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Originally Posted by Taunton
On infinity: thanks for the well elaborated explanation. I think there's one point where we aren't on the same page, and I'll try to explain what I mean:
The way that you're explaining it, to me anyways, it seems like infinity is being described as a tangible "thing" which can be "reached", which it obviously cannot. Something like infinity, which cannot be tangibly "reached" (at least based on the concept of infinity that I'm accustomed to) can't be explicitly demonstrated, which I accept.
My point is that, at least in my mind, you can always add or remove a number (for simplicity's sake, let's say 1) from or to a number. So, in a way, you're never going to "reach" infinity, but it can be concluded that infinity must be a valid concept anyways because there's nothing that can prevent you from adding (or subtracting) from a number to infinitum.
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This is the beauty, and the insanity, that is Mathematics. In a technical sense, the approach you're describing below is what's termed a "Successor function." Basically this means you 'add one' to something...ie. S(0) = 1, S(1) = S(S(0)) = 2, and so forth. (The reason we use a 'function' and not just the notion of adding 1 is because mathematics is built very formally...out of
sets, and not numbers).
Then Mathematics goes to the next level:
Let's suppose infinity IS a number, aleph (which looks like a squiggly N). What is S(N)? S(S(N))? ... and we get an entirely new class of number called the Ordinal Numbers, which allows for a more advanced proof technique called Trans-finite Induction.
Pictorially, we're doing something like this:
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0 S(0) ... N S(N) ...
|---------...)------ ...
And what this means is, there is no number M such that S(M) = infinity...ie. there is no number "1 less than infinity" (otherwise we could count to infinity), but nothing stops us from adding 1 to it. Eventually you hit another wall, and get another infinity. So you add one to it...etc.
It turns out that, mathematically, the existence of one infinity implies the existence of infinitely many infinities...each one strictly containing the previous.
So even though you can't count to it, it literally is like a 'tangible thing' in mathematics.
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I suppose it's more of a philosophical concept than a scientific concept, since by it's own definition, infinity cannot be explicitly reached.
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But this is exactly like God...so again I put it to you, why is it any less absurd? In all honesty, what it comes down to is the fact that you personally can fathom infinity but not God, but there are people who can do the exact opposite.
(Note: I'm not trying to get you to believe in God or anything here...infact, I'm just trying to spawn some critical thought on the subject)
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I'll express what I mean with your example: let's say each generation of people had a "counter" who counted their whole lives. Very likely (in reality) the tradition would likely break (ending at a number, rather than "infinity"). BUT, what's to stop someone from picking back up again and continuing to count? Nothing, right? THAT'S why infinity must "exist". There's nothing, that I know of, that could stop a number from being added to. There's no "barrier" (that we know of at least) that could stop you, or me, or anyone from simply adding more numbers to a pre-existing number. Again, I understand that this isn't scientific, and it's more philosophical...
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The irony of it is, your
proof, which isn't grounded in strict axioms or anything verifiable, comes down to philosophy, as you've mentioned. But again, why is a philosophical argument for, say, God "obviously rubbish" while this argument for infinity (which I agree with, but I acknowledge that it's more of a 'belief' in infinity) makes sense to you?
And of course I'm not saying accept any specific argument, etc. because there are decent, as well as crappy, arguments for both sides...I'm just saying, neither side is really down for the count beyond reasonable doubt.
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and maybe it's a different (possibly even new?) definition for infinity? I'd like to see your thoughts on this.
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The irony is, this philosophical definition of infinity you're pitching, that infinity is that which is unattainable but always striven for, is one possible definition for God and was actually what I was refering to when I said some closely associate infinity and God.
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On proving non-existence: I accept that the sweeping generalization that "you can't prove something doesn't exist" doesn't apply in all cases. You provided one example of a math problem with no solution. To that I say: maths is the only scientific way to actually "prove" anything.
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A few years back I would have agreed with you...but after looking into the foundations of Math, looking at some of the history behind it, I can't put my full trust in it.
In the early 1900s I believe (the math is true, not necessarily the history/dates :p) Bertrand Russell found a fundamental flaw in the current model of arithmetic by creating a paradox. The statement is:
"Let X be the set of all sets which are not elements of themselves. Then, is X an element of X?"
A layman's example of this paradox is "This sentence is false." It is true, then when you reread it, it becomes false...then true...etc. There is no answer.
This essentially broke mathematics and sent mathematicians, logicians and physicists into a panic, everyone thought Math was breaking. It turns out that years later, Math was reformulated using (the modern day) Zermelo-Frankel set theory. It resolved the paradox by ultimately deciding that X could not be a set, and no set can be an element of itself.
So today we have this theory, and we have no known holes...no
known holes. This does not mean there are none, and likely there are many problems with our current theory, as with science as you pointed out below.
But the point is, even a mathematical truth, which to some extent is more valid than a scientific truth as you mentioned, is still to be taken with a grain of salt...and this is because if we do find some fundamental flaw with the system we're using, we may have proven things which were actually false, or disproven things which were actually true.
We'd essentially be back at square 1.
Personally, I
believe math is well-formed, and that it isn't a big walking contradiction (otherwise I wouldn't be studying it), but it is something I believe without realistic grounds. Infact, the odds of this theory being 'the correct theory' are rather slim, because hey, we already found problems in the past, why not again?
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Remember that in science, we don't "prove" things, we "disprove" them (which I should be more careful about the use of these terms). We collect evidence for a theory, and accept the theory which has the most evidence and hasn't been disproven. You can have a theory with hundreds of years worth of work and evidence behind it, but a single finding can disprove it and the old theory and evidence is worthless!
So, on these grounds, the existence of a "god" (or any other thing, be it a rock, a teacup, or a leprochaun) cannot be disproven!
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Correction:
By your set of rules they cannot be disproven.
But who's to say science is the correct method of analysis? Science? Scientists?
See where I'm going with this? No I can't think of anything better, no one can and that's the whole problem...but people, even scientists who understand the inherent flaws of their method of deduction (as you clearly do, based on your explanation) must acknowledge that everything could and perhaps even
should be reworked into a more powerful system.
And thus, the postulation that something may lie
externally to this system of rules, of measurements, is not entirely absurd. I'm not going to explicitly state that it's God, or an afterlife, but to conclude with absolute certainty "God cannot exist because we cannot detect him" is in my opinion, naive...and given your grasp of science, I really can't figure out why you think science is all-encompassing. Your example (or rather one much like it) is why I lost respect for science in some sense...not that I don't think it's a remarkable tool, but I no longer look at it with those innocent "Science knows everything! ^_^" eyes.
Because it is exactly that...a tool.
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An example: I tell you that there's a wild pink rabbit living in Antarctica. It seems ridiculous, but you can't prove me wrong... how do you prove there's no wild pink rabbit living in Antarctica? You could look all you want, but when you come back with nothing, I can say "you didn't look hard enough" or "it was behind you the whole time". The only "proof" we can have in this situation is me (the believer) bringing you to Antarctica and showing you the wild pink rabbit. That's the only way to settle the disagreement.
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Yep, it's the "all crows are black" paradox. I'm confused here though as to what your point is. You've shown me an inherent flaw, a
problem with science...essentially you're saying science, in its current form, will never know the truth and does not claim to. Like I said above, something very well may lie externally, and we'll never know unless we re-vamp the criteria for scientific truth (which may not even be possible).
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It is on these grounds that I say, in the case of a "god", the burden of proof is always on the believer, and until such proof can be afforded there is no reason to believe in a god.
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You're only saying that because you're a non-believer.
Put the shoe on the other foot...to a believer, the burden of disproof is on the non-believer.
And as I've shown above, both perspectives are naive. To be precise, I gave a formal argument which says "You can only prove theorems which you can prove." If something is suggested to lie outside a system, it cannot be proven or disproven, and as a special case, God, who if He exists, is above and beyond science, cannot be proven or disproven by science.
To give a silly analogy, it's like trying to measure an angle with a ruler, then saying "The angle does not exist because I can't measure it." The rules of science, the scientific method, are just a means of deduction, a system of measurement.
As you've suggested (I didn't even have to), it's far from perfect.
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Finally, on blind faith: The example you provided is really just the scientific method.
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That was my whole point though...I'm saying the scientific method is based on faith. Do you know
any scientific principle is actually the truth?
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The current model of the atom is accepted because it has the most compelling evidence behind it, and it hasn't been disproven (ie it has stood up to rigorous testing by many, many people). These are reasons to believe that the theory may be correct, or even could be the most correct theory. This I would define as faith, not blind faith.
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The problem is, it's your arbitrary definition. Why is 'faith' any different from 'blind faith' ? In either case, one is blind to the truth, and only uses their best judgment to approximate truth.
All you're doing here, is making a new 'inferior' demographic and labelling yourself as external to it for an arbitrary reason. It's like a grade 9 saying "Look at all those
minor niners."
Faith is faith is faith: Belief in absence of proof.
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In the case of believing in a "god" and/or any religous dogma, there is no evidence or reason to believe these are true or real...
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Correction: No
scientific evidence to support them.
Suppose a miracle occured, I dunno...like it rained fire or something equally dramatic. Something which made everyone go "Whoa" and was convincing beyond reasonable doubt that there are supernatural forces at play.
This would not be repeatable and hence not scientific. Evidence sure, but not testable, verifiable evidence.
Again: Are you trying to argue that science is perfect? You really were arguing the exact opposite a moment ago.
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they're essentially untestable hypotheses. Since they have no evidence behind them (and apparently no way to provide evidence), basing your life around them is, (in my humble opinion), not an intelligent way to live. This is what I define as blind faith. There are very few, if any, situations in life where you are forced to live your life based on blind faith (you can always learn/do reasearch ahead of time).
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Here's how to sum up the discrepancy here:
Life is a game. A casino, infact. You, a master of Blackjack (science) stumble upon a master of Gin Rummy (religious theism).
Whose deck of cards do you play with? What table do you play at?
Being masters of each game, when playing blackjack, obviously you win...when playing Gin Rummy, obviously you lose.
So naturally, you and the other master start to get frustrated. "I want to play with
my deck" "No...we're going to play with
mine."
Little do you both realize, you're actually playing Roullette, and you both lose.
The moral of the story is, a scientist can demand the universe to bend to their terms, a religious theist can demand that the universe specifically does not bend to a scientist's terms. Both have no real reason to believe what they do, and the universe is likely so remarkably complex that they're both wrong.
The concepts of being testable, verifiable, and all that good scientific stuff, are quite frankly
the best we can do. That does not mean however, that they are
consistent and complete (see my previous post).
Suppose everyone but two scientists dies in a nuclear holocaust. How do these scientists prove they do indeed exist? How does scientist 1 know that scientist 2 isn't some schizophrenic embodiment of his emotions (and vice versa)?
Specifically, if it was only one scientist who was schizophrenic, how would he know? To him, the external being is testable and verifiable...it responds to his speech, it reacts to him...so it's real, right?
But...he's schizophrenic...so an
external view of the situation shows that he's not all right in the head. But what is an external view to science itself?
What about a blind scientist, the only one left after the holocaust? He can no longer test and verify say, colour...do we conclude colour no longer exists in the universe?
No...it just means not everything is
necessarily testable. And to believe it is, is in my opinion, pretty damn worthy of being labelled
blind faith. I'm not going to say it's a silly belief...but to say "It's my way or the highway" is what's silly.
Not to mention, supposing evolution and the big bang and the cosmological model are all true...do you really believe we are the pinnacle of evolution? I mean as you so far-gone to believe that we can see everything, and that which we can't see/perceive does not exist? I can't see my mother at work right now (again, silly example).
Six blind men and the elephant?
That's the same logic I used when I figured it out after gr. 11 genetics. 
)
