How do atheists get around determinism?

[warpspeedpetey]

Consider arithmetic sentences of the form (Forall x, H(x)), where H() is an easily testable predicate, e.g., you can find out if H(17) is true or false just by pressing a few buttons on your calculator. Let U be the set of all such arithmetic sentences.

Chaitin is using the principle of the excluded middle here, so he is assuming that (Forall x, H(x)) is either true or false. If it is false, then there is a specific value n such that H is false, and you can use your calculator to verify this. Call n a counter-example. Let CU be the subset of all sentences in U that have counter-examples.

Also consider proofs of (Forall x, H(x)). These are verifiable as well, because proofs must start from given axioms and must use sound rules of inference. Let PU be the subset of all sentences in U that have proofs, i.e., reasons.

What mathematicians have shown is that PU union CU is a proper subset of U, that is, there are an infinite number of arithmetic sentences in U that are neither in PU nor CU. Chaitin has some extension/variation of this result that I’m not really familiar with. I’ve seen his talk on Omega, but I haven’t really read his work.

Anyway, let RU = the rest of U, i.e., the subset of all sentences in U that are neither in PU nor CU. Mathematicians refer to sentences in RU as true because of the principle of the excluded middle, as we know that the sentences in RU have no counter-examples. In terms of the PSR, sentences in RU are true because they are true – there is no other reason for them being true other than that they are true.

It’s kind of like saying the reason there is a sandwich on my table is that, look and see, there is a sandwich on my table. It’s not lunch time, no one put it there, …, there are no reasons for the sandwich other than that it clearly exists because I can see it. Chaitin finds this to be a disproof of the PSR.

if there is no reason for them to be true, then how do we know they are true? Chaitin seems to take mathematical objects and their manipulation apart from reality as something more than machination, i wonder, do you think that it occured to him that there is no example of this in reality, yet there is an infinite set of RU? it shouldnt we have a universe full of sndwhiches popping into and out of existece?

 

[Just_Lurking]

if there is no reason for them to be true, then how do we know they are true?

It’s a non-constructive existence proof: (1) Assume that mathematical statements of the form (Forall x, H(x)) are either true for a proof/reason, or false by means of a counter-example; (2) Derive a contradiction, via a diagonalization argument; (3) Conclude that there must be a mathematical statement of that form that is not false, because there is no counter-example, yet it doesn’t have a proof either.

This proof does not show us how to construct such a mathematical statement, so we can’t write one down. In fact, the proof does not show us how to recognize such a mathematical statement if it was right in front of our faces. (In fact, prior to Andrew Wiles’ proof of Fermat’s Last Theorem, there was plenty of speculation that Fermat’s Last Theorem was one of these true but unprovable mathematical statements.) Yet the assumption that the PSR applies to mathematics leads to a define contradiction.

Chaitin seems to take mathematical objects and their manipulation apart from reality as something more than machination, i wonder, do you think that it occured to him that there is no example of this in reality, yet there is an infinite set of RU?

Chaitin is using mathematics to investigate the nature of mathematics, rather than metaphysics, and he is getting different answers than metaphysics.

it shouldnt we have a universe full of sndwhiches popping into and out of existece?

The status of the members of RU doesn’t change randomly over time. So the appropriate metaphor would be a universe full of sandwiches that exist for no reason other than they are there.

 

[warpspeedpetey]

I have no need to refute a claim which lacks sufficient support. I simply decline to accept it until such time that said support is proffered.

sure you do, you have to show that its arguments are insufficient. simply asserting so is nothing but dodging.

so why is it in sufficient? do scientists not expect a cause for an observed effect? do they think that things simply happen for no reason? if so how do you explain the massive amount of scientific research

I’m not sure what you mean by this. Probability theory is about as solid as a science gets, short of pure logic. I wouldn’t know what to tell you if you doubted its applicability.

in other words probability doesnt lead to a particular outcome, just a probable one, how is that trustworthy? maybe you mean something else, but probability simply means not knowing or being able to calculate all the factors involved in an event. if you flip a coin, but had all the relevant information to the event, the outcome would be a certainty. but what doesn this have to do with anything?

The PSR is a principle–that is, a statement, which can be true or false, not a behavior to be acted out or suppressed.

its the principle or reason for their behavior.

I’m afraid you misunderstood me. Scientists needn’t care one bit about the PSR, regardless of their field of expertise. As I mentioned previously, the PSR is simply beyond the scope of scientific relevancy, given current technology.

ummm…how so?, it seems to me regardless of technology, scientists reserch the causes for events all the time.

Now, in the field of cosmology, I would suspect (although I do not know for certain) that you will find more scientists aware of the PSR than in other fields, and thus in cosmology you may (or may not) find open denial of the PSR.

However, open denial is just icing on the cake, so to speak. Regardless of whether scientists are aware of the PSR and/or talk about it, the PSR is not a prerequisite to their research, or to a rational interpretation thereof.

im not sure what you may think scientists being aware of aor talking about the PSR has to do anything? why is that important?

but yes it is a prerequisite to research investigating any observation, and implicit in research to find a way to cause an effect.

why are you even denying this? no one does, are you just being contrary? your going against even those who generally hold the PSR to be false in the sense that it can explain the universe. even mackie would admitted it. its not even something debatable. the debate is to whether or not it can be an explanation for the universe.

Any particular explanation starts with premises which state `brute facts,’ and although the brutally factual starting-points of one explanation may themselves be further explained by another, the latter in turn will have to start with something that it does not explain, and so on however far we go. – the miracle of theism

now, mackie was an atheist, and in general atheist are the only set interested in denying the PSR, but here you see that he does not deny the PSR in relation of one fact to another, when attacked by adler for the same reason, he says that the PSR cannot be extended to G-d, in that some fact must be unexplainable. his arguments from there are weak in my view. but for this point even he admits the PSR to the method of scientiffic inquiry.

in short, your picking the wrong battle.

 

[warpspeedpetey]

It’s a non-constructive existence proof: (1) Assume that mathematical statements of the form (Forall x, H(x)) are either true for a proof/reason, or false by means of a counter-example; (2) Derive a contradiction, via a diagonalization argument; (3) Conclude that there must be a mathematical statement of that form that is not false, because there is no counter-example, yet it doesn’t have a proof either.

its just a bunch of word games to me. the premise are restricted to form the desired conclusion, yet we find no such examples in nature. i understand that you may see mathematical objects as real in some fundamental way that i as a lay person do not, but do you find this convincing?

This proof does not show us how to construct such a mathematical statement, so we can’t write one down. In fact, the proof does not show us how to recognize such a mathematical statement if it was right in front of our faces. (In fact, prior to Andrew Wiles’ proof of Fermat’s Last Theorem, there was plenty of speculation that Fermat’s Last Theorem was one of these true but unprovable mathematical statements.) Yet the assumption that the PSR applies to mathematics leads to a define contradiction.

im not sure that it is a proof in any way but the narrowest mathematical sense. there are some pretty hokey premise’ that one would have to agree to.

Chaitin is using mathematics to investigate the nature of mathematics, rather than metaphysics, and he is getting different answers than metaphysics.

it seems he is creating a very specific strict model that is built to reach a certain conclusion, as opposed to a robust model that can handle stronger premise’

The status of the members of RU doesn’t change randomly over time. So the appropriate metaphor would be a universe full of sandwiches that exist for no reason other than they are there.

technically we are shamelessly switching metaphors, in this scenario, we are dealing with the form, if something is true there is a reason it is true. though i think in some strange way he is claiming the necessity of the sanwiches, clearly they could have been hoagies. lol

 

[Just_Lurking]

its just a bunch of word games to me. the premise are restricted to form the desired conclusion, yet we find no such examples in nature. i understand that you may see mathematical objects as real in some fundamental way that i as a lay person do not, but do you find this convincing?

It’s a pretty standard proof in recursion theory. It’s one of the more useful results from studying the arithmetic hierarchy (see here).

im not sure that it is a proof in any way but the narrowest mathematical sense. there are some pretty hokey premise’ that one would have to agree to.

I don’t see what premises you are talking about. As I said, this is a standard proof, using standard mathematics. I had to answer questions about this and about Godel’s Incompleteness Theorem in my dissertation defense. One can question the application of this branch of mathematics to the metaphysics of PSR, which is why most mathematicians avoid metaphysics. Chaitin is one of the few mathematicians that tries to reach into the metaphysical consequences of math.

it seems he is creating a very specific strict model that is built to reach a certain conclusion, as opposed to a robust model that can handle stronger premise’

No one is creating any specific model. This is a proof in and about the standard model that all of modern mathematics uses.

Also, this is a very general result, applicable across a wide range of applications. Imagine that it is just saying that the set of true things is much bigger than the set of reasons that things are true, therefore there must be some true things left without reasons. The theorem is just like this, except that instead of “bigger”, substitute “more complicated”.

technically we are shamelessly switching metaphors, in this scenario, we are dealing with the form, if something is true there is a reason it is true. though i think in some strange way he is claiming the necessity of the sanwiches, clearly they could have been hoagies. lol

Yes, the metaphor is straying deep into metaphysical territory. I’m much more comfortable in the mathematics side, which is why I find computational metaphysics so interesting. It’s all based in math.

 

[warpspeedpetey]

I don’t see what premises you are talking about. As I said, this is a standard proof, using standard mathematics. I had to answer questions about this and about Godel’s Incompleteness Theorem in my dissertation defense. One can question the application of this branch of mathematics to the metaphysics of PSR, which is why most mathematicians avoid metaphysics. Chaitin is one of the few mathematicians that tries to reach into the metaphysical consequences of math.

the premise’ you listed.

(1) Assume that mathematical statements of the form (Forall x, H(x)) are either true for a proof/reason, or false by means of a counter-example; (2) Derive a contradiction, via a diagonalization argument; (3) Conclude that there must be a mathematical statement of that form that is not false, because there is no counter-example, yet it doesn’t have a proof either.

im not a mathematician, so i may not know the right words, but these are the basic structures from which he draws conclusions. though he isnt reaching into metaphysics in a sense that means something to a metaphysician, in that it is the study of the nature of reality, the conclusions he reaches have no reality, they arent even demonstrable in the sense that there are any examples reflected in the real world. it just looks like word games to me.

No one is creating any specific model. This is a proof in and about the standard model that all of modern mathematics uses.

Also, this is a very general result, applicable across a wide range of applications. Imagine that it is just saying that the set of true things is much bigger than the set of reasons that things are true, therefore there must be some true things left without reasons. The theorem is just like this, except that instead of “bigger”, substitute “more complicated”.

after alot of rereading, i get it, but i still dont see it as a meaningful statement of anything.

Yes, the metaphor is straying deep into metaphysical territory. I’m much more comfortable in the mathematics side, which is why I find computational metaphysics so interesting. It’s all based in math.

and im much more comfortable on the metaphysics side. to me if math doesnt reflect in reality, then the abstraction becomes to great to matter until such a situation exists. i suppose the same may be said for a number of ontological abstractions. im just more comfortable with those.

 

[James_S_Saint]

How do atheists get around determinism??? - How do you get around anything? - With practice and determinism.

 

[johankrava]

1. The world is rational, and everything can be sufficiently explained.
2. Everything has a knowable cause.
3. Nothing can go against the laws of nature and thus everything acts according to those laws

Ironically another thing most everyone believes is

1. We have free will

OK, here is how I see the world / I will limit myself to physics:

Everything can be sufficiently explained.
Not yet. We try to find law that run the world - scientific approach…
There are still unanswered questions (origin of big bang, fundamentals of gravity, origin of mass…)
We experiment to find the rules.

Everything has a knowable cause.
It has, however, we still don’t understand some causes.

**Nothing can go against the laws of nature and thus everything acts according to those laws.
**oxymoron?
We observe and try to find rules/laws and explain every phenomena.
If something behaves differently than expected then we have to change/modify the law.
A typical example is Newton’s mechanics. Works perfectly in our world.
But if we have speeds near the limit (speed of light), then we have to take into account effects of relativity.

And finally, We have free will
Yes and no. We thing we have.
We believe that we decide because we have free will.
We are just a bunch of tissue / molecules / atoms / particles.
There are fundamental physical laws that define relations between particles in our body.
However, the system of particles in our body is SO COMPLEX that we can not treat it this way.
On the other hand if we look at the particle level, there is no certainty. We have to deal with randomness. We still do not understand quantum physics enough.

And now the answer - How do atheists get around determinism?
I think there is no need to go around.
All you need is understanding of the world. And each has it’s own.