[edited]How to account for the Laws of Logic?

[onemangang]

I just can’t see any way to** account** for logic outside of God.

[edited]

 

[Perplexity]

I just can’t see any way to** account** for logic outside of God.

So how does an atheist account for the laws of logic?

I think if we got technical, like how Logicians understand these laws, you’d see that they’re just arbitrarily chosen rules for invented mathematical languages. They really don’t bear any metaphysical implications per se.

But, as you’re using the phrase ‘laws of logic’, I’d say if they’re necessarily true, then they’re grounded in themselves. That is, nobody (whether atheist or theist) has to account for them. Why not ask how the atheist accounts for the truth of ‘2+2=4’? etc.

If logic must be grounded in something like God (as you seem to indicate), then they’re not necessary, they’re contingent. That is, you’d have to say if God didn’t exist, laws like non-contradiction, excluded middle or identity would be false. But, of course, they’d still be true if God didn’t exist.

Atheist philosopher Micheal Martin formulated this into an argument known as TANG (transcendental argument against God’s existence) in response to certain Calvinist philosophers who use TAG (Transcendental argument for God’s existence).

Essentially, Martin argued:

1. If God exists, then the laws of logic aren’t necessary.
2. But, the laws of logic are necessary.
3. Therefore, God does not exist. (1), (2), M.T.]

 

[tonyrey]

1. Mathematics entails the falsity of materialism because it is concerned with intangible facts.
2. Mathematics is based on the objective reality of numbers, i.e. different quantities.
3. The success of science is due to the mathematical precision with which physical phenomena are described.
4. Mathematics implies Design because it presupposes intelligence and order.

 

[empther]

If there were no God,
we would be nothing but animals with no more individual personalities than a herd of buffalo.

 

[empther]

Essentially, Martin argued:

1. If God exists, then the laws of logic aren’t necessary.
2. But, the laws of logic are necessary.
3. Therefore, God does not exist. (1), (2), M.T.]

[edited]

Logic is necessary whether or not there’s a God.
But our ability to even talk about it proves there is, because no organization of matter could fill the Library of Congress.

 

[Iron_Donkey]

I think if we got technical, like how Logicians understand these laws, you’d see that they’re just arbitrarily chosen rules for invented mathematical languages. They really don’t bear any metaphysical implications per se.

True. But they (or rather, the most common rules) appear to apply to reality as we can see it and, indeed, are generally chosen as rules because of this appearance. But the fact that these rules are, from the logician’s viewpoint, somewhat arbitrary (though carefully chosen so that they are really only arbitrary in the strictly formal sense) seems to suggest that some of those rules may or may not really apply or that some other system than the standard one we use intuitively might apply.

This means that the statement

If logic must be grounded in something like God (as you seem to indicate), then they’re not necessary, they’re contingent. That is, you’d have to say if God didn’t exist, laws like non-contradiction, excluded middle or identity would be false. But, of course, they’d still be true if God didn’t exist.

Needs some qualification. For example, even in the standard logic systems, you can drastically change things by allowing or disallowing the rule “falsehood implies [anything]”. Obviously, if the formal rules could be changed and be valid in the strictly logical sense, we can ask “which systems of rules apply, which don’t, and why?” The mere fact that you can ask that question makes it at least a non-trivial assertion that they are not contingent, or that they would apply if God did not exist.

That is, taken as an unknown for the purpose of argument, a change in the existence of God from whatever it is to whatever it isn’t could potentially change anything that could possibly be changed. Since the laws of logic could be changed, then it is unclear whether or not they would be among those that did. (Or rather, it is unclear from this argument. I have a very clear idea: nothing would exist at all. But anyway.)

Atheist philosopher Micheal Martin formulated this into an argument known as TANG (transcendental argument against God’s existence) in response to certain Calvinist philosophers who use TAG (Transcendental argument for God’s existence).

Essentially, Martin argued:

1. If God exists, then the laws of logic aren’t necessary.
2. But, the laws of logic are necessary.
3. Therefore, God does not exist. (1), (2), M.T.]

I’m not so sure that the laws of logic are necessary (and certainly not sure that they are necessary in the form they seem to take). I mean, they are necessary for the world to be as it is now, but it’s not, strictly speaking, necessary that the world be as it is now. So while you could say that the logic must exist because without it and with all other things the same things would be otherwise, but that does not really tell you much.

I mean, the electricity situation would be different without the Hoover Dam, but it would be much more different without the water that powers it. So the Hoover Dam is necessary for the current state of things to be validly explained, but that certainly does not mean that there is no explanation for it. And even if we knew it was there, knew what it was, and knew what it would do if some unknown substance started the generators spinning (and had no way of knowing, so did not ask, whether or not there was an explanation for it), we would still be unable to completely explain why there is power coming out of it without also knowing and explaining the water.

 

[Perplexity]

True. But they (or rather, the most common rules) appear to apply to reality as we can see it and, indeed, are generally chosen as rules because of this appearance. But the fact that these rules are, from the logician’s viewpoint, somewhat arbitrary (though carefully chosen so that they are really only arbitrary in the strictly formal sense) seems to suggest that some of those rules may or may not really apply or that some other system than the standard one we use intuitively might apply.

That’s true, a big part of logic is trying to make an accurate model of natural languages, so that when a logic tells us that a form is valid, we can be justified in saying its instantiation in a natural language is likewise valid (or invalid as the case may be).

That is, taken as an unknown for the purpose of argument, a change in the existence of God from whatever it is to whatever it isn’t could potentially change anything that could possibly be changed. Since the laws of logic could be changed, then it is unclear whether or not they would be among those that did. (Or rather, it is unclear from this argument. I have a very clear idea: nothing would exist at all. But anyway.)

Well, this gets complicated. Generally, propositions and mathematical entities are understood as abstracta which are necessary entities: they exist in every possible world. So, you couldn’t make a proposition stop existing. In that sense, propositions describing the ‘laws’ of logic would exist regardless of whether God did or not. However, what I think most folks want to say is those propositions known as the laws of logic are true in every possible world, and therefore not only necessarily existent, but necessarily true.

I’m not so sure that the laws of logic are necessary (and certainly not sure that they are necessary in the form they seem to take). I mean, they are necessary for the world to be as it is now, but it’s not, strictly speaking, necessary that the world be as it is now. So while you could say that the logic must exist because without it and with all other things the same things would be otherwise, but that does not really tell you much.

Something exists necessarily if it’s in every possible world, and it’s necessarily true if it’s true in every possible world. I don’t think many dispute whether the ‘laws’ exist in every possible world; but, the interesting question is whether they’re true in every possible world.

I mean, the electricity situation would be different without the Hoover Dam, but it would be much more different without the water that powers it. So the Hoover Dam is necessary for the current state of things to be validly explained, but that certainly does not mean that there is no explanation for it. And even if we knew it was there, knew what it was, and knew what it would do if some unknown substance started the generators spinning (and had no way of knowing, so did not ask, whether or not there was an explanation for it), we would still be unable to completely explain why there is power coming out of it without also knowing and explaining the water.

I think we might be working with different understandings of ‘necessity’.

 

[TheTrueCentrist]

Something exists necessarily if it’s in every possible world, and it’s necessarily true if it’s true in every possible world. I don’t think many dispute whether the ‘laws’ exist in every possible world; but, the interesting question is whether they’re true in every possible world.

Indeed. That is an interesting question. I think we could say that in order for life (or sufficient complexity for life) to exist the rules must have certain properties. Since we exist, our universe’s rules must have those properties. It is tempting for us to say “since our universe has these rules, they must be the only rules, or the most common.” However, since it would have been impossible for us to exist in universes with non-life-supporting rules, we would never be able to find ourselves there and can therefore not make any conclusions about them.

I think the rules for complexity are explored in the “Game of Life”
en.wikipedia.org/wiki/Conway%27s_Game_of_Life

 

[Iron_Donkey]

Well, this gets complicated. Generally, propositions and mathematical entities are understood as abstracta which are necessary entities: they exist in every possible world. … Something exists necessarily if it’s in every possible world, and it’s necessarily true if it’s true in every possible world. I don’t think many dispute whether the ‘laws’ exist in every possible world; but, the interesting question is whether they’re true in every possible world.

Problem is, we don’t actually know what is necessary (or necessarily true, to use that terminology) in every possible world. My whole point is that I don’t think the laws of logic necessarily are true, because we can create mental scenarios in which they are different.

I have two points:

1. It may be true that such things as the law of excluded middle are unnecessary because we can create systems which do not assume these laws are true, and there is no particular reason to believe, as far as I am aware, that those systems aren’t instantiatable, or that there is not a model in which truth and provability at least don’t contradict each other, even if the sets of stuff which satisfies the two are different. Of course, it could be that in any such model, the things actually are true but that this fact is simply not deducible from those sentences which we forced the model to obey, but I do not think we have any reason to say that.

I am avoiding the case of assuming directly that the law of excluded middle is violated by something because I personally haven’t seen an example where that works, but if there is one of those then it shows that, using your definition, that law is not necessarily true.

1. It may be true that these laws are true in every world. But this does not in fact mean that they have no logical causes - something which is true that, if false, would change the truth of those statements. That cause would have to be true in every world also of course, so it’d be hard to talk about it being false since that would, in fact, be impossible.

For example (and yes, this is a stupid analogy using things on a completely different level, but still), if it was a fact that every single conceivable world had a fountain that constantly spat water 10 feet up in the air, then it would also be true that every single world had a constant stream of water going 10 feet up in the air.

Suppose you were in one of these worlds, and all you could see was the water (the fountain was invisible or something). Suppose further that you came up with a way of telling that that exact stream of water would have to exist in every possible world. You know it is there. But if you removed the fountain (which would in fact be impossible, since the possibility of doing so would mean that there was a world which didn’t have it, but if you could) then the water would also have to be gone even though that’s not actually possible either.

(And yes, having a world without the water would necessarily mean that you didn’t have a fountain which always shot up water, but it would be clear that the absence of the water did not cause the lack of fountain, but the other way around. That is, it’s the one thing causes another that I’m focusing on - something which doesn’t make much sense in a the standard purely mathematical way of phrasing things, since the difference between a theorem and an axiom is more or less that of point of view - but something that nonetheless makes sense to talk about.)

In short(er) I’m simply saying that the mere fact that something is true in every single world does not mean that it either explains its own truth, or that it needs no explanation.

I think my original use of the word necessary(/ily true) was not simply that it was true in every conceivable world, but that it would have to continue to be true even if it were somehow magically possible to change the truth of other things which cannot be changed.

(Apologies if I inadvertently butcher any terms that actually mean something, I have some back ground in mathematical logic, but no meaningful background in philosophy.)