Are the existence of logical paradoxes evidence that logic is not Universal truth?

October 14, 2009 9:54 AM

Are the existence of logical paradoxes evidence that logic is not Universal truth, or simply symptoms of incomplete or inaccurate semantic systems?

I.e., if the Universe is infinite, then everything is possible and every possible scenario happens not only at least once, but an infinite number of times. Within this set of "Everything" is the possibility that "Nothing exists." But obviously something does exist, or I wouldn't be writing this and you wouldn't be reading this. One could say the Universe is not infinite, but then what is outside of it? It would be either Something, or Nothing. And if it is Something what is outside of that Something? If it is Nothing, then how can Something exist "within" it when Nothing has no "within." But this digression would be beside the point of this question. There are other paradoxes out there that have no resolution.

The reason I ask this is that I have recently moved from a "liberal" college town in my state to a rural "conservative" area for a job. I am surrounded by people who easily accept religion as an answer to questions such as this, and am attempting to separate my belief in Logic from their belief in God, and keep coming to holes in my system of thinking which require blind faith, and am trying to reconcile these holes so that my faith in Logic is founded rather than blind.

Please, no responses that I should find God =)

posted by idyllhands to religion & philosophy (37 comments total)

"I.e., if the Universe is infinite, then everything is possible and every possible scenario happens not only at least once, but an infinite number of times."

Could you have an infinite number of pop tarts without any of them being Pickle flavored?
posted by ian1977 at 10:02 AM on October 14, 2009 [2 favorites]

Firstly, one commonly accepted theory of the universe is that it is expanding. If it is expanding, it cannot be infinite.

Secondly, restrictions do not necessarily mean gaps in logic. Think of mathematical equations: what is the square root of a negative number? It cannot be done. This is not because the logic behind square-rooting something does not hold up, it's because you try to apply one logical method to an area that it simply should not be applied to (math buffs, I know that this is not quite true, given i values). Some equations have asymptotes: points that can never be reached. What I'm getting at is that boundaries and restrictions are not the same as disproofs.

The logical way to deal with this is to look for what the answer really is. Imagine for isntance if we didn't know why people look the way they do. We have two options: "natural selection" or "created in God's image". Now take your situation: Solve the holes in the logic or let God. If you cannot solve for what you think you are missing, does it mean that God is the true answer?
posted by battlebison at 10:08 AM on October 14, 2009

one does not believe in logic in the same way that one believes in religion. logic is kind of like believing in history--you see the results of the logic. religion requires faith in an unknown. you can't use logic to answer the question of life after death--only use it to give an estimate. religion, on the other hand, has a substantive answer to the question.
posted by lester's sock puppet at 10:13 AM on October 14, 2009

The universe is a fractal information wave oscillating in 10 dimensions, there is no concept of "outside" and "inside" except for the 3d shadow we live in, "something" is "nothing" wrapped in constraints over time, and the setup "If the barber cuts everyone's hair who does not cut his own, who cuts the barber's hair" does not disprove the existence of an ultimate truth, so one vote for unhelpful semantic systems from me.
posted by sandking at 10:15 AM on October 14, 2009 [1 favorite]

Paradoxes don't necessarily reflect reality, do they? Contradictions can appear to exist, but I challenge you to find one that actually is wholly true. I suspect that you'll find that there's some re-definition or misunderstanding somewhere in a paradox that makes it not a contradiction in reality.

Your Russel's set-of-all-sets paradox says more about the idea of sets than it does of the rules of existence.

The Universe is space, and it may have finite area. There is no outside, but there is no border either. Think of 2-D critters crawling along a sphere, and extrapolate to 3-D.

My short avoid-the-question heuristic is that one only encounters paradoxes when talking about remote, abstract, impossible-to-confirm ideas. If one needs to construct such a likely-bogus paradox to refute some near, personal, and relevant idea, argumentum-ad-absurdum style, then it's probably false.

I've seen such arguments for theism, and while it's bad form to quote oneself, I hope you'll forgive this. "You're pretending to know something about the fartherest reaches of the Universe to poorly hold up a shaky proposition about the existence of a really powerful being who wants nothing more than our attention and worship, yet, is utterly impotent to do something unambiguous to show that it exists, right here, right now. This should bother you."
posted by cmiller at 10:19 AM on October 14, 2009

"If it is expanding, it cannot be infinite."

So I couldn't throw an apple onto a pile of infinite apples?
posted by ian1977 at 10:20 AM on October 14, 2009

I hope you take this as it is intended: as helpful. My best advice to you is that if you want this question, and questions like it answered in a way that will make sense to you, it would be best to prepare yourself. The best preparation would be to read some introductory texts in philosophical conceptual analysis. When you pose the question properly, understanding the concepts involved, you stand a much better chance at receiving an intelligible answer. Many questions, such as the ones you asked may seem to be real questions with real answers. However, because the concepts involved are poorly defined or because they only apparently belong together, a real answer is simply not possible. A famous philosophical example is the statement: "colorless green dreams sleep furiously". The statement may seem to have content, is grammatically correct, but in fact is nonsensical. You could put it in form of a question "do colorless green dreams sleep furiously?" and an answer would not be possible. Philosophical conceptual analysis can help you illuminate the basic concepts involved and their relationships, so that you can spot when a question actually makes sense or not. So, again, I'd start with basic texts in that field. It will be helpful not just in this case, but in many questions you may have or come up with in the future.
posted by VikingSword at 10:21 AM on October 14, 2009 [1 favorite]

Battlebison: one commonly accepted theory of the universe is that it is expanding. If it is expanding, it cannot be infinite.

Does that necessarily have to be true? From my understanding, aren't there different scales of infiniteness? For example, the set of reals is more infinite than the set of Integers. Or are there different physics rules that make your assumption true?
posted by azarbayejani at 10:22 AM on October 14, 2009

^Yes you could, the same way there are an infinite number of rational numbers, but none of those numbers are irrational.

Same thing for your question, it is very possible for an infinite set to fail to be all-inclusive. In addition, the universe isn't known to be infinite. The most popular idea goes that the universe expands at the speed of light.

Personally, I believe the later conclusion("simply symptoms of incomplete or inaccurate semantic systems"). However, you have to realize that even with logic, the essentials have to be assumed. How can you prove something like "If a statement is true, then it cannot be false"?
posted by fizzzzzzzzzzzy at 10:23 AM on October 14, 2009

I am surrounded by people who easily accept religion as an answer to questions such as this, and am attempting to separate my belief in Logic from their belief in God, and keep coming to holes in my system of thinking which require blind faith, and am trying to reconcile these holes so that my faith in Logic is founded rather than blind.

I think you're confusing logic for something like science or determinism. Logic as you have described it (taking a premise and thinking about the consequences that fall from it) is required for any kind of religious view too. If you accept the premise that God exists or any tenets of a given religion, there are a lot of logical beliefs and practices that result (such as following the rules of a given religion).

The point of science is to test various premises and see if actual evidence in the real world support them. So really you should be checking if your premises or logical arguments are faulty, rather than trying to figure out if logic itself is worth depending on.
posted by burnmp3s at 10:23 AM on October 14, 2009 [4 favorites]

crap, its a bad idea to walk away from your comp while commenting... Sorry... :P
posted by fizzzzzzzzzzzy at 10:24 AM on October 14, 2009

am attempting to separate my belief in Logic from their belief in God, and keep coming to holes in my system of thinking which require blind faith, and am trying to reconcile these holes so that my faith in Logic is founded rather than blind.

Godel proved that any consistent mathematical system that is powerful enough to prove anything interesting will include true statements that can't be proven via that system. So from the standpoint of any logic, there will be elements that must be taken "on faith"

A healthy way to think about proof systems (where "proof systems" is intended to stand in for a host of mathematic and scientific concepts as well) is that though they are imperfect in the Godel way, they are the best tool that we have for understanding the world and they get great tangible results in terms of science and technology in a way that nothing else does.

This doesn't mean that religion "wins", just that religion and math are playing different sports. Math attempts to define the rules of the game as clearly as possible and comes up a little short, while religion tends to wave its hands at rigorous rule systems. You can still take comfort in the fact that if we're to have a game at all, math seems like the best way to construct the rules such that all the players can have the best time. Pointing out from religion's perspective that it's still possible to "cheat" starts to seem like less of a compelling criticism when you look at the alternative. CalvinBall seems like a lot of fun sometimes, but there's a reason why it is played by a creative six-year-old and his imaginary tiger and not in professional leagues by adults.

This is not the sort of dialectic that you're likely to engage in productively with your rural conservative friends and colleagues, but I recommend seeing them as people and not ideological opponents and talking about the weather and children and Steve from accounting's terrible new haircut, because it turns out that most people are pretty ok and you kind of have to make your way in this great big old world of ours. BTW, the answer to your above the fold question is "both."
posted by Kwine at 10:27 AM on October 14, 2009 [7 favorites]

Semantics.

I'll use your example, "The Universe is Infinite". And apologies to any cosmologists in the audience: I'm about to say a bunch of stuff that probably isn't technically true for the sake of argument.

"Universe" and "infinite" have a lot of wiggle room in the definitions. Basically, the statement "the universe is infinite" is incredibly ambiguous and depends on your definitions. It is nowhere near robust enough to base any kind of argument on.

You can decide that when you say "the universe is infinite" you mean a particular definition of infinite - perhaps "contains all possibilities" but then all you're doing is defining the term "the universe" as "that which is infinite" because a cosmologist will take their practical definition of the universe and compare it to your definition of infinity and say "err, no it doesn't."

You might instead say that you're going to define "the universe" as "the observable universe" instead, and some mathematician is going to walk along and point out that that's not a proper infinity (mathematicians are scary - did you know that some infinities are larger than others?).

Long story short, by itself "The universe is infinite" is unverifiable. If you define your terms properly so that they coincide with reality, any paradox disappears as the phrase is revealed as either tautological, or false.

Top tip: infinity is a really wonky idea. It's the logical equivalent of dividing by zero. It breaks any argument you include it in and leads to silliness like Pascal's Wager and Zeno's tortoise Paradox. If the paradox of infinity is a challenge to your atheism, then ask whether God in his omnipotence can create a rock so heavy that he cannot lift it. (The rock argument is also bullshit by the way)

Human beings are really, really, really bad at thinking about infinity.
posted by Lorc at 10:33 AM on October 14, 2009 [1 favorite]

Azarbayejani and Ian1977: Before I start I should clear things up: I'm not a mathematician, nor am I a logician, nor am I really anything that gives me authority to speak about this.

But throwing an apple into a pile of infinite apples means that the once infinite pile is still infinite. You have added an apple to it, but its quantity remains the same: infinity. You have expanded the pile in a direction which it was not initially infinite. This is not the same as expanding infinity. If the pile were truly infinite in all directions, there would be no you to speak of. Literally everything would be apples.

The set of reals has an infinite number of values. The set of integers has an infinite number of values with restrictions. They both have the same number of values: infinite. The set of integers however is part of the set of reals and the set of reals therefore covers more numbers. But these sets never expand, they just are. And they are infinite.
posted by battlebison at 10:35 AM on October 14, 2009

"Logic is the beginning of wisdom, not the end."
-Spock
posted by Jon_Evil at 10:41 AM on October 14, 2009 [1 favorite]

Are you familiar with Godel's Incompleteness Theorems? As I understand it (and I'm not sure that I really do) its been proven that no logical system can prove all truths. So all logical systems are incomplete. The second theorem says something about consistency and paradoxes, but I don't understand it very well. Godel Escher Bach is an excellent book that hits upon this subject.
posted by no_moniker at 10:47 AM on October 14, 2009 [1 favorite]

The set of reals has an infinite number of values. The set of integers has an infinite number of values with restrictions. They both have the same number of values: infinite. The set of integers however is part of the set of reals and the set of reals therefore covers more numbers. But these sets never expand, they just are. And they are infinite.

See Georg Cantor.
posted by VikingSword at 10:48 AM on October 14, 2009 [1 favorite]

The set of integers has an infinite number of values with restrictions. They both have the same number of values: infinite.

Actually, they don't. The reals are way more infinite than the integers.

GOOGLE GEORG CANTOR
posted by Dr Dracator at 10:48 AM on October 14, 2009

The set of integers however is part of the set of reals and the set of reals therefore covers more numbers.

In addition to what VikingSword and Dr Dracator (correctly) pointed out, this is not a true statement either. In addition to the cardinality of the integers being less than the cardinality of the reals, the fact that one set contains another does not imply it has greater cardinality. For instance, the set of all integers and all half numbers (ie, ..., -1, -0.5, 0, 0.5, 1, 1.5, ...) contains all integers, adds more numbers, but happens to have exactly the same cardinality as the integers (aleph-zero).
posted by saeculorum at 10:53 AM on October 14, 2009

VikingSword, Dr Dracactor and Sarculorum: That'll learn me for trying to talk about things I don't know about. Fortunately, I think Cantor's theories (laws? rules?) aren't in opposition to my views, only to examples that I tried to use. Thanks for the tip, this cardinality stuff seems interesting. I'll read more when I get home!
posted by battlebison at 11:01 AM on October 14, 2009

Logic is not Universal Truth, not just for the Godelian reason already mentioned, but because logic is applied via operations on a set of axioms which may or may not have various correspondences to reality. Logic and math are the theorems you prove based on the axioms you invent; reality is what you observe.

However, one of our most frequent observations of reality is that the mathematical rules we've invented apply very well. Make quantitative measurements, apply the math that corresponds to a good physical theory, and your later observations tend to match the mathematical predictions. Combine logical statements based on a number of different claims and theories, and if you arrive at a contradiction then it turns out that one of the claims was wrong or one of the theories was.

But yes, layman's "logical contradictions" are often problems of semantics. The "set of all sets" paradox came down to the fact that you can't build a self-consistent logic if you include self-referential definitions of "sets" or "propositions". Math no longer allows such definitions, but English still does, which is one of the many reasons why attempting to apply logic to English is very dicey. "This sentence is false, and Santa Claus does not exist."

Another big reason is that English words don't always correspond precisely to mathematical definitions. Just in this short thread people have confused "infinity" in its multiple cardinality senses with each other, and with "infinity" in the metric sense, and with "infinity" in a vague probabilistic sense...
posted by roystgnr at 11:07 AM on October 14, 2009 [2 favorites]

"If the pile were truly infinite in all directions, there would be no you to speak of. Literally everything would be apples."

So saying the universe is infinite is the same as saying it is infinite in all directions?

Couldn't an infinitely long snake grow?
posted by ian1977 at 11:14 AM on October 14, 2009

So Russell and Frege walk into a bar. Can someone please complete the joke?

idyllhands, my suggestion would be not to engage your neighbors in these kinds of discussions. There will be a lot of hurt feelings, and nobody will be convinced of anything.
posted by VikingSword at 11:15 AM on October 14, 2009

Practical problem: you are surrounded by religious people and want to feel smarter than them, or at the very least less "faithy."

Practical solution 1: Do not have philosophy discussions with them that run on the level of stoned college freshmen. See "not a practical solution" below.

Practical solution 2: Ridicule them privately for any of the following: (A) The inconsistency of their beliefs (homosexuality is an abomination but shrimp isn't). (B) The inconsistency of their beliefs (Various facially self-contradictory parts of the Bible such as multiple genealogies of Jesus). (C) The inherent ludicrousness of the claims their religion makes. (D) Their inability to update their beliefs when evidence against their God or idea of God comes into play.

Practical solution 3: Ridicule them privately for other aspects of their worldview or lifestyle that you find simplistic or abhorrent.

Not a practical solution:

You write this. if the Universe is infinite, then everything is possible and every possible scenario happens not only at least once, but an infinite number of times. Within this set of "Everything" is the possibility that "Nothing exists."

But this is just plain wrong, and sloppy thinking. The set of all positive integers is infinite. Literally infinite, as infinite as an infinite thing and a fully paid-up member of The Infinite Club. But yet, the set of all positive integers doesn't include "everything." Only all positive integers. You can look and look and look, but you won't find any negative numbers, or the numbers pi or e. And even the positive integers that do occur only occur once, not an infinite number of times. There's only one "one," or one "eighty seven million billion trillion and four."

Second, there's no real reason to think the universe is literally infinite. So thinking about the properties of a literally infinite universe is about as useful as thinking about a the properties of a literal unicorn.

Third, even if it were, there would be lots of things that don't happen, and lots of things that don't happen more than once. Consider the sequence of digits of pi. It's infinite and never repeats, but that doesn't mean that anywhere in there will you find an encoding of the Kama Sutra. Might be, but its mere infinity is no guarantee that it will ever be there.
posted by ROU_Xenophobe at 11:18 AM on October 14, 2009 [7 favorites]

"Logic ultimately exists to make sure you can never arrive at a wrong answer from true premises. As such it is supposed to make sure that you don't make errors in your reasoning, for example by contradicting yourself. It won't, however, make up for incorrect or incomplete information. If the premises you start with are false... then logic can't be relied upon to give you a true answer..."

Logic requires axioms to work from—statements which are not proved, but are simply accepted. If you're concerned purely with symbolic logic, you can take one set of axioms, deduce some things from those axioms, and say, "hmm, that's interesting." Another day you might take a different set of axioms, and find you can deduce exactly the opposite thing you deduced the first time. That does not make it right or wrong; they are both right given the axioms you started with. Different axioms, different conclusions.

Now, if you're trying to reason about the real world, rather than just taking logic as an intellectual exercise, the axioms you choose are even more important, and yes, you'll have to take them on faith; without an unsupported belief in some axiom or other, logic will take you about as far as Descartes' "I think, therefore I am" and that's it. You can't prove that you're not just a brain in a jar and everything you perceive as the real world isn't just the result of some demented scientist sending impulses to your brain to create the illusion of the world you perceive.

I take it as an axiom ("on faith," if you will) that what we observe about the world (either directly, or indirectly through instruments which allow us to detect things we can't perceive directly) is a reasonably accurate, if incomplete, representation of the world as it is; I suspect you share this axiom. If you accept the scientific method as a valid way to learn about the world and make predictions about the future, you probably accept it as axiomatic that induction is a valid method of reasoning. Suppose you hold a ball out at arm's length, and you let it go, and it falls to the ground. Suppose you do this a hundred times, and each time the same thing happens. What will happen if you do it for a 101st time? You and I would probably agree that it is very very likely that the ball will fall to the ground again, and very very unlikely that it would float in mid-air, or shoot off into the sky, or anything else. But there's no logical basis for such a conclusion unless we've taken it as an axiom that inductive reasoning is valid.

My point is, you can't escape "faith" entirely, unless you want to stop your logic at "I think therefore I am" and go no further. If you want to believe in anything at all beyond that, you have to take something on blind faith.

Next, belief in God is not incompatible with logic, unless you have taken it as an axiom that God does not exist (or axioms from which "God does not exist" can be deduced). Religion is not inherently illogical. Some particular varieties of religion may be illogical (if they can be shown to result in self-contradiction), but religion in and of itself is not.

I won't suggest you find God, but I will suggest that it's ultimately futile to try to free yourself from all unsupported beliefs, and instead it's more productive to think about which unsupported beliefs you want to accept.

----

I've spent the bulk of this talking about the nature of logic (note the lowercase "l." This is not insignificant, as there is not one single universal system of Logic, but many possible systems of logic), but as to some of your particulars:

I.e., if the Universe is infinite, then everything is possible and every possible scenario happens not only at least once, but an infinite number of times.

This does not follow. For example, the universe might be infinitely large yet hold only a finite amount of mass and energy. Just because the universe is infinitely large does not mean every possible thing that could happen must happen somewhere.

One could say the Universe is not infinite, but then what is outside of it?

The general view is that there is no "outside" of a finite universe. You are assuming that space extends infinitely in all directions even if the universe does not, but that is not the case. Space itself is defined by the universe; there is no outside. Oh, you might define a coordinate system for the universe and pick numbers in that coordinate system that do not fall within the universe, but the fact that you can pick numbers doesn't mean that the space described by the number exists. It's like asking what's north of the North Pole, or what happens below absolute zero. I can type out "91°N latitude" or "-274°C", but just because I can type out those numbers doesn't mean that they have any real meaning. What's "outside" a finite universe? The same thing that's located at 91°N. It's not even "nothing" because "nothing" would imply at least empty space; "outside a finite universe" and "91°N" are as meaningless as "alkjhfjklah89r4jkbfh."
posted by DevilsAdvocate at 11:39 AM on October 14, 2009 [4 favorites]

battlebison: Firstly, one commonly accepted theory of the universe is that it is expanding. If it is expanding, it cannot be infinite.

My understanding (not a science guy, mind you) was that the expansion of the universe is omnidirectional, i.e. that on a large enough scale there is more distance between created between heavenly bodies more or less equally everywhere. Or, as my astronomy prof put it, imagine a loaf of raisin bread-- as it rises in the oven, the more-or-less uniform spacing between all of the raisins becomes greater simultaneously. The universe is an infinitely large loaf of raisin bread, spreading out.
posted by shakespeherian at 12:10 PM on October 14, 2009 [1 favorite]

Wow, thanks for all the responses. I am working 72 hours per week for the next month, and was involved in a long argument with myself on the 45 minute drive home from work, and due to my schedule, I have to skim through them for now, but in my current skimming, I have concluded that my inclusion of the apparent (to me) paradox of the Infinite Universe may have been a mistake, but I didn't have sufficient time to make sure my question was phrased in a way that made sense and thought including an example would clarify. But I don't think my example was a good one.

@ROU_Xenophobe: in quickly reading your response, I think you mistook my intent. What I hope to do, ultimately, is make my thought patterns less of a "blind faith" type of belief system so that I do not feel as though I must defend it against the prevailing "blind faith" belief systems that surround me. In essense, remove myself from "the game" of religion which is, of course, unwinnable. Logic and religion cannot compete, but I feel as long as I am unable to reconcile the "blind faith" holes that I come up with in my introspective drives home from work, then I am still just as "bad" as they are. (and by bad I mean allowing my worldview to be affected by false premises). It is disturbing when premises which I know to be true lead me to conclusions that are paradoxes..

I will probably wait a month until this crazy overtime subsides and try to rephrase my question, but I think that several of you have gotten my intent and I look forward to being able to read and fully consider your responses.

@cmiller: don't apologize for quoting yourself, I lol'd at this: "You're pretending to know something about the fartherest reaches of the Universe to poorly hold up a shaky proposition about the existence of a really powerful being who wants nothing more than our attention and worship, yet, is utterly impotent to do something unambiguous to show that it exists, right here, right now. This should bother you."
And the fact that paradoxes don't reflect reality is what troubles me about Logic..if that makes sense.
posted by idyllhands at 12:19 PM on October 14, 2009

It is disturbing when premises which I know to be true lead me to conclusions that are paradoxes.

Sure -- but you haven't offered one up, which is what ROU_Xenophobe is pointing out. An infinite universe doesn't mean that everything is possible, nor does "nothing exists" have any understandable meaning. Your reliance on logic hasn't led you into a confounded state.
posted by ellF at 12:35 PM on October 14, 2009

I.e., if the Universe is infinite, then everything is possible and every possible scenario happens not only at least once, but an infinite number of times

as others have pointed out, this isn't logically necessary (there are infinite primes, but there are also infinite numbers which are not primes - i.e., there can be infinite possibilities which do not happen, even if infinite possibilities must take place).

However, probably the reason this is confusing is the idea of infinity, which has been considered something of a paradox in itself. (take Kant's "four antinomies" - too much to get into here but if you're interested in the limits of logic & empiricism's relationship, Kant is a non-faith-based option)
posted by mdn at 12:53 PM on October 14, 2009

I apologise for getting tunnel vision on your throwaway example. I'll try again.

You always have to take some things for granted. This is distinct from the idea of capital-F-Faith.

It's not that you accept them unquestioningly, it's that the world is huge and and we are small and life is short. It is impractical to fully examine every single thing about what we believe to be true. So we settle for assuming based on what seems to make sense and works. When out assumptions stop working, we come up with new ones. This is not faith, this is a shortcut to save time and sanity.

Science, logic, religion and other systems of thought that try to explain the world are about creating a common body of best-guesses that work well enough that they are fit to be shared, to save everyone from having to re-think the wheel. The fact that we don't know everything - and that a lot of the stuff we do know may one day be disproved - doesn't necessarily mean we take it on Faith; it means that it's a work in progress that has proven itself to be good enough so far.
posted by Lorc at 12:58 PM on October 14, 2009 [1 favorite]

I've always used a little argument that 'God' is a pseudonym for ignorance.

Now I know that sounds harsh, but I don't mean it like it sounds, exactly.

I think the line where current knowledge ends and what we can't know NOW begins is where we always draw the line. "God" is what's on the other side of the line.

The line moves, every time humanity learns something. God shrinks further into the distance.

In my own life (as a radical athiest), I place things in three categories; what we know, what we don't know (yet), and maybe, what we can't know (ever).

In some ways, this is a semantic cop out. In other ways, a charitable reach to my religious (and good) friends who have a god that is some nice old man (of course?) with a beard. In yet another way, equating god with ignorance is a pretty good match, based on history.

So yes, you can have logical paradoxes, and yes, it implies logic has descriptive limitations. Like all forms of human thought, at one point its basic tenets were unstated. Then some were formalized. Did we get them all? Apparently not. When will we? Who knows? Surely you aren't a proponent that we now know all that there is to be known? Or that we've uncovered all the basic truths about logic? Again, consider that at one time, there was no zero (0) nor was their a Cartesian plane. Both concepts were invented, and the latter, rather recently.

/musing.

Good luck! Nice question. Very nice.
posted by FauxScot at 1:10 PM on October 14, 2009

make my thought patterns less of a "blind faith" type of belief system so that I do not feel as though I must defend it against the prevailing "blind faith" belief systems that surround me.

A more practicable option is to look at your own feelings and work on not feeling like you have to defend your beliefs against anyone else's.

For the most part, your beliefs aren't under attack, and other peoples' beliefs generally won't pick your pocket or break your leg. Even in the churchiest parts of America, I'm reasonably confident that the local blind-faithers aren't going to kidnap you and force you to sit through their services tied to a gurney with eyelid-holder-openers like Alex in A Clockwork Orange. As well, I rather doubt that they're going to use orbital mind-control lasers or MK-ULTRA brainwashing to somehow turn you Lutheran against your will.

In those instances where their beliefs do pick your pocket or break your leg, just donate to opposing causes.

If you're trying to be strictly empirical and logical, you'll have to accept that there are many questions for which the only answer you can provide yourself is "There is at present insufficient evidence to conclusively support any answer." I'm trying not to be snarky, but you really do sound to me like you're kept up at night worrying about, given that Jesus is all-powerful, can he microwave a burrito that's so hot that not even he can eat it?

A good logical empiricist would simply reject the premise of an all-powerful Jesus as lacking evidence. Likewise, a good logical empiricist would look at questions regarding the infinity of the universe and say that none of those questions can be answered unless it has been shown that the universe is infinite, and infinite in some specific way. Unless there's good evidence that the universe is some specific kind of evidence, the sorts of questions you ask in the original question are simply immaterial.
posted by ROU_Xenophobe at 1:11 PM on October 14, 2009

The universe can be finite and infinite at the same time.

All things in nature are cyclical. Perhaps there is a Möbius twist to space and time somewhere along the loop of existence, which brings the finite and infinite together, allowing whatever is outside the universe to reside within it simultaneously.

Care to discuss this further at The Restaurant at the End of the Universe?
posted by Oireachtac at 1:21 PM on October 14, 2009

if the Universe is infinite, then everything is possible and every possible scenario happens not only at least once, but an infinite number of times.

No. Somewhat tongue in cheek, but: you can approach it from the opposite direction, and reach opposite conclusions. Let's call this example HRWTSS ("Hume Really Wants To Say Something"). Like this:

1)Whatever happens must happen for a reason - there is an unbroken chain of causality - regardless of how infinite the universe is, at no point does the chain break, at no point do things happen 'for no reason'*
2)Causality can be described with strongly deterministic rules
3)Therefore there is only one possible way in which the universe can be, and no matter how many times you repeat the run of the universe from start to finish and back again, it'll always do the exact same thing, the exact same events. As long as you don't alter the initial conditions, the same laws of physics will develop and the same events will unfold in a strictly deterministic fashion - and since there is no reason or force to cause an alteration, this will continue ad infinitum (and if the conditions were to be altered, they will be altered also depending on a set of rules, so that regresses infinitely too). So the conclusion is: the universe is a perpetual Ground Hog Day. Not only is it wrong to say "everything is possible", but you must say "only one thing is possible". What we are doing is collapsing logical, philosophical and technical possibilities into one. To have a single thing change, no matter how minute, you'd have to defy the laws of physics (plus if you make a leap or multiple leaps: logic).

Bottom line, you are mixing up classes of arguments and phenomena - philosophical, logical, physical, technical. You must disentangle it, or you'll make no progress - you'll be condemned to spin in circles rather as in the tongue in cheek example above.

*Neils is now spinning, but we trust Albert to stop him
posted by VikingSword at 1:49 PM on October 14, 2009

I am surrounded by people who easily accept religion as an answer to questions such as this, and am attempting to separate my belief in Logic from their belief in God, and keep coming to holes in my system of thinking which require blind faith, and am trying to reconcile these holes so that my faith in Logic is founded rather than blind.

Respectfully, could you maybe post a different example that illustrates a situation where you are forced to take something on blind faith? Because the whole "Given: everything exists inifinite number of times" is just plain wrong, so everything that flows from that might as well be wrong, too.
posted by 23skidoo at 3:11 PM on October 14, 2009

In the strict sense, there are no logical paradoxes. That's the point of logic. Most paradoxes are mistranslations. A simple example would be how the English language "or" could mean the logical "inclusive or" or the "exclusive or". You have to be precise in your translation of thoughts into logic or you will get errors.

A paradox means there is an error in your application of logic. It's adding 2+2 and getting 5. It's programming a computer and getting a bug. It means you have to go through your working and find out where you went wrong.
posted by -harlequin- at 3:31 PM on October 14, 2009

> And the fact that paradoxes don't reflect reality is what troubles me about Logic..if that makes sense.

It makes perfect sense. My only point is that it's not a problem with logic or the universe, but our fuzzy language, or use of undefined terms, or operation in a manufactured domain with strange rules that create paradoxical puzzles. If you encounter a paradox then I bet that when building up to it, at some point you stopped accurately describing reality.

---

Maybe you will be happier just accepting that almost no one is rational. Your new neighbors have specific areas of their lives, like their jobs, where they have to really understand the rules of the universe. Postulating the nature of the unknown isn't one of them. Try not to let it bother you. They are curious, strange, people with rich lives in many respects, and they also profess to believe kooky things. i say just make peace with it and give it a chuckle or deep belly-laugh from time to time and take it as seriously as it deserves, which is not very much at all.
posted by cmiller at 6:35 PM on October 14, 2009