Pre-amble: Recovering RC (old-school German version no less). Took 30+ years to finally break free and become an atheist, through negative religious experiences, gradual self-reflection and rationalization (I suspect my degree in Math/Computer Science also had something to add).

Now to my paradox. My (and Dawkins', and probably every other atheist's) quest for truth (resulting in atheism) has been fundamentally based on rationalization. But I cannot mentally get past my own following (ironically rational) argument:

- Rationalism is based on logic.
- Logic is ultimately based on set theory (like most math).
- Sets are groupings of like entities.
- No two real entities exist alike (due to Heisenberg uncertainty, or other quantum-level concept).
- So sets cannot exist (except for abstractions).
- So logic has no foundation.
- So rationalism is impossible.

Seriously, this personal paradox is vexing me - someone please help with where my rationale is breaking down!


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Replies to This Discussion

It looks like you are using "set" with different definitions on separate lines of inquiry. Why would two items have to be identical at the quantum level to be considered a set?

Additionally, even if we can never show that logic is actually how the universe works, it sure seems to get stuff done. Its pragmatic to use logic in the real world, as it works. As far as we can tell, its the real universe, but perhaps behind the logic we see there isn't actually logical processes. We can't see them, so why assume they are there? Additionally, until we have evidence of the failure of logic, even if we can't prove it is the basis of reality, we might as well go with it. Maybe someday we'll be proven wrong, but that's just part of being a fallible mortal.
Johnny, atheism is the absence of theism, something that was invented by irrational people. I think a long bow is being drawn in connecting a non-entity with rationalism. Though I am not familiar with mathematical definitions it seems from your argument that sets can exist for abstractions, a fine home for rationalism. Perhaps I am not sure what you mean by "exist", or "impossible".
Instead of trying to find a completely rational basis for your beliefs or lack of them, you might want to consider them as working hypotheses. In the absense of evidence for the existence of gods, the null hypothesis (i. e. atheism) seems to be the correct one. What Stephan says above is spot on: the rational operations that lead us to conclude that there are no gods may be unsound, but they work most of the time. It doesn't get any better than that.
How bout logic is based on rational arguments. The ability to put an argument together to prove anything is critical. The problem with logic based arguments in this reality is that everything is in flux. It's hard to argue your point when everything is in flux. I think the most important thing for me to keep in mind is even though I've worked through to a logical conclusion on one issue, to keep open to new input. Truth is complex. I think we do ourselves a disservice to try and simplify too much or set our minds solid in one area. That said. You can't prove anything unless you assume a solid foundation in 'something'.

OK, I'm getting lost in my definition and my kids are trying to drive me crazy. Bottom line, I read that you may be putting two and two together but they are apples and oranges?
Stephen, sounds like you are suggesting that atheists just have to take logic "on faith"! :-)

It has since occurred to me that perhaps I am falling into the same trap as "prove/disprove the existence of God".

Something I also recall from my Math years is the concept of "metalogic", which formulates the system of logic you are using. But then what is the meta-metalogic for that metalogic? And we just fall back into the same old "first mover" problem again.

So I guess everything comes down to the mental models and base principles that form one's belief system of reality. In the past, it was top-down god-entities. Now it is logic, math, scientific method, and bottom-up self-organizing systems. Perhaps the next leap is quantum physics & statistics, which humanity is only now transitioning through!

Regardless, the human-created model will always live in ours heads and not in actual reality (at least as far as we will be able to know). I have probably been mixing the two. So I guess I will just have to be satisfied with my human limitations (and be thankful for the privilege). The important difference from the religious folks is that I remain open to the possibility of a paradigm shift - a new base model for how things work (as Pablo suggests below).

Thanx folks!
I assume when you said Stephen you meant me. Note how I said nothing like faith. I said, IT WORKS. Based on the evidence, it seems true. Using logic and rational thought processes gets the same answers (or predictable ones at least) from the universe time and again.

I do not for an instant assume that it is true, I simply have no evidence to the contrary and all of modern science in support.
Did I hit a nerve with an "idiotic metaphor"? :-)

BTW, what are you blathering on about? Not sure I see the relevance of most of what you wrote.
Something I also recall from my Math years is the concept of "metalogic", which formulates the system of logic you are using. But then what is the meta-metalogic for that metalogic? And we just fall back into the same old "first mover" problem again

Methinks you're adding to the confusion with another false analogy. It's true that both meta-disciplines and the "first mover problem" have an infinite regression aspect, yet I don't think they're at all comparable. In the latter, you're walking along a line of causal elements, trying to determine if or where this line begins. In the latter it's "thinking outside the box": like you're adding dimensions to an already existing space. There's no causal relationship between the 'meta' layers. It makes no sense to try to find a first mover cause here (as we could always add an extra dimension, so we're mathematically certain there's no first mover in this case). And thus, while metalogic is a potent and interesting tool in itself, this potency and interest quickly wanes as you add more 'metas'.
I do not disagree... I just threw in that meta-logic thing because I wanted to mention it originally, but forgot. I have since moved on to a more general separation of reality on the one hand and human mental models of reality on the other.

Thanx though! I appreciate your "waning potency" description.
Well, for starters, there is NO WAY to show that the universe doesn't work by logic. How would you do it?

"Look! I've proven that logic doesn't work!" [as you explode in a puff of greasy black smoke]

Besides, you talk about sets of LIKE entities, not EXACT entities.

I can has a set of all kittehs, but no one presumes that they are all quantum-identical kittehs (not even if they're from the set of "all the times my family has sat down at the Thanksgiving Dinner Table and discussed Schroedinger's Cat"-type kittehs).

So your logic still stands. Even though your logic (as I've just shown) is wrong.

Johnny said: "- No two real entities exist alike (due to Heisenberg uncertainty, or other quantum-level concept)."

I agree with Boothby171 who said: "Besides, you talk about sets of LIKE entities, not EXACT entities."

And I would add that Johnny seems to be getting into icky metaphysical *entitlement* land. As though close scrutiny of rationality and how it comes together in a materialistic universe were ever guaranteed to validate any preconceived notions about how perfect it is "supposed" to be. It's called "rounding" or "heuristics" or "close enough for practicality sake." It appears that (surprise, surprise) evolution didn't consult Kant or Hume before just making something that got the job done. Thank God! And even our formalizations of raw rationality the conventions of our minds present are only "perfect" hypothetically, but not ever in actuality. One wonders why anyone would care. Alas, lots of n00bs do. Rather than being an "undermining" of rationality, the common sense approach (given that you can't refute reality with expectations) is to *understand* what is actually going on and to what extent it is going on and why. Pocket calculators are under the same materialistic constraints as our brains. We don't doubt their conclusions because of "set theory" or "quantum mechanics." And we don't call them magic either just because we're being philosophically inept. We just do our bills regardless of whether 1 + 1 = 2 varies at an absolutely unnoticeable subatomic level from calculator to calculator. "Oh noes! Only 99.999999999999999999999999999999999999999999999999999999999% accuracy!!??! Throw out materialism!"

Then we can pick on the alternative as well if for whatever reason good sense has yet to kick in (if you are at all familiar with the various "arguments from reason" floating around out there). What exactly is the irreducible rationality that theism tends to promote? Rationality is a very complicated process and they want to melt the entire concept in their pan of magic, just because they don't notice atoms at work when they think thoughts. One fallacy of composition later (since a thinking brain "can't possibly" be made up of all non-thinking parts, *eyeroll*) and they are suddenly not responsible for the philosophical monstrosity they've backed themselves into "necessarily." They churn out so much nonsense (despite even critics on their own side of the argument pointing out how ridiculous much of it is) contrary to evolution, brain science, and computer science to defend their arguments from psychological appearances.

I guess you'd have to know a lot more about what they say before debunking it further would make any sense and I've probably already gone too far. If not let me know.

I was not very clear in what I was trying to say I guess... let me try again using the kitten motif:

You can never have more than one real "kitten", because you can never define "kitten" accurately enough, or compare two (or more) entities to your definition (or to each other) accurately enough to conclude absolutely that you have two real kittens (i.e., a set of kittens). The only way for that to happen is via *abstract* kittens in your mental model of reality.

In other words, humans make things equivalent as a convenience because they are unable to detect (or do not care) about the error between the things (as Ben indicates).


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