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I generally agree .. however, both axiomatic systems and theology accept the belief in statements held as being true .. whereas science doesn't .. science tests and verifies then moves forward on those results.@essentialsaltes is right: Gödel's Incompleteness Theorem is about the limits of systems in which one reasons deductively from a set of axioms. It is not about the kind of inductive reasoning one does in science, nor is it about the kind of reasoning one normally sees in theology. Gödel's theorem tells us nothing about the existence of God or the accuracy of the theory of evolution.
The distinction is assumed truth. Verified, 'tested' doesn't require assumed truths.Please make difference between your word "proven" and my word "confirmed, tested".
It was the ignorance of what the theorem actually said that gave me the facepalm headache.That certainly appears to be the inescapable conclusion when going up against Gödel's Incompleteness theorem whilst simultaneously demonstrating total ignorance of the depth of thinking behind it!
I'll confess that I'm a bit of a Gödel fan .. the depth of thinking this guy achieved, I think, stands alone. Never mind my admiration either .. he has the admiration of some of the all-time absolute masters of mathematics .. and I don't think any of them have ever come close to challenging the logic in his various works. Simply amazing legacy.It was the ignorance of what the theorem actually said that gave me the facepalm headache.
Strictly speaking, confirming a particular instance doesn't make a general truth. Something like gravity may be beyond all reasonable doubt, but - as Hume pointed out - the problem of induction applies to all such observations of the world. Truth and proof apply to statements of logic (which can refer to observations of the world) and mathematics.LOL. If you walk off a cliff, you may test the truth of gravity.
Yes - although, as is often the case with masterful insights - his was primed by prior self-referential set-theoretic work, e.g. Zermelo & Russell's paradox, etc.I'll confess that I'm a bit of a Gödel fan .. the depth of thinking this guy achieved, I think, stands alone. Never mind my admiration either .. he has the admiration of some of the all-time absolute masters of mathematics .. and I don't think any of them have ever come close to challenging the logic in his various works. Simply amazing legacy.
Strictly speaking, confirming a particular instance doesn't make a general truth.
Appeal to Strawman. I was responding to the statement that truth cannot be tested. To deny the truth of my example on the grounds that it does not confirm a "general" truth is a Strawman.
Walking off a cliff is a test of the truth of gravity. From a known truth, one can begin to use the powers of logic to arrive at a "general" truth.
OK, my mistake - I thought when you said 'test the truth of gravity' you were referring to testing the theory of gravity as a general truth about the world, i.e. a specific universal attraction between masses. It's trivially true that we have observed things falling towards the earth and have called this phenomenon 'gravity'; that really doesn't need testing, it's observational fact.Appeal to Strawman. I was responding to the statement that truth cannot be tested. To deny the truth of my example on the grounds that it does not confirm a "general" truth is a Strawman.
Walking off a cliff is a test of the truth of gravity. From a known truth, one can begin to use the powers of logic to arrive at a "general" truth.
Are you speaking about logic? Or science? Or the more casual meaning of "truth"?
The theory of gravity can never be proven, as scientific theories arent.
Gravity itself however is a fact. Just like evolution is a fact and the ToE explains how it works.
My friend. Saying over and over again that scientific theories cannot be proven is not becoming and is wrong. Gravity is not a theory but a scientific law.
The parsing you are doing between logic and science is nonsense. Science IS the application of logic. Logic IS the non-contradictory identification of truth. To parse truth in some way different from casual meaning of "truth" suggests you are playing all manner of word games.
My friend. Saying over and over again that scientific theories cannot be proven is not becoming and is wrong. Gravity is not a theory but a scientific law.
You have been corrected on this already by two other members. However, your misunderstanding here is so egregious that a third correction should not go amiss.My friend. Saying over and over again that scientific theories cannot be proven is not becoming and is wrong.
This is not correct.My friend. Saying over and over again that scientific theories cannot be proven is not becoming and is wrong. Gravity is not a theory but a scientific law.
The parsing you are doing between logic and science is nonsense. Science IS the application of logic. Logic IS the non-contradictory identification of truth. To parse truth in some way different from casual meaning of "truth" suggests you are playing all manner of word games.
Walking off a cliff is a test that gives meaning to the term 'gravity'.... Walking off a cliff is a test of the truth of gravity. From a known truth, one can begin to use the powers of logic to arrive at a "general" truth.
Just wanted to repost the above words. They capture the delicate interplay between the 'hardness' of math logic (linguistically .. 'models') used in science, and the never ending human quest to improve on their accuracy by way of comparison with observational measurements.... The equations are examples of a mathematical model which by definition is not as rigorous as pure mathematics.
The reason is straightforward; mathematical models are approximations and are not designed to prove anything.
Theories that are built on mathematical models are not subject to “proof” or “truth”, but on observations and experiments which either supports the theory or contradicts it.
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Each successive theory of gravity is more accurate than the theory it replaces; it is not based on truth.
Yes .. 'twas a very important phase of history in that they were probing the limits of math's applicability to 'giving access to' what they accepted as being 'reality' (aka Realism).Yes - although, as is often the case with masterful insights - his was primed by prior self-referential set-theoretic work, e.g. Zermelo & Russell's paradox, etc.
Any physical system can be described by the case of Gödel, e.g., a model of a car is formal axiomatic system.First, Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. They are not all inclusive of every axiomatic system you can think of.
Hmm. Okay, then. Can you give me the axioms you would use as a starting point, and some examples of theorems that you would prove about cars?Any physical system can be described by the case of Gödel, e.g., a model of a car is formal axiomatic system.
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