Abstract
In Chaps. 5, 6 and 8 it was suggested that non-classical methods may help to solve certain difficulties which might not be accounted for by the theories examined in those chapters. It was seen that Montague’s possible-worlds account was such that logically equivalent expressions were required to be intersubstitutable salva veritate in attitude contexts. As noted several times already, this requirement would seem at odds with common intuitions. Though the details were sketchy, it was seen that Montague may have thought that a non-classical approach would avoid the lately-mentioned problem. It has also been suggested elsewhere that non-classical methods might be used to account for certain difficulties surrounding (so-called) fictional entities. The trouble with fictional entities is that they may be subject to inconsistency and/or incompleteness. This was seen as a problem for Montague’s possible-worlds theory, as well as Cresswell’s possibilist account. But it was shown that Zalta’s Meinongian theory might be adapted so as to incorporate logically impossible worlds. It was suggested that this non-classical amendment might offer a solution to the lately-mentioned problem.
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Notes
- 1.
This system is based upon the propositional relevant logic N 4. The system N 4 was developed in Chapter 9 of Priest’s Introduction to Non-Classical Logic (2001).
- 2.
If these constraints are only relaxed at logically impossible worlds, one gains the semantics of a relevant logic ; in which case neither ╞ A → (B V ~ B) nor ╞ (B & ~ B) → A. If one relaxes these constraints at all worlds, one gains a theory that is both relevant and paraconsistent; in which case neither A, ~ A╞ B nor A╞ B V ~ B. Or one might relax these constraints only at worlds other than the actual world. In this case, while A & ~ A will not on any interpretation be true in the base world, ⃟(A & ~ A) might; and while in this case╞ B V ~ B, it will be false that ╞ ⃞ (B V ~ B) (Priest 2005, p. 20).
- 3.
Especially in fiction created by non-classical logicians; see Priest’s own fictional story Sylvan’s Box in his (2005), pp. 125–133.
- 4.
Apparently, SI simpliciter is a valid principle in Priest’s system (Priest 2005, p. 32). However, he claims that it fails in the context of the intentional operators. It is the latter claim which is being addressed here.
- 5.
However, doubts are raised below about whether the introduction of identities does result in a correct modeling of all intentional states.
- 6.
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Parsons, D. (2016). Priest’s Noneist Approach. In: Theories of Intensionality . Springer, Singapore. https://doi.org/10.1007/978-981-10-2484-9_9
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