The philosophical significance of Godel's slingshot

Mind, Oct, 1995 by Stephen Neale

1. Introduction

A collapsing argument is an argument designed to show that there are fewer items of a given kind than might be supposed. Alonzo Church (1943a, 1956), W. V. Quine (1953c, 1953e, 1960), and Donald Davidson (1967a, 1967b, 1967c, 1969a, 1969b, 1990, forthcoming) have used collapsing arguments to undermine several philosophical theses, most notably (i) the thesis that there are facts to which true sentences correspond, (ii) the closely related thesis that sentences designate propositions, states-of-affairs, or situations, (iii) the seemingly unrelated thesis that expressions such as "necessarily", "possibly", "probably", "because", and "before" are (on some of their uses) non-truth-functional sentence connectives, and (iv) the thesis that quantifiers and modal operators may be fruitfully combined. In each case there is meant to be some sort of collapse: (i) the class of facts collapses into a singleton (the "Great Fact"); (ii) the class of items capable of serving as the designata of sentences collapses into a class of just two entities (which might as well be called "Truth" and "Falsity"); (iii) the class of sentence connectives satisfying a simple logical condition collapses into the boring class of truth-functional connectives; and (iv) modal distinctions collapse--i.e. "p [equivalence] []p" is valid--in systems that combine modality and quantification.

On the face of it, the threat of such collapses goes well beyond embarrassing certain approaches to natural language semantics. If there are no facts to which true sentences correspond, it is not obvious how facts can function (as some have suggested) as truth-makers, causal relata, and objects of knowledge. If sentences do not designate states-of-affairs or situations, then it is not obvious how such entities can be characterized in ways that make them (as some have suggested) the sorts of things that can be perceived, desired, and brought about by our actions (and inactions). And if words like "necessarily", "because", and "before" cannot be treated as non-truth-functional sentence connectives, and if there is no prospect of combining modality with quantification, how can philosophy's favourite non-truth-functional logics be used to elucidate appeals to events, times, causes, facts, states-of-affairs, situations, and propositions, or to tackle problems in metaphysics, ethics, and the philosophy of mind?(1)

According to Davidson (1984b, 1989, 1990, forthcoming) and Rorty (1992a, 1992b), the demise of facts produces further problems. Our thoughts, utterances, and inscriptions often are taken to have content in virtue of being representations of reality. These representations can be accurate or inaccurate: those that are accurate are said to be true, to correspond to the facts, to mirror reality (nature, the world). Davidson and Rorty find such locutions unfortunate: not only are they thoroughly intertwined with talk of facts, correspondence theories of truth, states-of-affairs, counterfactual circumstances, and possible worlds, they also underpin talk of scepticism, realism and anti-realism, the subjective-objective distinction, representational and computational theories of mind, and talk of alternative conceptual schemes that represent reality in different ways. Davidson and Rorty reject the representationalist presuppositions of modern philosophy. The time has come, they suggest, to see only folly in the idea of mental and linguistic representations of reality; and with this realization philosophy will be transformed as many of its staple problems and posits evaporate.

I do not want to dwell on these claims here, but I should stress one point: an examination of Davidson's case against representations must include an examination of his case against facts, for Davidson's position is basically this: in order to give any substance to the idea of representations of reality, reciprocal substance must be given to the idea that there are facts (that true utterances and beliefs represent). Once the case against facts is made, Davidson believes the case against representations (and the case against correspondence theories of truth) comes more or less free:

The correct objection to correspondence theories [of truth] is ... that

such theories fail to provide entities to which truth vehicles

(whether we take these to be statements, sentences, or

utterances) can be said to correspond. If this is right, and I am

convinced it is, we ought also to question the popular assumption

that sentences, or their spoken tokens, or sentence-like entities

or configurations in our brains, can properly be called

representations," since there is nothing for them to represent.

If we give up facts as entities that make sentences true, we

ought to give up representations at the same time, for the legitimacy

of each depends on the legitimacy of the other. (1990, p.

304)

Davidson's critique of the fact-representation distinction is a challenge to the presuppositions of much work in modem philosophy, a challenge that can be met by the construction of a viable theory of facts.(2) But there is a collapsing argument, says Davidson, that precludes the articulation of such a theory. The style of argument--used earlier by Church and Quine--is sometimes called the "Frege Argument", a label that has something to do with the fact that Church and Davidson see it in Frege's work, and something to do with the fact that Frege's way of maintaining intuitively plausible compositionality assumptions involves postulating just two entities ("Truth" and "Falsity") to serve as the designata of sentences. In deference to the minimal machinery and presuppositions of the argument, Barwise and Perry (1981, 1983) have dubbed it the "slingshot." In view of the difficulty involved in attributing the argument to Frege, I shall use this label.