4 ms·

All knowledge ultimately relies on some self-evident first principals which are not demonstrable.

• alasdair_ 3y ago
  ALL knowledge does? Can you prove that? :)
  • ducttapecrown 3y ago
    Well, all knowledge capable of modeling the natural numbers is incapable of proving every true statement, so in a sense there can be no universal axiom set.
  • kdmccormick 3y ago
    Sure, I'll take a swing! If we define "knowing" some fact F as "we have proven that F follows from prerequisite facts A1..AN", then we can imagine all knowledge forms a graph where prerequsities point to the facts that they prove. Either this graph is cyclic, or there are nodes with no inbound edges. Therefore, there are facts which are either non-demonstrable, or only demonstrable via cyclic logic. I think this works, unless of course you have another definiton of "knowing" :)
    • alasdair_ 3y ago
      I see no reason why knowledge needs to come from prerequisite facts. Showing my ignorance here, but isn't this the whole point of "cogito ergo sum"? The "fact" that we are thinking is a first principle that comes from nothing else without a prerequisite axiom.
      • prox 3y ago
        That is still a presupposition you are taking, you are making a statement “that thinking is the first principle that comes from nothing.” There are host of ways to debate that philosophically.
  • T-A 3y ago
    https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
  • agensaequivocum 3y ago
    If first principals were demonstrated by definition they rely on some other first principles (see syllogisms). Hence you have an infinite regress which is unknowable. Thus no knowledge could be acquired. Therefore the first principals in syllogisms must be self-evident.
• zmgsabst 3y ago
  > Dubito ergo cogito ergo sum. Technically, we can derive one fact — there is something rather than nothing: Asking the question is itself proof.