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Slater H.

Logic and Logical Philosophy

2011

vol. 20

issue 4

275-283

There were already confusions in the Middle Ages with the read- ing of Aristotle on negative terms, and removing these confusions shows that the four traditional Syllogistic forms of statement can be readily gen- eralised not only to handle polyadic relations (for long a source of diffi- culty), but even other, more measured quantifiers than just ‘all’, ‘some’, and ‘no’. But these historic confusions merely supplement the main con- fusions, which arose in more modern times, regarding the logic of singular statements. These main confusions originate in the inability of the mainline modern tradition to supply the ‘logically proper names’ which alone have the right to replace individual variables; an inability which has resulted in the widespread, but erroneous replacement of individual variables with or- dinary proper names, i.e. names for contingent beings, in many if not most contemporary logic texts. The paper includes the exhibition and grammat- ical characterisation of the logically proper names that are required instead, specifying just how they differ syntactically from ordinary proper names. It also shows how ontologically significant is the distinction, since not only do logically proper names refer to necessarily existent objects (showing there are no ‘empty domains’ for Classical Logic to fail to apply to), but also thereby central features of Realism become considerably clarified.

A Fregean conception of singular existence

63%

Sayward C.

Logic and Logical Philosophy

2015

vol. 24

issue 1

3–18

A perplexity about singular existence statements (for example, ‘Socrates exists’) is that for their negations to be true their subject terms do not name anything. For example, in ‘Pegasus does not exist’ ‘does not exist’ is not said in respect to the referent of ‘Pegasus’ since there is none. But, then, in respect to what is that said? The paper answers the question by proposing a metalinguistic interpretation of singular existence statements, according to which singular existence statements are about names. It is argued that this interpretation fits in well with Frege’s views on existence, presupposition, and his idea that names have senses.

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A Fregean conception of singular existence