Can anything really be true/false? - General

Why is it that we trust science, and maths etc. if it's thought out, and made by us? You can say; well, we can prove this and this with empirical evidence, and years of research. But it's all so human. All we know as truth, and everything we can prove and disprove, has it's origin from our surroundings, and the human mind. I believe, for instance, that God was created by man, and not the other way around. But does it really matter? Religous science (Creationism etc) can be disproven, as it has been many times, but is either side really true? Both sides of the discussion rely on a human mind to prove their respective points, but can anything really be called true/false? I realize that these questions are like saying: "Yeah, I see this colour as red. Maybe for you it's what I see as blue.", but I'm still interested in hearing your views on this. I hope some advanced, highly intelligent life-form comes to Earth before I die. It'd be an interesting perspective shift, for sure.

true = true true != false false = false Im pretty sure all of them statements are true.

Relativism (what you're talking about) is a very valid point of view, but there is no need to actually discuss it in this fashion because the way we study the world ALREADY takes it into account. The scientific method is built in such a way that, for our purposes, it works. No theory can be proven to be "true," only tested and stated to be "not yet proven false." Because of this, there is no such thing as scientific fact; the theory of gravity is still a theory, and always will be, even though it works perfectly well. The reason for this is that as we discover more facets of the universe, we will have to make modifications to even these most long-standing and useful theories to allow them to continue to work for us.

Yes. An axiomatic system of inference can prove statements true or false, and tautologies are always true by necessity.

Well first of all we understand physics and maths. And masses and gravitation and what you have, they are true and we've crunched the numbers to an understandable form, on a paper or on a computer. Also, scale of measurement?

[QUOTE=Bat-shit;33908145]Well first of all we understand physics and maths. And masses and gravitation and what you have, they are true and we've crunched the numbers to an understandable form, on a paper or on a computer. Also, scale of measurement?[/QUOTE] They aren't "true." They're just, in their current state, not yet false. We will continue to add on and take away rules as we discover more information.

[QUOTE=Bat-shit;33908145]Well first of all we understand physics and maths. And masses and gravitation and what you have, they are true and we've crunched the numbers to an understandable form, on a paper or on a computer. [/QUOTE] Yes, that's all well and fine, but the numbers we gathered and crunched, still went through our human minds. Is anything that's 'not yet false', ever going to be completely true/false? Are there any absolute truths at all?

[QUOTE=Benstokes;33908044]Relativism (what you're talking about) is a very valid point of view, but there is no need to actually discuss it in this fashion because the way we study the world ALREADY takes it into account. The scientific method is built in such a way that, for our purposes, it works. No theory can be proven to be "true," only tested and stated to be "not yet proven false." Because of this, there is no such thing as scientific fact; the theory of gravity is still a theory, and always will be, even though it works perfectly well. The reason for this is that as we discover more facets of the universe, we will have to make modifications to even these most long-standing and useful theories to allow them to continue to work for us.[/QUOTE] I'm pretty sure the fact that gravity exists is a fact, but how and why it works would be described by a theory.

Peano axioms. Problem solved.

OP u r teh confuzed. True and false, being relative words like most words, have varied meaning in different context. In math, an equation is true if it does not violate mathematical laws under whatever conditions its given. a + a = 2a for example is always true for all real numbers. In computer science, a statement is true if the processor evaluates it as so. In science, a theory is true if there are no known or reasonably speculated ways that it could be false.

These are all human truths. Science, math, and the very concept of true/false was created by us. Therefor; can anything be true/false?

[QUOTE=Benstokes;33908218]They aren't "true." They're just, in their current state, not yet false. We will continue to add on and take away rules as we discover more information.[/QUOTE] Yes yes absolutely but so far we've accumulated a hell of a lot of consistent information.. Information that sticks. [QUOTE=Pampers;33908869]These are all human truths. Science, math, and the very concept of true/false was created by us. Therefor; can anything be true/false?[/QUOTE] I.. It doesn't work like that. You nitpick when you are the single most intelligent being. Kinda.

[QUOTE=Slight;33908782]OP u r teh confuzed. True and false, being relative words like most words, have varied meaning in different context. In math, an equation is true if it does not violate mathematical laws under whatever conditions its given. a + a = 2a for example is always true for all real numbers. In computer science, a statement is true if the processor evaluates it as so. In science, a theory is true if there are no known or reasonably speculated ways that it could be false.[/QUOTE] but what if science itself is flawed? we created science, so it could be a flawed ideology. but how would we prove science can prove things? using science? we can't use science to prove that science can prove things. That would require us to assume that science can prove things. But we can't assume in science. So to prove science can prove things, we have to break the rules of science.

[QUOTE=The Kakistocrat;33908963]but what if science itself is flawed? we created science, so it could be a flawed ideology. but how would we prove science can prove things? using science? we can't use science to prove that science can prove things. That would require us to assume that science can prove things. But we can't assume in science. So to prove science can prove things, we have to break the rules of science.[/QUOTE]I aint flawed. I am completely truthful.

Only maths can be proven 100% true. With science the best we can do is remove any reasonable doubt to something like 99% certainty. Most of the time we hardly notice the difference, so who cares if we're 100% certain or not?

[QUOTE=Darth_GW7;33909757]Only maths can be proven 100% true.[/QUOTE] Your statement isn't mathematical, so how can we know it's 100% true? (sort of joking)

[QUOTE=Darth_GW7;33909757]Only maths can be proven 100% true.[/QUOTE] what if a!=a. Then math can't be proven, can it?

[QUOTE=The Kakistocrat;33910891]what if a!=a. Then math can't be proven, can it?[/QUOTE] If a != a then a implies ~a implies a or "math is proven true" implies "math is proven true" because ~a. Logic'd.

-snip-

The proof is analogous when ~a is true. [editline]26th December 2011[/editline] [QUOTE=The Kakistocrat;33910979]I know I sound stupid, but what is ~a?[/QUOTE] It means "a is not true."

hmm. but doesn't a also imply ~a implies a implies a implies ~a? the cycle continues. so wouldn't "math is proven" imply both "math is proven" and "math is not proven"?

Yes but it doesn't matter. Math is proven. If you begin from a contradiction, anything can be proven true. The fact that its contradiction is also proven true is immaterial. [editline]26th December 2011[/editline] Basically it just shows that one of your axioms is wrong. If you try to prove something is true and you use a contradiction to do it, the other guy can always prove that you're wrong as well you you have to scrap it and restart with consistent axioms.

okay, seems logical. anyways, you said earlier that things can be proven via axioms. But what if an axiom is false? and since you can't prove an axiom, by definition, there is always a possibility (however small) that your axiom is false. doesn't taht mean nothing can be proven, with the exception of a=a?

An axiom cannot be false. They are assumed to be true, are necessarily unprovable, and form the absolute basis for a system of inference.

This sentence [i]is[/i] false.

[QUOTE=JohnnyMo1;33911336]They are assumed to be true[/QUOTE] what if the assumption is false?

[QUOTE=The Kakistocrat;33911362]what if the assumption is false?[/QUOTE] It can't be. An axiom is impossible to prove false unless you have inconsistent axioms, but in that case the axiom is still taken to be true, even if another axiom states that it's not true. I used that fact in the proof earlier. The fact that a was true allows me to say "either a is true, or 'math is proven,' or both are true." This has to be correct because a is true, so at least one is always true. But then another axiom says that a is not true, so to keep the previous statement true, "math is proven" must be true. This is called the principle of explosion.

[QUOTE=JohnnyMo1;33911478]It can't be. An axiom is impossible to prove false unless you have inconsistent axioms, but in that case the axiom is still taken to be true, even if another axiom states that it's not true. I used that fact in the proof earlier. The fact that a was true allows me to say "either a is true, or 'math is proven,' or both are true." This has to be correct because a is true, so at least one is always true. But then another axiom says that a is not true, so to keep the previous statement true, "math is proven" must be true. This is called the principle of explosion.[/QUOTE] I never said if an axiom could be proven false, I meant if it is false. Axioms are assumed true. But you can never [B]know[/B] that they are true.

It depends in what sense you're talking about axioms. If you're trying to create some sort of model that corresponds to reality, sure, but in terms of proof theory it's immaterial whether the axioms are "true" or not. All a set of axioms does is define some sort of deductive system.

[QUOTE=JohnnyMo1;33911843]It depends in what sense you're talking about axioms. If you're trying to create some sort of model that corresponds to reality, sure, but in terms of proof theory it's immaterial whether the axioms are "true" or not. All a set of axioms does is define some sort of deductive system.[/QUOTE] Yes, I am talking about reality. Axioms that correspond to reality can not be proven. and since we use those axioms to describe reality, our descriptions can not be proven.