Logic and contingent existence

It is argued here that Prior's non-standard modal system Q, and the Parry–Dunn system of analytic implication, though entirely independent and independently motivated systems, together provide a rationale for explicating the concept of validity in a non-standard way; their implications are explored for the theory of natural deduction as well as for modal logic and the concept of entailment. I give an account of formal logic from this non-standard viewpoint, together with an informal presentation of the system that unites the insights of Prior (drawing on Russell) and, Parry (drawing on Kant), and the motivations for both in the concept of the contingent existence – as opposed to the contingent truth or falsehood – of a proposition.     

Vagueness and Quantification

This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided which bear on three debated issues concerning quantification.     

Quantification and Ontology

Quineans have taken the basic expression of ontological commitment to be an assertion of the form ' x ', assimilated to theEnglish 'there is something that is a '. Here I take the existential quantifier to be introduced, not as an abbreviation for an expression of English, but via Tarskian semantics. I argue, contrary to the standard view, that Tarskian semantics in fact suggests a quite different picture: one in which quantification is of a substitutional type apparently first proposed by Geach. The ontological burden is borne by constant symbols, and truth is defined separately from reference.     

Temporal existence and temporal location

We argue that sensitivity to the distinction between the tensed notion of being something and the tensed notion of being located at the present time serves as a good antidote to confusions in debates about time and existence, in particular in the debate about how to characterise presentism, and saves us the trouble of going through unnecessary epicycles. Both notions are frequently expressed using the tensed verb ‘to exist’, making it systematically ambiguous. It is a commendable strategy to avoid using that verb altogether in these contexts and to use quantification and a location predicate instead.

     

Quantification and Realism*

This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers an assessment of just how implausible the thesis really is. It argues that the intuitions against the thesis come down to a few special cases, which can be given special treatment. Finally, the paper considers some metaphysical ideas that might surround the thesis. Particularly, it might be maintained that an important variety of realism is incompatible with the thesis. The paper argues that this is not the case.     

Quantification and semantic memory

Two models are considered for how people verify explicitly quantified sentences, such as All fathers are parents and Some fathers are parents. The models share the same second stage, but have different first-stage mechanisms. In the Predicate Intersection Model, suggested by Meyer (1970), the first stage involves a serial, self-terminating search among names of categories that intersect the predicate category. In the Feature Comparison Model (Smith, Shoben & Rips, 1974a), the first stage involves evaluating the overall relatedness between the subject and predicate categories by comparing their semantic features. To test the models, three reaction time experiments required subjects to verify statements quantified by Some or All. In the first experiment, the semantic relatedness of categories in false Some-statements was varied. Contrary to predictions of the Predicate Intersection Model, related categories increased reaction time for both true and false Some-statements. While the first experiment revealed that All-statements took longer to verify than comparable Some-statements, the second experiment demonstrated that the All-Some difference can be eliminated by presenting both statement types in the same block of trials, also disconfirming the Predicate Intersection Model. Finally, Experiment III examined the meaning of Some-statements in more detail by having subjects interpret the quantifier Some as “some but not all.” With this interpretation, Some-statements took longer to verify than All-statements. Overall the results support the Feature Comparison Model.