Classical positions on central topics--mind/body, epistemology, freedom/determinism--are presented in a series of imagined discussions between renowned philosophers and critical interlocutors.

Is pure mathematics - arithmetic as well as geometry - reducible to formal logic? Russell answered in the affirmative, considering this so significant as to constitute a fatal blow to Kant's synthetic-apriori philosophy of mathematics. But either pure arithmetic and pure geometry include the full, extra-logical content of their unique axioms and hence their unique theorems, or they do not. If they do, then this reductionism is trivially unsound. It they do not - if they include only the logic of (...) demonstration and exclude everything else - then it is trivially true, but insignificant. In fact this would accomplish no reduction at all, but rather a harmless formalization. (shrink)

Is pure mathematics - arithmetic as well as geometry - reducible to formal logic? Russell answered in the affirmative, considering this so significant as to constitute a fatal blow to Kant's synthetic-apriori philosophy of mathematics. But either pure arithmetic and pure geometry include the full, extra-logical content of their unique axioms and hence their unique theorems, or they do not. If they do, then this reductionism is trivially unsound. It they do not - if they include only the logic of (...) demonstration and exclude everything else - then it is trivially true, but insignificant. In fact this would accomplish no reduction at all, but rather a harmless formalization. (shrink)

According to Hume’s classical definition of causal relations, a cause must fulfill two distinct conditions: a) be a sufficient condition for the occurrence of its effect; b) be temporally prior to it. However, a careful logical analysis shows that the combination of sufficiency and temporality is impossible. This is because if a complete cause is a sufficient condition for its effect to occur-then the effect is a necessary condition for the occurrence of its own complete cause! Thus, there can be (...) no complete cause for anything to occur, which means that causal determination is logically impossible.The paper goes on to examine some possible responses to this argument, and then concludes with a nontemporal version of the paradox that shows that even the first of Hume’s above conditions cannot be fulfilled on its own. This is because if something (e.g., the cause) is a sufficient condition of something else (e.g., the effect), then it cannot be a sufficient condition of itself. (shrink)

According to Hume’s classical definition of causal relations, a cause must fulfill two distinct conditions: a) be a sufficient condition for the occurrence of its effect; b) be temporally prior to it. However, a careful logical analysis shows that the combination of sufficiency and temporality is impossible. This is because if a complete cause is a sufficient condition for its effect to occur-then the effect is a necessary condition for the occurrence of its own complete cause! Thus, there can be (...) no complete cause for anything to occur, which means that causal determination is logically impossible. The paper goes on to examine some possible responses to this argument, and then concludes with a nontemporal version of the paradox that shows that even the first of Hume’s above conditions cannot be fulfilled on its own. This is because if something is a sufficient condition of something else, then it cannot be a sufficient condition of itself. (shrink)