Browse Papers

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉).

The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker.

The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another.

I argue for an account of vagueness according to which the root of vagueness lies not in the type of semantic-value that is best associated with an expression, but in the type of linguistic practice that renders the expression meaningful. I suggest, in particular, that conventions about how to use sentences involving attributions of vague predicates to borderline cases prevail to a lesser degree than conventions about how to use sentences involving attributions of vague predicates to clear cases.

On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts.

Orthodoxy has it that mereological composition can never be a vague matter, for if it were, then existence would sometimes be a vague matter too, and that's impossible. I accept that vague composition implies vague existence, but deny that either is impossible. In this paper I develop degree-theoretic versions of quantified modal logic and of mereology, and combine them in a framework that allows us to make clear sense of vague composition and vague existence, and the relationships between them.

In this paper we outline and discuss various solutions to a restricted, but we think, more interesting version of the infamous Caesar Problem. This restricted version, labelled C-R Problem, occurs in contexts where we have two distinct abstraction principles:

AP_{@_{1}} (\forall X)(\forall Y)[@_{1}(X)=@_{1}(Y)\leftrightarrow E_{@_{1}}(X,Y)]

AP_{@_{2}} (\forall X)(\forall Y)[@_{2}(X)=@_{2}(Y)\leftrightarrow E_{@_{2}}(X,Y)]

and want to settle cross-sortal identity claims of the form:

@_{1}(P)=@_{2}(Q)

Both abstraction principles, however, are silent with regard to this identity -- a special instance of the Caesar Problem. In what follows, we outline two distinct strategies to resolve the C-R problem. The first strategy decides such cross-abstraction identities in terms of whether or not the equivalence relations appearing on the right hand side of the abstraction principles are identical, while the second strategy settles such identities by appeal to the relevant equivalence classes. We then focus our discussion on the latter approach and offer three ways of implementing this strategy. Ultimately, we argue that this strategy fails, as each attempt to appeal to equivalence classes faces unsurmountable difficulties.

On the difficulty of extracting the logical form of a seemingly simple sentence such as ‘If Andy went to the movie then Beth went too, but only if she found a taxi cab’, with some morals and questions on the nature of the difficulty.

Brogaard and Salerno 2005 have argued that antirealism resting on a counterfactual analysis of truth is flawed because it commits a conditional fallacy by entailing the absurdity that there is necessarily an epistemic agent. Brogaard and Salerno’s argument relies on a formal proof built upon the criticism of two parallel proofs given by Plantinga 1982 and Rea 2000. If this argument were conclusive, antirealism resting on a counterfactual analysis of truth should probably be abandoned. I argue however that the antirealist is not committed to a controversial reading of counterfactuals presupposed in Brogaard and Salerno’s proof, and that the antirealist can in principle adopt alternative readings that makes this proof invalid. My conclusion is that no reductio of antirealism resting on a counterfactual analysis of truth has yet been provided.

Category theory can be a tool used in philosophical theories and itself has an ontological status. More, there is a kind of categoricism. To justify these propositions is the scope of this paper.