Online research in philosophy

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.

Summary This paper will attempt to integrate (1) some new reflections on the implications for ontology of Monistic interpretations of formulae in quantification theory, with (2) a review of earlier material that I have published on such implications, and with (3) a sketch of several points made by others which bear on related issues.

Adding branching quantification to a first-order language increases the expressive power of the language,without adding to its ontology. The present paper is a defense of this claim against Quine (1970) and Patton (1991).

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?

This paper is a reaction to G. Küng's and J. T. Canty's Substitutional Quantification and Leniewskian quantifiers'Theoria 36 (1970), 165–182. I reject their arguments that quantifiers in Ontology cannot be referentially interpreted but I grant that there is what can be called objectual — referential interpretation of quantifiers and that because of the unrestricted quantification in Ontology the quantifiers in Ontology should not be given a so-called objectual-referential interpretation. I explain why I am in agreement with Küng and Canty's recommendation that Ontology's quantifiers not be substitutionally interpreted even if Leniewski intended them to be so interpreted. A notion of an interpretation which is referential but yet which does not interpret as an assertor of existence of objects in a domain is developed. It is then shown that a first order version of Ontology is satisfied by those special kind of referential interpretations which read as Something as epposed to Something existing.

Based on her earlier ground-breaking axiomatization of quantified modal logic, the papers collected here by the distinguished philosopher Ruth Barcan Marcus cover much ground in the development of her thought, spanning from 1961 to 1990. The first essay here introduces themes initially viewed as iconoclastic, such as the necessity of identity, the directly referential role of proper names as "tags", the Barcan Formula about the interplay of possibility and existence, and alternative interpretations of quantification. Marcus also addresses the putative puzzles about substitutivity and about essentialism. The collection also includes influential essays on moral conflict, on belief and rationality, and on some historical figures. Many of her views have been incorporated into current theories, while others remain part of a continuing debate.

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.