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Graham Priest, Karel Lambert. Free Logic: Selected Essays. Cambridge: Cambridge University Press, 2003. Pp. xii + 191. ISBN 0-521-81816-8., Philosophia Mathematica, Volume 13, Issue 3, October 2005, Pages 326–328, https://doi.org/10.1093/philmat/nki031
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Classical logic (at least according to its orthodox interpretation) endorses the claim that: !!...!! By classical logic, here, I mean first-order logic, as derived from Frege's Begriffsschrift and Russell's and Whitehead's Principia Mathematica. (1) is certainly not the standard view in the history of logic. Terms that appear to have no denotation, such as ‘1/0’, are all too obvious. And even if a term denotes something, many held that this need not exist. Aristotle wrote: ‘Even non-existents can be signified by a name’ (An. Post. 92b 29–30). Most later medieval logicians held that the denotation of a term need not exist; thus, for example, Paul of Venice: ‘The absence of the signification of a term from reality does not prevent the term's suppositing for it’ ([1978], p. 13). And Russell himself—at an earlier period—held that
The origins of the classical view can perhaps be traced back to Kant's discussion of existence in the Critique of Pure Reason. However, it was not until the work of Frege and the later Russell that the new orthodoxy emerged in logic.whatever may be an object of thought, or can occur in a true proposition, or can be counted as one, I call a term … Existence … is the prerogative of some only among [terms] ([1903], pp. 43 and 449).
