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What is truth?

lostmyway

Curt Godel, the famous mathematician, showed that in any sufficiently complex system of mathematics, there are statements that are true in the sense that they work and describe a pattern of nature that is consistent, but that cannot actually be proved mathematically using the internal logic of the axioms involved.

So, my question is, how can we know that mathematics really describes reality and that reality may simply be a construct that human beings invent on order to stay alive? In other words, more or less "subjective" representations of the way evolution has shaped our perceptions?

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  • I know nothing of maths but this is a fun question I posed to readers: 'if two people are on a desert island and an observor claims one is 'mad', whose reality is the true one?' The best explanation of any kind of 'truth' is the one accepted by the majority in that particular society; it would not apply to every society.

    ps I envy you maths genii! I find it hard balancing my bank account, let alone complex calculations. I wish there were a microchip you could insert, to make you expert in a chosen field.

  • in reply to Marianne72

    Yes, good point.

    All Godel was saying is if a rule based system avoids contradicting itself, it admits that some things are outside of its known rules and cannot be answered.and cannot be proven.

    If it tries, then it will inevitably contradict itself because it will have to break its own rules and therefore be inconsistent.

    So a system of rules can either be consistent but incomplete or complete but inconsistent. And no matter how much you enhance the rules there will still be further truths the system can't handle

    This is why there can be no "final truth" since there are always going to be truths that cannot be proven by any rules based system.

  • in reply to lostmyway

    There's a jump somewhat from the first two paragraphs. Gödel is referring to a particular aspect of mathematics. Applying this to broader questions is making a leap that requires substantial justification.

  • in reply to lostmyway

    Can you share where Gödel expresses the "idea hat there will always be some truths that cannot be mathematically expressed, at least in the foreseeable future"?

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