Is everything Provable? AngelRo may have an excellent point

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I do not believe everything is provable and here is why.

Let's say I have some theorems{t1..t4} which are derived from axiom 1. Is axiom 1 provable? If it is what is the proof and assertions that lead to it? Does axiom 1 have axioms(g) that lead up to it? Does axioms(g) have presuppositions and other axioms that lead up to it? Can one ever have everything in a given set be provable without a starting axiom that requires acceptance without proof? If this was possible would we not have an infinite amount of regressive proofs one would have to do?

Therefore, how is it possible to eliminate faith entirely? One has to accept something as a starting point without proof does he not?

Ultimately, can one prove proof meaning can one prove something without proving it? One has to accept that things can be proven without proof of this. I think we all have faith in something.

It depends on what you mean by "proof".

1. Axioms in a proof system can be proved merely by their assertion, because they were taken as axioms. Obviously this doesn't suffice to establish a proof of the soundness of the axioms, which I assume is what you mean, but my point merely is that this kind of proof is a different sort from the formal sense. (For Peano Arithmetic and ZF set theory we also have incompleteness phenomena, but I think discussing this would side track us at this stage)

2. It sounds like you're instead asking about whether we have to justify everything we can assert, and in a roundabout way running into the regress problem which is one of the central problems in philosophy. There are a few moves to go about establishing first principles, or even side-stepping the need for them, depending on where you're coming from philosophically (foundationalism, coherentism, infinitism).

Or one could simply adopt the scientific approach.

http://en.wikipedia.org/wiki/Falsificationism

For justification in science, or all justification in general?

The Godel theorem prove somehow that some mathematical true can't be proved.

Science.

As for anything else... well, look at my signature...

Very little can be proven with absolute certainty. But that doesn't mean that faith is a virtue. Faith has many meanings, and I think it's used wrongly when applied to scientific matters that are incompletely known. Faith in a religious context means believing in something without evidence or even in light of contrary evidence. Science doesn't do that. The most you can say about belief in some theories is that it constitutes tentative trust.

Sure. But you still have to ASSUME the axioms of the scientific approach/falsificationism. Falsificationism cannot be falsified, thus from a strictly empirical POV it cannot be proven.

The only real certainties are logical and mathematical ones, i.e., those which don’t state anything about the real world. Virtue is a subjective concept, and science can’t tell anything about whether faith is one or not, but it can study how faiths which consider themselves virtues fare better under memetic selection than those which don’t, so it’s no surprise that the most successful current ones do.

We all DO have faith in something. There's nothing wrong with that. I mean, take science as an example. Science depends upon human senses representing the world as it is. If the world as we see it isn't the world as it IS, then all we have left is solipsism. So even if we are all just heads floating in jars somewhere, it's not really relevant, is it?

It is true that the existence of a Supreme Being can be proven logically. But the problem that a theist will consistently run up against in a dialogue with an unbeliever/non-believer/atheist/anti-believer is there is never a shortage of counterarguments that the opponent will never admit to being faulty (the problem of evil, or the problem of suffering, for example, which are pathetically weak counterarguments--there were already scriptural answers to these before those issues even came up). And that exposes the inherent flaw in logical proofs for the existence of God: Any argument in favor of God that starts from the assumption "no God" and then sets out to prove "God" is doomed to fail. In order to believe in God, one must first accept that there is even a God at all to believe in. If your mind is made up that "no God," not even the best logic is going to be remotely convincing. And, I mean, the counterarguments can get pretty absurd. The toughest one I ever faced took an intellectually dishonest deconstructionist position that essentially held that words had no meaning, therefore terms such as "good," "evil," and "God" were essentially meaningless. My response was that all words, according to that line of pseudo-reasoning, are meaningless thereby leaving us nothing else to discuss. I became convinced that the guy was a troll and abandoned the discussion.

Scientific reasoning makes sense because of pragmatic conclusions. I don't believe that religious faith and science are inherently opposed. I have no issue with good science. I do, however, reject the idea that only what is physical is real. It's impossible to prove that idea with anything but itself. Therefore empiricism is an ultimate fail by way of petitio principii. However, that empiricism is wrong doesn't invalidate science. We just need to accept it for what it is rather than turn it into what it is not. Part of that means that we accept the scientific method as fact despite our inability to falsify it. If we can accept axiomatically the scientific method, then we can accept axiomatically the God of the Bible. Like it or not, we all put our faith in something.

No, and that isn't being argued here.


Again, not what we're talking about. The question is one of why we even bother to rely on the scientific method when we can't even scientifically prove it.


Wrong. I think faith in SOME religious contexts means believing without evidence or in light of contrary evidence, but this isn't always true. I would think...hope, even...that even religious thinkers would have at least enough wisdom to understand how foolish it would be to believe something in light of contrary evidence.

Why SHOULD a Christian believe the way he does? Is there a precedent for Christian faith? Yes. Why? Because people witnessed events that convinced them Jesus is the Son of God. If that is enough to convince you, then you have established the foundations of your faith on EVIDENCE. Faith need not be blind.

Now, it may not be evidence that you yourself have seen, or it may be evidence that fell to the ravages of time long ago. But it IS evidence that other, real people found quite tangible in their own time.


Religion is no different. Think about it: If you were raised in a religious home and had to do everything your parents said to include going to church, temple, whatever, odds say that you'll likely continue in the faith your were raised in. So how do you know, for example, if there is only one God and thus only one way to heaven, that you're even on the right track? I became convinced early on in life, so this was easier for me than probably for most. But that doesn't mean that I didn't ask myself from time to time whether I was on the right track--after all, the wrong idea about God could mean an eternity in Hell, right?--or if it was possible I was in a dangerous cult and being "lied" to the same way I was "lied" to about Santa, the Easter Bunny, and the Tooth Fairy. Or even about where babies come from. Seriously, how would you KNOW? And later on I got exposure to other cultures, religions, not to mention my brief studies in philosophy in college and getting to know people who were, um..."different." So it's not like I didn't have the opportunity to explore whatever else was out there the world had to offer. I just never could reconcile other approaches to spirituality with anything better than what I already had. What I DID find out along the way was that were things I'd been taught that really were just plain WRONG. I learned to make up my own mind, not live in fear because of what one mistaken teacher or another said about salvation. Even in religious faith, at least the way I know it, many times "tentative trust" is all you have as you grown in faith. Related to this is something mentioned in a different thread--the Kingdom of Heaven is like a mustard seed. "Tentative trust" is often the "little faith" described in the Bible. Peter didn't need a huge amount of faith to walk on water. Despite his momentary lapse of faith and getting distracted, he STILL had faith enough in Jesus to call out from beneath the waves for Jesus to save him. Faith in science, faith in Jesus...it's never been about how MUCH faith you put into it, but rather if you've put any faith at all into it.

AngelRho, I believe in God and his son Jesus Christ. I believe in the scientific method as well and it does have limitations as to what it can do. I am in a state of major depression, confusion and close to despair but I think of Jesus and it helps. If you do not mind, I would like to pm you and talk to you about some things.

When I used to be a Christian, I used to misunderstand this concept as well. I don't know of any one advocating science and empiricism who believes that anything can be proven beyond the shadow of a doubt. And if they do, I disagree with them.

When it comes to faith, faith is something you only rely on for things you cannot sense/perceive in any empirical fashion. So science is not faith in the same way believing in God is faith. I trust the scientific method exactly because it's the most effective method to rely on to discover facts and such as it relies on empirical sensing + replication and other forms of confirming to establish facts and truths.

I don't have faith (belief) in science as science is clearly real to my brain (albeit abstract), but I do have faith (trust) in it as the best method to discover truths.

Nothing is provable beyond the world of paper logic and mathematics.

We assume axioms (based on our senses or intuition or because it's accepted by practically all of us).

However, make no mistake, if we are to rely on the principle of simplicity, it's more logical to believe there is no God than there is one.

There are some proofs that don't have any premises. In other words, they "output" that something is true without requiring any "inputs". Here is an example, a proof of the statement "either nothing exists or something exists".

Under a certain interpretation of mathematics (the correct one! ), every mathematical proof is also like this.

But lots of other proofs aren't like this. They require premises, and so they only tell you "if the premises are true, then the conclusion is true".

You can PM me any time. I can't promise that I'll have all the answers, but I'll do what I can!