Notes of Donald Davidson: "Truth and Meaning"

The main point of this article concerns the goal of supplying a theory of meaning for language L that shows how the meanings of sentences in L depends on the meanings of words in L. Davidson thinks that the way to build such a theory is by constructing a (recursive) definition of truth-in-L. (p. 98) The point of these notes is to explain what this means and how Davidson argues for this conclusion.

WHAT THIS MEANS

A theory of meaning for a language L would be a theory such that if anyone understood the theory, they would thereby understand the language L. If the theory showed how the meaning of sentences depended on the meanings of words, then the theory would have to tell you, given a language consisting of a finite lexicon of words and syntactical rules for the combinations of words into sentences, how to figure out the meaning of any sentence.

Davidson tells us how to build such a theory: define, for the language L, a predicate true-in-L, like the predicate in English "is true" such that you could generate theorems of the form, for instance:

"Grass is green" is true if and only if grass is green

for every true (declarative) sentence that can be formed in English.

DAVIDSON'S ARGUMENT

Much of Davidson's argument proceeds by a combination of elimination and bold conjecture: X won't work, Y won't work, therefore Z. Not the greatest form of argument. But sometimes you take what you can get.

As far as I'm concerned, the arguments all take place on pp 92-98 (the article takes up pp 92-110)

I will break this down in several steps

Remember, the goal is a theory of how (a potentially infinite collection of) sentences can be meaningful (understandable) based on understanding the way a finite collection of words and other pieces of syntax contribute to the meaning (understandability) of a sentence. First I will just name the steps. Then I will explain them.

Step 1: Maybe every part of a language (words and other pieces of syntax) has a meaning (p.92)

Step 2: Not every part of a language (words and other pieces of syntax) has a meaning. (pp. 92-93)

Step 3: Maybe the meanings of some words are their referents and you can just figure out how words without relate to the words with referents. (p.93)

Step 4: This won't work either: because of the slingshot argument. (p. 96)

Step 5: A bold leap (p. 97)

Step 1: Maybe every part of a language (words and other pieces of syntax) has a meaning (p.92)

So take a sentence like "Theatetus flies". How do you explain the meaning of the sentence in terms of its parts? You might try to say the meaning of "Theatetus" is the person Theatetus, and the meaning of "flies" is the property of flying.. . .

Step 2: Not every part of a language (words and other pieces of syntax) has a meaning. (pp. 92-93)

. . .but Davdison says this won't work because it leads to regress. . . He doesn't really spell this out. He goes on to give another reason against using this strategy: he thinks that it is unnecessary to assign a meaning to every word. This is the point of the discussion of “the father of Annette”. All that is needed is to figure out how to assign referents to “Annette”, “the father of Annete”, “the father of the father of Annette” and so on. No part of the strategy involves assigning a meaning or referent to “the” or “of”.

Step 3: Maybe the meanings of some words are their referents and you can just figure out how words without relate to the words with referents, and maybe this will work for whole sentences by assigning referents to entire sentences. (p.93)

But the problem with this is that , according to the slingshot argument, every true sentence has the same referent. And if meaning just is reference, then every true sentence means the same thing.

Step 4 The slingshot argument pp 93-94

The slingshot argument will probably strike you as extremely weird and extremely hard. The point of the argument is that the meaning of a sentence cannot be what it refers to because all true sentences end up referring to the same thing. The way the slingshot leads to the conclusion that all true sentences refer to the same thing is so difficult to follow for many students because the conclusion seems so bizarre.

Here is a long quote on the slingshot argument from an article on the web by E.J. Lowe ("Philosophical Logic" web address:

http://www.dur.ac.uk/~dfl0www/modules/logic/PHILLOG.HTM

BEGIN QUOTE

Facts will only serve as the truth-making correlates of sentences or propositions if they can be individuated and identified in a principled way. However, there is an important argument—now often referred to as the 'slingshot' (Barwise & Perry 1981)—attributed by Alonzo Church (1956, p. 25) to Frege and subsequently espoused by such philosophers as Donald Davidson (1969, pp. 41-2) and W. V. Quine, the implication of which is that facts cannot be non-trivially individuated. The argument purports to show that if a 'fact' is what a true sentence or proposition 'corresponds' to, then all true sentences or propositions correspond to the same fact—so either we should avoid an ontology of facts, or else we have to accept that there is only one fact, the 'Great Fact'. The latter position, however, is of no use to a proponent of the correspondence theory of truth, since it entirely trivializes that theory. The argument (or one version of it) goes as follows. If facts exist, and a certain sentence, P, is true, then it is surely undeniable that

(1) The fact that P is identical with the fact that P.

However, it is surely also the case that the singular term 'the fact that P' should not change its reference if we substitute for P another sentence Q which is logically equivalent to P, nor if we substitute for any singular term in P another singular term with the same reference. This being so, let Q be any true sentence distinct from P and let a be any arbitrarily chosen object. Then it is easily provable that P is logically equivalent to the following sentence: '{a} = {x: x = a & P}'. (This may be read in English as follows: 'The set whose sole member is a is identical with the set every member x of which satisfies the condition that x is identical with a andP is the case'.) Hence, from (1) we can deduce

(2) The fact that P is identical with the fact that {a} = {x: x = a & P}.

However, in exactly the same way it can be proved that Q is logically equivalent to '{a} = {x: x = a & Q}'. It follows that the two singular terms '{x: x = a & P}' and '{x: x = a & Q}' have the same reference, since both have the same reference as the singular term '{a}'. Accordingly, we can substitute the second of these terms for the first in (2) to give

(3) The fact that P is identical with the fact that {a} = {x: x = a & Q}.

Finally, using the already established logical equivalence between Q and '{a} = {x: x = a & Q}', we can deduce from (3)

(4) The fact that P is identical with the fact that Q.

Thus, starting out from some highly plausible assumptions and an apparently trivial premise, (1), we have been able to deduce that any two true sentences, P and Q, correspond to the same fact, if indeed facts exist. There are various ways in which one might attempt to block this argument—for instance, by rejecting the assumption that so-called set-abstracts like '{x: x = a & P}' are genuinely singular referring terms, or by allowing that the substitution of one singular referring term for another co-referring one within P may alter the reference of the term 'the fact that P'. But none of these strategies is particularly compelling.

Frege's own conclusion from this line of reasoning (to the extent that Church is correct in attributing it to him) was that, rather than saying that every true sentence corresponds to a fact which makes it true, we should say that every true sentence has as its reference the True (and that every false one has as its reference the False). (See Frege 1892b, p. 63.) That is to say, the reference of every (assertoric) sentence is a truth value, of which there are just two. (The only exceptions to this rule, for Frege, would be assertoric sentences containing names lacking a reference, such as 'Zeus': such a sentence, he thought, must itself lack a reference and hence have no truth value.) Frege did not believe that one could define 'truth', holding it to be a primitive and irreducible notion. Of course, the idea that a sentence can have a 'reference' may seem odd, though only if we take names as our paradigms of expressions having a reference (this, then, is a case in which the term 'semantic value' may be less misleading than the term 'reference'). It should be pointed out here that between Frege's extreme of taking all true sentences to have the same reference and the opposite extreme of taking all logically non-equivalent true sentences to 'correspond' to different 'facts' there are many intermediate positions. Consider, thus, the case of negative and disjunctive true sentences of the forms 'Not P' and 'P or Q', respectively. A correspondence theorist need not say that 'Not P' is made true by a negative fact, the fact that not P, nor that 'P or Q' is made true by a disjunctive fact, the fact that P or Q. He can say that 'Not P' is true because there is no fact that P for it to correspond to, and he can say that 'P or Q' is either made true by the fact that P or else made true by the fact that Q. Thus, on this view, logically non-equivalent true sentences can, but need not, have the same 'truth-makers'.

END QUOTE

Step 5: A bold leap (p. 97)

This is pretty much contained in the second full paragraph on p 97.