Online research in philosophy

Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that absolutely everything is self-identical and the truth that the empty set has absolutely no members. Various metaphysical views too appear to involve unrestricted quantification, such as the physicalist view that absolutely everything is physical.

This Thesis addresses issues that lie at the intersection of two broad philosophical projects: inferentialism and contextualism. It discusses and defends an account of the logical concepts based on the following two ideas: 1) that the logical concepts are constituted by our canonical inferential usages of them; 2) that to grasp, or possess, a logical concept is to undertake an inferential commitment to the canonical consequences of the concept when deploying it in a linguistic practice. The account focuses on the concept of universal quantification, with respect to which it also defends the view that linguistic context contributes to an interpretation of instances of the concept by determining the scope of our commitments to the canonical consequences of the quantifier. The model that I offer for the concept of universal quantification relies on, and develops, three main ideas: 1) our understanding of the concept’s inferential role is one according to which the concept expresses full inferential generality; 2) what I refer to as the ‘domain model’ (the view that the universal quantifier always ranges over a domain of quantification, and that the specification of such a domain contributes to determine the proposition expressed by sentences in which the quantifier figures) is subject to a series of crucial difficulties, and should be abandoned; 3) we should regard the undertaking of an inferential commitment to the canonical consequences of the universal quantifier as a stable and objective presupposition of a universally quantified sentence expressing a determinate proposition in context. In the last chapter of the Thesis I sketch a proposal about how contextual quantifier restrictions should be understood, and articulate the main challenges that a commitment-theoretic story about the context-sensitivity of the universal quantifier faces.

Alternative readings of quantification are considered. The absence of an unequivocal translation into ordinary speech is noted. Some examples are cited which, in the opinion of the author, are a result of equivocal readings of quantification, or unnecessarily restrictive readings which obscure its primary function.

This paper is a critical evaluation of Kuenne's attempt to define truth via quantification into the position of a sentence.

.  Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in this way: losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication and classical quantification is preferred here.

This paper argues that ‘that’-clauses are not singular terms (without denying that their semantical values are propositions). In its first part, three arguments are presented to support the thesis, two of which are defended against recent criticism. The two good arguments are based on the observation that substitution of ‘the proposition that p’ for ‘that p’ may result in ungrammaticality. The second part of the paper is devoted to a refutation of the main argument for the claim that ‘that’-clauses are singular terms, namely that this claim is needed in order to account for the possibility of quantification into ‘that’-clause position. It is shown that not all quantification in natural languages is quantification into the position of singular terms, but that there is also so-called ‘non-nominal quantification’. A formal analysis of non-nominal quantification is given, and it is argued that quantification into ‘that’-clause position can be treated as another kind non-nominal quantification.

We here establish two theorems which refute a pair of what we believe to be plausible assumptions about differences between objectual and substitutional quantification. The assumptions (roughly stated) are as follows: (1) there is at least one set d and denumerable first order language L such that d is the domain set of no interpretation of L in which objectual and substitutional quantification coincide. (2) There exist interpreted, denumerable, first order languages K with indenumerable domains such that substitutional quantification deviates from objectual quantification in K and this deviance remains for all name extensions I of K. We show these assumptions have actually been made, and then prove the refuting theorems.

Is second-order quantification legitimate? For Quine, it was pure non-sense, unless construed as first-order quantification in disguise, ranging over sets. Boolos rightly maintained that it could be interpreted in terms of plural quantification, but claimed that it then ranged over the same individuals as singular, first-order quantification. I protest that plural quantification ranges over what I call multiplicities. But what is a 'multiplicity'? And does this idea itself not fall prey to something like Frege's paradox?