From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

1. Between language and mind: a logic of propositional attitudes ...

The statement in §5.542 concerns the logical form of peculiar propositional attitudes, viz. belief-statements:

But it is clear that "A believes that p", "A thinks p", "A says p", are of the form " 'p' says p": and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co- ordination of their objects.

This formulation sounds queer, and we will attempt to see why Wittgenstein did state it so before considering Hintikka's replies in favor of epistemic modal logic.

The core problem concerns truth-functions theory: is any meaning-function a truth-function? (Russell 1923) made a distinction between two sorts of occurrence for a proposition, namely: meaning-functions that contain propositions as a member are also truth-functions whenever the component proposition occurs as expressing a fact (i.e. an ontological entity); they are not so whenever the proposition occurs as a fact in its own right, given that the whole sentence then talks about the component proposition itself. It is precisely the case with propositional attitudes, where the fact in consideration is the form of words uttered by the speaker. It thus seems that not every meaning-function is truth-functional and, in this respect, Russell's position is to be compared with what Frege argued about the change of denotation in a context of indirect discourse.

Nevertheless, (Wittgenstein 1922) does not accept any other meaning-functions than the truth-functional ones: not only “Propositions are truth-functions of elementary propositions” (§5), but also “There is one and only one complete analysis of the proposition” (§3.25). If so, the preceding logical analyses as suggested by Russell and Frege cannot be accepted because they go beyond truth-function theory, the only one for Wittgenstein (“In the general propositional form, propositions occur in a proposition only as bases of the truth-operations”, §5.54). Therefore, the point is not to delimit one context of application for truth-functional propositions while ruling out some propositions of an intensional sort; rather, the point is to streamline every meaningful proposition within the unique pattern of truth-functions. There cannot be any exception to the theory of extensionality, from a Tractarian perspective.

For one thing, the analysis of "A believes p" excludes the subject A from its logical form while replacing it by a mention of the proposition within single brackets, 'p'. The result seems to be counterintuitive, reducing belief to an impersonal relation between a linguistic expression (i.e. the propositional sign) and that what it designates (i.e. the propositional fact that constitutes a thought). Why such an exclusion of the thinking subject, and how to analyze a belief while eliminating the psychological side of an attitude? (Russell 1923) did not reject it from his own analysis, given that he conceived the believer as a sequence of psychological facts expressed by means of sentences. But those beliefs were then associated with a single subject; now Wittgenstein's account definitely cancels this particular subject and talks instead about some arbitrary sentence in the form 'p'.

In order to understand such a mysterious statement as §5.542, several writers accounted for it in two steps, namely: Wittgenstein's theory of object and his subsequent distinction between an empirical and a metaphysical subject.

2. … is not a problem of mind (no psychologism!) ...

In (Russell 1923)'s account, each proposition was treated as a class of psychological facts that introduce A's mind through the analysis of propositional attitudes. The logical form of "A believes that p" thus corresponds to the correlation of a fact, i.e. the propositional fact that p, and an object, i.e. A's mind. However, any object is simple, Wittgenstein claims (“The object is simple”, §2.02), whereas A's mind is complex (as a sequence of psychological facts), so that the logical form assigned to propositional attitudes is not correct. The logical form required for any states of affairs (“An atomic fact is a combination of objects (entities, things)”, §2.01) thus leads Wittgenstein to discard propositional attitudes as states of affairs, in their current reading as a co-ordination of a fact and an object. Such a position leads him to the equally queer statement: “This shows that there is no such thing as the soul – the subject, etc. – as it is conceived in superficial psychology. A composite soul would not be a soul any longer” (§5.5421).

Isn't the price to pay for accepting Wittgenstein's logical analysis too expensive, if the rejection of propositional attitudes apparently leads one to a rejection of psychology? (Favrholdt 1964, 559) notes that this result directly follows from the Tractarian theory of objects:

For the superficial psychologists that maintain this it would be reasonable to say that "A says p" is a coordination of a fact in the Wittgensteinian sense, namely a propositional sign, and an object, namely the thinking, presenting soul, which being simple is to be called an object. This view Wittgenstein is bound to reject. According to the picture theory in the Tractatus no co-ordination could ever be established between a fact and an object. The two entities in question have to be equally articulated in order to be co-ordinated. Objects can be co-ordinated with objects (because they are simple) and facts can be co-ordinated with facts in so far as they can be analysed into the same amounts of elements. (559)

This prevents Wittgenstein from viewing propositional attitudes in the usual way, to be found in epistemic modal logic. Hence his second argument that accounts for §5.542: the distinction between an empirical and a metaphysical subject.

(Hintikka 1958) puts such a distinction to avoid some misunderstanding in Wittgenstein's language theory, namely: his thesis of solipsism, ordinarily considered as an argument for private language. In order to clarify the following passage: “That the world is my world, shows itself in the fact that the limits of the language (the language which I understand) mean the limits of my world” (§5.62), (Hintikka 1958) argues that Wittgenstein's concern

is not the empirical subject but the "metaphysical" subject discussed in philosophy. In other words, he is interested only in what can be said to be mine necessarily; for otherwise he would only be doing empirical psychology. But the only necessity there is, according to the other doctrines of the Tractatus, is the empty tautological necessity of logic. (89)

As a matter of fact, solipsism suggests the private character of our current thoughts: “The limits of my language mean the limits of my world” (§5.6). Now Wittgenstein doesn't support the view of a private language altogether. As a way to disentangle this wrong connection, Hintikka argues that the Tractarian "I" is not a psychological ego or single thinker. It is not the agent of Hintikka's later epistemic logic, but an abstract subject embodying the whole set of propositions: “The subject does not belong to the world but it is a limit of the world” (§5.632). Wittgenstein's picture theory of language should recall us that the limits of the world are determined as the limits of language, where the projective relation between both stands for the correspondence between a pictured fact and a picturing proposition.

Moreover, the metaphysical subject cannot talk about itself within the very language it embodies, contrary to the case of propositional attitudes: “No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the "whole theory of types")” (§3.332). In virtue of such an impossible self-reference for the Wittgensteinian subject, believing that p is the case is thus confined to the impersonal relation between a propositional sign and a proposition: 'p' says p, meaning that the propositional sign expresses p's being the case. Consequently, solipsism means the obvious impossibility for the metaphysical subject to go beyond the limits of language, given that the latter is a precondition to the former; but solipsism does not mean the impossibility for a psychological subject to express her own thoughts. On the contrary, Wittgenstein's thoughts are as public as Frege's ones (the Gedanken) and his solipsism does not mean at all that thoughts are private representations (Vorstellungen). Nevertheless, such public thoughts are separated from the psychological subject that grasps them in the Tractatus, hence the resulting logical form in §5.542.

Now (Favrholdt 1964) recalls in the same time that the thinker implicitly occurs in the relation expressed in §5.542 between 'p' and p:

"'p' says p" says nothing more than p. It states that the propositional sign is being thought, and this is the same as asserting the proposition p. Therefore, according to Wittgenstein, in sentences as ‘A says p’, p is not occurring in a proposition in a special way which is in conflict with his general theory of truth-functions. (560).

3. ... but a problem of language (no metatheory!)

It will be attempted to show in the following that epistemic logic amounts to some compromise between both topics: it introduces belief into logic while presenting it as the public occurrence of a statement, or assertion. But the Tractarian view of logic excluded to do so.

Assuming that assertion refers to the occurrence of a belief by means of a statement, it does not add anything to propositions that serve to make it explicit and is to be located in the domain of psychological events. The very project of a "doxastic logic" is therefore absurd, in the light of the Tractarian language theory:

The thought makes a une proposition out of the propositional sign p and this is the same as asserting p. If p is not thought it remains a propositinal sign and the expression "├p" in this case is absurd; you cannot at the same time assert, that is to say think p, and not think p. Hence the assertion sign is logically altogether meaningless (see 4.442). (560)

As to the rules of logic, they specify the limits within which subjects do and can express themselves: inferences and tautologies don't say anything but embed propositional forms that subjects cannot think of, because either these forms don't depict any particular image (excluded middle) or cancel any of them (non-contradiction). The projective nature of language according to Wittgenstein makes his logical theory appear as a sort of transcendental frame for thinking. Such a view could be interpreted as reminiscent of Kant's transcendental logic, to be defined as an inquiry into the conditions of a priori possibility for experience according to the categories of understanding. Apart from the notion of understanding, Kant's criticism is found again here in the impossibility for any empirical subject to know the limits of language; empirical subjects think within language, and they cannot depart from it in order to contemplate outwardly what makes a distinction between logical and illogical thoughts.

Logic is thus characterized as a method of projecting true or false propositions of a language into states of affairs (Tatsachen) or mere situations (Sachverhalte), respectively; but these methods are inexpressible by themselves. Formal semantics cannot be described in the latter: the rules for applying a set of formulas into some given model, as depicted in every metalanguage from a model-theoretical semantics, couldn't be conceived in a Tractarian line. If any subject A believes in a contradiction, for example, (Favrholdt 1964) recalls that the distinction between a propositional sign and a thought makes such a belief meaningless (its projection is impossible, as pointing out no plausible direction):

Wouldn't it be possible for A to say "p . ~p" thus violating the laws of logic? The answer is no (...) A can think "p" or he can think "~p". In the first case the first link of p . ~p will become a proposition but the last part (~p) will remain a propositional sign, because it is not thought (…) Therefore if one cannot think anything unlogical he cannot present anything in language which "contradicts logic" either. For language is not the physical facts that we call propositional signs, but these facts in their projective relation to other facts. (561-2)

Epistemic modal logic is in total agreement with this, when forbidding any two contradictory propositions to be embedded into one and the same "model". The metaproperty of consistency says no more than Wittgenstein did here; it does the same thing but in saying it with terms, that is, within a construed formal semantics.

4. Conclusion: metatheory as a
precondition for modal logics

Universality of language and ineffability of semantics are two preconditions that Hintikka will rule out from his very view of logic, in accordance with his distinction between logic as a universal language and logic as a calculus; the same does for other modal logics than epistemic logic, given that any judgment about a proposition was made impossible by Wittgenstein. Such a Tractarian impossibility came from ineffability as a unknowable relation between language and reality. It also follows from this a crucial nexus between symbolism and formalism: language symbolizes the world, nothing else, and any formalized language should yield a genuine picture of reality.

The point with epistemic logic is that it becomes acceptable only when the preceding preconditions have been qualified. Such a qualification is allowed only within a model-theoretical framework that Wittgenstein refused for philosophical reasons, so that Suszko's initial objection pointed to the right direction while assuming uncharitably something justifiably refused by the Tractatus.

In a nutshell: only God can rule in logic, for Wittgenstein; but Suszko was an atheist and God is (officially) dead with Tarski, so to say.