EPTWhat constitutes proof? - Page 2
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Thengel
156 Posts
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tontontonba
59 Posts
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mitsy
United States1792 Posts
the problem with this question is that it already brings a notion with it, the notion of "actual proof" or "real proof," already working with a notion of objective reality that we can get to and then "proof" meaning that we are "sure" we "got to it." how do we justify any of these other than that they "work in general" with others? because our existence, our reason, our language, etc. all fall in line with "whatever has worked" to propogate the species, the answer for "what is sufficient proof?" would simply be "whatever convinces sufficient people." | ||
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BigBalls
United States5354 Posts
On November 12 2005 19:17 LTT wrote: Proof outside of an axiomatic system does not exist. Knowledge certainly does. What is knowledge outside of an axiomatic/logical system? | ||
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Luhh
Sweden2974 Posts
Recursive "proofs" aren't true proofs. They only show that the statement holds true. | ||
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BigshoT
United States171 Posts
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PlayJunior
Armenia833 Posts
 I have so many non-mathematician friends/acquaintees that do not know the meaning of word "proof". The use it like we use "is likely to be". The humanitarian/social sciences have prooved so many false statements... About Godel theorem. I think the theorem you are talking about was formulated for axiomatic theory called "formal algebra". I remember we were prooving(FORMALLY!) that 2*2=4. Took us 2 hours. The most conviencing result for Godel's theory is certainly not the completeness of formal algebra. He has another remarkable result, that says that, say W is a statement that cannot be prooved or disprooved in formal algebra S. Let's add W(or not W) to the axioms. Then, there exists another statement that cannot prooved or sidproved...and so on. The result is: if system is rich enough, then it is incomplete. While formal mathematical systems are strong enough to produce some real proofs, the non-formal sciences do not have such oppurtinity. Mostly they use stastical methods to proove/disprove something. While they are unable to take into account every factor that impacts the experiments, some sciences have really remarkable results. Biology is the example. Others, like, say, psycology(I believe) are really lacking methods. I believe that it is not only due to the very complex nature of the objects they deal with, it is due to their methods(please psychology students don't turn this into a discussion, this is my very subjective opinion). I believe that ALL sciences will gain if they put some math into. | ||
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SurG
Russian Federation798 Posts
On November 12 2005 23:30 HeadBangaa wrote: It simply means that S cannot be ordinary in the first place. It's an extraordinary set that contains all ordinary sets. Did you just try to resolve Russell's paradox? =) Think again P.S. BigBalls, you screwed up the definition a little... | ||
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Prawned
United Kingdom794 Posts
On November 13 2005 00:05 TruthBringer wrote: Please, think I'm smart, please, pretty please. I'll show off math problems that I just learned in class. The opinion my fellow TL.netters hold of me is very sacred to me. You guys will love me, won't you? Hahaha. You're great | ||
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MoltkeWarding
5195 Posts
On November 13 2005 08:57 PlayJunior wrote: I have so many non-mathematician friends/acquaintees that do not know the meaning of word "proof". The use it like we use "is likely to be". The humanitarian/social sciences have prooved so many false statements... I would like to see an example of this. Sounds like absolute BS to me. | ||
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DaN[SES]
United States167 Posts
The simplest answer to this question is "it depends." The question depends on the area of study in which one is seeking proof. In most analytical contexts (i.e. mathematics, logic, etc.) one can deductively prove something based on deductively valid proofs. These a priori proofs rely on syntactical patterns in logic that always yield a certain result. There are some complications here, but let’s just leave it at that for now. In the sciences, deductive proof is usually impossible. Proofs in the sciences are rather inductive proofs, or more accurately abductive proofs- proofs to the best explanation. These proofs rely on a finite set of data, and the building up of this data to support some hypothesis. As such, very few scientific proofs reach the status of deductive proofs. Thank you for posting this topic. I see this issue confused so many times due to simply misunderstandings of these issues. The intelligent design thread is a perfect example of people misunderstanding that scientific proofs or theories are not deductively valid proofs as one would see in logic problems or mathematics. | ||
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danmooj1
United States1855 Posts
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mitsy
United States1792 Posts
On November 13 2005 08:14 BigBalls wrote: What is knowledge outside of an axiomatic/logical system? Experience? The senses? Perceptions? Most knowledge isn't even in an axiomatic/logical system, it simply can be interpretted that way post hoc, but that doesn't mean that's how it is. describing is not explaining. | ||
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matamata
United States133 Posts
On November 13 2005 07:36 mitsy wrote: why stop at cartesian notions of mind-body etc. first of all there's kant. and u have to at least acknowledge heidegger. the problem with this question is that it already brings a notion with it, the notion of "actual proof" or "real proof," already working with a notion of objective reality that we can get to and then "proof" meaning that we are "sure" we "got to it." how do we justify any of these other than that they "work in general" with others? because our existence, our reason, our language, etc. all fall in line with "whatever has worked" to propogate the species, the answer for "what is sufficient proof?" would simply be "whatever convinces sufficient people." Of course we could, at any time, say this for any argument. Since anything we observe is filtered through our senses and anything we think is just the behavior of our minds, then how do we know anything that we are convinced of is nothing more than a mass delusion? How is any restriction on a proof anymore valid than any other, since those restrictions are just human creations? Well... you could always take the minimalist approach, and restrict it to the axioms you define and the "common sensed belief" of logic | ||
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matamata
United States133 Posts
On November 13 2005 10:50 mitsy wrote: Experience? The senses? Perceptions? Most knowledge isn't even in an axiomatic/logical system, it simply can be interpretted that way post hoc, but that doesn't mean that's how it is. describing is not explaining. What happens when two people percieve different things, or know two contradictory statements? | ||
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matamata
United States133 Posts
On November 13 2005 07:36 mitsy wrote: why stop at cartesian notions of mind-body etc. first of all there's kant. and u have to at least acknowledge heidegger. the problem with this question is that it already brings a notion with it, the notion of "actual proof" or "real proof," already working with a notion of objective reality that we can get to and then "proof" meaning that we are "sure" we "got to it." how do we justify any of these other than that they "work in general" with others? because our existence, our reason, our language, etc. all fall in line with "whatever has worked" to propogate the species, the answer for "what is sufficient proof?" would simply be "whatever convinces sufficient people." Of course we could, at any time, say this for any argument. Since anything we observe is filtered through our senses and anything we think is just the behavior of our minds, then how do we know anything that we are convinced of is nothing more than a mass delusion? How is any restriction on a proof anymore valid than any other, since those restrictions are just human creations? Well... you could always take the minimalist approach, and restrict it to the axioms you define and the "common sensed belief" of logic Edit: I also think that the main question lies in the validity of the belief in logic and the definition of axioms, as well as the concept of what is true vs. not true. Truth in axiomatic systems has the luxury of not based on any perceived reality outside the functionality of logic. We can always just describe it as some abstract property. Now... if someone was to reject logic and the whole axiomatic system thing, then that would be their right, imo. But, then they couldn't really use it to prove anything to themselves. Additionally, pretty much everyone will agree with the founding statements of logic as being absolutely true, all the time. (ie A->B B->C means A->C, whenever A,B,C are true or not true, and with the accepted definition of implies. So if A is true, then B is true, as is C. Or equivalently, if A->B means "if A has some property, then so does B", then most people would also agree we can deduce if A has some property, then so does C). But if they accept this, then they already accept the mathematical notion of proof in an axiomatic system, since that is all you can do to prove something. So in short, you'll either accept logic and axioms and therefore the ultimate standard for proofs, or you won't ;] | ||
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aseq
Netherlands4007 Posts
On November 13 2005 08:57 PlayJunior wrote: Bigballs, I love you! I have so many non-mathematician friends/acquaintees that do not know the meaning of word "proof". The use it like we use "is likely to be". The humanitarian/social sciences have prooved so many false statements... About Godel theorem. I think the theorem you are talking about was formulated for axiomatic theory called "formal algebra". I remember we were prooving(FORMALLY!) that 2*2=4. Took us 2 hours. The most conviencing result for Godel's theory is certainly not the completeness of formal algebra. He has another remarkable result, that says that, say W is a statement that cannot be prooved or disprooved in formal algebra S. Let's add W(or not W) to the axioms. Then, there exists another statement that cannot prooved or sidproved...and so on. The result is: if system is rich enough, then it is incomplete. While formal mathematical systems are strong enough to produce some real proofs, the non-formal sciences do not have such oppurtinity. Mostly they use stastical methods to proove/disprove something. While they are unable to take into account every factor that impacts the experiments, some sciences have really remarkable results. Biology is the example. Others, like, say, psycology(I believe) are really lacking methods. I believe that it is not only due to the very complex nature of the objects they deal with, it is due to their methods(please psychology students don't turn this into a discussion, this is my very subjective opinion). I believe that ALL sciences will gain if they put some math into. Could you give me a link to a not too difficult formal proof? I'm certainly interested in something like this, i want to know what it looks like and how difficult it is to prove anything using it. also, what axioms does it use. The humanitarian/social sciences have prooved so many false statements... I think this is true, although by logic is it hard to find one which is false, otherwise it hasn't been proven. But we can watch the tendencies of the past (newton for example claiming that speed at which objects fall down was dependant of weight). Many past 'proofs' have been found to be wrong, and there are undoubtedly many more... | ||
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sith
United States2474 Posts
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Krzych
Poland693 Posts
On November 12 2005 19:43 BigBalls wrote: You're thinking of the statement: This statement is false. It's a contradiction, it has no true or false value. It's a recursive defintion but it makes sense. Let G be the statement that "This machine will never show G is true". G is a statement about itself. G is a statement which is a contradiction within the system. It's a weird way to disprove something, but its valid. Somehow it reminds me the halting problem (is that the name?) that was developed by Alan Turing regarding his machine. | ||
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BigBalls
United States5354 Posts
double major in math and computer science what's interesting to me is what angles people approach the question from, based on their different backgrounds. let me sort of rephrase the question. since there is no formal proof outside of an axiomatic/logical system, what is accepted as a proof? I suppose an overwhelming amount of evidence and data supporting a theory that cannot possibly be a statistical anomoly could be considered a loose proof. any way we can generalize proofs in different areas of study? | ||
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