Speakpigeon a faculty is a thing presumed in the brain that carries a capacity to perform some, in this case, some ethereal task. In my post I provided significant evidence that the terms insight and intuition where terms of presumption rather than terms describing some material capability that can be found even by aggregating known human brain capacities. They are like God they are presumptions covering numerous sins.
Better that if you read again.
But, point by point here goes.
Mathematicians use externally defined symbols to prove theories and theorems. I'm going to concentrate on the material, ergo, theory. Tanner explains thatIn every instance materiality continuity is maintained."...a scientific theory is the framework for observations and facts. Theories may change, or the way that they are interpreted may change, but the facts themselves don't change. Tanner likens theories to a basket in which scientists keep facts and observations that they find. The shape of that basket may change as the scientists learn more and include more facts. "For example, we have ample evidence of traits in populations becoming more or less common over time (evolution), so evolution is a fact but the overarching theories about evolution, the way that we think all of the facts go together might change as new observations of evolution are made,"
A mathematical theorem isfrom https://www.mathsisfun.com/definitions/theorem.html note parenthesis conditions.a result that has been proved to be true (using operations and facts that were already known).
Intuition is neither an operation, fact, already materially known. It is a cover capturing some presumed ability like those presumed by examination of bumps on one's head. Not a very satisfying way to establish facts a history has shown. May I say falsified?
As for conjectures it's kind of like "I know this is true but I don't have the evidence or knowledge to prove it yet". Time passes, information is gathered, proof generated IAC with operations and facts already known.
For instance we are beginning to understand why self organization of matter occurs. Self-organization Simply put it's a mechanism for conservation of energy in matter given the structure of our reality.
However this isn't a science forum it's a philosophical forum so I'm done. Now that you have a nice discussion going with Jokodo I expect I'll learn more. I do see why he chooses to discuss your comments on the proposition you post since the proposition is so unanchored and you aren't. It's in the commentary where one expects to find linkage between immortal and die.
Last edited by fromderinside; 11-10-2019 at 07:41 PM.
A match made in heaven.
Theorem...
For the few people who understand logic here, a theorem is never proven true. Mathematicians like to say you can't falsify a theorem.In mathematics, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms, or on the basis previously established statements such as other theorems. A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system. As a result, the proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.
Well, they are wrong, but it is still true that a theorem is not proven true since a theorem is nothing but the conclusion of a valid proof (at least in principle, since it may be that some proofs are not valid that are believed valid).
This means that the theorem is not proven true. It is proven.
The theorem, if proven, will be true IF the premises of the proof are true. Conditional IF.
So, no, a theorem is not proven true. Maybe a theorem is true, but it is not proven true. A theorem is the conclusion of a valid proof. That is, if you accept the premises of the proof as true, then you should logically accept the conclusion, and therefore the theorem itself.
Yet, that you believe the premises true doesn't mean they are true. Typically, mathematical theorems are all conclusions from some arbitrary set of axioms which might or might not be true, making the theorems themselves possibly true, possibly false.
Again, a theorem may well be true, but it is not proven true. Proven, yes, in the sense that there is a proof which is valid, but since we don't know that the premises are true, the truth of the proven theorem is conditional on the truth of the premises. Which is definitely not what we mean when we say that something is true. Of course,we can all believe otherwise, but then this will be a belief.
EB
So you are saying that the Pythagorean Theorem is not proven true?
Wiki presents evidence by many that show otherwise. You know Euclid, Einstein, .....
Pythagorean theorem
falsified again you are.
I enjoy your correct recitation of a general philosophical discussion. However we are dealing with math which is often applied in science practice. Things are often different there which is why you seem to be so often bumping up against this reality wall.
Maybe too much philosophy and too little math? Or, as you might say too much science too little philosophy.
As for your previous post Speakpigeon my point is your assertion(s) about intuition are built on sand which is known to shift.
Now I'm not going to say that many so called theorems are constructed in the manners which you suggest. They often are. But that's why I tend to go with scientific practices which usually avoids such blue sky tactics.
Induction? You must have bumped in to that concept. https://plato.stanford.edu/entries/hume/ Even Hume accepts that reality is not proven true it's just that we've found a way to show that it can explain ever more by applying a building block process as we build theory theorem by theorem based on observation built on previous observation. And I accept that the Pythagorean Theorem breaks down in different dimensional arrangements only to be rescued by adding theorems bridging those revealed gaps.
Sorry if I appear as unsympathetic. It's just that when one includes every manner of of speculative approach which you convey as intuitional. We differ there. Most theorem building in the past 400 years has been based on inductive processes rather than deductive processes. Sure, the a scientific argument begins with a deductive statement. However that statement is always based on preceding inductive processes rather than some speculation from whence no one knows. If you accept that we have no difference to discuss.
FDI
Last edited by fromderinside; 11-11-2019 at 07:50 PM.
Indeed. It is proven, many times over, again and again by successive generations of mathematicians and school children. It is never proven true.
If you understood logic you'd know that logic doesn't prove anything true. We have to rely on our premises which can never be proven if not by assuming other premises, and so we have our classical regress argument.
Like it or not, understand it or not.
LOL. This is a very impressive argument.
LOL. You are assuming a lot.
This is typical of a certain kind of people. People who have an axe to grind. Dogmatic people.
So here you are thinking without the least foundation that I believe intuition pops out of a clear blue sky. YET, did I ever suggested that much? No. Please quote me where I suggested intuition pops out of a clear blue sky!
Me, I think from personal experience that people who understand intuition because they rely heavily on it for their work, like indeed mathematicians, but essentially any intellectual workers, which includes many manual workers, know that intuition is made possible by the familiarity we have with the subject matter, which requires essentially hard work, such as reading, observing, discussing, pondering, trying this and that.
Please quote me where I suggested intuition pops out of a clear blue sky!
You are truly appalling .
Where did I claim the process was based on deduction?
You are appalling.
Look again at the definition of intuition I already provided twice:
And try to see where you went wrong.Intuition
1. The faculty of knowing or understanding something without reasoning or proof.
Clue:
EB
If something is proven, it is taken to be true.
You need to read the Wiki piece again. There are two explicit declarations that the theorem is true. It's for you to figure out why.
What can I say. I agree one has the ability to acquire the knack for often saying the right things which I agree is what might be the situation with intuition. Not the same as faculty - suffers from formerly fate - at all and not inherent at all. The other bolded terms are not demonstrated in any measured way. Whereas hearing had been verified as being a faculty. So failing to hitch ones star to any definition that holds water Speakpigeon's argument for intuition dies of thirst.Definition of faculty
1: ABILITY, POWER: such as
a: innate or acquired ability to act or doman … how infinite in faculty— William Shakespeare
b: an inherent capability, power, or function the faculty of hearing
c: any of the powers of the mind (such as will, reason, or instinct) formerly held by psychologists to form a basis for the explanation of all mental phenomena
d: natural aptitude
has a faculty for saying the right things