Are the terms "atheism" and "theism" logically consistent or useful?

[ynot]

I can try to simplify it further.

T: Are you an atheist?
D: What is an atheist?
T: You are an atheist if you don't believe in God.
D: Which god are you referring to?
T: There is only one god.
D: How do you know?
T: It says so in the Bible.
D: Then aren't you just asking me if I'm a Christian?
T: Well, you could believe in some other god.
D: You said that other gods don't exist so why would it matter?
T: You would be theistic if you believed in some god; that is important.
D: If theism is believing in something that doesn't exist then how is it different from just being crazy?


Are they "mostly agreed-upon concepts" or are they "variably understood"?

Your story is all wrong. It should go like this . . .

T: Are you an atheist?
D: What is an atheist?
T: You are an atheist if you don't believe in God gods.
D: Which god are you referring to?
T: I'm not referring to any actual gods. I'm referring to belief in any gods.

Continue from there . . .

 

[ehcks]

Your story is all wrong. It should go like this . . .

T: Are you an atheist?
D: What is an atheist?
T: You are an atheist if you don't believe in God gods.
D: Which god are you referring to?
T: I'm not referring to a god. I'm referring to belief in gods.

Continue from there . . .

If we're going with "What's an atheist," then we also need to go with
D: Which god are you referring to?
D: What's a god?

 

[ynot]

If we're going with "What's an atheist," then we also need to go with
D: Which god are you referring to?
D: What's a god?

True. My bad

Does Barhl mention "belief" anywhere?

 

[Brian-M]

You are the first person I've ever talked to who stated that his beliefs were chosen at random.

But I didn't state that my beliefs were chosen at random.
I only stated that choosing at random is a valid selection method.

(I also think that choosing beliefs at random would be pretty silly. Only someone who didn't care whether or not their beliefs are likely to be true would adopt their beliefs that way.)

There are situations which don't involve forming beliefs where using randomness as a selection criteria can be useful. In a situation where you need to take action, but have no way to determine which course of action is best, then selecting a course of action at random would be better than taking no action at all.

For example, you're lost in a maze and decide to follow one wall until you find the exit. Which wall do you follow? The one to your left, or the one to your right? And which way do you follow it? The direction you're facing or the direction from which you just came? There's no way to tell which decisions will get you to the exit fastest, so you may as well select one at random.

 

[Lowpro]

If what you said was true then I would agree with you. However, a comparison of selection criteria for an infinite set would take an infinite amount of time. Even something as simple as choosing a random number from an infinite set would take an infinite amount of time. If you feel that you can disprove this you are welcome to give it a try.

I see your confusion

We'll turn it around then. If a theist believes in a subset of Gods, does the selection of one in that subset exclude the rest, making them "atheist" to the rest of those selections? This is because that dependency of "atheist" relies the Gods subset.

That becomes an interesting, if academic, semantics issue. It's like working from Totatheist, polytheist, monotheist or pantheist (pantheist being ambiguous monotheism), and then the atheist.

Again it's an issue of semantics. We are arguably all atheists to Gods we are unaware of (certain cults that deify their leaders for example), though we need not declare it. The question becomes whether atheism is the default state with no selection criteria needed.

 

[phiwum]

If what you said was true then I would agree with you. However, a comparison of selection criteria for an infinite set would take an infinite amount of time. Even something as simple as choosing a random number from an infinite set would take an infinite amount of time. If you feel that you can disprove this you are welcome to give it a try.

I promise that your bizarre ideas have no correspondence to set theory and infinite sets. From what you've just said, it is not only impossible to pick a natural number (23. There. Done!), but it is also impossible to choose the least natural number (0. Done!).

This is just utterly divorced from how mathematics deals with infinite sets. It is your own personal delusion.

ETA: You've spuriously added the word "random" here. Why should we worry about randomly selecting elements?

 

[Lowpro]

I promise that your bizarre ideas have no correspondence to set theory and infinite sets. From what you've just said, it is not only impossible to pick a natural number (23. There. Done!), but it is also impossible to choose the least natural number (0. Done!).

This is just utterly divorced from how mathematics deals with infinite sets. It is your own personal delusion.

ETA: You've spuriously added the word "random" here. Why should we worry about randomly selecting elements?

I'm guessing because computer programs rely something nonrandom to seed a random sequence. Computers producing one number from an infinite set is easy, but to know that the number produced was random would take an infinite amount of time (true regardless of computers; it's central to entropy). The probability of the one number being chosen at random from an infinite set means there's infinite entropy.

In other words, to program a computer to choose a random number from an infinite set is more than just telling it to choose any number, but to actually know/guarantee it to be random too.

Again this is an interesting discussion with respect to Kolmogorov Complexity but equivocating the logic to a semantics issue is a cardinal sin. Essentially, if I gave you a questionnaire that asks: "Do you believe in <insert God>" for every god or deified figure, you'll get responses that answer "no" to at most all but one for theists, and across the board no's from atheists.

 

[Brian-M]

In other words, to program a computer to choose a random number from an infinite set is more than just telling it to choose any number, but to actually know/guarantee it to be random too.

But it's impossible for a computer, or even a person, to pick any number out of an infinite set, due to practical limitations. This is true whether or not you're picking randomly.

Sure, you can say something like "I choose option number five-seven-nine-nine-two-three...." and continue spouting digits for the rest of your life, but you're still limited to the finite number of options which can be described by a short enough string of digits for you to be able to finish giving within your lifespan, so there will always be an infinite number of options you can't select because it would take longer than your entire lifespan to describe even one of them.

The same applies for computers, which may have a larger range of options because of longer possible working lifespans and vastly quicker communications, but these are still finite as well.

But you (and your computer) can still pick randomly from the finite subset of the infinite set which you and it are capable of choosing from.

 

[Lowpro]

But it's impossible for a computer, or even a person, to pick any number out of an infinite set, due to practical limitations. This is true whether or not you're picking randomly.

Sure, you can say something like "I choose option number five-seven-nine-nine-two-three...." and continue spouting digits for the rest of your life, but you're still limited to the finite number of options which can be described by a short enough string of digits for you to be able to finish giving within your lifespan, so there will always be an infinite number of options you can't select because it would take longer than your entire lifespan to describe even one of them.

The same applies for computers, which may have a larger range of options because of longer possible working lifespans and vastly quicker communications, but these are still finite as well.

But you (and your computer) can still pick randomly from the finite subset of the infinite set which you and it are capable of choosing from.

Yup, with a strange caveat. I was wracking my brain for a bit trying to find a way to express what I was saying more elegantly. It's not expressing a number from an infinite set that's difficult, it's knowing that it was expressed with equal proportion to all numbers in that set that makes it infamous.

I guarantee that if you were to say a new number to yourself every second until you die, you will have expressed a number within an infinite set, as infinite sets are wont to have any number. What's difficult is formally computing it.

If I were to place you inside the center of a sphere and have you point to any part of that sphere, you have selected a point in an infinite set. Now what's difficult is actually formally identifying that geometric point in that space (the sphere; a Cantor Space really) even though you just selected it; random or otherwise actually.

 

[fuelair]

I realize you worked hard on this, but I really don't see it as anything more than a semantic game. There are a couple of words and they generally represent mostly agreed-upon concepts. You are then trying to subject the words to math. Math is precise and requires precise inputs in order to generate anything useable. I just don't see being able to do operations on words that are so variably understood.

Got the problem in one. Well done!!!

 

[Tommy Jeppesen]

Are the terms "atheism" and "theism" logically consistent or useful?

barehl, what is the status of the both the "or" and "useful"? I.e. it maybe that the terms in question "atheism" and "theism" are useful, but not logically consistent?

 

[phiwum]

I'm guessing because computer programs rely something nonrandom to seed a random sequence. Computers producing one number from an infinite set is easy, but to know that the number produced was random would take an infinite amount of time (true regardless of computers; it's central to entropy). The probability of the one number being chosen at random from an infinite set means there's infinite entropy.

In other words, to program a computer to choose a random number from an infinite set is more than just telling it to choose any number, but to actually know/guarantee it to be random too.

Again this is an interesting discussion with respect to Kolmogorov Complexity but equivocating the logic to a semantics issue is a cardinal sin. Essentially, if I gave you a questionnaire that asks: "Do you believe in <insert God>" for every god or deified figure, you'll get responses that answer "no" to at most all but one for theists, and across the board no's from atheists.

There are, of course, well-known issues when it comes to probability distributions on infinite sets, as well as interesting interpretations of randomness.

But this has nothing to do with whether I can select an element from an infinite set. Certainly, when we apply "existential elimination" (that is, when we go from "There is an x such that..." to picking such an x), there is no onus on putting a uniform distribution on the set in order to select an element at random.

 

[Norman Alexander]

Perhaps this hypothetical conversation will help:

Atheist to Deist: Do you believe in ten gods?
D: No, less than that.
A: Five gods?
D: No, less than that.
A: Two gods?
D: No, less than that.
A: One god?
D: Yes, just the one!
A: Well I believe in fewer gods than that.

 

[phiwum]

But it's impossible for a computer, or even a person, to pick any number out of an infinite set, due to practical limitations. This is true whether or not you're picking randomly.

With due respect, Brian, poppycock.

Here's a simple example. Take the obviously infinite set of natural numbers. I pick 23. Done.

Now, perhaps what you mean is that one can't pick an element of an uncountable set, like the set of real numbers. But, of course, that's nonsense too. Again, I pick 23. Or pi. Either of these numbers can be specified in a perfectly finite description.

Oh, well, perhaps you meant that it is impossible to describe an arbitrary element of an uncountable set in finitely many words. This might be so. But so what? Since when did we require such a restriction when doing mathematical proofs? (Hint: we don't -- unless we buy into certain minority views about philosophy of mathematics, perhaps including intuitionism[1].)

How many proofs shall I show you which depend on selection of elements from infinite sets? Are we to rewrite textbooks to excise such proofs?
Do you seriously think that mathematicians balk at going from "S is non-empty (possibly infinite)" to "let x be an arbitrary element of S"?

I promise you that they do not. For reference, just please look up, oh, let's say Existential Instantiation (also called existential elimination). Note carefully the fact that there is no requirement that the domain of discourse be finite. (For this fact, you might have to look into models of predicate logic.)



[1] I'm honestly uncertain whether this is really a part of intuitionism. It has been a long time since I studied that school, but it sounds a little like it.

 

[phiwum]

Yup, with a strange caveat. I was wracking my brain for a bit trying to find a way to express what I was saying more elegantly. It's not expressing a number from an infinite set that's difficult, it's knowing that it was expressed with equal proportion to all numbers in that set that makes it infamous.

By "yup", you mean, "nope".

Please recall what Brian said.

But it's impossible for a computer, or even a person, to pick any number out of an infinite set, due to practical limitations. This is true whether or not you're picking randomly.​

What you're talking about is the problem of uniform distributions on countably infinite sets[1]. He's talking about the pseudoproblem of describing an element of an infinite set in finitely many characters.

[1] Not exactly a problem on uncountably infinite sets, where each element can have probability 0, but let us recall that probability 0 does not mean an event is impossible. Therefore, even interpreting the problem in terms of randomness gets us the surprising result that there's no sense to be made of the question for countably infinite sets (since no uniform distribution exists), but there is no problem with selecting a particular element of an uncountable set (though each such element has probability 0 of being selected).

 

[phiwum]

But it's impossible for a computer, or even a person, to pick any number out of an infinite set, due to practical limitations. This is true whether or not you're picking randomly.

Sure, you can say something like "I choose option number five-seven-nine-nine-two-three...." and continue spouting digits for the rest of your life, but you're still limited to the finite number of options which can be described by a short enough string of digits for you to be able to finish giving within your lifespan, so there will always be an infinite number of options you can't select because it would take longer than your entire lifespan to describe even one of them.

The same applies for computers, which may have a larger range of options because of longer possible working lifespans and vastly quicker communications, but these are still finite as well.

But you (and your computer) can still pick randomly from the finite subset of the infinite set which you and it are capable of choosing from.

Ah, I think I see what's going on here. Your response (which, again, plays no role at all in classical mathematics and in terms of the existential quantifier) is, I think, badly misstated, though there may be a simple semantic issue here.

Let S be a subset of T. That is, every element of S is also an element of T. Now, if I select an element of S, then I have also selected an element of T. Do you disagree?

What you meant to say is this: the number of elements which can be described by a finite string is necessarily finite. And that is true[1]. And therefore, I cannot select every element of an infinite set, if selection requires description. But I can sure as heck select some of them, and so it is nonsense to say that this act (selecting an element of an infinite set) is impossible.

[1] But we must be careful here, since if we are allowed to change the interpretations of the descriptions in the middle, so to speak, this is no longer true. I think that someone who studies complexity theory, as Lowpro mentioned earlier, would bring some needed rigor to this discussion.

 

[Manopolus]

I think part of the problem is that when someone is asked their religion, theists don't use "theism" as their response. Atheists are just as diverse in their beliefs (even more so, since many reject dogma of any sort and are very much individual, or one could say in their own category alone), but somehow it's treated as a catch all category where the nuances don't matter.

The fact that it is by nature a completely non-organized belief (or lack thereof) system sort makes it even more insulting to be all thrown into one box categorically. That's good part of why I have issues with the term. I would much rather say that my "religion" is unique to me as an individual, and not properly describable by category. To me, that's a much more accurate way of describing my worldview. Although technically, you can use the term "atheist" and be relatively accurate, the category itself is not useful as far as I'm concerned.

 

[phiwum]

Since this list does not include a common selection criteria, I'm not sure how a selection would be possible. To obtain a selection, it appears that you would need to either make a random choice, choose the entire list, or restrict the list in some fashion until one common criteria is available. People seem to use the term "atheism" as though it has a strong definition but I'm not sure how it would have any definition if "god" is not first defined.

Re-reading your post, I see that this nonsense about selection has nothing to do with your primary claim, which is this: It makes no sense to declare "There is no god," unless the term "god" is well-defined.

And, there is something to be said for this. I wouldn't have an opinion on whether any numbers are flurbles, absent a definition of flurble.

On the other hand, of course, atheism does not occur in a vacuum. Rather, it occurs in a cultural context. The overt atheist is reacting to more or less commonly known alternatives, namely (in most Western cultures) that there is a single all-perfect, all-knowing, all-powerful, all-good diety. The atheist denies this[1].

The atheist denies more, of course. He denies, roughly speaking, that there are any beings worthy of the term "god". Does this require that he have a clear definition of the term? I think not. I think that there are certain characteristics which distinguish gods from non-gods, among them the ability to act contrary to the laws of physics, their immortality, their emphatically spiritual rather than physical nature. Now, not every purported god possesses every such trait, but there is a more or less common theme.

The atheist isn't committed to the view that there is a well-delineated class of gods, and that he doesn't believe in any of them. It's enough that he knows a god when he (metaphorically) sees one, and that that's the sort of thing he disbelieves.

[1] I am phrasing this in terms of so-called hard atheism, since I don't think the issue arises for soft atheism, sometimes called agnosticism.

 

[pgwenthold]

Why does something have to be defined to lack belief in it. In fact, there are an infinite number of undefined things you don't believe in most of which you've never heard of. I can guarantee that right now, you do not believe in an asdlenttocik, because until I wrote it down, the concept never even existrd. However, the mere fact I wrote it down does not make youe lack of belief in it illogical just because you don't know what it means.

In fact, the lack of a definition makes it even more logical to reject it. How can I believe in something if I don't know what it is?

Let those with the belief define it, because they claim to know what it means. I can only go from there.

 

[Brian-M]

With due respect, Brian, poppycock.

Here's a simple example. Take the obviously infinite set of natural numbers. I pick 23. Done.

That only proves that you can pick an element, not that you can pick any element.

I'm pretty certain that there are many natural numbers which would require many googleplexes of digits to describe that you're not capable of picking because you lack the time and means to describe those selections.

What you meant to say is this: the number of elements which can be described by a finite string is necessarily finite. And that is true[1]. And therefore, I cannot select every element of an infinite set, if selection requires description. But I can sure as heck select some of them, and so it is nonsense to say that this act (selecting an element of an infinite set) is impossible.

I wasn't saying that you can't select some of them, my point was that you can only pick from a finite subset of the infinite set, and so therefore Lopro's argument about requiring infinite entropy to know that the computer actually is randomly picking from an infinite set was inapplicable because a computer can't pick from infinite options, but only from the finite subset of those options which it is capable of selecting from.