Can Logic Alone Prove Anything?

[AnnaM]

God violates non-contradiction and material naturalism, which are logical necessities of existence.  Aristotiliean metaphysics.

[Kyuuketsuki]

God violates non-contradiction and material naturalism, which are logical necessities of existence.  Aristotiliean metaphysics.

Maybe but metaphysics is rubbish!

I accept that philosophical reasoning can on occasion feed into science but I think current day philosophy has very little to do with the original Greek idea of a search for knowledge and nowadays it's largely people with huge ego's blowing deductive sunshine up each other's arses ... metaphysics is philosophy's bastard child!

My stated position (elsewhere) on metaphysics is this (apologies in advance for the language but I was hyped when I said this), "Metaphysics is unnecessary, it is intellectualised hyper-bollocks, total psychobabble and has no (zero, nada, zip) bearing on reality. It is worthless to man and beast (harmless fun but couldn't prove the existence of a gnat's bum whether it wanted to or not)."

What use is a form of logic that can be used to prove something for which there is no evidence?

Kyu

[AlP]

Logic is certainly useful in mathematics and other related areas. It works particularly well in math I think because it is often possible to prove things with certainty. Math doesn't have to deal with the muddle and uncertainty of the natural world that is the domain of science.

It is less useful in science because it is rarely possible to actually prove something with certainty. You can usually only disprove things. So I don't think it's common to, for example, take some scientific theories that seem true (perhaps based on overwhelming supporting evidence, like Newton's laws) and try to draw other conclusions from them using logic. You might use it to help form a new hypothesis but you would still have to test that new hypothesis experimentally before it anyone would consider it scientific fact. Logic alone wouldn't be very convincing in many cases.

I don't know enough about philosophy to contribute on the applicability of logic in that area. I'm guessing they use it but where they could draw their axioms from I don't know! I would be skeptical of philisophical conclusions "proven" with logic. I would be wary that it was actually based on questionable axioms or applied pseudo-logic.

Theologians? I expect they will continue to misuse pseudo-logic to "prove" all kinds of religious "truths", just like those who promote intelligent design will continue to misuse pseudo-science.

It's pseudo-logic we need to be wary of, not logic. Logic is a useful tool in the rational persons toolbox. Pseudo-logic is not.

[SteveS]

Okay, I know this topic has been dead for a bit, but I've been reading over some recent postings and this one in particular really catches my attention.  I'm sort of shocked at some of this discussion.  Logic is not only capable of proving things, it is required to prove things.

Look - just suppose that the answer to the OP's question was "no".  In other words, let's say that we decide that logic is incapable of proving anything.  This just pleads for someone to then ask the question: how would we prove anything without logic?  

So, how about it - what would count as proof?  How would we know that an argument is valid or invalid?  That reasoning is sound or unsound?  That a conclusion "stands to reason" or is "pure poppycock"? :hmm: )

3) Law of the Excluded Middle (Either Or)

All things are either "A" or "not A".  All statements are either true or false.  There is no third choice.  A statement cannot be neither true nor false.  It is either or.

Okay - now, go ahead and convince me that these principle are wrong without accepting the truth of them.  If you say to me "logic might not always apply", but pretend that you don't accept the law of identity, then what is logic?  What is always?  What does "might" mean?  Are the words interchangeable?  Could they mean other things?  Or, when you say "always", or "apply", or "logic", do you have a specific idea in your head that isn't interchangeable with other ideas and means a specific thing that you're identifying with a word?

If you don't accept the law of non-contradiction, then what if your statement is both true and false.  The laws of logic both always apply and don't always apply.  Can you think of an analogy to explain this meaningless expression?    Another meaningless proposal that is impossible to understand because understanding is only possible with logic.

Hopefully I'm making my point.  Using words, ideas, and thoughts; forming sentences; attempting to communicate meaningful ideas; all these endeavors implicitly accept the validity of logic.  In fact, they depend upon it.

Wow, what a rant.  Believe it or not, there's a few more things I'd like to get off my chest:

Anyone can try to use logic to prove the existence of some god or other.  In fact, I approve of this endeavor.  At least this makes the attempt valid for discussion.  If a god can be proven to exist, then that proof will need logic.  If a "proof of god's existence" is not valid, then logic will clearly illuminate this.

This is my appeal to all atheists:  don't condemn logic.  If you do, then you condemn reason.  You condemn rationality.  Why?  Because these are the direct descendants of logic.  If atheists disavow logic, then we disavow reason.  If we disavow reason, then we're just another pact of mystics and the only thing separating us from the religious mystics will be our conclusions; not how we arrived at them.

Being an atheist doesn't make me rational.  Being rational makes me an atheist.  Logic works, and you already count on it.  So stop pretending you don't!

[AlP]

Look - just suppose that the answer to the OP's question was "no". In other words, let's say that we decide that logic is incapable of proving anything. This just pleads for someone to then ask the question: how would we prove anything without logic?

I can't speak for anyone else but for my part I was certainly not claiming that logic cannot prove things. And to be clear I was thinking about propositional logic (which I think is also what you are talking about) at the time. My concern was simply that you have to be careful that you aren't applying it inappropriately and that outside mathematics and related fields you're on much shakier ground in that respect. In my education in and professional practice of computer science I don't remember encountering a logical proof in an academic paper outside the domain of mathematics. My reading includes science and engineering research too.

So, how about it - what would count as proof? How would we know that an argument is valid or invalid? That reasoning is sound or unsound? That a conclusion "stands to reason" or is "pure poppycock"?

Outside of mathematics, there are other ways to determine if a statement "stands to reason". I'll give two examples. You can perform an experiment and determine whether the results are consistent with the statement. If they aren't and the experiment was performed correctly then that indicates the statement is false. Once enough experiments and observations have been made you might be convinced that it is fact. It's rational and it doesn't involve propositional logic (except perhaps trivially). Another example is statistics. One might state that two things (like taking a drug and better health) are correlated. You can conduct an experiment and use a statistical analysis of the results to see if they really are correlated and that the correlation is statistically significant. Again, it's rational and it doesn't involve propositional logic.

[SteveS]

Hey AlP - Re-reading my post I realize it may have come off a bit "preachy", so apologies in advance.  Also, I have no issue with the empirical scientific methods you present (I heartily approve!) and I wasn't really aiming my response directly at any one person (certainly not you in particular).  Anyway, regarding science, I think that logic (propositional logic is fine - the three laws I listed are frequently expressed in propositional terms) underlies and informs the more empirical methods that you are talking about.  I'll get into that in a bit.

Minor gripe,

It is less useful in science because it is rarely possible to actually prove something with certainty. You can usually only disprove things.

Disproving is the same as proving something false, right?    ) that an axiom is really supposed to be self-evident.  Scientifically, we realize that we don't know for sure whether our beliefs are correct and we can't just puzzle them out in our head because we don't know what axioms we should accept.  So we go out into the world and try to find out with observation and experimentation.  Science is powerful and convincing because our conclusions and theories are demonstrable.  If somebody questions our conclusions about gravity and planetary motion, we can perform future predictions of the position of planets and then go outside and look: and there everything will be right where we said it would be.  I can demonstrate why I should accept my theory.  As Carl Sagan has pondered: what would religion give to be able to predict the future with such certainty?  

Two things about this:

1) Science embraces an axiom that there is an objective reality.  In other words, "reality is real", or "existence exists".  I think nearly everyone, unless they are nuts, probably agrees with this.  If they claim they don't, and they don't otherwise seem nuts, then they're going to have a hard time convincing me.  In particular, they probably act as though they do believe that things around them are real, which seems to betray their true feelings on the subject:

[lame attempt at humor]
Dude-at-bar: I don't think all this stuff that we think we see around us, that we think exists, actually like, exists, man.
SteveS:  Really?  <chucks beer mug at Dude's face>
Dude-at-bar: <dodges beer mug>  What the hell, man?
SteveS: Hah!  Liar.....
[/lame attempt at humor]

This is why science is so powerfully convincing to people - because they all (minus the nutters) accept this axiom that "reality is real".  But, it's not the only reason.  Also:

2) Science embraces the validity of logic.

Look at this statement, for example:

You can perform an experiment and determine whether the results are consistent with the statement. If they aren't and the experiment was performed correctly then that indicates the statement is false.

I agree, of course, but why does this indicate the statement is false?  Because of logic.  This is what I mean about accepting the "Law of Non-Contradiction".  If the results contradicted your statement (i.e. are inconsistent with it), why would this bother you or motivate you to conclude anything at all if you didn't accept the capability of logic to prove something?  So, even though you can use empirical demonstration to prove something, you can only do so by accepting that empirical demonstration requires the validity of logic.

You just aren't usually calling it out explicitly.  This is probably the part you feel is trivial.  Trivial, or so deeply ingrained in our minds that we don't normally take note of how frequently and to what extent we rely on it?  Either way - it doesn't seem that there's very much substantive disagreement between us.

Cheers,
Steve

[AlP]

Stave, I agree with everything you said in your last post. I apologize for my sloppy language regarding proof versus disproof. Unfortunately I do it all the time I did not reply to your initial post because I disagreed with you. I replied because I thought the case for reason needed some clarification. You said your language was preachy. I personally think I should be careful to be clear about the meaning and applicability of things such as propositional logic and the scientific method, which really shouldn't need to be argued in our circle. IMHO, there is already too much confusion in the world in this regard. On the other hand, there are plenty of areas in secularism where I am quite unclear. These are the things I want to talk about.

[Ninaa]

This is an interesting subject!

I'm new here, and I would like to share my story with you

[SteveS]

Hey AlP - I'm with you man.

[athiest12]

logic alone cannot prove anthing. logic can help but most often it only brings about confusion. loic can seek to prove anything but it needs reason to prove it. reason doesn't need to seek it only resolves

[Recusant]

I'm new here, and I would like to share my story with you.   there is a place here for that very purpose.  I look forward to seeing your post in "Introductions."  Until then, may I be the first to say welcome to HAF, Ninaa.

[SteveS]

Sorry, atheist12, but I'm not getting any of your comment.

logic can help but most often it only brings about confusion.

Would you suggest that behaving or arguing illogically would somehow be less confusing?

loic can seek to prove anything but it needs reason to prove it. reason doesn't need to seek it only resolves

What, if anything, is the meaningful difference between logic and reason?

Consider a typical dictionary definition of reason: http://dictionary.reference.com/browse/reason.
Note in particular things like the following:

to think or argue in a logical manner.
to form conclusions, judgments, or inferences from facts or premises.

Reason is thinking in accord with logic.  Using logic to guide your thinking.  Not relying on something else like faith, emotion, feeling or intuition.  You can't advocate for reason if you're going to toss logic out the window.....