Philip Hugly

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.

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.

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.

OBJECTIVISM AND REALISM IN FREGE’S PHILOSOPHY OF ARITHMETIC

This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one central debate in the philosophy of mathematics. Non-realism, i.e., the view supported by Hugly and Sayward in their monograph, is an original position distinct from the widely known realism and anti-realism. Non-realism is characterized by the rejection of a central assumption shared by many realists and anti-realists, i.e., the assumption that mathematical statements purport to refer to objects. The defense of their main argument for the thesis that arithmetic lacks ontology brings the authors to discuss also the controversial contrast between pure and empirical arithmetical discourse. Colin Cheyne, Sanford Shieh, and Jean Paul Van Bendegem, each coming from a different perspective, test the genuine originality of non-realism and raise objections to it. Novel interpretations of well-known arguments, e.g., the indispensability argument, and historical views, e.g. Frege, are interwoven with the development of the authors’ account. The discussion of the often neglected views of Wittgenstein and Prior provide an interesting and much needed contribution to the current debate in the philosophy of mathematics.

A fregean principle

Frege held that the result of applying a predicate to names lacks reference if any of the names lack reference. We defend the principle against a number of plausible objections. We put forth an account of consequence for a first-order language with identity in which the principle holds

Non-Objective Truth

We shall focus on thesis 2 which entails the basic redundancy theory: the claim that for any sentence A, A and “it is true that A” say the same. There are three objections to this claim which we shall take up. The first is that not all truth is realist or objective truth, and that thesis 2 does not fit non-objective truth. The second is an objection put forth by Michael Dummett. Dummett argues against thesis 2 using principles he thinks are found in Frege’s philosophy. The third objection against thesis 2 is that thesis 2 is inconsistent with truth value gaps. In this chapter we take up the first objection. In the next chapter we take up the second and third objections.