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LOGICISM AND PARADOX II.

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Kolman V.

Organon F. medzinárodný časopis pre analytickú filozofiu

2005

vol. 12

issue 2

121-140

This is a sequel to my article devoted to the development of Fregean logicism. The first part dealt with its 'rise and fall', i. e. its initial success in analyzing the concept of number and its subsequent fall at Russell's antinomy. In the course of the previous article we did not (have to) leave the area of the classical Fregean research. On the contrary, Russell's paradox and its analysis bring us now to the second part of the whole story - the (alleged) resurrection of the logistic idea in the works of Crispin Wright and George Boolos. We find ourselves in the middle of a neo-Fregean - structuralistic - approach based on the techniques of modern model-theoretical logic and (meta)mathematics. We do not want to criticize it yet, but only present some of the most important results such as the consistency of Hume's Principle or categoricity of Frege's (and Peano's) second-order arithmetic.

DOUBTING THE TRUTH OF HUME'S PRINCIPLE

72%

Dozudic D.

Organon F. medzinárodný časopis pre analytickú filozofiu

2010

vol. 17

issue 3

269-287

Hume's Principle (HP) states that for any two (sorted) concepts, F and G, the number of Fs is identical to the number of Gs if the Fs are one-one correlated with the Gs. Backed by second-order logic HP is supposed to be the starting point for the neo-logic program of the foundations of arithmetic. The principle brings a number of formal and philosophical controversies. In this paper author discusses some arguments against it brought out by Trobok, as well as by Potter and Smiley, designed to undermine a claim that HP and its instances (such as 'the number of the forks on the table is identical to the number of the knives on the table if the forks are one-one correlated with the knives') are true. Their criticism starts from distinguishing the objective truth from a weak or stipulated one, and focusing on fictional identities such as 'Hamlet = Hamlet' or 'Jekyll = Hyde.' They argue that numerical identities (as occur in instances of HP) are much the same as fictional identities; that we can attribute them only a weak or stipulated truth; and, consequently, that neo-logicists are not entitled to ontological conclusions concerning numbers they derive from HP and its instances. As opposed to that, the author argues that such a criticism is ill-conceived. The analogy between the numerical and fictional identities is far-fetched. So, relative to such a criticism, HP has more prospects than some authors are prepared to admit.

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2 Organon F. medzinárodný časopis pre analytickú filozofiu

1 2010

1 2005

1 Dozudic D.

1 Kolman V.

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LOGICISM AND PARADOX II.

DOUBTING THE TRUTH OF HUME'S PRINCIPLE