Monday, January 21, 2013

On reality and logic

Cogito ergo sum, right?

A chief goal of religious apologists, and indeed, any philosopher that plays in ontology, is to demonstrate logical necessity that something must exist. The problem with this is that it puts the cart before a really big horse. The following commentary on this phenomenon appears largely as is in a comment on John Loftus's Debunking Christianity blog, on a post about the use of mockery and ridicule.

Generally speaking, I find this to be an enormously common fallacy, more common the more of a philosopher one considers him/herself to be. Again, this error is not limited to theists, though exceptionally common amongst them since ontological arguments are often central to their efforts.

Indeed, as weird as it is, a philosopher could prove "logical necessity" for the existence of some entity, say a deity, and yet no such entity must actually exist. If the logic used doesn't really match reality, we can prove all sorts of things are logically necessary and yet physically meaningless.

Indeed, it is actually easy to think of examples of this if one is properly prepared for and then spends any serious time studying mathematics, particularly transfinite math. Take, for instance, numbers that are so large as to be essentially meaningless, and I'm not talking about cute little big numbers like googolplex or Skewes's number. Sure, those are fantastically big, but they're smaller than most. There's an entire branch of mathematical philosophy known as "ultrafinitism" that says that at some point, those numbers really don't mean anything. Certainly, just because we can produce some sort of notation that indicates what they are, and because the axioms underlying number theory guarantee that they "exist," it is not incumbent upon the universe to produce or house any sort of structure that can be enumerated by those numbers. Indeed, it is easy to come up with numbers that dwarf any number that can represent the size of anything that a finite universe can create (as the countable infinite cardinal represents a strong limit cardinal, if you want to know why).

Other examples are copious: what do fractions of super-large numbers really mean in reality? How about irrational real numbers like π (which is also transcendental)? One could argue that π must exist in the universe because of how useful it is, but that's not correct if very, very good approximations of it (say to millions or billions of decimal places) are actually what's really going on (i.e. there is no requirement on the universe for a perfect circle to exist). What about the infinitely many infinities? At some point, even if the universe is infinite, logic dictates that there exist concepts with sizes that are literally beyond comprehension. Must these exist because logic says so? Or is it more reasonable to see logic as what it is: a construction that allows us to create an abstract representation of reality, rather like a map, and even extend it beyond reality's true boundaries?

To emphasize: "This must necessarily exist" only ensures the abstraction, which exists in a logico-axiomatic framework, we're talking must necessarily "exist" in the abstract sense and confers no responsibility on reality whatsoever.

Reality is not dictated, nor is it influenced, by our logical constructions. Indeed, it is the other way around, as is so often the case with really good illusions (like the illusion of intelligent design in the natural world). Our entire conception of logic has been built around the idea of how we see the universe, not the other way around. The universe appears to follow logical rules because while formulating what has become logic, if what we were saying didn't really match up with how the universe works, we called it "illogical." Sure, we've extended that now into the purely abstract, but all of our basic axioms (from which logical systems get their utility) ultimately have to be grounded in our best guesses about reality itself. Furthermore, the responsibility rests on our shoulders to realize that our abstract representations, though very, very useful (and thus justified), are abstract representations of reality, not statements about reality itself.

All along, it's been our system of attempting to understand the world (which is all logic is) getting nudged into a neater and neater fit, so far as we can tell, by the brute force of a non-agent universe (I'd say "an indifferent universe," but some fairly annoying Christian apologists have already proved to me that they try to exploit that term as if I'm implying agency by saying "indifferent"--sickeningly trite).

Now is an exciting time of sorts. We face a problem in that our highly successful map to reality (logic, and its fruits) has run into one of these places where, ultimately, we may have to reexamine the foundations of our intellectual cartography. Quantum mechanics presents evidence from reality that can be described with the tools we have, but it appears not to be able to be properly understood. It's possible that nature doesn't really present the basis the kind of logic we've been pretending it does all along. This means it's a good time to impress the lesson again: the universe, reality, is not subject to our logic. Our logic is an abstract construct via which we attempt to understand what actually is.


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4 comments:

  1. Agreed. Well written explanation, too. The concept of meaningless numbers is helpful to illustrate the point. I've also considered using different axiomatizations of logic to represent the fact that it is ultimately humans who choose what logic to use, not some 'universal logic' that dictates what logics we can have. These kinds of arguments tend to be useful when arguing with certain kinds of presuppositionalists.

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  2. First, I must say that I just discovered your blog and love it; your series of posts on Bayes Theorem are awesome and have me obsessed with exploring bayesian reasoning!

    Second, this post is fascinating (so, I take it that you are not a fan of physicist Max Tegmark's "Mathematical Universe Hypothesis" (MUH)), but critiquing logic seems to me to be very risky business; for the success of your critique ultimately depends on the logic you are criticizing--you do purport the argument of your post to be a logical one, correct?

    My problem, i.e., is that it appears that any (anti-realist) argument which concludes that "logic is a chimera" is self-refuting, for if the argument is sound and the conclusion true, then the argument is unsound and the conclusion is ultimately ambiguous...[the same critique holds for anti-realists who critique science: "science consists of only theories--mental constructs of reality--which must not be mistaken for reality; all theories are unreal and fundamentally not true!" But this itself IS a theory about reality (namely a theory about theories), and a self-refuting one at that.]

    Third, if reality either is some kind of formal system (e.g. MUH) or is governed by a formal logic, why would you discount that all possibilities of the system were not actualized in reality? It seems to me that such an ontological limitation would be bizarre and requires an explanation.

    I.e. the only conceivable explanation for such a limitation of reality (particularly if we are atheists) would be a logical one; but if logic tells us that no such limitations exist, then on what grounds does one believe that in fact such limiting barriers exist over the ontology of the Universe, none the less?

    (I agree that ontological arguments for God are silly; but they are silly, not because they rely on logic, but because they assert, or rhetorically define, what it is that they ultimately intend to prove--they do not demonstrate that, e.g., the proposition 'God is a necessary being' is true; thus the arguments are either fallacious, or simply unsound due to highly ambiguous premises.)

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    Replies
    1. Thanks for the insightful comment. I don't have room to talk about all of this in a reply, but it's good food for thought.

      My essential claim is that reality itself is not dictated by what or how we think about it and that what and how we think about reality is, instead, dictated by reality. If we decide to "think something into existence," for instance, the onus of explanation rests upon what "existence" means there. Of course, this is where ontology becomes a useful endeavor.

      The usual metaphor applies nicely, though: a mud puddle with self-reflective agency is likely to feel as though the pothole it is in happens to be perfectly formed for its existence, but the situation is precisely the opposite. The mud puddle is the shape it is because it has conformed to the hole, which means it has conformed to the shape of the boundary of the physical reality that defines it.

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    2. Got it--I'm on board with that!

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