• Agent Smith
    5.2k
    Here's the deal, using Fermat's Last Theorem as a case in point.

    Mathematicians, since Fermat wrote those mysterious lines in the margin of his book, have spent a considerable amount of time & energy trying to prove/disprove Fermat's Last Theorem - all were unsuccessful until Andrew Wiles proved it in the 1990s.

    This got me thinking about problem solving and question answering in general, one pertains to math mostly and the other to philosophy; however the implications of what I'm about to say extend beyond these domains into living itself.

    What do I want to say/discuss?

    Well this: Wouldn't it be absolutely amazing if we had a method of determining, before we dive headlong into solving/answering problems/questions, whether the problem/question is solvable/answerable in the first place?

    If someone does come up with an easy method/technique that would allow us to know whether a problem can be solved/a question answered, it would save us a whole lot of trouble in my humble opinion.

    Got any ideas? Spit it out! :grin:
  • Outlander
    1.5k
    Well this: Wouldn't it be absolutely amazing if we had a method of determining, before we dive headlong into solving/answering problems/questions, whether the problem/question is solvable/answerable in the first place?Agent Smith

    Non-math questions? Wouldn't that be impossible without the use of absolutes (even if you can "plug in" subjective values)?

    Not a math guy (I'm sure you can tell), but after looking into it I find it remarkable how he came up with it and it remained unsolved (neither proven nor disproven) for so long. Quite cool. But say a represents the idea of happiness (subjective) and b represents likely consequences that may result from pursuing a, while c represents the current state of being (contentedness, resignation, boredom, despair, what have you). Is this like trying to determine if based on c what it would require to reach a, being b is worth it aka a reasonable pursuit?

    For example, if your subjective absolute for c is "just about happy" and your subjective absolute for b is "losing all wealth and ending up homeless, it would not be reasonable to pursue b to achieve a seeing as the difference between a and c is very small, lesser than the risk of b. However if your subjective absolute for c is "miserable" and your subjective absolute for b is "having to downsize to a smaller apartment which I enjoy anyway" then it would be worth pursuing b in order to achieve a seeing as the difference between a and c in this example is greater than the risk of b. Is that something like what you mean or am I way off here?

    Edit: Basically kind of a fancy way to say "is the potential risk of an endeavor worth the potential(?) reward of it?". I'm thinking you mean something else.

    A = problem (let's say a flat tire)
    B = resources available to solve it (an incomplete jack set, and a cell phone I can call a tow truck with)
    C = solution (the tire being functional/changed and the vehicle being able to drive)

    In this scenario, C can be reached using B (thanks to the cell phone to call the tow truck) thus alleviating A. Or no? Give an example, if you please.
  • Agent Smith
    5.2k
    Interesting angle to my thesis. All I can say is you've managed to keep it real, kudos!

    To get to the point, the so-called continuum hypothesis (math) can't be proven/unproven i.e. it's undecidable. This, paradoxically, has been proven. Think along these lines please. Danke for your input.
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