Tuesday, 7 April 2009

My Thesis: Section 3, part 2

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The target of the criticisms

Given what I have said above, a criticism of the GFP must recognise that it aims to uncover the logical form of thought. However, on my interpretation, not only do the criticisms in the Investigations recognise it but they depend on it. It is its very inability to uncover the depth grammar of our propositions that render the GFP empty. When we are implored to look, we are not being asked to look at the surface of language but we are being asked to assess whether analysis, as conceived in the Tractatus, can help us understand the logic of our language. What we need to remember is that the depth grammar, or the body of thought, resides in understanding how we use the proposition with sense. For a philosophical elucidation to uncover the meaning of a proposition, what is uncovered must already be there in its application. As we learnt from TLP 4.112, philosophy cannot discover facts about reality or produce true propositions which justify what sense something expresses. Instead, it can only logically clarify the thoughts that are already expressed/ expressible.

When he highlights that “‘p’ is true = p”, he is pointing out that unless we are able to discover the way in which ‘p’ is used then all we have done is enunciate a rule for signs. That is to say, we have remained on the surface of language rather than looking at how propositions symbolize. This is important to point out in order to guard against two potential errors. The first is that the later Wittgenstein held a purely deflationary or redundancy theory of truth, if by that we mean “that the sole explanation that can be given of the notion of truth consists precisely in the direct stipulation of the equivalence thesis”[1]. On the contrary, coming to know the sense of a sentence comes along with knowing how to assert its truth. In fact, his earlier work comes under criticism for ignoring how truth is used in relation to actual cases in our language. The point being made is simply that “’p’ is true = p” is all that can be said advance. As Winch says, “the real work is done by a detailed examination of how it is applied in particular cases.”[2] We can’t start with a notion of truth and then say something is a proposition only if it fits that mould.

The second error to be avoided is the mirror-image of the first, although it is slightly more complicated. It would be to say that in the Tractatus he had a specific notion of truth that a proposition must fit. In the Notebooks he said ““p” is true, says nothing else but p”. There is nothing further to know about what it is for a proposition to be true once one knows its sense. Here, one could only add ‘is true’ to a legitimately constructed proposition and all propositions are so constructed because they have a sense (TLP 5.4733). To see the sense clearly one has to see in what way it is a logical fact and this means uncovering its ‘logical scaffolding’ (TLP 4.023). After this, the only thing left to find out is whether the proposition is true and to do that one must compare it against reality (TLP 2.223). Either what is shown by its sense obtains or its negation does. Now I said it is more complicated. That is because he does have a substantial view of what it is for a proposition to be true or false. This is because of a particular pre-philosophical conception of what it is for a proposition to tell us ‘how things stand’- that there must be an agreement between something in the propositional sign and something in the situation. However, in the GFP this finds expression, not in a theory of truth but in how we can lay out the sense of any proposition in such a way that it can be compared to reality for truth and falsity.

Logic and understanding

I am claiming that, the Tractarian position that there is a GFP amounts to the view that the sense of our sentences is manifest in how we use them and that logical analysis can uncover what the sense is. It is then vulnerable if we are not given a method for uncovering the logic of our everyday propositions in this way. If so, the GFP fails by its own lights. Such an analysis might be surprising if we take it to tell us something substantial, a priori, about the nature of propositions. As Wittgenstein says, “The general propositional form is the essence of a proposition” (TLP 5.471). Moreover, it is something abstracted from the particular content of a proposition or its internal structure. This is because, in giving the ‘essence’ of a proposition, the GFP informs us what it is in virtue of which a sign can be regarded as a propositional-sign in the first place. In other words, it gives us a necessary feature by which our words have content (are about something) rather than being gibberish. For Wittgenstein, this investigation is directed towards looking at the logical syntax of our language, the status of logical constants, and how propositions are formed, one from the other. This is due to the contention that “logic covers everything that is necessarily true, and so can be said in advance of experience; or to put this in the old terminology, everything that is a priori[3]. As such, in claiming that the GFP is all that can be said in advance about a proposition having sense, it is the ‘sole logical constant’ (TLP 5.47).

The view that meaningful language depends on its logical form is a view that bears the impress of his predecessors, Frege and Russell. Consider that it seems necessary but not sufficient, in understanding the sense of “The ball is red”, to understand its constituent expressions. We also need to understand how, in the sentence, the expressions are put together; and this depends on certain semantic rules. These rules embodied in ‘logical syntax’ will show why we understand “The sandals are red” but not “The sandals are red and green” or “The good is red”.

In what way though does having a thought then depend on logical laws? Consider this quote from Frege:

In this way it is shown that our eight primitive names have denotation, and thereby the same holds good for all names correctly compounded out of these. However, not only a denotation, but also a sense, appertains to all names correctly formed from our signs. Every such name of a truth-value expresses a sense, a thought[4]

It looks like first we could have signs with denotation, and then if they are correctly conjoined, they have a sense. However, if at first we only knew the denotation, we would only know it and not know anything about it (e.g. its present conjunction with other objects in a fact; the logical role its name plays in any true proposition). How then can we use them in a proposition to state a fact? After all, a proposition is not just a blend of names and only a [propositional] fact can express a sense. As such, we would also have to be in possession of logical laws that tell us how we can put the names together in such a way that they can match the way things in reality in combine. Sandals are the kind of thing that can combine with redness whilst good isn’t.

In this regard, there is a tension between Wittgenstein and his predecessors. Consider that for Frege, logic has “the task of discovering the laws of truth, not the laws of taking things to be true or of thinking”[5]. Here logic is prescriptive: if one wants to think logically, one should put the signs together according to certain rules such that it expresses a thought. However, as Wittgenstein points out, one cannot think illogically (TLP 3.03-3.032). If logical form defines the limits of sense, it delineates what can be said and thought. To think illogically would require us to transgress that limit (i.e. to think what cannot be thought). Thus, the logical laws cannot be merely prescriptive but present in our ability to think and use language in the first place.

This leads Wittgenstein to believe that we couldn’t know the denotation of signs independently of their role in a proposition. The reason is that we our understanding of the components and how they are conjoined would not be enough for the proposition to have a sense, but also the fact that it is a legitimate combination. However, whether a proposition makes sense cannot depend on whether another (the one about whether they can combined in this way) is true. If it were otherwise 1) it could turn out we were thinking illogically if the proposition of logic turns out to be false and 2) we could only be said to know the sense to the extent that we became acquainted with the logical constants through logical analysis. This, as I said, is unacceptable because we can’t think illogically and we don’t need a logical analysis to use our propositions with sense.

Given this, we can only look at the logic of our language by seeing analysing how we use propositions with sense. We start with thoughts- propositions we understand- and then see what role the parts play in that rather than vice versa. To cut a long story short, the propositions at the end of analysis must be of the sort where there is no question whether they express a sense. That is, they don’t depend on any external logical glue that says that the simple signs can be in that combination. These elementary propositions show their sense (how things stand if it is true) through their components parts; and to know the meanings of the component parts is just to know the propositions it is possible for them to take part in. We can’t know their denotation independently of the possibilities of logical form. Given that through repeated negations on sets of elementary propositions we can derive the other logical constants, and because negation is an operation (something that we do) rather than representing anything there is no external logical glue needed for language to represent at all.

Here it is clear that in the Tractatus “’p’ is true”, doesn’t give us any more information than ‘p’ and nothing tells us what it is in virtue of which language makes sense, that is separate from our ability to use and understand language. The GFP doesn’t rely on any logical glue that allows our propositions reach out to reality. As McGinn says, the GFP “is given as soon as language in which we express judgements about the world is given. In acquiring language we have already grasped the general form of the proposition, that is, we have already grasped the whole of logic”[6]. This is something that Wittgenstein realises in the Investigations and is re-iterating. “This is how things are” and other formulations of the GFP are pseudo-propositions which give us nothing other than what is given in the individual sense of elementary propositions. They are not something stated but only shown in how we use our propositions with sense. If the GFP isn’t what is revealed by the elucidation of language it reveals nothing at all.

[1] Dummett as cited in (Winch, 1981) p.164

[2] (Winch, 1981) p.161

[3] (Pears, 1971) p.46

[4] Frege, Grundgesetze der Arithmetik, section 32 cited in (McGinn, 2006) p.242

[5](Frege, 1997) p.326

[6] (McGinn, 2006) p. 240


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