Atheism's Burden of Proof

[Silmarien]

I don't really have an exact definition. Its a problem that comes up because I'd need to disprove all gods from all religions to be an atheist the way I understand it. But the one unifying feature is a belief that consciousness can exist independently of matter/the brain. God is simply one version of that theme, primarily as a "creator" or first cause.

I'm a theist, and I don't think consciousness can exist independently of matter. I would specify, however, that consciousness as we experience it is quite clearly an embodied phenomenon, mediated by biological processes. An ontologically fundamental analog to it could probably not be considered consciousness in a meaningful sense.

That said, I don't see how it's possible for purely physical processes to give rise to subjective experience even in principle. The ability of living things to transcend their physicality seems to be a strong hint in favor of divine immanence, which is one of the major reasons I find arguments for atheism unconvincing. (Mind you, I like what the panpsychists have to say, but their form of naturalism looks a lot like a de-spiritualized pantheism to me.)

I would say that one of the best thinkers to study to get a grasp on theism in general is actually Plotinus, the founder of Neoplatonism. Many of his ideas worked their way into Christianity, particularly through Saint Augustine, and Neoplatonism is actually disturbingly similar to Vedanta Hinduism, which is the other side of philosophical rigorous theism. You really do not have to disprove every religion independently--I would say that Aristotelian-Thomism would provide a clear picture of theistic rationalism, and Neoplatonism a paradigmatic look at mysticism, both East and West.

I think there are at least two things that have value. The First is simply pleasure. Pleasure gives meaning and to some extent purpose in something to aspire for. I would say that Pleasure is real and is not an illusion of the mind. The fact I may be a single organism on one planet doesn't mean that pleasure is so insignificant that it has no value. It means that my life is part of a much bigger context and what I feel about the world is simply part of a larger picture.

The second is a sense of "consequence". So, its the sense that my life and my actions have consequences. This is probably more like a "transcendental" sense of self because it means that I can "escape" death to the extent that I have consequences that last beyond my own existence, so I leave something behind. Now, in 1000 years time, no-one will remember me or even know my name, but I am part of a stream of cause and effect that flows through history and that gives me a sense of being connected to everyone and everything else beyond my own immediate sensations. [edit: There is a darker undercurrent in that in order to have more consequence you must necessarily have more power. That on the one hand can mean self-improvement, but there is a danger of seeking the illusion of power as a way to escape the fear of death.]

There is a large background noise of potential nihilism but you learn to block it out because it isn't healthy and as an animal, you need to believe your own survival matters. It doesn't have to be rational, but the combination of being happy and being part of something "larger" than yourself satisfy both your immediate and long-term needs.

Does it, though? I've found that embracing the idea that life has inherent meaning and is not merely accidental and ontologically empty reduces my own issues with depression. It's not an easy idea to accept, because I'm naturally pessimistic, but the anxiety of doubt is more positive and productive than the underlying conviction that nothing really matters. ("What if it does?" is a pretty serious Pascalian wager.)

But yes, obviously all I see is the nihilism. I see no consequences, since what follows after me has no more inherent meaning than my own existence--everything disintegrates into triviality. You can hide from that reality, but it will still be lurking in the depths of your psyche. The pursuit of pleasure is an interesting point, though if you spoke to the Buddhists about it, they would say that one seeks pleasure to alleviate suffering, and that liberation is to be found in the cessation of craving. And of everything else. I've come to find the pessimism of Eastern religions very dehumanizing, but I think it is something that needs to be grappled with if you're going to reject theism.

Sort of an after thought...

The "Courage to be" sounds very similar to some of the works of Erich Fromm (a member of the Frankfurt School and a Freudo-Marxist psychoanalyst). He is probably one of my favourite authors and looks like him too.

Heh, well, Paul Tillich is one of the major theologians who was influenced by Heidegger. I'm not really sure to what extent Heidegger influenced the Marxists, but I would expect there to be connections.

Another thing you might be interested in is Immanent Transcendence: Reconfiguring Materialism in Continental Philosophy, by Patrice Haynes. I'm not sure what her religious background is, if any (continental philosophers of religion can be tricky to pin down--our Christians look like Hindus and our non-Christians get mistaken for atheists), but I was reading some of the excerpts from it on Amazon and I think it would be interesting from a dialectical materialist perspective.

 

[Radagast]

... Plotinus, the founder of Neoplatonism. Many of his ideas worked their way into Christianity, particularly through Saint Augustine

I wouldn't quite say that. Augustine did regard the Neoplatonists as the "least wrong" philosophical school, but he was very strongly against certain aspects of Neoplatonism, which are incompatible with Christianity.

There was a big Neoplatonist influence on Judaism, however, and you are correct in pointing out that Plotinus and Porphyry make a strong philosophical case for theism.

and Neoplatonism is actually disturbingly similar to Vedanta Hinduism

The Greeks and North Indians are fundamentally the same people-group, and India was further influenced by Greece post Alexander. It's not surprising that there was a similar philosophical road away from polytheism. That said, there are different schools of Vedanta.

I The pursuit of pleasure is an interesting point, though if you spoke to the Buddhists about it, they would say that one seeks pleasure to alleviate suffering, and that liberation is to be found in the cessation of craving.

I think that many religions share an understanding that the pursuit of pleasure is ultimately futile.

 

[Nihilist Virus]

Well, no, "Amillennialist" doesn't mean that, it means someone who rejects the belief in a literal 1,000 year reign of Christ



Well, no, "Gnosticism" doesn't mean that.

0/2 on this post.

 

[Silmarien]

I wouldn't quite say that. Augustine did regard the Neoplatonists as the "least wrong" philosophical school, but he was very strongly against certain aspects of Neoplatonism. There was a big Neoplatonist influence on Judaism, however.

And on Sufi Islam as well. We may be taking different things from Augustine, though--I'm more Eastern than Western in terms of my understanding of Christianity, and there's a lot more Neoplatonism over there. And Augustine is read differently. When he isn't tossed out the window in a rage, that is.

I would really associate Aristotle with theistic realism and Plotinus with theistic antirealism, though the latter is probably going to be of more interest to a Marxist initially.

The Greeks and North Indians are fundamentally the same people-group, and India was further influenced by Greece post Alexander. It's not surprising that there was a similar philosophical road away from polytheism. That said, there are different schools of Vedanta.

Yeah, but I would say that Advaita probably informs all of them, even the ones that are reacting against its excesses.

 

[Radagast]

And on Sufi Islam as well.

Of course.

I'm more Eastern than Western in terms of my understanding of Christianity, and there's a lot more Neoplatonism over there.

One of the key differences is that, like Christianity, Neoplatonism sees a gulf between God and humanity. However, Neoplatonism and Christianity see that gulf being bridged in radically different ways. For Christianity, it is bridged through the Incarnation.

Yeah, but I would say that Advaita probably informs all of them, even the ones that are reacting against its excesses.

Well, but monist Advaita is really very different, philosophically speaking, from monotheist Dvaita.

 

[Silmarien]

One of the key differences is that, like Christianity, Neoplatonism sees a gulf between God and humanity. However, Neoplatonism and Christianity see that gulf being bridged in radically different ways. For Christianity, it is bridged through the Incarnation.

Oh, absolutely! But I think the concept of God is pretty similar across these religions and philosophies, so an atheist does not need to attempt to disprove them separately. If you can't take down the various forms of philosophical theism, you're in trouble before you've begun.

Well, but monist Advaita is really very different, philosophically speaking, from monotheist Dvaita.

About as different as Spinoza and Leibniz! I'm still not really sure they're ways of looking at God that need to be disproved separately, though--my problem with Spinoza is that he doesn't take into account the universe we see around us, not the picture he paints of the divine. I have a similar problem with Advaita, but I don't think it's relevant to the question of theism vs. atheism.

 

[Radagast]

so an atheist does not need to attempt to disprove them separately. If you can't take down the various forms of philosophical theism, you're in trouble before you've begun.

Indeed! And for a theist, the next question is: Which theism?

 

[ToddNotTodd]

I agree that language evolves, but ultimately language has to correspond to something.

Language "corresponds" to how the various uses of words are strung together to form meaning within groups.

4 (the concept) has to equal 4 (the real property/measurement), and that's why Mathematicians don't arbitrarily change 4 to 5.

"4" isn't a concept, it's a label that we give a concept. You could just as easily say 2 + 2 = cheeseburger, if a group wants to change the label to that.

Why would they want to do that?

Who cares? If it happens it happens, and would be dealt with.

Given that the definition of atheism as "denial" of the existence of god was acceptable for many centuries, what has changed in the past twenty to forty years to mean that an "evolution" of the definition of atheism to "lack of belief" is now necessary?

The evolution of words isn't "necessary". It may be the case that some words retain their same meanings throughout time. It's just the case that words often do change meaning.

As for "atheism", the short answer is, again, who cares why it changed. The "non-belief" version seems to have taken over the "belief in non-existence" definition, as no atheist I've talked to in the past 30 years says that "atheist" must only mean someone who believes gods do not exist. The chart I have below makes sense to most atheists I've dealt with, and so those definitions seem reasonable.

The people I primarily see arguing about it are theists who both insist that language never change (which is nonsensical) and should reflect their definition, which conveniently is an easily knocked down straw man.

People like that seriously remind me of whack job talk show hosts insisting that the word "gay" only means "happy", and that homosexuals are involved in some insidious plot to co-opt the word for some nefarious agenda.

 

[Radagast]

As for "atheism", the short answer is, again, who cares why it changed. The "non-belief" version seems to have taken over the "belief in non-existence" definition.

I don't think the meaning has changed, but sure, use the word however you want. I wasn't interested in talking to you anyway.

 

[ToddNotTodd]

I don't think the meaning has changed, but sure, use the word however you want. I wasn't interested in talking to you anyway.

Do you always tell people who aren't even talking to you (since my post wasn't to you) that you weren't "interested in talking" to them? Seems incredibly rude...

 

[Nihilist Virus]

As I said earlier, I had carefully picked out an example proposition, namely (P => R & Q => R) => (P \/ Q => R), which is constructively true. I can prove it without the law of the excluded middle and without truth tables. But the law of non-contradiction is indeed unquestionably true.

A truth table is just a convenient diagram. You're going to have to rely on an assumption somewhere to prove it. So I don't see your point.

What makes you think that? Nothing in quantum mechanics contradicts the law of non-contradiction.

Simple.

First observe that the law of excluded middle is logically equivalent to the law of non-contradiction:

The law of excluded middle:
Av~A

Apply double negation:
~(~(Av~A))

Distribute:
~(~A~v~~A)

Simplifying the interior yields the law of non-contradiction:
~(~A·A)


How does this relate to quantum mechanics? Well, I'm sure you've heard of Schrödinger's cat. Basically, if a particle is unobserved then it is in a superposition of all possible states at once, but these states are discrete and mutually exclusive. Particles naturally violate the law of excluded middle, and hence they violate the law of non-contradiction. Also look at the double slit experiment.

Huh? I thought I threw in enough brackets to make it unambiguous. And, as it happens, I virtually never use "·" for logical "and."

It would have been unambiguous if you said,

[(P => R) & (Q => R)] => (P \/ Q => R)

or

(P => R, Q => R) => (P \/ Q => R).

When you say

(P => R & Q => R) => (P \/ Q => R)

it can be taken to mean

(P => R·Q => R) => (P \/ Q => R)

I don't know why I'm supposed to understand the "&" to be informal when every other symbol you typed was from the formal language, and when you already went through the trouble of grouping terms. Water under the bridge. But... yeah, you're wrong on this one.

Never said that. I have a PhD,

And on this one I'm in the wrong. I could swear you said you didn't have a PhD. But I looked through the thread and you never said any such thing. So... I apologize, my mistake. You are indeed a mathematician... provided, of course, the PhD is in mathematics.

but obviously I'm not going to post a scan of my certificate or anything like that.

I've never asked you to dox yourself here. If you want to be a private person, I don't care. I was just trying to get your claims straight. Like I said, I apologize for the confusion, and it was my fault.

You did? Was that what that thing about families was meant to prove?

It's an axiomatic system. See, when you say things like this, it makes me wonder what your PhD is actually in. Every mathematician can consider a hypothetical logical system.

It is? Are you using Euclid's definition, or one of the more modern ones?

I was using Euclid's definition, and that's probably not the best idea. If we just define everything with set theory and linear algebra then my position will be unassailable.

In fact, it is an eternal truth about the Euclidean plane.

OK, but if you allow us to define lines with linear algebra, then your eternal truths fall flat. The plane is just RxR, and R is constructed from the Dedekind cuts of Q, and Q={(a÷b)|a,b in Z; b nonzero; gcd(a,b)=1}, and Z=NxN, and N is a set for which *we assume based on nothing* there exists a function f:N-->N such that f is injective but not surjective. This assumption is absolutely not obvious, and intuitively impossible; it is taken as an axiom. Is this one of your eternal truths? Or how about the existence of Ø, the only term which we are actually sure is in N? Ø, shorthand for {}, has no actual definition and is a primitive term. The set itself, the entire basis of mathematics, is a primitive notion which is undefined. Eternal truth?

As far as I know, the only definition of truth in mathematics is "that which follows from the axioms." To say that the axioms are true is to say that they follow from themselves, which is to say nothing at all.

For great circles on the surface of a sphere, it is an eternal truth that any two will intersect. But a sphere, or indeed any Riemannian manifold, can be seen as an object embedded within Euclidean space, so one must distinguish the lines within the manifold from Euclidean lines.

There are no eternal truths.

 

[Radagast]

First observe that the law of excluded middle is logically equivalent to the law of non-contradiction

They're not actually. You're obviously familiar with the range of geometries that exist, and there's a similar range of logics. In particular, constructive logic has the law of non-contradiction but not the law of the excluded middle.

How does this relate to quantum mechanics? Well, I'm sure you've heard of Schrödinger's cat. Basically, if a particle is unobserved then it is in a superposition of all possible states at once, but these states are discrete and mutually exclusive.

OK, I see where you're going, but that doesn't actually violate the law of the excluded middle. And the states aren't exactly "mutually exclusive" either.

It would have been unambiguous if you said,

[(P => R) & (Q => R)] => (P \/ Q => R)

OK, now I get you. What I meant was, in your notation, [(P => R) · (Q => R)] => ((P \/ Q) => R)

I don't know why I'm supposed to understand the "&" to be informal

Of course you weren't. It was a formal "and." My apologies for being unclear and confusing. Mea culpa.

I've never asked you to dox yourself here. If you want to be a private person, I don't care. I was just trying to get your claims straight.

I'm fully aware that I could just as easily claim to be the Pope. You can really only judge me based on my words.

It's an axiomatic system.

It was an axiomatic system, but about people, not mathematical objects. I didn't quite see the point (and I didn't have the time to recast it using modal logic in a form I'd be happy to endorse).

I was using Euclid's definition, and that's probably not the best idea. If we just define everything with set theory and linear algebra then my position will be unassailable.

Up to a point. You can define a line as the set of (x,y) in R^2 satisfying ax+by+c=0 for some a,b,c, but that basically assumes you're in a Euclidean space.

OK, but if you allow us to define lines with linear algebra, then your eternal truths fall flat. The plane is just RxR, and R is constructed from the Dedekind cuts of Q

That's one way of constructing R. There are others.

And the Euclidean plane can still be tackled axiomatically, using the 5 axioms of Euclid.

N is a set for which *we assume based on nothing* there exists a function f:N-->N

I would basically start with N and the Peano axioms, myself. I see them as axiomatising what I learned in kindergarten.

Or how about the existence of Ø, the only term which we are actually sure is in N? Ø, shorthand for {}, has no actual definition and is a primitive term.

Oh, I really don't like that. I consider the Peano axioms for N all intuitively obvious (I can explain most of them to kids). The axioms of set theory, not so much. So I don't much like the Russell approach of defining N in terms of set theory.

You've obviously done a lot of what I call "school mathematics." This tends to assume one specific "official" way of doing things (probably the influence of Bourbaki). In the actual literature, a number of approaches tend to coexist.

As far as I know, the only definition of truth in mathematics is "that which follows from the axioms."

I'm a Platonist (as I said). For me, "true" means "corresponding to reality." For individual steps of a proof, that involves direct intuition. "Yes, I see that," my colleagues and I will say, or "that's obvious."

But if you say Q follows from P, then you're saying that (P => Q) is true. Now either that means "true" in my sense, or it means "following from the axioms" again (the axioms of logic this time), in which case you have a bit of a regress problem.

There are no eternal truths.

In that case, without the laws of logic, I can't see how you can have contingent truths either. In which case we're not communicating, we're just grunting.

 

[KCfromNC]

Well, the quote in blue does express mathematical Platonism, which includes the idea that mathematics is discovered. Most professional mathematicians tend to hold some version of that (and, when it comes to natural numbers, most kindergarten teachers too).

The idea that mathematics is a man-made creation is fairly common, but mostly outside of mathematics itself.

You seem to be implying that being trained in mathematics makes one an expert in philosophy - as if matthematician's opinions are somehow to be trusted more than others? I'm not sure that makes sense. And in any case, it doesn't really matter since like much of philosophy there's no established method to determine which opinion is true.

 

[KCfromNC]

As I said earlier, I had carefully picked out an example proposition, namely (P => R & Q => R) => (P \/ Q => R), which is constructively true. I can prove it without the law of the excluded middle and without truth tables.

But you can't prove it without certain particular rules humans made up. Make up different rules for how => works and you get a different answer.

 

[Nihilist Virus]

They're not actually. You're obviously familiar with the range of geometries that exist, and there's a similar range of logics. In particular, constructive logic has the law of non-contradiction but not the law of the excluded middle.

OK. So which of the logics is the one that is unquestionably true?

OK, I see where you're going, but that doesn't actually violate the law of the excluded middle. And the states aren't exactly "mutually exclusive" either.

I won't pretend to understand quantum mechanics, but everything I've read has indicated that an electron having both an up spin and a down spin at the same time is like a person being both alive and not alive at the same time.

OK, now I get you. What I meant was, in your notation, [(P => R) · (Q => R)] => ((P \/ Q) => R)



Of course you weren't. It was a formal "and." My apologies for being unclear and confusing. Mea culpa.

OK.

I'm fully aware that I could just as easily claim to be the Pope. You can really only judge me based on my words.

Fair enough.

It was an axiomatic system, but about people, not mathematical objects. I didn't quite see the point (and I didn't have the time to recast it using modal logic in a form I'd be happy to endorse).

I fail to see the problem.

Up to a point. You can define a line as the set of (x,y) in R^2 satisfying ax+by+c=0 for some a,b,c, but that basically assumes you're in a Euclidean space.

I think the notion of a line can be generalized further than that. R is just a go-to example of a set with certain "nice" properties.

That's one way of constructing R. There are others.

And the Euclidean plane can still be tackled axiomatically, using the 5 axioms of Euclid.

Two things.

First, that's exactly my point. There are multiple ways of constructing mathematics. So which set of axioms has the "unquestionable truths"?

Second, it would be silly of me to bounce back and forth between DP and ZF when constructing everything, wouldn't it?

I would basically start with N and the Peano axioms, myself. I see them as axiomatising what I learned in kindergarten.

Here, you're responding to your own strawman. You snipped my sentence in half, right in mid-thought, and you completely removed the other half without addressing it.

Oh, I really don't like that. I consider the Peano axioms for N all intuitively obvious (I can explain most of them to kids).

Uh, then why do you cherry pick in your replies? You snipped out the function f that I described. Its existence is not obvious. I would say that if the existence of f is obvious to someone, then they're not a genius but rather they're insane. Yet its existence is absolutely necessary if you want to have an infinite set. Infinite sets exist if and only if some such f exists.

Is the existence of some such f an eternal truth?

The axioms of set theory, not so much.

So... there are some axioms which are not obvious. OK, good. You said that the axioms for N are intuitively obvious. Whether you take the existence of f to be a precondition for N's existence or a consequence of N's existence, I still don't see how it is obvious that f must exist - even to someone for whom it is obvious that there are infinitely many natural numbers.

Do you intend to tell me that the axioms generating N are obvious and intuitive, but that there are some non-arithmetic truths about N which are not obvious?

So I don't much like the Russell approach of defining N in terms of set theory.

Why? Because set theory axioms are not intuitive? Well if you just ignore the ones that aren't intuitive like you did before, you'll be fine.

You've obviously done a lot of what I call "school mathematics." This tends to assume one specific "official" way of doing things (probably the influence of Bourbaki). In the actual literature, a number of approaches tend to coexist.

Again:

First, that's exactly my point. There are multiple ways of constructing mathematics. So which set of axioms has the "unquestionable truths"?

Second, it would be silly of me to bounce back and forth between DP and ZF when constructing everything, wouldn't it?

Do you really expect me to list all characterizations of mathematics all at once in a single post?

I'm a Platonist (as I said).

My condolences.

For me, "true" means "corresponding to reality."

In a scientific sense, that's what true means. But in a mathematical sense, you'd have to be joking to say that. I thought it was clear which of the two topics we were on here.

For example, is it true - in the sense that you're saying - that there is no largest prime? We can show this mathematically - since it follows from the axioms - but can you show me how this corresponds to reality? Because in reality, infinity is a fiction as far as we can tell. There is a finite number of particles in the observable universe, and a finite number of Planck volumes. If we count everything up and we come up with the maximum integer, n, and then you want to discuss n+1, I could say, "What are you talking about? n+1 does not correspond with reality, so it is not true that it exists."

For individual steps of a proof, that involves direct intuition. "Yes, I see that," my colleagues and I will say, or "that's obvious."

Your point being what, exactly? The limit of the sequence 3, 3.1, 3.14, 3.141, ... is obviously pi. What does this have to do with reality? Every time I look under a rock, I fail to find an infinite sequence of numbers.

But if you say Q follows from P, then you're saying that (P => Q) is true. Now either that means "true" in my sense, or it means "following from the axioms" again (the axioms of logic this time), in which case you have a bit of a regress problem.

I'm well aware of the regress problem. In mathematics, everything is ultimately given in terms of undefined symbols. Logic and mathematics, ultimately, is just the pushing of symbols. Hence my nihilism.

But it is a fantasy to think that physical reality does not share this problem. Maybe start with this interview of Dr. Richard Feynman.

Spoken language has the same problem as well, of course. Instead of using primitive terms, so that a successive sequence of definitions ultimately terminates, spoken languages go in circles. Every word is defined in terms of other words.

There is no escaping the regress problem.

In that case, without the laws of logic, I can't see how you can have contingent truths either. In which case we're not communicating, we're just grunting.

Sort of a cartoonish reality you're presenting there. But ultimately you're just making an appeal to consequences: "I prefer that there is something that is unquestionably true, and that words have meaning, so these things must be so."

 

[Radagast]

You seem to be implying that being trained in mathematics makes one an expert in philosophy

I'm suggesting that, in the philosophy of mathematics, the opinions of mathematicians deserve respect.

 

[Radagast]

But you can't prove it without certain particular rules humans made up. Make up different rules for how => works and you get a different answer.

If you think the laws of logic are made up, gronkle squarb. Slurgz.

 

[Radagast]

OK. So which of the logics is the one that is unquestionably true?

I'm happy with classical logic.

is like a person being both alive and not alive at the same time.

"Alive" and "dead" are mutually exclusive, but the cat being in-a-superposition-of-alive-and-dead is fine.

There are multiple ways of constructing mathematics. So which set of axioms has the "unquestionable truths"?

I'm not going to argue the truth of the axiom of choice.

You snipped out the function f that I described. Its existence is not obvious.

N does not have a mysterious "f." It has a successor function, which I learned in kindergarten.

But in a mathematical sense, you'd have to be joking to say that.

Not at all. Like I said, and like most professional mathematicians, I'm a Platonist.

Because in reality, infinity is a fiction as far as we can tell. There is a finite number of particles in the observable universe, and a finite number of Planck volumes.

Like I said, and like most professional mathematicians, I'm a Platonist. Numbers exist, but not in the physical universe.

Your point being what, exactly? The limit of the sequence 3, 3.1, 3.14, 3.141, ... is obviously pi. What does this have to do with reality? Every time I look under a rock, I fail to find an infinite sequence of numbers.

Maybe I could make a constructivist of you...

I'm well aware of the regress problem. In mathematics, everything is ultimately given in terms of undefined symbols. Logic and mathematics, ultimately, is just the pushing of symbols. Hence my nihilism.

If that's all logic and mathematics are, the foundation of science vanishes, so your nihilism has to be total.

And it's logical of you, I guess -- historically a non-nihilist view is connected to theism.

But this is starting to get boring. Merry Christmas, and goodbye.

 

[Radagast]

.

 

[Nihilist Virus]

I'm happy with classical logic.

OK... thanks for that... but I was asking which logic is actually true beyond question.

If I want to get a piece of artwork insured, and the insurance salesman asks me what it's worth, I can't just say, "I'm happy with $1B." He'd want some documentation.

Being as charitable as possible, should I assume that you mean to say that you affirm classical logic is the form of logic that is true beyond question? But then when I ask for your supporting evidence, you will have none - you cannot support axioms with evidence unless you have even more axioms, and obviously we have a regress problem.

So I'm left thinking that you actually mean what you literally said. And if that's the case, all onlookers should see how vacuous your views are.

"Alive" and "dead" are mutually exclusive, but the cat being in-a-superposition-of-alive-and-dead is fine.

Interesting. Could you elaborate?

I'm not going to argue the truth of the axiom of choice.

I said,

There are multiple ways of constructing mathematics. So which set of axioms has the "unquestionable truths"?

Your answer is a non sequitur here. I don't see the relevance, unless you intend to say that there exists some meta-axiom which allows us to choose from existing equivalent axiomatic systems. But even then, the axiom of choice is something else entirely.

N does not have a mysterious "f." It has a successor function, which I learned in kindergarten.

You've misidentified the axiom of choice, and now you are saying that there does not exist a function on N which is injective but not surjective. I don't know what your PhD is in, but I'm finding it difficult to believe that it's in mathematics.

The Hilbert Hotel thought experiment explains why f exists on infinite sets.

Not at all. Like I said, and like most professional mathematicians, I'm a Platonist.

I never met a PhD in mathematics who sympathized with Platonism.

Like I said, and like most professional mathematicians, I'm a Platonist. Numbers exist, but not in the physical universe.

But infinite quantities don't exist in physical reality, do they? So would you argue that infinite sets don't exist, since they cannot correspond to reality?

Maybe I could make a constructivist of you...

You'd have to start arguing a convincing case, but yes, you could. Unlike the Christians here, I don't start with a conclusion and work backwards to support it with evidence; rather, I follow evidence where it leads.

If that's all logic and mathematics are, the foundation of science vanishes, so your nihilism has to be total.

As a nihilist I do not lend absolute credulity to invented concepts. I only allow for degrees of certainty. That's all nihilism is to me.

As for how this plays out in reality, I find nihilism to be irrelevant. I'm not going to leave my hand on a hot stove because I'm not 100.000% sure of what is happening. I'm not going to slash someone's throat because I want their pair of sneakers and I'm not 100.000% of what is happening to them.

And it's logical of you, I guess -- historically a non-nihilist view is connected to theism.

Nonsensical. I assume you meant to say that it is consistent of me to be a nihilist. Even then, it's a silly thing to say.

Most people throughout history have been theists. You go back before the age of Christianity, and most people were polytheists. So when the trinity was invented, there could have been scoffers saying, "Ha! Only one, er, three, but yet one god? How could there only be one(ish) god?"

In any case, it's clear that atheism is the winning side if this is how you want to measure things. Theism is dying, and everyone knows it.

But this is starting to get boring. Merry Christmas, and goodbye.