A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...) but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

I investigate substitutional interpretations of quantifiers that count existential sentences true just in case they have true instances in a parametric extension of the language. I devise a semantics meeting four criteria: (1) it accounts adequately for natural language quantification; (2) it provides an account of justification in abstract sciences; (3) it constitutes a continuous semantics for natural and formal languages; and (4) it is purely substitutional, containing no appeal to referential interpretations. The prospects for a purely substitutional theory of (...) quantification are thus no worse than for a referential account. (shrink)

All sides in the recent debates over the Quine‐Putnam Indispensability thesis presuppose Quine's criterion for determining what a discourse is ontologically committed to. I subject the criterion to scrutiny, especially in regard to the available competitor‐criteria, asking what means of evaluation there are for comparing alternative criteria against each other. Finding none, the paper concludes that ontological questions, in a certain sense, are philosophically indeterminate.

Ontology is the study of what there is, what kinds of things make up reality. Ontology seems to be a very difficult, rather speculative discipline. However, it is trivial to conclude that there are properties, propositions and numbers, starting from only necessarily true or analytic premises. This gives rise to a puzzle about how hard ontological questions are, and relates to a puzzle about how important they are. And it produces the ontologyobjectivity dilemma: either (certain) ontological questions can be trivially (...) answered using only uncontroversial premises, or the uncertainties of ontology are really a threat to the truth of basically everything we say or believe. The main aim of this dissertation is to resolve these puzzles and to shed some light on the discipline of ontology. I defend a view inspired by Carnap’s internal-external distinction about what there is, but one according to which both internal and external questions are fully factual and meaningful. In particular, I argue that the trivial arguments are valid, but they do not answer any ontological questions. Furthermore, I propose an account of the function of our talk about properties, propositions and natural numbers. According to this account our talk about them has no ontological presuppositions for its literal and objective truth. This avoids the ontology-objectivity dilemma, and solves the puzzles about ontology. To do this I look at quantification and noun phrases in general, and at their relation to ontology. I argue that quantifiers are semantically underspecified in a certain respect, and play two different roles in communication. I discuss the relation between syntactic form and information structure, the function of certain non-referential, non-quantificational noun phrases, the uses of bare number determiners, and how arithmetic truths are learned and taught. The more metaphysical issues discussed include: inexpressible properties, logicism about arithmetic, nominalism, Carnap’s view about ontology, the problem of universals, the relationship between ontology and objectivity, different projects within ontology, non-existent.... (shrink)