Atheist VS Naturalist - the latter sounds more appealing to me...

[The Grand Nudger]

My point is that within the story they are natural.

I don't think that we read the same stories.  That's certainly one way that an author can take it, though, sure.  It's up to the author to decide whether they're telling a sci fi story about werewolves, or high fantasy.

[Succubus#2]

Don't be so sure.

A precambrian rabbit would certainly overthrow our ideas in biology. But we could still pick up the pieces and do the science of biology.

No! A precambrian rabbit would void everything we have ever learened.

[The Grand Nudger]

I think that it's fair to say, in all cases, that we'd have to rewrite enough to call it a new science or new math or new logic of some other x - though we have a habit of keeping the names when we learn things that overturn our previous understanding. It's happened before, we know that it could happen again. That's a big part of supernaturalists gripe about naturalism or materialism. They'll let you have the rocks, but they want the energy, lol.

If we found a precambrian rabbit the unifying theory of biology is false.

If we noticed in reality that every time we threw pebbles into a pile, four from one hand, three from the other, we ended up with a pile of ten pebbles - it would be clear that the system of numbers we use to describe those interactions is false.

Poly had a good example of the limits of propositional logic, there are tons more we could add to the pile that we already know about....and insomuch as any of our statements lean on items that may not accurately describe reality - they would be false.

The contents of logic and math are as descriptive and potentially falsifiable as the contents of any given science, or..at least, they could and should be. This is the contention of pancriticalism. We're being asked to consider the supernatural as an unfalsifiable proposition. This is being compared to the contents of science, math, and logic - and if the comparison is accurate, it's contended that the respective positions would then all be reduced to faith, or belief alike.

This obviously cannot be the case if we're able to point out both positivist and falsificationist justifications for holding a position, and can simply and honestly note the limits of any given inference, system, or observation. The contents of the supernatural remain faith based and different from the contents of science, math, or logic, until such a time as the proponents of the supernatural can do the same. It is by their own insistence alone that the propositions fail to have any merit to pancriticalism.

Just as we can set these examples up for the others, the supernaturalist must provide what they believe would constitute evidence for a thing as a sound proposition, show that this evidence has been observed, and that this evidence is not better attributed to some other thing. They must then do the same with what evidence would disqualify a thing as a sound proposition, show that this evidence has not been observed, or that this evidence is better attributed to some other thing. That's what it would take to turn the supernatural apples into cogent oranges.

[polymath257]

It should be pointed out that even math statements like 1+1=2 need to be tested in the real world to determine *when* they apply.

For example, if you pour 1 quart of water and 1 quart of ethanol together, you do NOT get 2 quarts of mixture. You get slightly less. So, in this case, 1+1=2 is NOT a good description of reality.

Another: If you smash 1 proton against 1 other proton, it is quite possible to end up 3 protons, 1 anti-proton, and a number of pions and other particles. The description 1+1=2 is simply not a good descriptor of what happens in this case.

Another: if you take 1 rock and forcefully smash it into another rock, it is quite possible to get 3 or more rocks out at the end. Once again, 1+1=2 is not a good descriptor of what is going on.

And, in fact, those cases where some quantity (like energy) *does* work in a way where addition 'works' consistently are known as 'conservation laws' and are quite important *because* the math works for those cases.

This is a very simplistic case, but the basic idea remains: the application of math to the real world and observations needs to be tested. It is quite possible that the phenomena being studied are not well described by any particular mathematical formalization.

This is why math is a *language* for helping us to understand the world. It alone is not and cannot be definitive about anything, but needs to be tested just like any other scientific issue.

[GrandizerII]

It should be pointed out that even math statements like 1+1=2 need to be tested in the real world to determine *when* they apply.

For example, if you pour 1 quart of water and 1 quart of ethanol together, you do NOT get 2 quarts of mixture. You get slightly less. So, in this case, 1+1=2 is NOT a good description of reality.

Another: If you smash 1 proton against 1 other proton, it is quite possible to end up 3 protons, 1 anti-proton, and a number of pions and other particles. The description 1+1=2 is simply not a good descriptor of what happens in this case.

Another: if you take 1 rock and forcefully smash it into another rock, it is quite possible to get 3 or more rocks out at the end. Once again, 1+1=2 is not a good descriptor of what is going on.

And, in fact, those cases where some quantity (like energy) *does* work in a way where addition 'works' consistently are known as 'conservation laws' and are quite important *because* the math works for those cases.

This is a very simplistic case, but the basic idea remains: the application of math to the real world and observations needs to be tested. It is quite possible that the phenomena being studied are not well described by any particular mathematical formalization.

This is why math is a *language* for helping us to understand the world. It alone is not and cannot be definitive about anything, but needs to be tested just like any other scientific issue.

I agree that math is a language, but when it comes to equations like 1 + 1 = 2, we not only expect this to be precisely true in math but also be unconditionally true in the real world as well, even if not perfectly (in a Platonic sense). The examples you provided aren't simply "1 + 1 = 2" examples, but rather "1 + 1 + some other stuff happening = outcome other than 2". The way I see it, a "1 + 1 = 2" example in real life is one where you assume if you have one particular object and you have another object that is identical to that, then (short of other factors involved that may interfere with their interactions or whatever) we must have only two of these objects, not more not less.

[Belacqua]

Another: if you take 1 rock and forcefully smash it into another rock, it is quite possible to get 3 or more rocks out at the end. Once again, 1+1=2 is not a good descriptor of what is going on.

The examples you've given aren't math problems. They're empirical problems. As such they have empirical tests, of course. 

You have two rocks, you smash them together. Do they merge into one rock? Shatter into a hundred? You're asking about rocks, not numbers.

Empirical statements about rocks need to be tested empirically. That's obvious.

But there are any number of math questions that can't be tested empirically. Negative numbers, irrational numbers, imaginary numbers, infinite sets, numbers larger than the quantity of particles in the universe. 

By declaring a priori that only empirical things are true, and math is always and only a language to talk about that, you are again begging the question. Karl Popper and Roland Penrose disagree with you that numbers are only descriptors of physical states. 

Popper's Three Worlds system shows how non-physical entities also have a kind of existence, not testable through empirical means. They exist, but they have no extension or location.

[The Grand Nudger]

That is not, at all, what three worlds refers to. Holy shit..........?

[polymath257]

Another: if you take 1 rock and forcefully smash it into another rock, it is quite possible to get 3 or more rocks out at the end. Once again, 1+1=2 is not a good descriptor of what is going on.

But there are any number of math questions that can't be tested empirically. Negative numbers, irrational numbers, imaginary numbers, infinite sets, numbers larger than the quantity of particles in the universe. 

By declaring a priori that only empirical things are true, and math is always and only a language to talk about that, you are again begging the question. Karl Popper and Roland Penrose disagree with you that numbers are only descriptors of physical states. 

Popper's Three Worlds system shows how non-physical entities also have a kind of existence, not testable through empirical means. They exist, but they have no extension or location.

Actually, negative numbers and complex (imaginary) numbers are very often used in our physical descriptions. For example, the interference properties of waves use negative numbers and quantum mechanics is a theory that uses complex numbers for the wave functions.

And, once again, math is not testable because *no* language is testable. it is either useful or not. And, in the case of math, a good part is, in fact, useful, but far from all of it.

You seem to be of the opinion that there is only one possible mathematics or logic. And that is quite far from being the case. In fact, after Godel, we know that *every* axiomatic system that is strong enough to talk about the natural numbers *has* to have undecidable questions. And, every such undecidable question splits math into at least two versions: one where the statement is true and the other where it is false.

I can even describe, if you wish, a number of those undecidable questions.

Popper was quite brilliant at one time, but he seems to have fallen off the back of the truck since he started thinking about consciousness. He is usually regarded as somewhat beyond his years now.

The three worlds mythology doesn't help at all.

[polymath257]

Popper's Three Worlds system shows how non-physical entities also have a kind of existence, not testable through empirical means. They exist, but they have no extension or location.

In math, there is a conflict resolution procedure for claims: If I prove something based on the axioms, another can challenge my proof by pointing out a flaw in the argument. I can respond by showing how that flaw does not apply. The ultimate authority is the assumed axioms (usually Zormelo-Fraenkl set theory for modern mathematics). if there is a lfaw in my proof, I have to retract the claim.

In the sciences, there is a conflict resolution procedure. if two people disagree, they find some observation (an experiment, for example) where their views would give different predictions. Then, the result of the observation determines who is wrong. Any views that cannot be tested in this way are considered to be equivalent: the differences don't matter.

So, what conflict resolution procedure do you propose for determining the truth or falsity of claims about the supernatural? If two people make conflicting claims about some supernatural topic, how can the dispute be resolved? It seems to me that in order to make truth claims, there has to *at least* be some sort of process to separate truth from falsity. Both math and science have such. What about the study of the supernatural?

---

It should be pointed out that even math statements like 1+1=2 need to be tested in the real world to determine *when* they apply.

For example, if you pour 1 quart of water and 1 quart of ethanol together, you do NOT get 2 quarts of mixture. You get slightly less. So, in this case, 1+1=2 is NOT a good description of reality.

Another: If you smash 1 proton against 1 other proton, it is quite possible to end up 3 protons, 1 anti-proton, and a number of pions and other particles. The description 1+1=2 is simply not a good descriptor of what happens in this case.

Another: if you take 1 rock and forcefully smash it into another rock, it is quite possible to get 3 or more rocks out at the end. Once again, 1+1=2 is not a good descriptor of what is going on.

And, in fact, those cases where some quantity (like energy) *does* work in a way where addition 'works' consistently are known as 'conservation laws' and are quite important *because* the math works for those cases.

This is a very simplistic case, but the basic idea remains: the application of math to the real world and observations needs to be tested. It is quite possible that the phenomena being studied are not well described by any particular mathematical formalization.

This is why math is a *language* for helping us to understand the world. It alone is not and cannot be definitive about anything, but needs to be tested just like any other scientific issue.

I agree that math is a language, but when it comes to equations like 1 + 1 = 2, we not only expect this to be precisely true in math but also be unconditionally true in the real world as well, even if not perfectly (in a Platonic sense). The examples you provided aren't simply "1 + 1 = 2" examples, but rather "1 + 1 + some other stuff happening = outcome other than 2". The way I see it, a "1 + 1 = 2" example in real life is one where you assume if you have one particular object and you have another object that is identical to that, then (short of other factors involved that may interfere with their interactions or whatever) we must have only two of these objects, not more not less.

And like I said, in any particular case, you have to *test* to see if the mathematical formulation fits the data or not. The whole game is in that phrase 'short of other factors involved that may interfere with their interactions or whatever'. You have to *test* to see if there are such 'interactions' and whether you broke things into 'objects' correctly, and whether there is 'conservation of objects'. Once again, the situations where the math does apply are the interesting ones because they are saying there is a conservation law of sorts.

[Belacqua]

So, what conflict resolution procedure do you propose for determining the truth or falsity of claims about the supernatural? If two people make conflicting claims about some supernatural topic, how can the dispute be resolved? It seems to me that in order to make truth claims, there has to *at least* be some sort of process to separate truth from falsity. Both math and science have such. What about the study of the supernatural?

It depends on how you're defining "supernatural." If you're defining it as that which is unknowable to humans, I'd say that no truth resolution is possible. Because we can't understand it, we can't make claims about it. We might claim that something which seems supernatural has happened, but this would also be untestable. Because that which is outside of nature -- the only purview of science -- can't be tested by science. 

Some people might dislike the idea of having a part of the world which can't by definition be tested. But we can't always get what we want. 

And like I said, in any particular case, you have to *test* to see if the mathematical formulation fits the data or not. The whole game is in that phrase 'short of other factors involved that may interfere with their interactions or whatever'. You have to *test* to see if there are such 'interactions' and whether you broke things into 'objects' correctly, and whether there is 'conservation of objects'. Once again, the situations where the math does apply are the interesting ones because they are saying there is a conservation law of sorts.

Again, you're not talking about math. You're talking about empirically-known situations which are measured by math. 

I want to know whether a googolplex is really smaller than a googolplex plus one. Do we need an empirical test to determine the truth of this? Or is it known through definitions and logic?