= 27d567bc2d48d9f40e9ccc20ea370b15)
Kaj_Sotala comments on Mainstream Epistemology for LessWrong, Part 1: Feldman on Evidentialism - LessWrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (82)
Why not? It's not actually hard to specify an infinite number of axioms to use in a first-order logic system. For example, "For any well-formed formula {x}, {x} -> {x} is an axiom" represents an infinite number of axioms by using a single sentence. So I don't see why a person can't have an infinite series of beliefs.
I don't have a dog in this fight, but you may be happy to know that there actually is a name for rejecting the assumption you quoted, "infinitism." In undergrad, my epistemology professor told us he knew of "one guy" who held this position. Make of that what you will.
infinite in the "the number of beliefs I hold is growing without bound" sense, but htat's not the relevant sense here. Growth over time doesn't cut it for this - in order to have an infinite regress of beliefs, you'd have to have all infinity of them at the same time. The set of all your beliefs would have to have cardinality
, AFAICT (oddly enough, I've never seen a mathematical analysis of this, but I can't see why it wouldn't be like this.)