For now, let us avoid any further metaphysical gymnastics of the arguments of Bad Company Objections. But if we abandon the search of the acceptability conditions, what lesson could we learn from Bad Company Objection? There is an analogous matter which Ebert and Shapiro (1999, p.298) labelled ‘Good Company’. Assuming we have successfully constructed an account of acceptability which helps us to rule out ‘bad’ principles; there is another question that neo-Fregean logicists to answer. Why is it that only the stipulation of ‘good’ abstraction principles earn such a special epistemic status and no other kind of stipulation does? The fundamental difference between Direct Stipulations and Bad Company Objection is that where former seeks conditions to rule out
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First, PA can be elaborated in pure second-order logic and contains no contradictions, and if it does, neo-logicsts would not use HP to derive PA. Second, PA is also conservative and there is no part that PA introduces any new mathematical and non-mathematical ontology to the universe. Third, although it is little hard to tell whether PA is harmonious but at least I do not find any conflict within the nine axioms of PA and clearly there is no non-logical rules or operators. Finally, the stipulation of PA fails in fixing truth-values at least in some contexts involves the primitives such as “N”, “0”, etc. As such, PA cannot fix truth-conditions of an expression such as “0 = Julius Caesar”. MacFarlane (p.452), however, concerns little about this issue and says that even Hale and Wright does not say that the range must be infinitely large. If MacFarlane’s proposal is true then there would be no problem in regarding the stipulation of PA as a true implicit definition, since PA fixes the meaning of expressions contain PA, and also satisfies the four conditions proposed by Hale and Wright (2001,
First, PA can be elaborated in pure second-order logic and contains no contradictions, and if it does, neo-logicsts would not use HP to derive PA. Second, PA is also conservative and there is no part that PA introduces any new mathematical and non-mathematical ontology to the universe. Third, although it is little hard to tell whether PA is harmonious but at least I do not find any conflict within the nine axioms of PA and clearly there is no non-logical rules or operators. Finally, the stipulation of PA fails in fixing truth-values at least in some contexts involves the primitives such as “N”, “0”, etc. As such, PA cannot fix truth-conditions of an expression such as “0 = Julius Caesar”. MacFarlane (p.452), however, concerns little about this issue and says that even Hale and Wright does not say that the range must be infinitely large. If MacFarlane’s proposal is true then there would be no problem in regarding the stipulation of PA as a true implicit definition, since PA fixes the meaning of expressions contain PA, and also satisfies the four conditions proposed by Hale and Wright (2001,