An Essay in Universal Semantics by Achille C. Varzi

By Achille C. Varzi

Like the magazine TOPOl, the TOPOl Library relies at the assumption that philosophy is a full of life, provocative, pleasant job, which continuously demanding situations our inherited conduct, painstakingly elaborates on how issues might be diversified, in different tales, in counterfactual events, in substitute attainable worlds. no matter what its ideology, no matter if with the purpose of uncovering a more true constitution of truth or of capturing our anxiousness, of disclosing myths or of following them via, the result of philosophical job is usually the destabilizing, unsettling iteration of doubts, of objections, of criticisms. It follows that this job is intrinsically a discussion, that philosophy is at first philosophical dialogue, that it calls for bringing out conflicting issues of view, paying cautious, sympathetic recognition to their constitution, and utilizing this dialectic to articulate one's process, to make it richer, extra considerate, extra open to edition and play. And it follows that the spirit which one brings to this job has to be considered one of tolerance, of continuously suspecting one's personal blindness and for that reason having a look with impartial eye in each comer, with no fearing to go a (fallible) judgment on what's there but in addition with out failing to teach curiosity and respect.

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If and only if Do=k. I. as the joint denial connective 'neither ... nor' relative to the given set of truth-values. 4(A). I. 22) 21 Since M may not be sharp, h(h(d(~,t),x),y)(c) will be well-defined only if d(~,t)e 1(0,(0,0», h(d(~,t), x)e 1(0,0), and h(h(d(~,t), x),y)e 1 0; similar considerations ap- ply to examples (B) and (C) below. 22 See above, note 9. For k=3, (*) amounts to a corresponding requirement in the 3-valued logic of Kleene [1938]. ' as 'neither ... nor' in the k-valued logic of the sequence of Dienes [1949].

For instance, with regard to expressions of type 1 (names) the non-emptiness requirement acquires a metaphysical connotation to the effect that there must be something rather than nothing. , a function yielding a unique value d(~,t)(C)E D t for each CE C-excludes the possibility that a symbol may, in some con15 This was Wittgenstein's concern in [1913], a concern that eventually led to the development of so-called inclusive logics (see Church [1951], Mostowski [1951], Hailperin [1953], and Quine [1954] for the seminal papers).

2o I shall return to these general issues in the next chapter, when the overall picture will be more complete. 2 includes as a special case those models that do not involve any kind of contextdependence. Such extensional models-as we may call them-may be 20 For more discussion on this point, see Varzi [1994b]. FOUNDATIONS 33 identified with those models M whose context set C is a singleton. In this case the notation introduced above is slightly redundant. For instance, it would be more natural to speak of a symbol as having no denotations or more denotations in M, rather than in the unique context of M.

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