Charles Sayward

A Possible Solution

12.1 The Possibility of an Account. Though he acknowledged no need to provide any account of truth for sentential quantifications, Prior’s text yet suggests a conception of quantification which coheres with the claim that sentential quantification is neither objectual (and thus certainly not referential) nor substitutional, and which may lend itself to an account of truth for such quantification.

A problem about conversational implicature

Conversational implicatures are easy to grasp for the most part. But it is another matter to give a rational reconstruction of how they are grasped. We argue that Grices attempt to do this fails. We distinguish two sorts of cases: (1) those in which we grasp the implicature by asking ourselves what would the speaker have to believe given that what he saidis such as is required by the talk exchange; (2) those in which we grasp the implicature by asking ourselves why it is that what the speaker said is so obviouslynot such as is required by the talk exchange. We argue that Grices account does not fit those cases falling under (2).

Frege on identities

The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an identity the terms flanking the symbol for identity do not have their ordinary contents, but instead have themselves as their contents. In ‘Uber Sinn und Bedeutung’ Frege became convinced that if an identity a=bis about the signs aand b, then it expresses no proper knowledge. So, since it is evident that many such identities do express proper knowledge, Frege concluded that identities are not about their contained signs. So he became convinced that his Begriffsschrift account was incorrect. What was the error in the argument that led Frege to that account? It was thinking that the content of a sentence is a function of the contents of its constituent signs, that is, the things it is about.

Does the law of excluded middle require bivalence

Determining whether the law of excluded middle requires bivalence depends upon whether we are talking about sentences or propositions. If we are talking about sentences, neither side has a decisive case. If we are talking of propositions, there is a strong argument on the side of those who say the excluded middle does require bivalence. I argue that all challenges to this argument can be met.

Why Substitutional Quantification Does Not Express Existence

Fundamental to Quine’s philosophy of logic is the thesis that (Q) Substitutional quantification does not express existence. We here consider the content of this claim and the reasons for thinking it true.

On Some Much Maligned Remarks of Wittgenstein on Gödel

In Remarks on the Foundations of Mathematics Wittegnstein discusses an argument that goes from Godel’s incompleteness result to the conclusion that some truths of mathematics are unprovable. Wittegnstein takes issue with this argument. Wittegnstein’s remarks in this connection have received very negative reaction from some very prominent people, for example, Godel and Dummett. The paper is a defense of what Wittegnstein has to say about the argument in question.

Prior On Truth-A First Look

Prior distinguishes two cases in which truth or falsity are attributed to propositions. In the first case the proposition is fully specified.

Quantifying over the reals

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geachs idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real numbers.

Moral relativism and deontic logic

If a native of India asserts “Killing cattle is wrong” and a Nebraskan asserts “Killing cattle is not wrong”, and both judgments agree with their respective moralities and both moralities are internally consistent, then the moral relativist says both judgments are fully correct. At this point relativism bifurcates. One branch which we call content relativism denies that the two people are contradicting each other. The idea is that the content of a moral judgment is a function of the overall moral point of view from which it proceeds. The second branch which we call truth value relativism affirms that the two judgments are contradictory. Truth value relativism appears to be logically incoherent. How can contradictory judgments be fully correct? For though there will be a sense of correctness in which each judgment is correct — namely by that of being correct relative to the morality relative to which each was expressed — if contradictory, the judgments cannot both be true, and thus cannot both be correct in this most basic sense of correctness. We defend truth value relativism against this sort of charge of logical incoherence by showing it can be accommodated by the existing semantical metatheories of deontic logic. Having done this we go on to argue that truth value relativism is the best version of relativism.

A Fregean conception of singular existence

A perplexity about singular existence statements (for example, ‘Socrates exists’) is that for their negations to be true their subject terms do not name anything. For example, in ‘Pegasus does not exist’ ‘does not exist’ is not said in respect to the referent of ‘Pegasus’ since there is none. But, then, in respect to what is that said? The paper answers the question by proposing a metalinguistic interpretation of singular existence statements, according to which singular existence statements are about names. It is argued that this interpretation fits in well with Frege’s views on existence, presupposition, and his idea that names have senses.