Way of the Mind Forum

I was wondering, do we have any reason other then "faith" that logic works? David Hume showed with the Problem of Induction that the inductive properties of logic had no rational basis, and we cannot prove the deductive properties of logic (and if we could prove it, we would prove it using logic, which would beg the question).


So is the belief that logic works simply an axiom we choose to go by which is not actually proven (or provable)?

No because logic works by not assuming anything unless it has previously been proven, logic states that 2 + 2 = 4, this is true it cannot be refuted unless you screw with the argument by changing definitions, which devoids the argument entirely.
The reason I KNOW that is true is because I can prove it is if I take pencils and add another two it will equal four.
You cannot simply state I have FAITH in logic because the very definition of faith is blind belief, belief without evidence, however logic works in all situations.

But what you are doing is using logic to prove logic. You say "2+2=4" then prove it by using induction (since 2 plus two always seems to equal 4, it must ALWAYS equal 4).

But there is the Problem of Induction, being that it is circular and therefore has no rational basis.

2+2 always =4. unless it's 1984.

Why is two plus two always four? It is an a priori logical truth, right? But if we denied the existence of logic, wouldn't two plus two equaling five be just as likely? Or ten? 100? A fish?

You assume logic holds in that statement, then use that assumption to show that logic must be true. It begs the question. "Since logic must always work, therefore logic must always work!"

sorry i couldn't respond sooner.... the damn logic circuits of my computer kept saying that since i had no faith in them, they didn't exist.

Just because you don't have faith in something doesn't mean it ceases to exist. That implies we like in a subjective universe that is controlled by your beliefs.

I hope you know that is not the case.

yeah i know.... just making a (bad) joke.

Okay, sorry lol. I'm new to this forum, as you can tell.

Well, (and sorry to jump in.) Only by throwing away the definition of 2 and + are you going to get FISH.

The begging the question thing doesn't work, because in any kind of language, even hand gestures, people have to agree (assume) that they are speaking of the same thing. If nobody agrees to the same language, in this case math, no conclusion could be possible, nor any real argument, or statement for that matter.

Humans rely on each other to understand, sympathize, communicate.
This isn't a stranger in nature: some birds need to SEE another bird in order to reproduce.

So, two plus two is always four because we agree (within the english language and blah blah blah.) that the definition of 1+1+1+1, or two pair, or 3+1 is called FOUR.

You can call it faith, sure... but it's still the general obliging that words mean what words mean.

Okay, even if we do concede that a priori truths are necessary, the majority of what we use is a posteriori. Does this not at least require faith?

It isn't. Logic is not only based on rules that allow us to come to conclusions in a verifiable manner, but also on the assumptions that we make. We can have a logically correct argument, but still have an invalid conclusion if the assumptions are wrong.

As for 2+2, that can equal 1 if you are working in a system modulos 3. Or, 2+2=1 (mod 3).

does anyone find it funny/ironic that we are using logic to defend logic?

That is the problem...logic would then be necessarily circular, and that is a logical fallacy in itself.


So is faith all that's left?

Actually, for a physicist, 2+2 = 5, given large enough values of 2.

Sorry, this my first post here. Hello all.

2 is a value.

2.3 is also a value, albeit with two apparent significant figures.
Hence the 2+2=5 thing.

It is to grin, not argue.

Throw out the whole 2+2=4 thing for a moment. Just think of this:

We believe the only way to prove something is via logic (use of evidence of course stems from the inductive properties of logic).

Now, if we wanted to prove logic works, what else could we use BESIDES logic? Do we have to resort to wishful thinking? To faith? Because if we do use logic to prove logic, this begs the question and is no different than using the Bible to prove God.

So why is the use of logic not based on faith as is the belief in the Bible? Do we not all resort to wishful thinking as the basis of our world view?

Because logical proofs can be refuted.

Natureie,

A proof is .. PROOF. In the very essence of the word PROOF it means that it CANNOT be refuted. Even in saying "Logical proofs" we just complicate it... I don't know of any proofs that AREN'T logical.

Esaul7, I think I understand the point that using logic to determine logic is itself a logical fallacy.


You say:

"We believe the only way to prove something is via logic (use of evidence of course stems from the inductive properties of logic).

Now, if we wanted to prove logic works, what else could we use BESIDES logic? Do we have to resort to wishful thinking? To faith? Because if we do use logic to prove logic, this begs the question and is no different than using the Bible to prove God.

So why is the use of logic not based on faith as is the belief in the Bible? Do we not all resort to wishful thinking as the basis of our world view?"


Which is very interesting, in the fact that your refutation against logic is logically correct. How could someone possibly use logic as a proof of logic?!

Well, it's because logic is all that there is to prove ANYTHING.

And it's all that we actually have to go by when it comes to ANYTHING in our daily lives. When it boils down to it, logic is the only thing that we CAN prove anything by. So yes, logic is used to prove logic. It's an exception to using the bible to prove the bible because logic, is proven (and has proven many things) as the bible is faith.. and has proven nothing. But using Logic we can do the whole 2+2=4 thing... and BUILD and BUILD and BUILD and as long as we keep to those specifics... we'll NEVER be wrong.

Well, this is the problem I have.

First, you never seemed to disagree that we had faith in logic. You, instead, just seemed to say we had faith in logic because we don't have anything better. To me that seems similar to saying it was okay to be a creationist until evolution was discovered. I would, however, praise Hume for thinking along the lines of: I do not know anything better, but I can still see why the creationist hypothesis is wrong.

Secondly, addressing a priori truths such as "2+2=4". These may be true, I do not wish to argue against their validity. But my complaint is instead that they do not so much appear to be using logic so much as simply taking a different viewpoint of the same "entity". For instance, if I look at a table from above I may see a simply circle, but looking at it from the side, I notice 4 table legs, and the circle seems to have vanished (appearing only as a horizontal rectangle when viewed head-on). But I am not exercising logic here, but simply changing how I look at things. Furthermore, I could even take apart the table and see it consists of one circular disc, and four cylinder-shaped legs. Again, I am not really invoking logic, but simply noting the make-up of table. Now, apply this to math. When I can look at the number 27, I could imagine it in different ways. Using a base-6 system I would see it as 43. In a base 5 system it would be 47. Also, sticking to base 10 however, 27 is still 3*9, 10+17, 54/2, etc. 4 is of course 2+2, amongst other things. All math I believe is reduced to this, along with all other a priori truths. This is not really even logic, they are tautologies.

Logic comes in with matters of fact, a posteriori, whose validity requires outside evidence, not just our mental faculties allowing us to dissect what we have created. In this category, science, as well as common sense and most day to day rational thought, lie. However, going back to Hume, the Problem of Induction (ask if you don't know of it) clearly shows that we have no rational basis for these matters of fact- no rational basis for induction.

After realizing all of this, I am really asking why faith is any worse then logic (or at least logic which is not a priori, if you wish to continue to believe these statements as actually using logic, and not just different ways of saying the same thing). It appears some of us take on a faith in logic, and others in God. Why is the former and better then the latter?

Ok, I looked up Inductive Reasoning... but I honestly don't REALLY understand it.
Either way, I am very inclined to answer THIS question:

It appears some of us take on a faith in logic, and others in God. Why is the former and better then the latter?

Because God will never hold any decidable answer.
Logic always works. (And maybe the 2+2=4 thing is a bit too simple, but in Algebra you use logic to deduce the answer.)
If a logical answer changes, that means that the things involved have changed.

Even the idea of Induction was brought upon by using logic.
You can't ask God how this, or that happened, you have to use logic, or ask someone who already has used logic to determine it.

It makes nobody the better person, because even people who have faith in God can be great people. But being a good person never makes you correct in anything.

Here is the problem, Kren. You are saying "since logic gives results, it must be the right thing to use". But that itself is using logic to reach that conclusion. If you didn't use logic, you would have no idea that something that gives right results is the right thing to use.

Also, with faith, you can read the Bible or something and take it as literal fact without logic based on pure faith.

I COULD take things I read from the bible as literal fact without using logic based on pure faith. But it would still make me WRONG.

You are correct though in stating:

"If you didn't use logic, you would have no idea that something that gives right results is the right thing to use."

...perhaps you have a better idea?

I could take logic to be perfect truth based on faith...how does that make me right. It only seems right because we already defined truth as stemming from logic. If one defined truth as from the Bible then the Bible would magically appear to be infallible and always right as well.

No, I unfortunately don't. But think, was the argument from creation sound before Darwin and evolution? No, we should have just admitted we don't know instead of creating a false entity and declaring it as infallible and the cause of all. One might argue we have created logic, said it infallible, and the source of all truth. How could we refute this?

Also, just a brief break down on inductive reason because you said you had a hard time coming to grips with it.

Imagine you and a group of 10 friends are stranded on an island. You find a tree with fruit. On of your friends eats the fruit, and dies in extremely painful ways. The second does the same, with the same result. So with the third, fourth, fifth...all the way to the ninth. You may come to reason that you should not eat this fruit, because this fruit will cause you to die in most unpleasant ways. This is not a deductive statement though (actually you you induction to go from the observations to conclude the fruit will kill you, then deduction to decide that since it will kill you you shouldn't eat it).

The Problem of Induction is that it is circular. The justification for induction working is that we've seen it works millions of times before in our lives. This is saying since induction worked before, it obviously isn't just going to stop. However, without induction, we cannot apply past results to the future at all. So this justification relies on the assumption of induction being valid, using it to prove itself. This obviously begs the question and is fallacious.

David Hume, who thought of this problem, decided that there was no rational basis for induction, but we should still use it (just for the record, Hume was an open atheist). This appears to me to be faith based.

Hey esaul7, sorry I've been away.

First and foremost:

"One might argue we have created logic, said it infallible, and the source of all truth. How could we refute this?"

This is basically a ploy (IMO) to get me to answer a question with no answer, and put my foot in my mouth.

You can only TRY to refute truth. There IS NO REFUTE TO TRUTH. Logic is USING truth to determine an unknown truth. (You basically said so yourself with your "2+2=4" isn't logic ... yet, refutation)

Probably the most interesting position I've come across though, with the induction thing.
I'm like, so regular when it comes to education and stuff, so like, tone it down a bit?

Nah, let me step up a bit, if I can't I'll just say so.

Whoa, I definitely learned something today.
So INDUCTION says, "this fruit will kill you", and DEDUCTION says "Don't eat the fruit, it will kill you."
I didn't know people were SO stupid, they needed someone to tell them that jumping off of a building kills them (induction) so they shouldn't do it (deduction). I would say both are forms of logic, one is just undercutting the obvious (when it comes to people who wish to live).

A few moments to let my brain recover from the seizure...

Sorry, I had no idea of this.

Okay, so my question is this:
Is deduction only something pertaining to safety?

Because someone could do the same thing in cooking.
Yeast makes bread raise faster... 10 times out of 10 times.
Using yeast when making bread makes the bread rise faster, (induction) so if you WANT faster rising bread, use yeast (Deduction).

So induction says what obviously already happened, and deduction says what WILL happen if you do the same?

How did I do?

If I get this right, then I disagree with David Hume. (All due respect of course)
Saying what definitely happened, happened, or what definitely is, IS, is rational. (Again, please correct any of my wrongs.)
The fact that he evidently states that we should use it, is evidence that he himself thought it WAS rational. Why would he say that then? It's not rational but we should still use it?! Hell, now I'm going to the nearest fortune teller.

OF COURSE that statement is faith based. There's no REASON in it.
He believes that we should just use something... without any reason. The very DEFINITION of faith.

Yet the REASON is obvious, it's LOGICAL that the same thing happening in the same circumstances will happen again. Thinking that a different result will happen while doing the same thing in the same circumstances is the DEFINITION OF INSANITY.


AAAAND I go back to the first question you asked:



"I could take logic to be perfect truth based on faith...how does that make me right."

Fortunately for people like me and many others, we can start logic using damn near anything. If I drop a plate made of clay from 10 feet and it breaks, logic tells me the next plate made of clay, dropped at the same hight or higher will also break. Then we can calculate distance from the ground, gravitation pull, terminal velocity, blah blah blah, and find out when the plate will be whole.

As long as we've got all of the calculations correct we would NOT BE WRONG.
That's the catch right there... FAITH has no logic, you can't tell what's GOING to happen, yet logic can tell you what's going to happen, and EXACTLY what's going to happen, unless you missed something.

Yes, you CAN take logic basd on faith, but there's no need to. You yourself can take logic as things you know to be true to determine other things to be true and as long as you keep things TRUE you'll be...



RIGHT.

Okay Kren. First, Induction is going from many example to predict the outcome. Deduction is then using the prediction to get the desired outcome, as far as I know. Induction is based on the past and deduction strives towards the future. Your example with the yeast was correct. But we would have to have tested yeast many times to inductively conclude it makes bread rice faster of course. Inductive claims are made based on experience and experimentation. Scientific laws revolve around inductive reasoning, then technology benefits from this using deduction.

"Saying what definitely happened, happened, or what definitely is, IS, is rational. (Again, please correct any of my wrongs.)"

Hume does agrees what happened, happened. He asks how do we know it will happen in the future? He agrees yeast sped up the rising of bread the first 100 times, but what about time number 101? Hume disagrees with going from the statement "yeast has always made bread rise faster" to "yeast will always make bread rise faster".

Now, Hume seems to see induction as working and thinks we should use it, but he cannot see any rational way for it to prove it true.

"Yet the REASON is obvious, it's LOGICAL that the same thing happening in the same circumstances will happen again. Thinking that a different result will happen while doing the same thing in the same circumstances is the DEFINITION OF INSANITY."

You say the reason is obvious, but you need to tell me why it is so obvious. We can play around with words and throw in "insanity" but you have to give an actual argument as to why things in the future will behave as they did in the past. The only reason we think they will is because they always have before- and that is circular.

"Yes, you CAN take logic basd on faith, but there's no need to. You yourself can take logic as things you know to be true to determine other things to be true and as long as you keep things TRUE you'll be..."

You see, the problem is you are using induction here. "Logic has always worked before, so it will work now!" This is an inductive statement. You cannot prove induction with induction...that is circular.

Hi again Esaul.

"
Okay Kren. First, Induction is going from many example to predict the outcome. Deduction is then using the prediction to get the desired outcome, as far as I know. Induction is based on the past and deduction strives towards the future."

It seems to me that you can deduce something that happened... in the past.
So I'm going to forfeit any argument about the definition of the two, because if we have different view of those words we could never come to a conclusion about such a thing.

"You cannot prove induction with induction...that is circular."
And you can't prove logic with logic, that's circular too.
What about this though, can you prove faith with faith? How about Logic with faith? Anything?

You can't prove anything with faith.
Logic however proves lots of things... you can argue continually that you can't prove logic with logic, but it proves SOME things... and faith proves NOthing.

I can almost hear a retort already though. Something like "If you can't prove logic with other things, or itself, than you are just using faith to prove logic, or logic is unprovable, unless we use circular reasoning, IE: logic."

Well let's throw away the words, "logic, and induction and deduction" and just use the word Truth.
What do you prove Truth with?
If you use a method to prove Truth, that works, why would you use another method? I for one would try to use the method that proves Truth more than any other method, if I was looking for the Truth.
If you had one thing that was true, and another thing that was true, and you used both of those to find out that something ELSE was ALSO true, you are using circular logic, but does that make the outcome untrue?

esaul7... i kind of think that you did this just to piss us off because we have to use logic to prove logic... and you have to use logic to prove that we have faith in it. circular logic......... drives me nuts!

(just kidding about the pissing off part)