Philosophy & math

[Bent-Winged Angel]

If there are degrees of infinity, as proven by Georg Cantor, a mathematician and father of Set Theory,would it not be unreasonable to thiink that for every thing one consides in his/her heart to be true contains at least one element of a falsehood?

[Sockratease]

If there are degrees of infinity, as proven by Georg Cantor, a mathematician and father of Set Theory,would it not be unreasonable to thiink that for every thing one consides in his/her heart to be true contains at least one element of a falsehood?

In formal logic, "Truth" is undefined!

It defies any attempt to define it, so I say truth itself is false...

[hobold]

I don't know what the philosophers think, but modern mathematicians, until recently, used to think that "true" and "provable" were the same thing. Then came Kurt Gödel and proved his incompleteness theorem. Since then, "true" and "provable" are recognized as different things.

In my humble opinion, the concept of "truth" can only be defined from some kind of utilitarian point of view. "True" are all the claims that you can reliably base predictions of the future on. "False" are those claims that don't help you to reliably predict the future.

This is why Newtonian physics was true in its day and age: there was no technology back then that exposed relativistic effects (nor could there have been such a technology, because no one had the know how).

This is why there is a grey area of claims that may seem to help predicting the future, but later turn out to be mere correlations rather than underlying truths. I.e. things that are "almost always true".

Philosophical and mathematical notions of truth would have evolved from there. So these days we are using the concept of truth for things that we cannot verify or falsify in the material world. The original utilitarian rule of thumb no longer helps us there. I guess "truth" is now mostly about consistency with the more mundane, verifiable truths. That drastically increases the likelihood that predictions of the real world, based purely on theory, will end up being correct in practice.

[Sockratease]

The Statement Below Is True.

The Statement Above Is False.

[Bent-Winged Angel]

The Statement Below Is True.

The Statement Above Is False.

THREAD KILLER!

[hobold]

Not a thread killer, just a contradiction. Gödel's thread killer would look more like:

"This statement cannot be proven".

True or false? And what are the consequences in either case?

[David Makin]

Not a thread killer, just a contradiction. Gödel's thread killer would look more like:

"This statement cannot be proven".

True or false? And what are the consequences in either case?

One could just ask if either of these are true or false:

1. "This statement is true"

or

2. "This statement is false"

Obviously if the first is false then it is incorrect so it's false, but if the first is true then it is correct so it's true but if the second is true then it's incorrect so it's false but if it's false then it's correct so it's true

"The meaning and purpose of life is to give life purpose and meaning"
(My own AFAIK, but if anyone's seen it elsewhere I'd like to know)

To me "Reality" or "existence" is essentially a manifestation of statement 2 !

I like this question: "I am, but is anything else ?".

Another, with answers: "What is, but is not ?" Answer 1:"Everything", Answer 2:"Nothing"

For those who want a deity, question to deity:"Why?" answer: "Because I could." or (better) "Why not?"

Which is correct: "Nothing never exists" or "Nothing always exists" ?

[David Makin]

If there are degrees of infinity, as proven by Georg Cantor, a mathematician and father of Set Theory,would it not be unreasonable to thiink that for every thing one consides in his/her heart to be true contains at least one element of a falsehood?

In formal logic, "Truth" is undefined!

It defies any attempt to define it, so I say truth itself is false...

In philosophy relating to existence then the only "absolute truth" is "I think therefore I am", though I prefer "I think, therefore something is, part of which may be me".

[jehovajah]

This is why Newtonian physics was true in its day and age: there was no technology back then that exposed relativistic effects (nor could there have been such a technology, because no one had the know how).

This is why there is a grey area of claims that may seem to help predicting the future, but later turn out to be mere correlations rather than underlying truths. I.e. things that are "almost always true".

Newton in fact understood relativity very well, he just did not see the significance of it to the speed of light and time in our modern sense. Newton was not alone in understanding relativity, as you can go back as far as the sumerians and Dravidians and Egyptians and find the concept.

Surprisingly non of these topics are new to discussion, being regularly discussed in various cultures throughout history. Our contribution to the discussion has been technological and passionate. From the reformation the west really felt it could master nature and bend it to human will. Former cultures were more respectful and more in sync with their environment, calling each element or process a god and respecting it that way.

Relativity really required Lorentz to take off in Einstein's mind, but the fundamentals of relativity were appreciated solely through proportion, and trigonometry and Quaternions. Thus it took another 100 or so years to make this obvious to modern scientists, but many scientists from Maxwell onwards had a good enough perception of it. Einstein was the one who captured the scientific imagination and brought it all together, contributing very little math i might add! It was his insight and praxis that were influential. We then have to go through Schroedinger and Dirac and Feynman to get to the modern understanding. Now they did contribute some math!

As to truth, scratch that! Congruence, similarity and accuracy/ approximation are utilitarian cognates. Adhere,inhere and cohere are also important verbs to framework discussions.

There are no Absolutes! And that is absolutely true!  
For the notion of moral relativism being a slippery slope, realise that all are hypocrites, and that takes care of that issue.

Empiricists have worked through these issues since greek times and before. John Locke is the modern founder of the movement.
There is nothing wrong with the old idea of "true" and nothing right with the old idea of "false", but this like any statement is to be taken with a pinch of salt.
Logic, particularly propositional logic is only utilitarian not "the  truth" as pointed out above. In fact i hold that "the truth" is one of the major lies we are told in our current culture!

We may enjoy ourselves if we will accept that that is a great thing to do and an end in itself. Moral questions can then be seen as critiques to  social mores as they indeed are. As a consequence of that mores are  imperfect and prejudicial, unless we work to make them "fairer" in some way, and by some measure.

[hobold]

Gödel's incompleteness theorem had to be about provability, not about truth. That's the only way he could show that those two are different. Let me bore you in more detail...

Remember: "this statement cannot be proven" was his target, formulated as rigorously as any other mathematical theorem.

Case 1: There indeed exists no proof of the statement. That implies we have found a truth that cannot be reached by logical deduction from the foundations of mathematics (a proof is an unbroken chain of deduction that starts at a small number of axioms and arrives at the claim). That in turn implies that our system of logic is fundamentally incomplete. (Adding the statement as an axiom won't fix it, but that's another long story.)

Case 2: There is a proof of the statement. That implies a contradiction can be constructed from a long chain correct reasoning, starting out at the foundations of mathematics. So our system of logic is fundamentally flawed, because it contradicts itself.


In other words, Gödel was able to show that mathematics, logic itself, is buggy one way or another and cannot be fixed.

[Melancholyman]

There is truth, truth is experience. Experience is not subject to judgement, I am of course talking about the experience itself. Experience is what it is and all the experience you have had and ever will have is true, it cannot be false. Then of course you could claim that it cannot be true either, only state that it IS. But what is must be, and if to be is not truth then there is no truth. Ehhr...This is precisely what Descartes meant with "I am a thinking thing", what he really meant in modern language is "I am experience"

[taurus]

... Experience is not subject to judgement ...

This is exactly the point. In other words you can say experience is irrelevant. Expierience is real, not true (and not false). Relevant are statements about expierience and they can be true, false or undecidable.

Those undecidable statements are by the way the reason, why we have today an axiomatic set theory. Modern logic still (and maybe will ever) base one a few unproovable assumptions. A fact, that might be important for all sorts of philosophic considerations.

greetz
taurus

[jehovajah]

It is near easter so like Pilate i pose the question: "what is truth?
For that matter what is experience? And finally what is logic?

Wherever we start from it s only ever a starting place.

Starting with experience  is the best starting place, is my opinion.

[visual.bermarte]

YES, you need experience for that! <--semantics

first order logic contains predicative logic and has a decidability's problem..propositional logic not.
Problem of 'decidability' arises for propositional logic as well just because of time needed solving very long propositions/sentences!
just depends on the method used...
When talking about logic+quantifiers is better to talk about 'satisfaction' instead of 'truth' AND we need semantics (experience) for that task..

see>http://en.wikipedia.org/wiki/Propositional_calculus

[Bent-Winged Angel]

analytic propositions are truth
for example

1. All triangles have three interior angles.
2. All bachelors are unmarried.
3. All whales are mammals.