tag:blogger.com,1999:blog-14117162.post500035980924413051..comments2024-03-28T02:29:26.853-07:00Comments on Obscure and Confused Ideas: Descartes on Mathematical Truth and Mathematical ExistenceUnknownnoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-14117162.post-79147283438519544272015-11-01T03:44:54.632-08:002015-11-01T03:44:54.632-08:00I don't like the QP argument. It contains a da...I don't like the QP argument. It contains a dangerous epistemic short-circuit. Our best theories rely on the truth of the foundations of mathematics, so any epistemological disconnect in the mathematics implies an ontological disconnect. An example is the idea of limits, introduced to circumvent problems with infinitesimals (e.g. Zeno's paradox, see Huggett in the SEP) for which Hilbert expressed grave concerns because he felt that introducing the epsilon delta definition just moved the problem one step to the left. Present ideas support this caution in that theories of the universe are a deal less problematic if spacetime is discrete. So, where QP say:<br />(P1) We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.<br />(P2) Mathematical entities are indispensable to our best scientific theories.<br />(C) We ought to have ontological commitment to mathematical entities.<br />I say:<br />(P1) We ought to have commitment to all and only those entities with a well-founded epistemic basis.<br />(P2) Neither mathematical entities nor our best scientific theories are currently well-founded.<br />(C) We ought not commit to mathematical entities or our scientific theories.<br />Stephen Anastasihttps://www.blogger.com/profile/04684536044880085246noreply@blogger.com