Although Peano arithmetic (PA) is necessarily incomplete, Isaacson argued that it is in a sense conceptually complete: proving a statement of the language of PA that is independent of PA will require conceptual resources beyond those needed to understand PA. This paper gives a test of Isaacon’s thesis. Understanding PA requires understanding the functions of addition and multiplication. It is argued that grasping these primitive recursive functions involves grasping the double ancestral, a generalized version of the ancestral operator. Thus, we can test Isaacon’s thesis by seeing whether when we phrase arithmetic in a context with the double ancestral operator, the result is conservative over PA. This is a stronger version of the test given by Smith, who argued that understanding the predicate “natural number” requires understanding the ancestral operator, but did not investigate what is required to understand the arithmetic functions.

This paper presents two cases demonstrating that theories allowing the environment to partially determine the content of moral concepts (such as the causal theory of reference) that provide incorrect truth-conditions for moral terms. While typical Moral Twin Earth cases seek to establish that these theories fail to account formoral disagreement, neither case here essentially involves interpersonal disagreement. Both involve a single person retaining moral beliefs despite recognizing actual or potential mismatches with the purportedly content-determining facts. This lets opponents of such theories grant objections that standard Moral Twin Earth cases fail to demonstrate disagreement, and argue more straightforwardly that they generate implausible truth-conditions for moral claims.

The combinatorial theory of modality has long been dogged by the supposed problem that it entails that S5 is not the correct logic for metaphysical modality. In this paper, I suggest a modification to combinatorialism, to eliminate this tension with S5. I argue that the resulting view is more in the spirit of combinatorialism than the original position.

Recently several philosophers have argued that racial, gender, and other social generic generalizations should be avoided given their propensity to promote essentialist thinking, obscure the social nature of categories, and contribute to oppression. Here I argue that a general prohibition against social generics goes too far. Given that the truth of many generics require regularities or systematic rather than mere accidental correlations, they are our best means for describing structural forms of violence and discrimination. Moreover, their accuracy, their persistence in the face of counterexamples, and features of the contemporary socio-political context make generics useful linguistic tools in social justice projects.

A number of philosophers deny that contradictions can be believed. Are they correct? In this note, I showthat even in quite weak logics, on pain of inconsistency, if there are false beliefs, either there are propositions which are true but unbelievable or contradictions are believable. Since the antecedent clearly holds, I offer some considerations in favor of the latter disjunct. Objections and variants of the main argument are considered.

The consequence argument is among the most influential arguments for the conclusion that free will and determinism are incompatible. Recently, however, it has become increasingly clear that the argument fails to establish that particular incompatibilist conclusion. Even so, a version of the argument can be formulated that supports a different incompatibilist conclusion, according to which free will is incompatible with our behavior being predetermined by factors beyond our control. This conclusion, though not equivalent to the traditional incompatibilist thesis that determinism strictly precludes free will, is something many incompatibilists have had in mind all along and, indeed, is arguably the more central incompatibilist position. The consequence argument thus remains philosophically important, even if, as several of its critics have argued, it can’t be used to establish the strict incompatibility of free will and determinism.

It is a received view of the post-Fregean predicate logic that a universal statement has no existential import and thus does not entail its particular (existential) counterpart. This paper takes issue with the view by discussing the trespasser case, which has widely been employed for supporting the view. The trespasser case in fact involves a shift of context. Properly understood, the case provides no support for the received view but rather suggests that we rethink the ‘quantity view’ of the existential import of quantifiers

For sentences such as "(1) Columbus knows that the sea is unpredictable" there is a face-value theory, according to which ‘that’-clauses are singular terms denoting propositions. Famously, Prior raised an objection to the theory, but defenders of the face-value theory such as Forbes, King, Künne, Pietroski and Stanley urged that the objection could bemet by maintaining that in (1) ‘to know’ designates a complex relation along the lines of being in a state of knowledge having as content. Is the theory safe, then? The aim of this paper is to show that a new problem for the theory arises if we consider some clauses other than ‘that’-clauses.