14 Nov 06
Originally posted by PalynkaBecause a proof demands 100% accuracy.
Fine by me. Let's split some hairs.
There's no 100% accuracy about the present or the past, why demand it for the future?
We knew for a long time that Fermat's Last Theorem was probably right by searching for cases and not finding any. But for a long time it remained unproven.
14 Nov 06
Originally posted by spruce112358Mathematical proofs are all ultimately axiomatical.
Because a proof demands 100% accuracy.
We knew for a long time that Fermat's Last Theorem was probably right by searching for cases and not finding any. But for a long time it remained unproven.
The problem is that in reality all axioms are fallible.
15 Nov 06
Originally posted by PalynkaExactly! In mathematics axioms are defined and proofs follow. But what is axiomatic about Life?
Mathematical proofs are all ultimately axiomatical.
The problem is that in reality all axioms are fallible.
So proving that some Thing will happen is likely impossible because we have no axioms on which to ground the proof.
15 Nov 06
2 edits
Originally posted by spruce112358My point was that strict definition of proof renders it pretty useless. There are always axioms in our everyday reasoning. Without them, we would hardly make sense of the world. I'm not saying these axioms are random, they are the best explanation that makes sense out of the evidence. This reasoning is somewhat circular, yes, (that's why we need axioms) but nonetheless justifiable.
Exactly! In mathematics axioms are defined and proofs follow. But what is axiomatic about Life?
So proving that some Thing will happen is likely impossible because we have no axioms on which to ground the proof.
Examples: The universe exists, what we perceive is reality (allowing for the possibility of misinterpreting perceptions), what I define as myself, etc, etc.
With only these 'standard' axioms, you can disprove a negative by providing a case for the positive. In this case, the question "Is there proof that the future can be predicted? If so, what is that proof?" can be answered by any case where the future was successfully predicted, under the 'standard' axioms.
I don't see why we should be more demanding about proof about the future than we are about the present or past.
15 Nov 06
Originally posted by PalynkaOK, but the way the question was posed -- 'actual proof' I figured we were going whole hog.
My point was that strict definition of proof renders it pretty useless. There are always axioms in our everyday reasoning. Without them, we would hardly make sense of the world. I'm not saying these axioms are random, they are the best explanation that makes sense out of the evidence. This reasoning is somewhat circular, yes, (that's why we need axioms) but ...[text shortened]... d be more demanding about proof about the future than we are about the present or past.
Yeah, sure we make guesses about what will happen, and a lot of the time we are right. I'm not sure that we prove anything by that except that we are good guessers. We know what happened in the past and assume it will go on happening.
Suppose I flip a coin 3 times and get heads each time. I predict I will get another heads -- and I do! Does that prove that I can predict the future?
Now if you could start with "the universe exists", "I exist", etc. and then eventually produce a proof that George Bush's war in Iraq would go off the rails -- I think you would be on to something.