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Craig's Applicability of Mathematics Argument

phantom
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2/28/2013 7:54:53 PM
Posted: 3 years ago
The Craig/Rosenberg debate was a few weeks ago so I can't remember exactly how the argument went but it was something along the lines of saying if God did not exist, the applicability of mathematics to the natural world would be a happy coincidence. The applicability of mathematics is not a happy coincidence. Therefore God does exist.

Now what exactly is Craig proposing? Well one thing seems to be that the natural world does not have to be mathematical, which I won't refute. In other words, nature could have been inconsistent with mathematics and the correspondence of the two is not a necessary law of the universe. While mathematics can be a completely objective system of laws, the way nature behaves does not have to conform to it. That's what Craig is assuming.

Quantum physics actually supports that premise since we know now that at the quantum level, mathematics is not applicable to nature. It's rather non-mathematical and random actually. It's partially unpredictable and reflects only probabilities but not inevitablities. Now I don't think that would refute Craig's argument since the quantum level does not really effect our life and Craig would just say God would only need to make mathematics applicable to every day life situations, so the inapplicability of mathematics to the quantum realm is irrelevant. I am just showing that quantum physics does seem to lead to the thought that nature need not be mathematical which seems to be a fundamental presumption Craig makes. If nature must be mathematical, Craig's argument would fail since the applicability of mathematics would be a necessary truth and thus would be present in reality regardless of whether God existed or not. Therefore, it couldn't be a happy coincidence since it would have a 100% chance of being true. So I don't think Craig would object for us to say we can assume that proposition as correct.

So now let's leave the applicability argument for a moment and go to Craig's more popular arguments, the Kalam Cosmological argument and the Leibnizean Cosmological argument. We could reference many others, especially Aquinas's, but since Craig made the mathematics argument, I want to focus on his other arguments (not that the Leibnizean or Kalam arguments are his originally. But he's a strong supporter of them).

I find that Craig's presumptions with the applicability argument overall make a plausible refutation of his cosmological arguments and I would have loved to see Rosenberg make use of the conflicting reasoning. For example, let's take premise one of the cosmological argument. "Everything that begins to exist has a cause". This, I think everyone would agree, is a judgement about nature. Craig uses it to support the conclusion that the universe must have had a cause since it began to exist, so it's purely a claim about the way nature behaves. But then again, Craig already supposes the applicability of mathematics to nature is contingent therefore possibly false at some other time or place (I don't mean like tomorrow, or behind the milky way. I mean such as in another universe or before our universe)...Hmmmm, so nature could have behaved in a non-mathematical way, as assumed by Craig, meaning nature does not have to be logical...Interesting. But if nature can behave in ways that don't conform to the laws of logic, how do you then infer by pure logic necessary truths about nature? That seems wholly inconsistent especially as the beginning/previous sate of the universe is/could have been completely different to how our current universe behaves. So while we can say a ball thrown into the air will fall to the ground in a way that is according to geometrical rules, can we say that just because it's true here means it's true everywhere in all possible worlds? According to Craig, no. So then how can we say the universe must have had a cause when our sole justification can be that logic necessitates it be so? You can't! At least Craig can't. If logic is not necessarily applicable to nature, such as it is with quantum physics, then you cannot possibly infer the necessary truth that everything that begins to exist has a cause. It follows necessarily that the contingency of applicability of mathematics, means we cannot infer logically necessary truths about nature, at least not truths such as universal causality or the principle of sufficient reason. You can't just assume the natural origin of the universe occurred logically just as we cannot assume when quantum particles are shot at two slits in a wall the outcome will be logical. Craig has to either drop the mathematics argument or drop the cosmological arguments. If he does drop the mathematics argument however, he'll still face the same problem of applying necessary laws of logic as necessarily applicable to nature.

Interesting thought experiment in my opinion.
Thoughts?
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
phantom
Posts: 6,774
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2/28/2013 8:06:00 PM
Posted: 3 years ago
"If logic is not necessarily applicable to nature, such as it is with quantum physics,"

By this I meant, logic is not necessarily applicable with quantum physics.
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
medic0506
Posts: 13,450
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3/1/2013 11:03:02 AM
Posted: 3 years ago
I always find arguments against causality to be the most illogical. If conditions existed that allowed things to just pop into existence from nothing, then I can't imagine how any scientific finding could be said to be reliable. It would have to be a condition where nothing could be known, just guessed.
Polaris
Posts: 1,120
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3/1/2013 1:22:04 PM
Posted: 3 years ago
At 3/1/2013 11:03:02 AM, medic0506 wrote:
I always find arguments against causality to be the most illogical. If conditions existed that allowed things to just pop into existence from nothing, then I can't imagine how any scientific finding could be said to be reliable. It would have to be a condition where nothing could be known, just guessed.

This is because you conflate causal agency with nomic necessity.
medic0506
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3/1/2013 2:41:39 PM
Posted: 3 years ago
At 3/1/2013 1:22:04 PM, Polaris wrote:
At 3/1/2013 11:03:02 AM, medic0506 wrote:
I always find arguments against causality to be the most illogical. If conditions existed that allowed things to just pop into existence from nothing, then I can't imagine how any scientific finding could be said to be reliable. It would have to be a condition where nothing could be known, just guessed.

This is because you conflate causal agency with nomic necessity.

What's your view??
phantom
Posts: 6,774
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3/1/2013 5:04:25 PM
Posted: 3 years ago
At 3/1/2013 11:03:02 AM, medic0506 wrote:
I always find arguments against causality to be the most illogical. If conditions existed that allowed things to just pop into existence from nothing, then I can't imagine how any scientific finding could be said to be reliable. It would have to be a condition where nothing could be known, just guessed.

Did you read the whole post? Because I essentially answered that.

But I'll add more. Scientists do know the principle of universal causality is false as the most tested theory on earth, which is always verified by the tests, quantum physics, demonstrates so. So scientists realize nature need not be causal but that doesn't matter to them because in everyday life, it is completely causal. Stephen Hawking explains that quantum physics, though partially random, does give us probabilities and patterns. At the quantum level the probabilities are not significantly high but they build up in ordinary life so that probabilities are essentially rather inevitbilities. In ordinary life causality holds true so scientists can trust predictions to a very reasonable extent. Plus there's no practical reason not to. Scientists don't try to refute the problem of induction but they still base all their theories on the uniformity of nature because it is essential for science. Your argument wouldn't convince any scientists because science progresses easily despite it.

Plus this just misses the point. According to Craig's assumptions with his argument, nature could have been non-mathematical but happens to be mathematical. We find ourselves in a mostly mathematical world therefore nature isn't just going to act all random (except in the quantum level). In other universes, perhaps it does, but not ours. Therefore we could say how our universe arose may not need to be completely logical as is how we observe nature in ordinary life. So scientists can trust their predictions because they do indeed observe that life around us is mostly logical.
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
phantom
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3/3/2013 11:08:54 AM
Posted: 3 years ago
Bump
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
KeytarHero
Posts: 612
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3/3/2013 10:16:28 PM
Posted: 3 years ago
At 2/28/2013 7:54:53 PM, phantom wrote:
The Craig/Rosenberg debate was a few weeks ago so I can't remember exactly how the argument went but it was something along the lines of saying if God did not exist, the applicability of mathematics to the natural world would be a happy coincidence. The applicability of mathematics is not a happy coincidence. Therefore God does exist.

Now what exactly is Craig proposing? Well one thing seems to be that the natural world does not have to be mathematical, which I won't refute. In other words, nature could have been inconsistent with mathematics and the correspondence of the two is not a necessary law of the universe. While mathematics can be a completely objective system of laws, the way nature behaves does not have to conform to it. That's what Craig is assuming.

Quantum physics actually supports that premise since we know now that at the quantum level, mathematics is not applicable to nature. It's rather non-mathematical and random actually. It's partially unpredictable and reflects only probabilities but not inevitablities. Now I don't think that would refute Craig's argument since the quantum level does not really effect our life and Craig would just say God would only need to make mathematics applicable to every day life situations, so the inapplicability of mathematics to the quantum realm is irrelevant. I am just showing that quantum physics does seem to lead to the thought that nature need not be mathematical which seems to be a fundamental presumption Craig makes. If nature must be mathematical, Craig's argument would fail since the applicability of mathematics would be a necessary truth and thus would be present in reality regardless of whether God existed or not. Therefore, it couldn't be a happy coincidence since it would have a 100% chance of being true. So I don't think Craig would object for us to say we can assume that proposition as correct.

So now let's leave the applicability argument for a moment and go to Craig's more popular arguments, the Kalam Cosmological argument and the Leibnizean Cosmological argument. We could reference many others, especially Aquinas's, but since Craig made the mathematics argument, I want to focus on his other arguments (not that the Leibnizean or Kalam arguments are his originally. But he's a strong supporter of them).

I find that Craig's presumptions with the applicability argument overall make a plausible refutation of his cosmological arguments and I would have loved to see Rosenberg make use of the conflicting reasoning. For example, let's take premise one of the cosmological argument. "Everything that begins to exist has a cause". This, I think everyone would agree, is a judgement about nature. Craig uses it to support the conclusion that the universe must have had a cause since it began to exist, so it's purely a claim about the way nature behaves. But then again, Craig already supposes the applicability of mathematics to nature is contingent therefore possibly false at some other time or place (I don't mean like tomorrow, or behind the milky way. I mean such as in another universe or before our universe)...Hmmmm, so nature could have behaved in a non-mathematical way, as assumed by Craig, meaning nature does not have to be logical...Interesting. But if nature can behave in ways that don't conform to the laws of logic, how do you then infer by pure logic necessary truths about nature? That seems wholly inconsistent especially as the beginning/previous sate of the universe is/could have been completely different to how our current universe behaves. So while we can say a ball thrown into the air will fall to the ground in a way that is according to geometrical rules, can we say that just because it's true here means it's true everywhere in all possible worlds? According to Craig, no. So then how can we say the universe must have had a cause when our sole justification can be that logic necessitates it be so? You can't! At least Craig can't. If logic is not necessarily applicable to nature, such as it is with quantum physics, then you cannot possibly infer the necessary truth that everything that begins to exist has a cause. It follows necessarily that the contingency of applicability of mathematics, means we cannot infer logically necessary truths about nature, at least not truths such as universal causality or the principle of sufficient reason. You can't just assume the natural origin of the universe occurred logically just as we cannot assume when quantum particles are shot at two slits in a wall the outcome will be logical. Craig has to either drop the mathematics argument or drop the cosmological arguments. If he does drop the mathematics argument however, he'll still face the same problem of applying necessary laws of logic as necessarily applicable to nature.

Interesting thought experiment in my opinion.
Thoughts?

No offense, but if you can't remember the argument, you ought not be responding to it. Chances are, you're responding to a strawman.
phantom
Posts: 6,774
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3/3/2013 10:33:03 PM
Posted: 3 years ago
No offense, but if you can't remember the argument, you ought not be responding to it. Chances are, you're responding to a strawman.

I couldn't recall it exactly but I remember what's necessary. If it's a strawman tell me what's wrong. If you read the post, it's not even a refutation of the mathematics argument, rather a refutation of his cosmological arguments by means of the assumptions he makes in the mathematics argument. I only need to be right about the assumption.
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)