F... {z} F F T... {x, y} T T F... {x, z} T F T....
KRITERION, Nr. 17 (2003), pp. 1-6 Indeed, Wittgenstein s view was not just that the logical constants do not represent. His idea was that the entire logical syntax does not represent. And Tarski s concept of satisfaction explores in point of fact, the same idea. If we accept all that, we have ipso facto something like the principle of extensionality. If the semantic values of compound sentences are functions of the semantic values of their constituents and the semantic values of atomic sentences are functions of the semantic values of their ultimate (sub-sentential) constituents, then it is clear that, for any constituent expression x involved in the compound sentence A, we can substitute any other expression y without any change of the semantic value of A, providing that x has the same semantic value as y. To have the standard principle of extensionality we need only to assume, that the semantic values in question are the same entities that are commonly called extensions. And so far, as we have seen, they were extensions. 2 Modalities But we know very well that the principle of extensionality holds only for a very rudimental part of our language. Consider modal contexts, It is possible/necessary that.... If we try to construct the truth-functional tables for the modal operators, we see that the truth-values of modal sentences are not always determined by the mere truth-values of their constituents and therefore are not functions of the truth-values of their constituents. Syntactically, the box ( ) and the diamond ( ) behave like the negation ( ). They are sentential operators building sentences out of sentences. But while for the negation we have the well known simple table: p p T F F T for the box and diamond we obtain positions at which the truth values are indeterminate: p p p T T? F? F We have two unknown values. Whatever is actual, is possible, and whatever is not actual, is not necessary, but not all non-actual is impossible, and not all actual is necessary. To extensionalize modal contexts we need some more fine-grained semantic values than the Fregean the True and the False. The standard procedure is to move to the ontology of possible worlds. The propositions are treated no longer as entities that simply have truth-values. They become functions from possible worlds to truth-values. In the extensional semantics operating in the frame of one world, sentences could be construed as 0-ary predicates (i.e. as 0-place functions). In the frame of the possibleworlds semantics, they become 1-ary predicates (i.e. 1-place functions from the possible worlds to the truth values). 1 The world-theoretic explanation of modalities is then as follows: The sentence p is true simpliciter, if p is true at the actual world (i.e. at the distinguished world w ). The sentence p is possibly true, if there is at least one possible world, at which p is true, and the sentence p is necessarily true, if p is true at all possible worlds. 2 The modal discourse has been thus extensionalized. The box and the diamond have been replaced by the quantifying over the possible worlds. The modal discourse p p p The extensionalized modal discourse p(w ) w[p(w)] w[p(w)] Not all philosophers, however, are happy with the abundant ontology of possible worlds. 3 And Wittgenstein has shown, how such an ontology could be simulated. The possible worlds need not 1 Every n-ary predicate becomes analogically n + 1-ary. 2 Alternatively, propositions could be construed not as functions from possible worlds to the truth-values but as sets of possible worlds at which they are true. 3 It is far from clear what the possible worlds are. Carnap construes worlds linguistically as state descriptions [1, cf. p. 9]. For Chisholm and Plantinga worlds are abstract entities (maximal states of affairs) [2, cf. p. 43] and [4, cf. p. 44f]. David Lewis [3] proposes to treat worlds as concrete individual entities. 2
Chrudzimski, A.: Contentless Syntax, Ineffable Semantics, and Transcendental Ontology. be construed as primitive individuals of the system, as in the orthodox possible worlds semantics. If we had a set of basic building blocks of the universe and a set of rules specifying how these blocks could be combined, we could develop a combinatorial theory of possibilities to the effect that possible is, as it were, all that could be constructed from the given material. In effect Wittgenstein proposes such a theory. The world is composed of simple objects which prescribe all possible configurations in which they could appear. (2.011, 2.012) illustrated by the following simple picture: 3 Semantics and ontology But why should all that be true? What guarantee could we have that the combinatorial ontology of possibility that we could formulate on the ground of our analysis of our world, is really valid. To mention just a few problems: Why could there be no alien objects that exist in some possible, but not in the actual world? How could we be sure that we know all the ways in which the objects could be combined etc.? The answer lies in the philosophical method of the Tractatus. The ontological theses formulated in this work are for the most part deduced from semantical considerations. The way the world is, appears thus, in a sense, as a consequence of the way the world is represented. In this sense the ontology of Tractatus is transcendental in the Kantian sense. Wittgenstein assumes that our thoughts refer, and seeks the conditions of possibility of this semantic relation. He claims that such a reference is only possible, if the thought has a structure that is able to mirror a structure of the (fragment of the) world. (2.151) But the very mirroring assumes that it must be in advance some correlation between the elements of the structure of the thought and the elements of the structure of the world. The main device of the tractarian semantics is thus an a priori correlation between the logical form of the language and the ontological form of the world that is explained by the metaphor of the correlation of the syntactically simple names with the ontologically simple objects. (2.1514, 2.1515) The ontology and semantics of Tractatus can be The world consists of facts that are configurations of ontologically simple objects (A, B, C, D, E, F). Conscious subjects think of the world by means of sentences that are configurations of syntactically simple names. Sentences are meaningful because of the semantical relation correlating every simple name with an exactly one simple object. The sentence is true, if the configuration of the involved names corresponds to the configuration of the objects in the world (cf. the left side of our diagram). Otherwise the sentence is false (cf. the right side of our diagram). (2.222) The simple objects are called the logical form of the world, the simple names the logical form of the language. A moment s reflection shows, however, that the Wittgensteinian concepts of a name and an object are technical concepts that have very little to do with their commonsensical ancestors. As we have said, Wittgenstein suggests that the set of the ontologically simple objects prescribe somehow all possible configurations in which the objects could appear and by means of that, generates the set of possible worlds. Indeed, this is the crucial feature of Wittgensteinian objects. They are just a label for something that generates the set of possible worlds, whatever the nature of this something might be. The talk of simple objects is just a picture. So, Wittgenstein is not persuading us that there are really Wittgensteinian objects a kind of Democritean atoms of which the world consists. Instead, he gives us a picture that is in- 3
KRITERION, Nr. 17 (2003), pp. 1-6 tended to help us to understand what the logical form of the world could be like, but the metaphor used should not be pressed behind its intended meaning. The logical form is just any thing (or better any aspect of the world) that would generate all possible worlds in an analogue way, as the Wittgensteinian objects would generate Wittgensteinian worlds, if there really were such Wittgensteinian objects and worlds at all. If we remember that the entire conception of the Wittgensteinian objects in point of fact flows from the semantical considerations in fact, from the assumption that the language refers at all and if we remember that the aspect of the language that is a priori correlated with the objects are names, that in an analogue way generate all that could be said in a given language, we see that we had better think of Wittgenstein s names and objects as something resembling rather a grammar than a set of building blocks. Wittgenstein s thesis is that the logical form of the language is somehow a priori correlated with the logical form of the world, and we understand why he claims this, if we remember that the logical form of the language is its logical syntax, and that this syntax does not represent anything. Syntax is essentially something that could not be false, because it is not semantically correlated with any correlate in the contingent world. Indeed, the logical syntax is perfectly contentless. The metaphor by which Wittgenstein tries to express this fact is the picture according to which the syntax-aspect of the language (i.e. the set of the simple names) is correlated with the eternal and unchangeable form of reality (i.e. with the set of simple objects), while the descriptive aspect of the language (i.e. the configurations in which the names could be placed) represent the contingent content of the world (i.e. the way the simple objects are arranged in facts). (2.024, 2.0271) But in point of fact the eternality and unchangeability of the semantical correlate of the syntax, consists in the fact that there is no such correlate. It is, as it were, the eternality and unchangeability of the nothingness. We can now clearly see the structure of Wittgenstein s transcendental argumentation. The point of departure is language by means of which we represent the world. The first assumption is that such a language must have something like a syntax. 4 The syntax is further claimed to be contentless. It does not represent anything. Consequently whatever is true on the ground of syntax alone, is necessarily true. The last thesis is that such syntactic truths are the only necessary truths. 4 Logical omniscience and intentionality This idea of the contentless logical syntax makes it understandable why Wittgenstein could claim that in a sense we could not be wrong in the logic. (5.473) The logical omniscience of a Wittgensteinian subject consists precisely in the fact that the logic is contentless (6.1, 6.11), and so there is no point at which one could be wrong. As long as a subject uses a given language, he must respect its grammar. If he, e.g., uses the conjunctive in a way that does not conform to the table for conjunction, then he is actually interpreting the sign not as conjunction. Consequently, he is not speaking a language in which means and. This is the sense in which the meaning of our words lie in their use. To speak of the logical omniscience of the Wittgensteinian users of language could be thus very misleading. Note that, as there are no separate logical objects, there is also no logical knowledge involved. To be logically omniscient and infallible means therefore not to know something. It means merely to speak a given language. The thesis of the logical omniscience is the reason why in the frame of the tractarian philosophy there are no problems of the ontology of intentionality in addition to the problems of the ontology of modalities. The Wittgensteinian analysis of modalities automatically gives us a solution of the problem of intentionality. But first of all we ask, why it is commonly believed that the intentional contexts pose such additional problems. The reason is simple. If we move from the modal structures (... and... ) to the constructions involving the so called mind. 4 It seems that this assumption is plausible for any finite 4
Chrudzimski, A.: Contentless Syntax, Ineffable Semantics, and Transcendental Ontology. intentional operators, i.e., to the constructions like John believes that..., Mary thinks of..., Jack wonders, if... etc., we seem to have an additional source of non-extensionality. The nonextensionality of the modal contexts consists in the fact that we have to take into account not only how the world actually is, but also how it could be. And it is an initially plausible idea that in the case of the intentional contexts we have to take into account not only how the world actually is, and not only how it could be, but also what the subject in question thinks the world is and could be. Accordingly, if we want to use a possible world semantics for the intentional contexts, we will expect that the doxastically possible worlds will be in general much more fine grained then the alethically possible worlds. The intentional contexts are thus nonextensional and they seem to be essentially more subjective than the modal contexts. The question, whether two given constituents could be substituted salva extensione, depends not on the question what their semantic values are, but instead on the question, what the involved subject believes these semantical values are. It seems therefore that the logical form of the belief-context must involve at least an additional reference to the subject in question. It does not have the simple form: B(p) where B is an intentional operator like S believes that but takes the form: B(S, p) where B stands for a two-place operator believes that and S refers to the believing subject. Wittgenstein believed, however, that a philosophically analyzed language poses no such problems. The analysis revealing the deep logical structure of a language must therefore lead to the language that is fully logically transparent. In this case we could omit the reference to the particular subject and refer simply to the language. His next important claim was that in point of fact, every language functions according to its deep logical structure. The functioning of a language is thus logically transparent, whether or not the language in question is actually analyzed, and to use a language is precisely to let the language in question properly function. (3.262) This is the meaning of the thesis that the mere using of a language implies in a sense, a logical omniscience. A subject who really uses the language L must thus conform to the logical syntax of L and consequently he could not think non-logically. (3.03) Now it is the logical syntax of L that prescribes what is possible and, as this syntax must be transparent for any subject using L, there could be no difference between (i) what is possible and (ii) what the subject think is possible. There is thus no need for an additional ontology of intentionality. (i) and (ii) collapse. 5 An ineffable semantics Transcendental argumentations are notoriously difficult to express. The reason for this difficulty is instead relatively easy to grasp. What we talk or think about, are by definition objects of our thought. But what a transcendental argumentation wants to concentrate on, is precisely the conditions of possibility of such objects as they emerge from the way they are thought about. The conditions that were identified by Wittgenstein were: (i) the logical form of the language, (ii) the ontological form of the world, and (iii) their a priori correlation. It is thus no surprise that all Wittgenstein could give us, is a handful of metaphors like simple objects, the form or the substance of the world the metaphors discredited explicitly in the last sentences of the Tractatus. (6.54) The conditions of possibility of a semantical reference the logical form of representation could only be shown (or mirrored ), but not described. (4.12) A sentence could be about the world, but not about its own aboutness. Still this being about the logical form of representation is mirrored in each use of a sentence. (4.121) In point of fact, the whole semantics is, according to Wittgenstein, principally ineffable. And the reason is easy to understand, when we think of Tarski s analysis of the concept of truth. According to Tarski the condition of the material adequacy of any theory of truth T T for language L is that for every sentence p of L the T T must imply the so called Tarski s biconditional : (T) p is true if and only if p. But to the conditions of the formal correctness 5
KRITERION, Nr. 17 (2003), pp. 1-6 of T T it belongs that the possibility of expressing the paradoxical liar sentence : (*) The sentence (*) is not true should be blocked. Tarski s proposal is that the truth-predicate for the language L could not belong to the language L itself. The biconditional (T) must be expressed in a language of higher order (in a meta-language) which contains the names for all sentences of L (that appear at the left side of the (T)) and the translations of all sentences of L (that appear at the right side of the (T)). We consequently obtain the following picture: References [1] R. Carnap. Meaning and necessity. The University of Chicago Press, Chicago, 1960. [2] R. Chisholm. On metaphysics. University of Minessota Press, Minneapolis, 1989. [3] D. Lewis. On the plurality of worlds. Basil Blackwell, Oxford, 1986. [4] A. Plantinga. The nature of necessity. Oxford University Press, Oxford, 1974. [5] A. Tarski. Pojecie prawdy w jezykach nauk dedukcyjnych. In A. Tarski, editor, Logic, Semantics, Metamathematics. Papers from 1923 to 1938, pages 152 277. Clarendon Press, 1956. English version. Originally published 1933 in Warszawa. [6] L. Wittgenstein. Tractatus logicophilosophicus. Routledge & Kegan Paul, London, 1922. We see that the semantical relations between an object-language and its universe could be cognitively accessed, only through the language of the higher order. But according to Wittgenstein there is only one universal language. The semantical relations are consequently principally ineffable. This is the next point that allows us to understand the special status of the logical omniscience of the Wittgensteinian subject. The logical form of the world and the language is a crucial element of the mechanism of the intentional reference. We see now that this mechanism principally could not be intentionally grasped. Now if there is any object of the logic, it is this mechanism itself. (Cf. 6.124) The thesis that the logic of the language L could not be described (by any sentence of L) but only shown (in each use of a sentence of L) becomes thereby much more understandable. And we also seem to understand better why to have a logical omniscience is simply to use a language. 6