Kurt Gödel and the romance of logic
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Kurt Gödel and the romance of logic
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Re: Kurt Gödel and the romance of logic
#2" He announced that he had studied the US constitution in detail, and—no doubt, forensically examining its propositions one at a time and perhaps testing it against thought experiments against wild possible futures in which the president was allowed to get out of control—he had discovered how the US could legally be turned into a dictatorship."
Re: Kurt Gödel and the romance of logic
#3[deleted]
Re: Kurt Gödel and the romance of logic
#4Actually, Gödel's theory is fairly accessible compared to, say, the General Theory of Relativity.
All you have to know that the process of proving a statement is a fairly mechanical, step-by-step process. At that point, "statements that can be proven true" and "statements that be proven false" are two fairly defined sets. At that point, "there are some true statements that cannot be proven true" is moderately clear.
Then you introduce the idea of a model and make the concept fully exact.
The thing to remember is Gödel himself never really liked this simple view and wanted truth to be more transcendent. He shared with Einstein the quality of not liking the results of his discoveries, perhaps a source of their friendship.
Re: Kurt Gödel and the romance of logic
#5> rescued the idea that there are truths that humans can never prove
This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic.
What Gödel showed was that proofs are relative to some underlying axiomatic model and that for any particular axiomatic model there are always truths unprovable by it.
That doesn't mean "there are truths that humans can never prove", all it means is that we have to extend our axiomatic systems in order to prove some truths. (And whether they are true or false "in reality" is another question, to be determined empirically.)
A more accurate (and just-as-click-baity) way of interpreting Gödel's theorem is that "mathematicians and logicians will always have a job".
Re: Kurt Gödel and the romance of logic
#6" He announced that he had studied the US constitution in detail, and—no doubt, forensically examining its propositions one at a time and perhaps testing it against thought experiments against wild possible futures in which the president was allowed to get out of control—he had discovered how the US could legally be turned into a dictatorship."
Suggestions as to what this found flaw might have been has been discussed on Quora a couple of times [1][2]
[1] https://www.quora.com/How-did-G%C3%B6del-believe-the-US-coul...
[2] https://www.quora.com/What-was-the-flaw-Kurt-G%C3%B6del-disc...
Re: Kurt Gödel and the romance of logic
#7> rescued the idea that there are truths that humans can never prove This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic. What Gödel showed was that proofs are relative to some underlying axiomatic model and that for any particular axiomatic model there are always truths unprovable by it. That doesn't mean "there…
"And whether they are true or false "in reality" is another question, to be determined empirically."
Mathematical and logic truths have highest apstraction level.By definition they can 't be proved or disapproved in reality they exist only in apstraction.
Re: Kurt Gödel and the romance of logic
#8> rescued the idea that there are truths that humans can never prove This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic. What Gödel showed was that proofs are relative to some underlying axiomatic model and that for any particular axiomatic model there are always truths unprovable by it. That doesn't mean "there…
This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic.
It is, it really is. Yet is also an interpretation that Gödel himself would indulge in.
Consider his most famous quote: "Either mathematics is too big for the human mind, or the human mind is more than a machine." (I remember reading this statement in the Time-Life book on mathematics when I was a kid).
Re: Kurt Gödel and the romance of logic
#9> rescued the idea that there are truths that humans can never prove This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic. What Gödel showed was that proofs are relative to some underlying axiomatic model and that for any particular axiomatic model there are always truths unprovable by it. That doesn't mean "there…
This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic. It is, it really is. Yet is also an interpretation that Gödel himself would indulge in. Consider his most famous quote: "Either mathematics is too big for the human mind, or the human mind is more than a machine." (I remember reading this statement in the Time-L…
What’s the problem with the disjunction?
Re: Kurt Gödel and the romance of logic
#10> rescued the idea that there are truths that humans can never prove This is a gross misinterpretation of Gödel's actual theorem that helps perpetuate irrational superstitious attitudes against science, mathematics, and logic. What Gödel showed was that proofs are relative to some underlying axiomatic model and that for any particular axiomatic model there are always truths unprovable by it. That doesn't mean "there…
> That doesn't mean "there are truths that humans can never prove", all it means is that we have to extend our axiomatic systems in order to prove some truths.
If you believe that the only consequence to Gödel's theorem is we need to "extend our axiomatic system", I do think you've missed the point.
For one thing, I think Gödel's theorem and Gödel's proof are unfortunately conflated.
Gödel's proof is lovely and elegant, and can be understood with minimal knowledge of logic, but, ultimately, all it does is provide a counter example. So when people read his proof and understand it, they tend to be unimpressed with its power because the counter example is very generic and seems an uninteresting barrier to our ability to discern "truth". But that says nothing about there may be lots of other kinds of unprovable statements.
Ultimately, Gödel's theorem tells us one absolute kernel of truth by saying all but very basic axiomatic models are necessarily incomplete. However which way you want to make the philosophical leap to connect that to our notion of "truth" seems far more up to interpretation, but it annoys me when people disrespect the theorem because they're unimpressed with the counter examples the proof constructs.