Two Arguments Against the Generic Multiverse
This talk will critically examine two arguments against the generic multiverse (GM) approach to set theory. Both of these are due to Hugh Woodin. Meadows will start by providing a general explanation of what GM is and why one might be motivated to accept it on the basis of recent results in set theory. He will then move onto the first argument against GM via Omega-logic. Followed by an original logical analysis of this argument that reveals the underlying philosophical commitments required to accept the conclusion. The second argument relies on an intuition that if V=Ultimate-L or something like it is true then the real action in set theory is taking place in Ultimate-L. Meadows will show that this holds in an extremely precise sense by demonstrating that Ultimate-L theory and the GM theory are equivalent in a very strong sense. Meadows will then close with some remarks about the relative strengths of these arguments and speculate on the kinds of philosopher to whom they should be persuasive.