This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

In this paper, I articulate and argue for a new truthmaker view of ontological commitment, which I call the “General Truthmaker View”: when one affirms a sentence, one is ontologically committed to there being something that makes true the proposition expressed by the sentence. This view comes apart from Quinean orthodoxy in that we are not ontologically committed to the things over which we quantify, and it comes apart from extant truthmaker views of ontological commitment in that we are not (...) ontologically committed to the truthmakers of our sentences. (shrink)

There is a puzzle about the use of paraphrase in philosophy, presented most famously in Alston's [1958] ‘Ontological Commitments’, but found throughout the literature. The puzzle arises from the fact that a symmetry required for a paraphrase to be successful seems to necessitate a symmetry sufficient for a paraphrase to fail, since any two expressions that stand in the means the same as relation must also stand in the has the same commitments as relation. I show that, while this problem (...) does undermine some conceptions of paraphrase, on a proper understanding of paraphrase the puzzle gets no purchase. Since paraphrase is an important component of Quinean approaches to meta-ontology, this paper constitutes a partial defence of Quinean meta-ontology. Since paraphrase is an important component of traditional methods of philosophical inquiry, this paper constitutes a partial defence of traditional modes of philosophizing as well. (shrink)

The syntactic priority thesis (henceforth SP) asserts that the truth of appropriate sentential contexts containing what are, by syntactic criteria, singular terms, is sufficient to justify the attribution of objectual reference to such terms (Wright, 1983, 24). One consequence that the neo-Fregean draws from SP is that it is through an analysis of the syntactic structure of true statements that 'ontological questions are to be understood and settled' (Wright, 1983, 25). Despite the significant literature on SP, little consideration has been (...) given to this bold meta-ontological claim.1 My concern here is accordingly not with specific applications of SP to debates in the philosophy of mathematics, but rather with the .. (shrink)

One major difficulty confronting attempts to clarify the epistemological and ontological status of abstract objects is determining the sense, if any, in which such entities may be characterised as mind and language independent. Our contention is that the tolerant reductionist position of Michael Dummett can be strengthened by drawing on Husserl's mature account of the constitution of ideal objects and mathematical objectivity. According to the Husserlian position we advocate, abstract singular terms pick out weakly mind-independent sedimented meaning-contents. These meaning-contents serve (...) as the ‘thin’ referents of abstract singular terms, but are ultimately founded in prior acts of meaning-constitution. (shrink)

The prevailing approach to the problem of the ontological status of mathematical entities such as numbers and sets is to ask in what sense it is legitimate to ascribe a reference to abstract singular terms; those expressions of our language which, taken at face value, denote abstract objects. On the basis of this approach, neo‐Fregean Abstractionists such as Hale and Wright have argued that abstract singular terms may be taken to effect genuine reference towards objects, whereas nominalists such as Field (...) have asserted that these apparent ontological commitments should not be taken at face value. In this article I argue for an intermediate position which upholds the legitimacy of ascribing a reference to abstract singular terms in an attenuated sense relative to the more robust ascription of reference applicable to names denoting concrete entities. In so doing I seek to clear up some confusions regarding the ramifications of such a thin notion of reference for ontological claims about mathematical objects. (shrink)

In this paper I further elucidate and defend a metaontological position that allows you to have a minimal ontology without embracing an error-theory of ordinary talk. On this view 'there are Fs' can be strictly and literally true without bringing an ontological commitment to Fs. Instead of a sentence S committing you to the things that must be amongst the values of the variables if it is true, I argue that S commits you to the things that must exist as (...) truthmakers for S if it is true. I rebut some recent objections that have been levelled against this metaontological view. (shrink)

This paper defends two claims about the criterion of commitment of W.V.O Quine. The first claim is that the criterion can be made extensional. The second is that a proper formulation becomes an analytic truth. We spend a few preliminary sections clarifying our intended notion of ontological commitment. We will not go very far in our investigation of the criterion if we do not distinguish the things a theory postulates, what its adherents, or anybody else, believe in, and which of (...) these entities we have compelling reasons to accept. A look at [Quine 1953] shows that the criterion concerned the postulation of entities by theories, but it is often misread as an attempt to say something about either or. The core of the paper is an exposition of two formulations of the criterion. I first state a schema improving on that of [Scheffler and Chomsky 1959]. The second formulation is a single principle and construes commitment as a relation between theories and predicates: ontological commitment to the entities that satisfy a given predicate. Both criteria are extensional and are formulated for constructional systems, in the sense of [Carnap 1928] and [Goodman 1951], rather than for theories construed as interpreted sets of sentences. This solves a problem raised by [Halvorson 2019]. Their analyticity is substantiated by showing that their most controversial consequences are instances of Tarski’s Convention. (shrink)