Why I am Not an Atheist

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Macbi
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Postby Macbi » Mon Apr 09, 2007 9:07 pm UTC

space_raptor wrote:I doubt they'd take an interest in humans. Maybe to the point where they'd create a planet with certain conditions, but I doubt they'd be interested in the activities of some tiny animals on it.

I think they might, like humans enjoy Conway's Game of Life etc.

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Postby LE4dGOLEM » Mon Apr 09, 2007 9:24 pm UTC

Macbi wrote:
space_raptor wrote:I doubt they'd take an interest in humans. Maybe to the point where they'd create a planet with certain conditions, but I doubt they'd be interested in the activities of some tiny animals on it.

I think they might, like humans enjoy Conway's Game of Life etc.


The one with the cells and the lonliness||overpopulation death and the 3-neighbor newlife thing? That's fun!
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Postby Pathway » Tue Apr 10, 2007 2:24 am UTC

What?

ArmonSore wrote:I am well aware that I cannot justify the claim that we are the greatest. And of course it's possible that someone has already gotten to the place that we're going to. But here's the punchline: I happen to think that we are unique. Only human beings can discover the secrets of the universe.

This is my opinion, nothing more. It cannot be argued.


That's the stupidest thing I've ever heard. If you can't justify it you have no business trying to make any sort of point with it as one of your premises. Just because you think that way and say it's not arguable doesn't mean you can expect an argument using that idea to be accepted as meaningful.

Macbi wrote:
space_raptor wrote:I doubt they'd take an interest in humans. Maybe to the point where they'd create a planet with certain conditions, but I doubt they'd be interested in the activities of some tiny animals on it.

I think they might, like humans enjoy Conway's Game of Life etc.


Oh dear. Whenever I play Conway's Game, I always clear the board after a sufficient period of time. :(

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Postby ArmonSore » Tue Apr 10, 2007 3:04 am UTC

Pathway wrote:That's the stupidest thing I've ever heard. If you can't justify it you have no business trying to make any sort of point with it as one of your premises. Just because you think that way and say it's not arguable doesn't mean you can expect an argument using that idea to be accepted as meaningful.


You point out the argument that I gave using my opinions and I'll actually respond to your statement. As far as I can tell, I only stated my opinion. I didn't make any arguments based on those opinions.
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Postby Macbi » Tue Apr 10, 2007 8:53 am UTC

ArmonSore wrote:
Pathway wrote:That's the stupidest thing I've ever heard. If you can't justify it you have no business trying to make any sort of point with it as one of your premises. Just because you think that way and say it's not arguable doesn't mean you can expect an argument using that idea to be accepted as meaningful.


You point out the argument that I gave using my opinions and I'll actually respond to your statement. As far as I can tell, I only stated my opinion. I didn't make any arguments based on those opinions.

I agree, but saying that something can't be argued because it's your opinion is arguable.

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Postby ArmonSore » Tue Apr 10, 2007 2:00 pm UTC

That's true, Macbi. But I didn't so much mean that opinion can't generally be argued, but rather that this particular opinion can't be argued. It would boil down to little more than conjecture piled up on conjecture. i.e. a waste of time.
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Postby Pathway » Wed Apr 11, 2007 12:04 am UTC

ArmonSore wrote:But I didn't so much mean that opinion can't generally be argued, but rather that this particular opinion can't be argued. It would boil down to little more than conjecture piled up on conjecture. i.e. a waste of time.


I may have come off a little harsh--but this is exactly what I mean. If it's based on nothing, a 'waste of time,' how can you consider it valid?

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Postby ArmonSore » Wed Apr 11, 2007 1:10 am UTC

[qoute="Pathway"]If it's based on nothing, a 'waste of time,' how can you consider it valid?[/quote]

You're telling me things that I already know. I don't consider it valid. I know it's just my opinion, and I won't even try to justify that human beings are the greatest in the universe.

But it's when we jump from "we are not the greatest in the universe" to "we can't know everything(read: anything)" that I have a problem. I not being the greatest means being incapable, then I choose to believe that we are the greatest. If only to preserve my faith in our potential.
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Postby duckshirt » Thu Apr 12, 2007 12:34 am UTC

Belial wrote:
yy2bggggs wrote:
duckshirt wrote:An atheist would say #2 is more because it uses fewer words and is simpler, but I say #1, because I would rather have a full explanation that gives an answer than a simple, unexplained one.

#1 explains no more than #2.


Pretty much. There's nothing *more* sensical about a sentient, omnipotent being coming into existence for no reason than an ordered, rational universe coming into existence for no reason.
Sure there is. It makes more sense for the reason I posted right after. Basically, it's illogical for a finite universe to come into existence from nothing, but it's also illogical for God to come out of nothing, but if God created logic, he wouldn't have followed it before he created it.
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Postby Belial » Thu Apr 12, 2007 12:38 am UTC

But if there's a time that predates logic, there's nothing *logically* preventing it from coming into existence on its own.

Possibly along with the universe.
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Postby Shadowfish » Thu Apr 12, 2007 12:45 am UTC

Logic came into existence when people made it up.

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Postby Belial » Thu Apr 12, 2007 1:04 am UTC

The underlying laws that logic emulates, then.
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Postby Shadowfish » Thu Apr 12, 2007 1:59 am UTC

You beg the question: are there such laws? But his has been discussed in other threads.

The question here is what relationship God has to the laws of the universe and of logic. Personally, I am agnostic. When I feel that there is a God, I view it as being these rules. This is why I disagree with the OP. man can become powerful, but he must work within the system.

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Postby Belial » Thu Apr 12, 2007 2:05 am UTC

When I feel that there is a God, I view it as being these rules.


If God is just the rules of physics/causality/logic/whatever, and not a separate, thinking entity, you're better off just calling it "The laws of physics, causality, logic, and whatever". Calling it "god" just confuses the issue and isn't terribly accurate.
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Postby Shadowfish » Thu Apr 12, 2007 2:49 am UTC

It may be that I should not use a word that has such a different meaning to most people.

But do tell me, if God(your version) thinks, how does (insert appropriate pronoun) think? It certainly does not think the way you or I do.

Edit: I'm not entirely sure what it means for a thing to think, in general.

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Postby Fluff » Thu Apr 12, 2007 3:03 am UTC

duckshirt wrote:
Belial wrote:
Pretty much. There's nothing *more* sensical about a sentient, omnipotent being coming into existence for no reason than an ordered, rational universe coming into existence for no reason.
Sure there is. It makes more sense for the reason I posted right after. Basically, it's illogical for a finite universe to come into existence from nothing, but it's also illogical for God to come out of nothing, but if God created logic, he wouldn't have followed it before he created it.


Why would the universe have had to come into existence or be created at all, if you can neither create nor destroy energy? What if it's just always been around? Also, with time not being a uniform phenomenon, how is the question even valid?

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Postby Belial » Thu Apr 12, 2007 3:08 am UTC

But do tell me, if God(your version) thinks, how does (insert appropriate pronoun) think? It certainly does not think the way you or I do.


I don't have a version. I'm an atheist. But the general definition of a God is an entity with phenomenal power. My general assumption is that it thinks like a very intelligent person (especially if you take that whole "created in his image" thing), with a lot of power.
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Postby Andrew » Thu Apr 12, 2007 10:09 am UTC

duckshirt wrote:if God created logic, he wouldn't have followed it before he created it.

No.

Something which is against the rules of logic is false. God didn't "create" logic. Logic is just truisms pumped through reason until you get non-obvious but nonetheless inevitable rules.

It was never created, principally because it doesn't in any material sense exist. It's like asking "what if god had never created the number six? What would five plus one be then?" It's still six. God has no say in it.

If there is a god, which for my money there isn't, then he can't break the laws of logic, and he never could. You can't tell me God created a set of rules so powerful God can't break them.

The whole argument is just nonsense.

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Postby bbctol » Thu Apr 12, 2007 8:48 pm UTC

Shadowfish wrote:Logic came into existence when people made it up.

Erm... no.
A=B
B=C
Aristotle didn't just make up A=C. Humans discovered logic, and learned to apply it. Which brings to mind a totally unrelated thought, which might turn into a new thread.
Let's say we all live in the Matrix. In the Matrix, there are rules such as A=B, B=C, A=C. Suppose that is an entirely false statement, planted in your head by the evil whatever. It makes sense, naturally, because you've been programmed to think that it does. You can't prove it, because it's an aphorism; it's OBVIOUS. But how do you know it's not false? How do you know that it "making sense" isn't a lie?
Ok, that was random.

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Postby Pathway » Thu Apr 12, 2007 8:56 pm UTC

bbctol wrote:Aristotle didn't just make up A=C. Humans discovered logic, and learned to apply it. Which brings to mind a totally unrelated thought, which might turn into a new thread.


Thank you for that.
bbctol wrote:Let's say we all live in the Matrix. In the Matrix, there are rules such as A=B, B=C, A=C. Suppose that is an entirely false statement, planted in your head by the evil whatever. It makes sense, naturally, because you've been programmed to think that it does. You can't prove it, because it's an aphorism; it's OBVIOUS. But how do you know it's not false? How do you know that it "making sense" isn't a lie?
Ok, that was random.


The answer might have something to do with consistency, which is something we should probably assume.

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Postby Shadowfish » Fri Apr 13, 2007 1:35 am UTC

Erm... no.
A=B
B=C
Aristotle didn't just make up A=C. Humans discovered logic, and learned to apply it. Which brings to mind a totally unrelated thought, which might turn into a new thread.

Well, I guess "made up" is not really what I meant. I was going for "invented". If you disagree that logic was invented,tell me, was the internal combustion engine discovered or invented?

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Postby Andrew » Fri Apr 13, 2007 11:01 am UTC

Shadowfish wrote:Well, I guess "made up" is not really what I meant. I was going for "invented". If you disagree that logic was invented,tell me, was the internal combustion engine discovered or invented?

The engine was invented.
The fact that materials made into the shape of an engine convert the chemical energy in petrol into useful motive force was discovered.

The means of expression we use to describe the rules of logic were invented.
The rules themselves were discovered.

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Postby Yakk » Fri Apr 13, 2007 12:55 pm UTC

Yes, A=C was invented. It didn't exist before humanity thought it up.

The concept of equality was invented. The abstractions that take the world and produce number (and other abstractions) is a human (or other intelligence, possibly sub-human animal) invention. Without that abstraction, A=C has no meaning.

No two things in reality are the same. There is no equality relation in reality. Any two rocks are different: they have different numbers of atoms, different crystal arrangement: they are different in a number of ways I cannot bound.

Even the fundamental particles like electrons are never the same. When we describe them via their Q-M state, we end up with a wavefunction that is not bounded by any known agent: it exists over the entire universe at trace levels. No two electrons have the same Q-M state.

Only by abstraction can we find equivilence in reality. By paring off the properties of things that we don't care about, we simplify reality. Once this is done, the two abstractions of things can become the same abstraction. If we have three things that are equivilent, we end up with:
A=B
B=C
then, in this abstract, simplified world, we end up with:
A=C
but without the abstracted simplified world, A=C is meaningless. And that shadow-world of abstraction and thought is the world that mankind invented, hence we invented A=C.

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Postby Scheaume » Fri Apr 13, 2007 4:20 pm UTC

I don't have anything particularly insightful to say =P but I read a book by C.S. Lewis called "Miracles" -- the entire book might not be of interest to you but at the beginning he spends a lot of time talking about the idea that Reason itself is a sort of miracle. It is related to all this stuff about logic being invented or discovered, and is fairly fascinating.

Dat iz all.

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Postby Shadowfish » Fri Apr 13, 2007 8:52 pm UTC

The engine was invented.
The fact that materials made into the shape of an engine convert the chemical energy in petrol into useful motive force was discovered.

The means of expression we use to describe the rules of logic were invented.
The rules themselves were discovered.

I think the difference between an invention and a discovery is this: a discovery is when we become aware of something that is happening. An invention is when we figure out how to make something happen.

The physics that causes an engine to work were happening before anyone noticed them. Then, after they were noticed, it became possible make engines happen(run, if you prefer). Notice how close this is to what you said.

One can try to say the same thing about logic. The rules of logic were happening before anyone noticed them. Then after they were noticed, people were able to find a way to express them.

This is true. People were reasoning before there was formal logic. The patterns of reasoning that lead to useful deductions were noticed, and a system of logic was invented to formalize them. Logic was not a discovery about how the universe works. It was a discovery about how to structure our thoughts to make them more useful. The reason I said invented, instead of discovered, is that logic became much more useful when it was formalized.

If you say otherwise, you imply that the rules of logic exist independently of the people who use them, which means that there is something that is reasoning in the absence of people.

This is why I find it hard to separate the idea of God from the idea that logic is universal.

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Postby Andrew » Fri Apr 13, 2007 10:38 pm UTC

Shadowfish wrote:People were reasoning before there was formal logic. The patterns of reasoning that lead to useful deductions were noticed, and a system of logic was invented to formalize them. Logic was not a discovery about how the universe works. It was a discovery about how to structure our thoughts to make them more useful. The reason I said invented, instead of discovered, is that logic became much more useful when it was formalized.

If you say otherwise, you imply that the rules of logic exist independently of the people who use them, which means that there is something that is reasoning in the absence of people.

This is why I find it hard to separate the idea of God from the idea that logic is universal.

I do indeed say otherwise, but I imply no such thing. A calculator uses logic to determine the answers to sums, but it doesn't reason. It arrives at the correct answer because it is bound to do so by the fundamental, intrinsic physical laws of the universe. They are immutable and independant of the presence of sentient life. The laws of logic have nothing to do with thought. If I see an object alone in a box, and then I take the object out of the box without looking, that box is now empty. I know this because logic tells me it is true. But the box isn't empty because I believe it is so; it's empty because I took the object that was inside it out and now the object is not inside the box, so it's empty. That's logic. And it works whether I know it works or not; indeed if there were no people anywhere, and no God, and the object was blown out of the box by wind the box it still empty.

It's hard to explain without it seeming circular, because logic is just that fundamental that the only framework that exists to explain these things is itself logical, but it's still true.

Yakk wrote:Yes, A=C was invented. It didn't exist before humanity thought it up.

The concept of equality was invented. The abstractions that take the world and produce number (and other abstractions) is a human (or other intelligence, possibly sub-human animal) invention. Without that abstraction, A=C has no meaning.


This is gibberish. Just because there isn't an example of somethig in nature doesn't mean the concept is meaningless, and if the concept of equality has meaning then the laws that go with it hold.

Besides which, if we invented "A=C", then logically we could change it. We can change engines and languages and toasters. Improve them. We could make A>C, say. Of course, by substitution that would mean that C>A, but we could invent it so that that's OK. Or invent it so that substitution doesn't work.

And indeed, we could construct a form of metalogic where all these things are true, as long is it was internally consistent (or held that internal consistency was for girls). But whenever we test it in real life, A does keep coming out as C, doesn't it? So from a philosophical point of view, sure, yeah, your point sort of stands. But from an experimental point of view, I think we've amassed enough evidence by now to dispense with all this sillyness and just accept the laws of reason.

Edit:

For example, the Zeroth Law Of Thermodynamics states, essentially, that if T1=T2 and T2=T3 then T1=T3. This is a rule so fundamental it precedes even the First Law of Thermodynamics. And it states that if A=B and B=C then A=C.

So it seems to me that the universe has some ideas about logic without people having to "invent" them.

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Postby Shadowfish » Sat Apr 14, 2007 5:02 am UTC

do indeed say otherwise, but I imply no such thing. A calculator uses logic to determine the answers to sums, but it doesn't reason. It arrives at the correct answer because it is bound to do so by the fundamental, intrinsic physical laws of the universe.

A handful of pennies can compute sums. I put three of them in a pile. Then, I add three more pennies to the pile. I count the pennies, and see that there are six of them. Look, the pennies just computed a sum without thinking!

What's wrong with this? Well, physically, you are just pushing zinc discs around. this whole business of how many there are is going on in your head.

Saying that a calculator can compute sums is the same as saying a pile of pennies can. The logic that went into computing the sum was actually done by a person. In order to design a chip that can do sums, you have to work out a combination of gates that will translate one set of pulses, which you assign a meaning to, into another set of pulses, that you assign meaning to. What happens inside a calculator is semiconductor physics, not logic.

If I see an object alone in a box, and then I take the object out of the box without looking, that box is now empty. I know this because logic tells me it is true. But the box isn't empty because I believe it is so; it's empty because I took the object that was inside it out and now the object is not inside the box, so it's empty. That's logic. And it works whether I know it works or not; indeed if there were no people anywhere, and no God, and the object was blown out of the box by wind the box it still empty.

The laws of physics also tell you that if you move an object, it won't be where it was before you moved it anymore. When you know something only because logic tells you it must be true, then you have knowledge of the shadow world Yakk talked about, not the physical world.

By the way, the laws of physics(in the form that we use) are also invented, but they do give us a symbolic handle on the real processes in the universe.

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Postby Andrew » Sat Apr 14, 2007 11:40 am UTC

Shadowfish wrote:A handful of pennies can compute sums. I put three of them in a pile. Then, I add three more pennies to the pile. I count the pennies, and see that there are six of them. Look, the pennies just computed a sum without thinking!

What's wrong with this? Well, physically, you are just pushing zinc discs around. this whole business of how many there are is going on in your head.


No, it isn't. For one thing, because pennies are made of copper and contain very little zinc at all. (Unless of course the chemical composition of objects is also "going on in your head".) I mean, take a smaller example. Produce acid rain. (Please imagine subscripts as appropriate)

H2O + SO2 = H2SO3

Note there that for hydrogens, 2+0=2, for sulphur, 0+1=1, and for oxygen 2+1=3. "This whole business of how many there" is going on right there in fundamental chemical reactions. It is intrinsic to reality. It is not something mankind has concocted for a laugh. If it were, we should expect to see chemical reactions ignoring it. (Or, say, the mixing of a large amount of copper atoms with a small amount of zinc atoms giving an alloy that could reasonably be called "zinc".)

Shadowfish wrote:The laws of physics also tell you that if you move an object, it won't be where it was before you moved it anymore.

Then that must mean that the laws of physics obey the rules of logic. They must; calculators can produce answers to sums, emptied boxes no longer have things in them, chemical reactions produce mathematically sensible amounts of the arithmetically correct substances. There is no recorded instance of physical reality behaving illogically. (Note that "illogically" is not the same as "counter-intuitively".)

If the laws of physics obey logic, then mankind can't have invented it, now can we?

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Postby Yakk » Sat Apr 14, 2007 2:05 pm UTC

Andrew wrote:
Yakk wrote:Yes, A=C was invented. It didn't exist before humanity thought it up.

The concept of equality was invented. The abstractions that take the world and produce number (and other abstractions) is a human (or other intelligence, possibly sub-human animal) invention. Without that abstraction, A=C has no meaning.


This is gibberish. Just because there isn't an example of somethig in nature doesn't mean the concept is meaningless, and if the concept of equality has meaning then the laws that go with it hold.

Besides which, if we invented "A=C", then logically we could change it.


Yes, we can. Odds are the abstraction defined by that would be less useful.

We can change engines and languages and toasters. Improve them. We could make A>C, say. Of course, by substitution that would mean that C>A, but we could invent it so that that's OK. Or invent it so that substitution doesn't work.


That doesn't mean toasters and engines would change. How we talk about them would. Language would change.

I make no guarantee that an arbitrary change in our habits and systems of abstraction and formalization would produce useful results.

Just like, if you invent a toaster, you could change it. You could remove the plug! ... and leave the rest the same. This new invention would be a pretty damn useless invention, but it doesn't mean that toasters where discovered.

And indeed, we could construct a form of metalogic where all these things are true, as long is it was internally consistent (or held that internal consistency was for girls). But whenever we test it in real life, A does keep coming out as C, doesn't it?


Yes, if we use the same habits and patterns of abstraction, and the same definitions for terms, a different system of formal logic can end up giving nonsense results.

On the other hand, you can create formal logic systems in which you can reason from contradition (ie, A and ~A does not imply false), or in which proof by contradiction isn't valid (Ie, ~~A does not imply A). Both of these varients can talk about the real world in a sensible way.

So from a philosophical point of view, sure, yeah, your point sort of stands. But from an experimental point of view, I think we've amassed enough evidence by now to dispense with all this sillyness and just accept the laws of reason.


I happen to personally find ~~A->A to be a particularly poor law of reason. Once you accept it, you end up with non-demonstrateable existence proofs: logic that prooves "X must exist", yet provides no reason to think that X can be actually found in reality when you create a physical analogue of the problem.

So no, the laws of reason are not holy and inviolate.

The abstraction of "number" or "counting" happens to be an insanely useful one. It is the one that underlies "A=B, B=C => A=C".

For example, the Zeroth Law Of Thermodynamics states, essentially, that if T1=T2 and T2=T3 then T1=T3. This is a rule so fundamental it precedes even the First Law of Thermodynamics. And it states that if A=B and B=C then A=C.

So it seems to me that the universe has some ideas about logic without people having to "invent" them.


Yes, Thermodynamics rests on our ability to generate abstractions about the universe.

Did you know that the laws of Thermodynamics are statistical laws? They are laws of large numbers. When you build them from more basic principles, you end up with "X is far more likely by a large extent in reasonably large systems" instead of "X always happens".

This isn't a level of detail that is all that useful, when using thermodynamics on "human" and above scales, simply because X is so insanely more likely to happen it isn't funny.

This doesn't mean that the law of thermodynamics is a bad law: rather, it is a set of laws that apply to an abstraction of the world.

That beautiful ability to abstract, then to manipulate those abstractions, is what provides mankind with it's ability to break down and understand chunks of the universe.

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Postby Andrew » Sat Apr 14, 2007 3:37 pm UTC

Yakk wrote:I happen to personally find ~~A->A to be a particularly poor law of reason. Once you accept it, you end up with non-demonstrateable existence proofs: logic that prooves "X must exist", yet provides no reason to think that X can be actually found in reality when you create a physical analogue of the problem.

So no, the laws of reason are not holy and inviolate.

I don't understand a word of that, but it appears that you're saying "just because the inverse of a statement is not true, that's no reason to assume the statement itself is true", yes? (Though you spelt "proves" wrong so your credentials in the study of logic should perhaps be questioned.) So you show me one example of a statement which is true and whose inverse is true, or which is false and whose inverse is also false, and I'll concede that logic is broken and abandon it. But until you do, I shall ignore this argument as based on nothing but crazy words.

Yakk wrote:The abstraction of "number" or "counting" happens to be an insanely useful one. It is the one that underlies "A=B, B=C => A=C".

Now, I agree with this. Counting is an abstraction; we're dispensing with a vast amount of information when we count things. "There are four people" is obviously a poor description of The Beatles, but from the abstracted view of "counting", it's exactly right.

But that's the point -- when we count things, we dispense with the detailed information; we don't add any new information. Everything we say when we count things comes directly from the universe; not from out minds.

Yakk wrote:Did you know that the laws of Thermodynamics are statistical laws?

I should hope I know that, or else I think I'd have failed my MPhys course.

Again, temperature is an abstraction; it's a single number that is used in lieu of a vast, vast amount of information about a system's microstate. The idea that taking that much information, processing it in a logical way and arriving at a logical answer as basic as "A=B and B=C therefore A=C" should describe natural phenomena so well if logic isn't very fundamental seems highly improbable to me.

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Postby Shadowfish » Sat Apr 14, 2007 3:57 pm UTC

The mint thinks pennies are made of 98% zinc, but what do they know?

I really don't see how molecules are any different from pennies. The reaction you gave can be explained completely in terms of quantum mechanics. Nature obeys quantum mechanics. Actually, quantum mechanics obeys nature, but let's not worry about that. The point is, nature does not care how many there are. You do.

Here's an example of nature not obeying arithmetic. A Radon atom decays, turning into a helium nucleus and a Radium A(I don't remember the real name) nucleus. One nucleus turned into two.

Oh me yarm! Nature says 1=1+1!

You might say I counted wrong. I should have been counting protons and neutrons, instead of nuclei. As it turns out, these aren't conserved in all kinds of decay either. But that's not the point. The point is, the validity of logic in talking about physical situations depends on your using the correct abstractions. In order for arithmetic to apply to things in the real world, you need pick things in the real world where arithmetic works.

If you know something only by logic, it is not certain that you know that about nature. It is true that physics has made predictions based on existing theories and logic. However, these predictions needed evidence before anyone would believe them. And rightly so.

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Postby Pathway » Sat Apr 14, 2007 4:55 pm UTC

Shadowfish wrote:
If you know something only by logic, it is not certain that you know that about nature. It is true that physics has made predictions based on existing theories and logic. However, these predictions needed evidence before anyone would believe them. And rightly so.


But if you know something by logic then you know it is true wherever the conditions apply. We know, from our counting principles that whenever things are conserved, they obey certain rules. Determining which abstractions apply when must be experimental, yes--but counting rules are obeyed in pertinent circumstances because the world's underlying structure is self-consistent and obeys logical rules. I think you guys are forgetting that most theorems are if-then statements: whenever these hypotheses are true, when our axioms hold, we have this result.

Yakk wrote:
Andrew wrote:
Besides which, if we invented "A=C", then logically we could change it.


Yes, we can. Odds are the abstraction defined by that would be less useful.



But why would it be less useful? Because the intrinsic rules of reality aren't in agreement with that abstraction, whereas they appear to be pretty solidly on our side when we say A=B and B=C implies A=C. Those rules of reality were there before human thought and will outlive us.

Also, I think there's a bit of confusion when you talk about A and ~A. I've been taking ~A to mean "A is not true." Truth and untruth are dual states; there's no demi-true. So if something is not untrue then it's true.

You're denying that--you say that if something hasn't been formally proven or disproven, and such a proof isn't possible, then it can't be true or false. But that's simply not the case. Take, say, Goldbach's conjecture. Either all of the composites can be constructed out of primes, or there's one or more that can't be. Our ability to prove one statement or the other is irrelevant to reality.

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Postby yy2bggggs » Sat Apr 14, 2007 5:25 pm UTC

Pathway wrote:Also, I think there's a bit of confusion when you talk about A and ~A. I've been taking ~A to mean "A is not true." Truth and untruth are dual states; there's no demi-true. So if something is not untrue then it's true.

So what would you say about the truth of the following statement?:
"If you take acetaminophen and have a fever, your fever will go down."

Is this statement true? Is it untrue?

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Postby Pathway » Sat Apr 14, 2007 5:33 pm UTC

It's untrue, because the statement says that it's a relationship which always occurs.

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Postby yy2bggggs » Sat Apr 14, 2007 5:47 pm UTC

Pathway wrote:It's untrue, because the statement says that it's a relationship which always occurs.

I missed where the statement says such a thing.

Edit: Clarification:
I think you're begging the question; specifically, you are changing the meaning of this statement when you say that it claims the relationship always holds. As such, you're artificially defending your original viewpoint that there are no "demi-true" claims.

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Postby Shadowfish » Sat Apr 14, 2007 9:43 pm UTC

Pathway wrote:But if you know something by logic then you know it is true wherever the conditions apply. We know, from our counting principles that whenever things are conserved, they obey certain rules. Determining which abstractions apply when must be experimental, yes--but counting rules are obeyed in pertinent circumstances because the world's underlying structure is self-consistent and obeys logical rules. I think you guys are forgetting that most theorems are if-then statements: whenever these hypotheses are true, when our axioms hold, we have this result.


what I read wrote:Logic always applies in some circumstances. In the circumstances where logic always applies, logic always applies. Therefore, the universe obeys the laws of logic.


I don't want to strawman you, but I really can't see the difference. Please clarify.

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Postby Yakk » Sat Apr 14, 2007 11:17 pm UTC

Andrew wrote:I don't understand a word of that, but it appears that you're saying "just because the inverse of a statement is not true, that's no reason to assume the statement itself is true", yes? (Though you spelt "proves" wrong so your credentials in the study of logic should perhaps be questioned.)


Naw, my credentials in the study of spelling should be questioned. :)

If you want credentials:
I have neither a master's degree nor a PhD in logic, so I am not an accredited expert at the subject.

I can (or I could) generate proofs for Godel's incompleteness theorem, Godel's completeness theorem, and some similar-level problems. I have spent 1000s of hours using logic to reasonably formally prove and disprove things (not at the computer-verifiable level).

So you show me one example of a statement which is true and whose inverse is true, or which is false and whose inverse is also false, and I'll concede that logic is broken and abandon it. But until you do, I shall ignore this argument as based on nothing but crazy words.


I don't claim there are statements which are true whose inverse is true.

I do claim that there are perfectly good abstractions of the universe in which there are statements which are false, whose inverse doesn't have to be true. As example, the intermediate value theorem: I accept that it is possible to prove that it is impossible to prove that a continuous function that goes from 1 to -1 does not touch 0 (ie, ~~intermediate value theorem) -- however, I am unwilling to take on faith that the point exists, when in at least some cases the only evidence we have that the point exists is a proof by contradiction.

You can build a model of mathematics in which all real to real functions are continuous is an axiom, and it is an abstraction that is just as consistent with the real world as the more common one.

Just because you can add an axiom, it doesn't mean you should. The axiom of choice is consistent with the axioms of a formal system -- one cannot find an example within ZF that contridicts the axiom of choice -- yet both ZFC and ZF~C are useful axiomatic systems.

I'm not saying standard mathematical logic is broken -- I think the universe is pretty damn consisent with it -- I just think that the law of excluded middle is not required to model the universe to testable levels.

Yakk wrote:The abstraction of "number" or "counting" happens to be an insanely useful one. It is the one that underlies "A=B, B=C => A=C".

Now, I agree with this. Counting is an abstraction; we're dispensing with a vast amount of information when we count things. "There are four people" is obviously a poor description of The Beatles, but from the abstracted view of "counting", it's exactly right.

But that's the point -- when we count things, we dispense with the detailed information; we don't add any new information. Everything we say when we count things comes directly from the universe; not from out minds.


When we build an internal combustion engine, we simply reorganize matter according to physical laws. We don't add any matter. Clearly we simply discovered how to build an ICE: how to build it was already manifest in reality.

Again, temperature is an abstraction; it's a single number that is used in lieu of a vast, vast amount of information about a system's microstate. The idea that taking that much information, processing it in a logical way and arriving at a logical answer as basic as "A=B and B=C therefore A=C" should describe natural phenomena so well if logic isn't very fundamental seems highly improbable to me.


Logic that wasn't useful was thrown out. The logic we use today isn't the only attempt at it, the math we use to day isn't our only attempt at it, and the physics we use today isn't our only attempt at it.

Newton's laws did not describe the motion of bodies. They described an approximation to the motion of bodies. They where amazingly accurate, having taken 1000s of years to produce the groundwork for. Very cool.

Yet Newton's laws are not the universe. They where invented by Newton.

I'm using ~A to mean "you can prove that you cannot prove A", or "you can derive ~T from A", depending on context.

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Postby Pathway » Sat Apr 14, 2007 11:23 pm UTC

Yakk wrote:I'm using ~A to mean "you can prove that you cannot prove A", or "you can derive ~T from A", depending on context.


I interpreted it as "'A is not true' is true."

Your definition and mine basically differ in that you use 'provability' and I use 'truth,' which are different notions. But if something isn't provable, that doesn't mean it isn't true.

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Postby Yakk » Sat Apr 14, 2007 11:50 pm UTC

If you hold that all statements are either true or not true, then your interpritation follows from mine. :)

Godel demonstrated that completeness in a formal system isn't a reasonable demand. So I see no reason to add consistent axioms that do not have verifiable consequences when you apply the abstraction to reality, like the ~~X->X and ~ForAll X ~P(X) -> ThereExists X P(X).

Basically, I hold that completeness is not a virtue worthy of adding otherwise unjustified axioms. I am willing to accept that there are formal statements that are neither true nor false.

I accept that you disagree with me: I understand that your logic will be able to prove more statements true and more statements false than my logic.

Both of our logics are models for reality. Yours just claims extra things to be true about reality that I don't see the need for.

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Postby Andrew » Sun Apr 15, 2007 3:18 am UTC

Yakk wrote:I do claim that there are perfectly good abstractions of the universe in which there are statements which are false, whose inverse doesn't have to be true. As example, the intermediate value theorem: I accept that it is possible to prove that it is impossible to prove that a continuous function that goes from 1 to -1 does not touch 0 (ie, ~~intermediate value theorem) -- however, I am unwilling to take on faith that the point exists, when in at least some cases the only evidence we have that the point exists is a proof by contradiction.

I was using Pathway's definition rather than yours, apparently:
If you hold that all statements are either true or not true, then your interpritation follows from mine. :)

See, I don't know what rules xkcd sets on posting while drunk, so I should explain that I've been out drinking for nine hours before posting this. But even so, it's perfectly obvious even in my mentally sub-par state that your last post is not true. Truth follows from provability, but that doesn't mean that falsehood follows from unprovability. If ~A means "you can prove that you cannot prove A", then ~~A means "you can prove that you cannot prove that you can prove that you cannot prove A". It does not follow from there that A is true.

You can build a model of mathematics in which all real to real functions are continuous is an axiom, and it is an abstraction that is just as consistent with the real world as the more common one.

Just because you can add an axiom, it doesn't mean you should. The axiom of choice is consistent with the axioms of a formal system -- one cannot find an example within ZF that contridicts the axiom of choice -- yet both ZFC and ZF~C are useful axiomatic systems.

I'm not saying standard mathematical logic is broken -- I think the universe is pretty damn consisent with it -- I just think that the law of excluded middle is not required to model the universe to testable levels.

For reference, I have no idea what the hell any of that means. What is C? What is ZF? What is "the law of excluded middle"? And what has any of that got to do with the topic at hand?

When we build an internal combustion engine, we simply reorganize matter according to physical laws. We don't add any matter. Clearly we simply discovered how to build an ICE: how to build it was already manifest in reality.

Yes, that's what I said. We didn't "invent" the fact that matter arranged into the shape of an engine converts chemical energy into useful motive force. We discovered that. The fact that matter arranged in that way can perform that task is an intrinsic property "already manifest in reality". We did indeed discover how to make one.

In a sense, there is no "invention" ever, since anything we build could, in theory, have been built by aliens the week before, so in a way all we did was discover how to build something that would have worked perfectly well anyway.

Again, temperature is an abstraction; it's a single number that is used in lieu of a vast, vast amount of information about a system's microstate. The idea that taking that much information, processing it in a logical way and arriving at a logical answer as basic as "A=B and B=C therefore A=C" should describe natural phenomena so well if logic isn't very fundamental seems highly improbable to me.


Logic that wasn't useful was thrown out. The logic we use today isn't the only attempt at it, the math we use to day isn't our only attempt at it, and the physics we use today isn't our only attempt at it.

Newton's laws did not describe the motion of bodies. They described an approximation to the motion of bodies. They where amazingly accurate, having taken 1000s of years to produce the groundwork for. Very cool.

Yet Newton's laws are not the universe. They where invented by Newton.


See now, I agree about the physics bit. Physics is indeed fluid. We take a stab and test it and then we have another go to fix the bits that didn't work.

But maths... no. Maths is by definition correct. You start with axioms, and then you apply the rules of logic until you end up with maths. If the maths is useful, then woohoo, you have something worth writing up. If not, then what the hell, I hope you enjoyed deriving it. (In reality, of course, what usually happens is that you design the maths and then work out what axioms are required to support it. But let's pretend that isn't true.) If it turns out not to be useful then the axioms are at fault, as those are the only information in mathematics.

And as for logic... I don't really know. I've never studied philosophy. Is Statement X true just because "Statement X is false" is false? Yes. Obviously it is. And the universe very clearly operates to that rule. So that rule is surely intrinsic and not invented.

Surely?


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