Badici on Inclosures and the Liar Paradox

Abstract

Badici [2008] criticizes views of Priest [2002] concerning the Inclosure Schema and the paradoxes of self-reference. This article explains why his criticisms are to be rejected.

Notes

¹1. Badici [2008]. Page references are to this unless otherwise stated.

²The prima facie nature of the IS conditions was not spelled out as clearly as I would now wish in the first, but is quite explicit in the second, edition of Beyond the Limits of Thought[2002: 277].

³I was not very clear about the distinction [Priest 2002]. Thanks to Badici for seeing its importance.

⁴In [2002: 9.5 and 17.6], I often used the ambiguous term ‘contradiction’, where it would have been better to use ‘paradox’.

⁵He gives two quotations from me suggesting that I think this. I forgo the pedantic task of going through them and pointing out why they do not do so.

⁶All this is discussed at greater length in Priest [2002: 9.5].

⁷He also glosses it [591] as ‘if one is willing to talk about the true sentences of English, one is thereby committed to there being a set of true sentences of English’. This is clearly not a fair paraphrase.

⁸As I put it: ‘No one would ever have doubted this connection, had it not been for the fact that it gives rise to contradiction in certain contexts’[2002: 280].

⁹What Badici actually says [592] is: ‘Priest tries to defend the idea that it is the Inclosure Schema that generates (and thus explains) the paradoxes by arguing that the diagonalizers are such that “there is a genuine functional dependence of the value of the function on its argument: the argument is actually used in computing the value of the function” Priest [2002: 136, fn. 18]’. This is not an accurate reading of the footnote, which addresses the question of how to distinguish between a real ψ and a gerrymandered one; and what it says is: ‘One way to get some handle on the issue might be to note that in the case of the bona fide diagonalisers that we have met, there is a genuine functional dependence of the value of the function on its argument: the argument is actually used in computing the value of the function. This is clearly not the case with the pathological example [f] we noted’.

¹⁰I was not very explicit about the matter [2002:10.2]. This is the reason.