Can anyone prove that logic is correct?

Decartes' meditations were based in the idea that if you can doubt something, it cannot be absolutly true. I doubt that anything, including myself really exist. So what makes logic more correct than faith? And isn't saying that "God does not exist because it is not logical" really just showing faith in the system of logic?

In a way yes. It illustrates the paradoxal view that logic is the end all be all by means of it simply being the end all be all.

I doubt that anything, including myself really exist
Hence: cogito ergo sum. keep working :D
Although, go far enough and you turn solipsist. But why am I telling a figment of my imagination? I already know this.

yeah, except that I don't think cogito ergo sum really works. Descartes' says he can doubt everything except that he is thinking. I seem to think that he should have doubted that as well. If you can doubt everything else, then why can't you doubt that it is actually you thinking, not some external force.

If he couldn't doubt he was thinking, he wasn't thinking hard enough. Or maybe he didn't know enough physics and chemistry to realise that 'thinking' is just patterns in the slush between your ears.

I seem to think that he should have doubted that as well. If you can doubt everything else, then why can't you doubt that it is actually you thinking, not some external force.
The "I" is that which was doing the thinking, not necessarily himself. But since that "I" was asking about Descartes himself then.... So something is thinking in what I think is my head? Okay, I'll invent another something (without any evidence) to describe what it is that actually is doing the thinking in my head. I don't perceive myself thinking in anyone else's head therefore the "I" must be me.
If he couldn't doubt he was thinking, he wasn't thinking hard enough. Or maybe he didn't know enough physics and chemistry to realise that 'thinking' is just patterns in the slush between your ears.
So what? There's still something thinking and/ or doubting. Doubting that you're thinking is a fairly good demonstration that something is going on.

If he couldn't doubt he was thinking, he wasn't thinking hard enough. Or maybe he didn't know enough physics and chemistry to realise that 'thinking' is just patterns in the slush between your ears.

What if these "physics" are just manifestations in my mind? Or your mind? There is not really a universe out there?

All humans know is what is experienced with our senses. Which begs the question... "what is knowledge?"

What if these "physics" are just manifestations in my mind? Or your mind?
So if physics is a manifestation of, say, my mind, then my mind is controlling the universe since you will get the same results as I do if you perform an experiment the way I tell you. Is that easier to accept - that you're also a manifestation of my mind?
The "fact" that physics gives the same answer to the same question no matter who asks it argues that it has an independant existence, or at least that the results/ subject of the experiment do, and that physics is a valid method of asking questions.

Well it could be some outside "being" is what creates this world in our minds, so it is nothing physical.

I guess the best way to see this is to "step outside" the universe and your own existance and just observe it. See the larger picture and you will soon just confuse yourself like I do.

It could be an external being, but Occam says probably not. And there's no actual evidence, especially for it creating worlds in our minds. You'd have to show that that could be done.
I guess the best way to see this is to "step outside" the universe and your own existance and just observe it.
Any suggestions on how to do that? Other than, say, 15 pints of Guinness (and my handwriting for taking objective notes gets a bit wobbly somewhere around the tenth...) :D

It couldAny suggestions on how to do that? Other than, say, 15 pints of Guinness (and my handwriting for taking objective notes gets a bit wobbly somewhere around the tenth...) :D

I have actually wrote a paper in my freshman English class trying to explain how to do that. Although I got an A on it, I still feel it was a failed attempt.

I guess the best I can do is this: if you can "see" and "sense" four spatial dimensions, then you are half way there :eek:

I guess the best I can do is this: if you can "see" and "sense" four spatial dimensions, then you are half way there
There was (apparently) a Brit mathematician (possibly E A Abbott - the author of Flatland, but I could be mistaken) who was able to hold images in his head of five, six etc. up to 11 (IIRC) dimensional constructs.
Although how he proved this I'm not sure.
And I haven't read anything on what (if any) insights that ability gave him to discern the existence of external beings... but the book was fun.

If you can doubt everything else, then why can't you doubt that it is actually you thinking, not some external force.

Because God wouldn't do that to you.
That was Descartes' Ace in the hole.

You did know that his meditations were not about proving the self or any such nonsense. It was about proving the existence of God. Yes?

There was (apparently) a Brit mathematician (possibly E A Abbott - the author of Flatland, but I could be mistaken) who was able to hold images in his head of five, six etc. up to 11 (IIRC) dimensional constructs.
Although how he proved this I'm not sure.
And I haven't read anything on what (if any) insights that ability gave him to discern the existence of external beings... but the book was fun.

The only way I can think of how he could do this was view, say a 4D object, on C(4,3) = 4 seperate 3-dimensional spaces. That is, if 4D has these axis: w, x, y, z, then he viewed them as 4 seperate 3D creations. Then, when he got the sense of those, manipulate them.

At least, that is how I would do it if I had to.

If you do not exist then what does your logic matter? Your using non existant logic, thus you can't really say you can't exist if you can't prove you can't exist, and if you don't exist what you say doesn't matter becuz you DO NOT exist.

If you do not exist then what does your logic matter? Your using non existant logic, thus you can't really say you can't exist if you can't prove you can't exist, and if you don't exist what you say doesn't matter becuz you DO NOT exist.

Well it seems that something exists... and SOMETHING uses "logic" to deduce "knowledge." And so far this "knowledge" is consistant with whatever it is that this "something" is experiencing.

Make sense? None at all to me :bugeye:

Well it seems that something exists... and SOMETHING uses "logic" to deduce "knowledge." And so far this "knowledge" is consistant with whatever it is that this "something" is experiencing.

Make sense? None at all to me :bugeye:Me neither, it's a cycle. Now you can see why I have this avatar. contemplating ideas on cycles is great. There's just no way around it lol.

Well I do not think it is really a cycle. You have something that creates "reality," in whatever sense it might be in. Then you create things that "experience" it.

It is a cycle though, think about it.

You do not exist, therefor your logic means nothing, therefor that means nothing becuz that's logic based on something that doesn't exist.

I think it's a cycle.

That's why I think you can't exactly say... "I can't exist". If you didn't exist, then you wouldn't know it, becuz you thus don't exist and can't form any opinion.

However, there's reason to deduce to say that you can't prove anyone else... exists.

Can anyone prove that logic is correct?

In so far as logic is a system, a set of rules it may of course be claimed that a propostion sticks to the rules.

Doubt is another matter, it being logical enough to propose that no logical statement is ever more true than a premise it depends upon.

That statement depends for instance upon the premise of truth ......... etc. ad infinitum.

--- Ron.

Can anyone prove that logic is correct?

Proof will require premises that must be true. Then you have to have to draw a conclusion (logic is correct). It seems to me you got to use logic to prove logic. In this case, no. It was shown by Godel, I think, that proving axioms and anything else about how a system works by using THAT SAME system is impossible.

And the first proof is that something (Descartes' "I") is thinking. If it did not exist it would not be able to think...
As for proofs for other things, isn't Euclidian geometry based on axioms rather than "proven" bases? But it is self-consistent and it works. That is why it is accepted.

And the first proof is that something (Descartes' "I") is thinking. If it did not exist it would not be able to think...

Until recently, I actually bought this "I am" statement. I am starting to see something more significant behind it all, yet I cannot get a finger on it.

As for proofs for other things, isn't Euclidian geometry based on axioms rather than "proven" bases? But it is self-consistent and it works. That is why it is accepted.

Well ALL math is based on a set of axioms. The thing is, the axioms need to be pretty damn obvious. Second, the proof would the current axioms is impossible by humans. If we find a proof for an axiom, than it is no longer an axiom. If we build math up so much in the next thousand years, for example, and we finally find a contradiction, and all the logic is consistant throughout, then it will mean an axiom contradicts another... and we need to do something about it.

0 != 1 is an axiom. Try to prove it.

Equality is more of a definition than an axiom, but I suppose you could call it an axiom.

Until recently, I actually bought this "I am" statement. I am starting to see something more significant behind it all, yet I cannot get a finger on it.
Breakthrough or breakdown coming up. Keep us informed.
0 != 1 is an axiom. Try to prove it.
Using calculator on "real numbers" setting, yep, it's 1. On "surreal numbers" it just says "fish". Close enough for me. :D
Slightly more seriously
It was shown by Godel, I think, that proving axioms and anything else about how a system works by using THAT SAME system is impossible.
I thought he'd shown that you can't prove that ALL of that sytem is true, which isn't QUITE as bad (although that probably includes the axioms). Bugger, now I've got to go off and read some more books.
But I think it comes back to being self-consistent and that the system does work. Which is why geometry (non-euclidean) and non-base 10 maths is used/ useful. Maybe there's an underlying system that we haven't found yet...

Breakthrough or breakdown coming up. Keep us informed.

I am a god ;)

Using calculator on "real numbers" setting, yep, it's 1. On "surreal numbers" it just says "fish". Close enough for me. :D
Slightly more seriously

I mean, you can show what happens when you let 1 = 0, (it's not hard to show that the real numbers collapse to {0}.) but that isn't proof.

I thought he'd shown that you can't prove that ALL of that sytem is true, which isn't QUITE as bad (although that probably includes the axioms). Bugger, now I've got to go off and read some more books.
But I think it comes back to being self-consistent and that the system does work. Which is why geometry (non-euclidean) and non-base 10 maths is used/ useful. Maybe there's an underlying system that we haven't found yet...

"Informally, Gödel's incompleteness theorem states that all consistent axiomatic formulations of number theory include undecidable propositions (Hofstadter 1989). This is sometimes called Gödel's first incompleteness theorem, and answers in the negative Hilbert's problem asking whether mathematics is "complete" (in the sense that every statement in the language of number theory can be either proved or disproved). Formally, Gödel's theorem states, "To every omega-consistent recursive class kappa of formulas, there correspond recursive class-signs r such that neither (v Gen r) nor Neg(v Gen r) belongs to Flg(kappa), where v is the free variable of r" (Gödel 1931)."

Taken from here (http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html) .

I am a god
I believe you. But prove it to ME.
Okay I read the link, and I suddenly remembered why I'm an engineer not a mathematician :D
I think I get the gist, and I'm bloody sure I'm going to have to read more so that it means something to me. (Other than, oh shit we're fucked from the start, but stated much more rigorously).
And I have a nasty feeling I'm going to not stop reading... bollocks, more books to buy just after the job finishes. :(
Can I join you in your (presumably correct) illusion that you're god? Maybe we could take it in turns?
Roughly speaking then, all the maths I know could be a lie? If the answer is yes then I'll forward details of my bank account so you can make regular payments to keep yourself informed of things I've designed, for you to avoid in case the calculations behind them suddenly become invalid. :D

No, I said I am A god, not the God. Perhaps I mean I am a god of my own creations. Perhaps we all are.

I used to want to be an aerospace engineer when I was deeply into rocketry. The math involved in rocketry was far more interesting to me than the actual product of the math.

Perhaps you will help me with the 3x+1 problem? Maybe we can prove P=NP by solving the traveling sales man problem? :D

No, I said I am A god, not the God. Perhaps I mean I am a god of my own creations. Perhaps we all are.
Oh, that. Yep. But certain figments of my imagination get stroppy when I inform of that. Unfortunately we also seem to be limited (or at least limited when compared with what my idea of a god should capable of...)
I used to want to be an aerospace engineer
As did I, but I got suckered on my apprenticeship scheme and ended up working for a subsidiary that made diesel engines for hospitals... not quite the cutting edge of aerospace technology I was hoping for. :mad: (OTOH I'm off to Duxford on Sunday to photgraph the newly-refurbished TSR.2 - heaven).
Perhaps you will help me with the 3x+1 problem? Maybe we can prove P=NP by solving the traveling sales man problem?
Gimme pointers as to what it is first :D I'm game for just about anything I can get my teeth into and don't mind reading to catch up.
Off to bed now, had a veeery long week. Catch you later.

Ponder this:

If logic is sophomoric, then this statement does not make sense.

I suppose there is no way to say whether or not that statement does make sense.

First off, the original question "Can anyone prove that logic is correct?" is, as defined (or not defined rather...) a category mistake. There seems to be in this question, some sort of assumption that 'logic' has an 'absolute' or 'innate' ontological status. Clarification of the term"correct" would help greatly here.


Proof will require premises that must be true. Then you have to have to draw a conclusion (logic is correct). ...

Not quite. This would mean that the argument satisfies validity , not proof.



...
It seems to me you got to use logic to prove logic. In this case, no. It was shown by Godel, I think, that proving axioms and anything else about how a system works by using THAT SAME system is impossible.

Exactly. As I noted above, the original question falls into a category mistake fallacy. Now, if we had clarification on the terms "logic" and "correct", then we might be able to move on, perhaps into a more linguistic approach.

Q. Is logic absolutely true

A. Doesn't matter. Experience shows us it works in many, many areas. It is a valuable way to analyse. That's all that matters, in the end.

The infalliability of logic can be found in two things:

1. All arguments against logic presume the validity of logic in presenting an argument. I.E. "What proof of logic is there?" implies consistancy and a lack of contradiction and the absurd. In essence: It implies logic.

2. The negation of logical laws presents us with absurdities. For instance, in order for something to violate the law of identity, one would have to say it ceases to be itself, in which case, you would be left with nothing. To go against and to say that A != A implies that one never is speaking of A to begin with. Similarly, if A = B and B is in absolute contradiction to A, then what are we left with? Something which so clashes as to not be able to exist. Consider, for instance, that a square cannot be a circle in the same way and at the same time, for in order to be one or the other, one must be opposed in practically all ways to the other, and therefore stating that they could be would deny that either has the necessary qualities to be themselves.

Logic's rules do not apply simply because, as Tyler has affirmed, they are of great utility, but to think of them as not holding true in all cases, would be to proclaim what is manifestly false.

Yeah, more or less what James said.
'Logic' is a tricky word to use for what we're talking about. Do we mean the symbols (^, v, =, <->, ->) and their functional purposes? Or do we mean some over-arching structure of the universe?

I think the fact that both questions can be asked makes it confusing for us. Under the first light, logic seems to be nothing more than a language system that happens to hold in all forseeable occurences. Under the second we dive deeper into the "nature of the universe" to ask if the structure we're use to always holds.

I think breaking it down into these two questions makes it much simpler.

1) Yes logic as a system holds. By definition (like James said) because 'holds' calls into play logical structure.

2) Is the universe always in consistency with logical structure? Is it the case that ((A->B) ^ (B->C)) -> (A->C) will be true in all the great expanse of existence? For this question I think we may need to just make a big ol' shrug of the shoulders and accept that we don't know. Keep in mind that logic makes perfect sense to us because in our observable universe it always, always works. Who knows what the universe has in store for us; there could be existence where A != A and yet A is. Before someone makes the obvious response of 'How, dumbass?' keep in mind that our language reflects the impossibility of observing such a phenomenon. Perhaps our minds do to.

Then again, I could of summed up all of that with "who knows?"

Can anyone prove that logic is correct?

Decartes' meditations were based in the idea that if you can doubt something, it cannot be absolutly true. Yeah but it is possible to doubt something that is in fact true.

Yeah but it is possible to doubt something that is in fact true.

This would lead to a contradiction at some point... if you build a system from doubting what is absolutly true. Could we recognize it? Maybe not.

This would lead to a contradiction at some point

Nope. A contradiction is to hold as true two things which cannot be true at the same time.

Ex.
a = T (true)

Bx = I believe x
Dx = I believe there is reason to doubt x

The contradiction would be Ba ^ B~a
There is no necessary contradiction otherwise.

But I mean... if you doubt something, we can take its negation as true. So, we do that. We build a system (much like you do in math) with these negatated statements. At some point, something should contradict what we see that follows and what it says follows. Like if we some how derived an evtire system that, in the end, says nothing exists in any form.. well we know that is false. How could we doubt that fact?

Well, for one I disagree on your meaning of the word doubt. To doubt - in my mind - simply means you suspend assigning a truth-value.

In fact, a 'belief system' built on Cartesian doubt would (traditionally) look something like this:

Class A = {the proposition that I exist)
Class B = {the propositions derived from the laws of logic which describe natural existence}
Class C = {observable phenomenon}

Yes there are many problems with this. For instance, the natural laws (mathematical laws) cannot be derived from logic. But that wasn't found out for many years after Descartes.

Tyler:

Are you here presenting a viewpoint that "natural laws" - I.E. the forces of nature, the laws of thermodynamics, et cetera - are "mathematical laws" in nature? That is, that we could intuit them from mathematics? Or are you saying that natural laws can be expressed as equations? For if the former, I must point out that you are slipping from your former appreciation of empirical analysis, as opposed to "metaphysical" speculation.

No, what I meant to imply is that natural law invokes or expresses or contains... (depending on which philosopher you are, choose your word) the mathematical laws.

Tyler:

In that the phenomena are generally reducible to mathematical equations describing in part their properties?

This would lead to a contradiction at some point... if you build a system from doubting what is absolutly true. Could we recognize it? Maybe not. I'm not writing that one should doubt what is true, rather that one could doubt what is true. I would argue that one could initially doubt the truth only to discover, through logical reasoning, that the doubt is in fact false, and the truth is in fact true; the truth can be found through doubt.

Can anyone prove that logic is correct?

Decartes' meditations were based in the idea that if you can doubt something, it cannot be absolutly true. I doubt that anything, including myself really exist. So what makes logic more correct than faith? And isn't saying that "God does not exist because it is not logical" really just showing faith in the system of logic?
‘Logic’ is a term denoting a manner of thinking based on the repetitive consistency of perceived phenomena.

Nope.
You could make a much stronger argument that logic is actually a system of analysis (the system of analysis) which is reflective or derived from our language.

Now, it's value may be in the repetitive consistency of perceived phenomena.

Reflective or derived from what language? Human thinking as a language or language as in Latin (for example)? In either case I would say that language developed with the help of a set of rules (which we call logic) being consistant. Not that we made up logic, with the help of language, to make sense of cause and effect. It always "was." We just gave it a name and constructed the rules out of language to help deal with it. We say "A causes B" because it is much easier than just ignoring it and hoping that everyone else is "on the same page."

Or I am missing your point...?

Reflective or derived from what language? Human thinking as a language or language as in Latin (for example)? In either case I would say that language developed with the help of a set of rules (which we call logic) being consistant. Not that we made up logic, with the help of language, to make sense of cause and effect. It always "was." We just gave it a name and constructed the rules out of language to help deal with it. We say "A causes B" because it is much easier than just ignoring it and hoping that everyone else is "on the same page."

Or I am missing your point...?

Interesting thoughts.
I would argue that, for the most part, language developed without a complete set of rules. Over time of course, the rule set was refined and completed.
Further, I would also argue that we indeed did 'make up' logic: an extracted symbolic system of analysis, derived from empirical data.
And causality is a pretty tough example to work with; given that implication is the weakest of all inductive rules, it would be much better to pick another to argue.