- 10 Mar '09 11:35Hi all, I've been having a debate with a religious cousin who claims that logic is based on faith because the fundamental Laws of Logic cannot be proved (and therefore are accepted by faith).

I think that the fundamental Laws of Logic are man-made laws which explain our observations (ie: everything I observe conforms to these Laws of Logic, therefore I accept them) but my cousin thinks Logic is not man-made and is intuitive.

Can anyone enlighten me about this or point me where to read more about it? Google has not been terribly helpful!

Thanks - 10 Mar '09 11:39

Does he think about Gödel? "Every axiomatic system cannot be proven without going outside said system."*Originally posted by marieclaire***Hi all, I've been having a debate with a religious cousin who claims that logic is based on faith because the fundamental Laws of Logic cannot be proved (and therefore are accepted by faith).**

I think that the fundamental Laws of Logic are man-made laws which explain our observations (ie: everything I observe conforms to these Laws of Logic, therefore ...[text shortened]... t this or point me where to read more about it? Google has not been terribly helpful!

Thanks

Meaning that we have always to start with something that 'feels' right, and build everything from there. - 10 Mar '09 11:46

That is basically his argument - you can't prove logic because using proofs and evidence is part of the logic system.*Originally posted by FabianFnas***Does he think about Gödel? "Every axiomatic system cannot be proven without going outside said system."**

Meaning that we have always to start with something that 'feels' right, and build everything from there.

And the fact that we have always to start somewhere is where he believes faith comes in. - 10 Mar '09 13:06

Both of these things are not true, to differing degrees.*Originally posted by FabianFnas***Does he think about Gödel? "Every axiomatic system cannot be proven without going outside said system."**

Meaning that we have always to start with something that 'feels' right, and build everything from there.

Goedel's theorems require the axiom system to have a specific property for that result to hold. They actually assert that if an axiom system is*sufficient to construct the natural numbers*, then either there is a statement derivable from the axioms whose negation can also be derived, or there is a statement for which neither itself nor its negation can be derived. They also assert that if an axiom system, with the same assumption about the natural numbers, asserts that is is consistent, then it is inconsistent. So your statement is pretty much correct, although in the application at hand, one wonders whether Goedel's theorems apply, because one wonders whether the "axiom systems" in question need contain a construction of the natural numbers.

As for the "feeling right", this is one way to view the construction of axiom systems. Another interpretation is "because I said so" or "because I have empirical justification for this choice of axioms".

This thread needs to clarify whether it is the choice of axioms in general which is being considered an article of faith, or whether the procedures by which we deduce things from axioms (which is itself axiomatised, although**a propositional calculus doesn't fall victim to Goedel**) is an article of faith.

Also, somebody's cousin is overloading the word "faith". Having faith in something like god, or the existence of one's own feet when they're numb and out of sight, is a whole different epistemological animal from the "faith" one has in a propositional calculus as far as I am concerned. - 10 Mar '09 13:08

Careful with what you mean by "logic". It seems like you and your cousin are both assigning more meanings to the word than it actually contains. Is your cousin asserting that inductive, deductive or abductive reasoning requires faith, for example?*Originally posted by marieclaire***I think he makes sense, but only if you accept that logic is some sort of universal truth. However I think that rather than logic being a universal truth, it is a man-made explanation of our observations (like science).** - 10 Mar '09 13:34

Nope; Logic is based on hypotheses that they are severely critisized, for there is a standard procedure in order to define what "is" and what "is not" in order to bring up a new theory/ philosophical system.*Originally posted by marieclaire***Hi all, I've been having a debate with a religious cousin who claims that logic is based on faith because the fundamental Laws of Logic cannot be proved (and therefore are accepted by faith).**

I think that the fundamental Laws of Logic are man-made laws which explain our observations (ie: everything I observe conforms to these Laws of Logic, therefore ...[text shortened]... t this or point me where to read more about it? Google has not been terribly helpful!

Thanks

Then the theory will be the subject of severe philosophical and scientific evaluation (scientific facts and evidence) in order to become clear if it copes better than the other, already known theories regarding the same problems that they are its object. If the theory can pass the test, we accept that it is logical and that its product is acceptable.

Therefore the product of a logical string of thoughts/ theory has nothing to do with "faith" as your cousin poses it, but with a state of understanding, which is constantly reconsidered due to the fact that the evolution of Philosophy and of Science at every field is never ending.

Aristotle was the first philosopher who arranged the whole issue by using the main hypothesis that, the logical thought and its product are finally logical since there are no contradictions at any level of understanding. Logic is a thing and Faith another; - 10 Mar '09 13:36

Yeah you're right - when I say logic I mean all reasoning in general.*Originally posted by ChronicLeaky***Both of these things are not true, to differing degrees.**

Goedel's theorems require the axiom system to have a specific property for that result to hold. They actually assert that if an axiom system is*sufficient to construct the natural numbers*, then either there is a statement derivable from the axioms whose negation can also be derived, or ...[text shortened]... from the "faith" one has in a propositional calculus as far as I am concerned.

And it is the choice of axioms in general which is here being considered an article of faith.

I'm not sure what to say about the definition of faith, but I guess here it's defined roughly as belief without evidence. - 10 Mar '09 13:51

Excellent. Everything is pinned down, now.*Originally posted by marieclaire***Yeah you're right - when I say logic I mean all reasoning in general.**

And it is the choice of axioms in general which is here being considered an article of faith.

I'm not sure what to say about the definition of faith, but I guess here it's defined roughly as belief without evidence.

The next step is to see in what sort of situations we reason from axioms and in what sort of situations we are generating axioms (via observation or faith or whatever). It seems like much of the reasoning we're called upon to do is pretty trivial, and much of the axiom-generating we do strains the use of axioms (in the sense of logic) as a metaphor.

A very interesting direction this thread could take would be to have somebody post a belief that they have, which they have thought carefully about, along with their justification for that belief. We could then peel the reasoning off of it until we reach justifying statements which that person would have to admit are "taken on faith". Then we could compare the sort of faith involved to religious faith, and see what kind of qualitative distinctions there are.

Ideally, this test case will be a belief which is strongly justified and not about a heated enough topic to turn this into a usual Spirituality Forum thread . Who's got one? - 10 Mar '09 14:00

I thought that Gödel's theorems was proved? That the theorem was therefore correct? No doubt about it? (Even if the matematicians of that time didn't like it and that Gödel committed homocide of the entire mathematical world. Nothing in maths would therafter considered as true? However, Mathematicians have recovered after that blow.)*Originally posted by ChronicLeaky***Goedel's theorems require the axiom system to have a specific property for that result to hold. They actually assert that if an axiom system is sufficient to construct the natural numbers, then either there is a statement derivable from the axioms whose negation can also be derived, or there is a statement for which neither itself nor its negation can b ...[text shortened]... whether the "axiom systems" in question need contain a construction of the natural numbers.**

Let's take the example of natural numbers and it's axioms. The whole foundations lies on a set of axioms. Everything above this is based of these axioms. One of them is "There is a smallest natural number." It cannot be proven, we hold that for true without being able to prove it. Everything else has to rely that this axiom in particular is true. If it is not true, we have to start from the beginning again.

(Some says that 1+1=2 is self evidentory, but it's not. It relies on the axoms as well.)

However, if we come to try to prove that there isn't a smallest natural number, and we succeed, then this proof in turn have to rely on a more basic axiom, which by definition is not proovable.

For short: All mathematics begin with a series of axioms that cannot be proven, but self evident in its nature. If this self evidentiary is concidered be based on faith, then I agree with everyone, even if this belief is of a non religious kind.

Now, am I right in this, or am I only ranting?

Edit: Yes, there are other ways to define natural numbers, set theory provides with an alternate one. - 10 Mar '09 14:02

X and ~X can never be simultaneously true. I don't see how anyone can call this man made. In fact I don't see how anything that will invariably be agreed upon by independent thinkers can be considered man made.*Originally posted by marieclaire***Hi all, I've been having a debate with a religious cousin who claims that logic is based on faith because the fundamental Laws of Logic cannot be proved (and therefore are accepted by faith).**

I think that the fundamental Laws of Logic are man-made laws which explain our observations (ie: everything I observe conforms to these Laws of Logic, therefore ...[text shortened]... t this or point me where to read more about it? Google has not been terribly helpful!

Thanks

Further even if you accept something on faith that does not make it faith, so to say "Logic is faith" would still be wrong even if you only accepted logic on faith. - 10 Mar '09 14:15

How do you know that X and ~X can't be simultaneously true? Because it is illogical. And the laws of logic were created by man to explain how things appeared to work in our universe.*Originally posted by twhitehead***X and ~X can never be simultaneously true. I don't see how anyone can call this man made. In fact I don't see how anything that will invariably be agreed upon by independent thinkers can be considered man made.**

Further even if you accept something on faith that does not make it faith, so to say "Logic is faith" would still be wrong even if you only accepted logic on faith.

I think it's like science - how do you know that if you drop an apple it will fall to the ground? Because of the man-made law of gravity. But if one day an apple didn't fall then man would have to amend the law to fit our new observations. - 10 Mar '09 14:35

Goedel's theorem is true, but your statement was incomplete, because it left out the requirement that the axiom system in question be sufficient to construct the natural numbers (this is an artifact of the proof of the theorem: Goedel uses prime factorisations of natural numbers in an essential way). I think this was an important point to raise, because I don't think Goedel-numbering can be applied to the sorts of axioms this thread is dealing with. However, I also think axiom-systems are not a very good metaphor for even our basic beliefs about most things outside mathematics, because we don't strive for or care about completeness in our ordinary beliefs (although consistency is of course desirable).*Originally posted by FabianFnas***I thought that Gödel's theorems was proved? That the theorem was therefore correct? No doubt about it? (Even if the matematicians of that time didn't like it and that Gödel committed homocide of the entire mathematical world. Nothing in maths would therafter considered as true? However, Mathematicians have recovered after that blow.)**

Let's take the exa ...[text shortened]... ere are other ways to define natural numbers, set theory provides with an alternate one.

Goedel's theorem does*not*have implications for the "truth" of mathematical theorems. Instead, it simply clarifies what we mean by saying that a theorem is true: we mean that the theorem*can*be deduced from the axioms, i.e. though the axioms are incomplete, the statement of the theorem is not an example of the incompleteness.

It's true that the axioms we use in mathematics are taken to be self-evident, but it's not "truth by faith" as much as "truth by fiat". Mathematicians don't claim that things are true, strictly speaking: they claim that things are consistent with axioms. The choice of axioms is based on history, utility and interest, and it is not made absolutely (nobody says that "nonstandard analysis" is false, for instance; they simply recognise that it derives from a different axiom-system).

In fact, axiom-systems and other such formal constructs are a terrible metaphor for most non-mathematical thinking. To equate the cognitive processes involved in choosing axioms with the cognitive processes involved in religious faith obscures and denigrates both. - 10 Mar '09 14:36

Well, X and ~X are statements in a language.*Originally posted by twhitehead***X and ~X can never be simultaneously true. I don't see how anyone can call this man made. In fact I don't see how anything that will invariably be agreed upon by independent thinkers can be considered man made.**

Further even if you accept something on faith that does not make it faith, so to say "Logic is faith" would still be wrong even if you only accepted logic on faith.