The necessary a posteriori: A response to Tichý

Conclusion

Some of Tichý's conclusions rest on an assumption about substitutivity which Kripke would not accept. If we grant the assumption, then Tichý successfully shows that we can discover true identity statements involving names a priori, but not that we can discover a priori what properties things have essentially. Many of Tichý's arguments require an implausible rejection of the possibility of indirect belief as described in Section III. 25

Are there necessary a posteriori propositions? I have argued that we certainly can discover necessary propositions a posteriori, but have left it an open question whether there are necessary propositions which we can only discover a posteriori.

What effect do the considerations here presented have on the positivist doctrine that the a priori and the necessary coincide? My explanation of how we discover necessary propositions a posteriori involves our believing them indirectly, in virtue of believing contingent propositions. I would argue that Kripke's examples of the contingent a priori involve, similarly, our believing the contingent propositions in directly, in virtue of believing necessary propositions.

This suggests that a reformulation of the positivist thesis along something like the following lines may well be correct. Let us say that someone directly believes a proposition just in case he could not fail to believe it without being in a different cognitive state. Then perhaps one can directly believe a proposition on the basis of a priori evidence only if it is necessary, and can directly believe a proposition on the basis of a posteriori evidence only if it is contingent.