Originally posted by FZ+
But it cannot be objectively true, as you have declared there that this does not represent anything in reality. The meaningful conversation relies on a shared set of definitions (called language) - and speaks nothing of whether the language has a true basis.
i never said it is objectively true. but you can't prove it's objectively false, either, it seems. i think "aleph0 = aleph1" may represent, in some sense, something in reality. aleph0 is the mathematical measurement of the infinity consisting of discrete elements (such as the set of natural numbers) while aleph1 is the mathematical measurement of the infinity consisting of a continuum (such as the set of real numbers). i don't know: is anything in reality continuous? i know time is no longer considered continuous...
Can we just look back over our concept of indeterminancy please? By indeterminancy, this means that I can't prove objectively it to be false - and neither can you prove it to be true. Whether it is true or false is a matter of subjective feeling and opinion.
In fact, you have perfectly captured the failure of most discussions about religion. Faced with this indeterminancy, it is simply impossible to have a meaningful conversation.
so the Heisenberg uncertainty principle, and whatever else in science that involves the indeterminate, can not be conversed about in a meaningful way?
btw, lots of people have meaningful conversations about religion. to say it is impossible to have such a discussion flies in the face of emprical data.
I don't see why you are consistently failing to get this point. Falsification has nothing to do with falsehood! Science has nothing to do with the unfalsifiable. What we get here is that mathematical axioms are non-scientific entities. What we do not get is a contest between science and mathematics, because neither can deal with the other. That is why there are no debunking maths posts, and that is why there should be no misguided debunking religion posts.
that's odd. then the name "falsification" is utterly misleading if it has nothing to do with falsehood. it should be called, "supercalifragilisticalization," if has nothing to do with something being true or false.
is it or is it not true that in science, one does the experiment without forming an expectation about the result? in other words, if you look for a certain outcome, then one may be tempted to see patterns that aren't there or fudge the data a little to get the conclusion that is desired? therefore, it should be standard scientific practice to conduct an experiment without having a desire for the outcome. when you title this thread "debunking religion," you have set a desired outcome. or at least, that's how it comes off. a better title would be "investigating religion."
I think you are failing to understand my point, as this is precisely what I meant. The idea of truth in this context is one of tautology - that in the formulation of the definition, we have forced the 1+1=0 statement to be true. In fact, it is probably more sensible to refer to this not as truth, but as consistency - like saying that 2 = 1+1 is consistent with 1+1=2. But what matters is the formulation of the rules itself. Does 1+1 = 0 represent something in nature. To that, if you follow a formalism based philosophy, you can only say that it is indeterminate, and that in exploring maths we dynamically change it to suit our needs.
The situation is wholly different in a platonic view of course. As far as the platonic view is concerned, this whole argument is moot because maths really is something that has tangible effects in the real world. 1+1=0 in some cases is a scientific discovery. Do you understand?
well, if I'm not understanding the statement, "insisting 1+1!= 2 is rather non-useful," i don't see how.
we should probably throw the word "objectively" in front of true or false if that's what we mean. I'm falling into the "trap" of often referring to "true" statements (in math or otherwise) as true, when, in fact, they're not objectively true (or objectively false). well, group theory is based on statements like 1+1=0; don't you think group theory is important in quantum mechanics, string theory, and other fields? to give a concrete example, that is the kind of arithmetic used on clocks. clocks occur in nature.
much of mathematics is not platonic.
Because it seems you don't.
Let's start off from basics.
False = Is contradicted by reality.
True = Is supported by reality so far.
Indeterminate = Unable to test for support/contradiction by reality. Neither false nor true.
Falsifiable = Can be tested for contradiction by reality.
Consistent = provides a logical framework with other claims.
Tangible = Interacts with what is observable. Can be detected or implicates behaviour that can be measured.
When we talk of true mathematics, we really mean consistent mathematics. A mathematical "proof" consistutes a search for that consistency. In this way, we can make the whole of mathematics one body. We cannot however, unless we adopt the platonic idea of mathematics being tangible in itself.
when can anything be contradicted by reality? this would require that we have a way to be objectively SURE that we have any awareness of reality. neo, in the movie "the matrix," had no awareness of reality whatsoever until he took the red pill (or was it the blue pill?). how can you say what reality is if you can't even prove you're not in a matrix in which the rules are subject to change at the whim of the robots who control it?
so far. so things can be true today and not tomorrow? that is not an acceptable definition of truth. i claim that ALL people with pictures of homer's boss as their icon have your beliefs. then, by your definition, this claim is true for it is true so far. to me, one instance hardly proves it's true. i guess we'll have to agree to disagree on what true means. furthermore, the word "supported." what does this mean? the predictions rarely EXACTLY match the observations, correct? there is some tolerance of DIFFERNECE to "reality" that is ACCEPTABLE. but, there is still a difference. technically, by your definition, this wouldn't make the claim true. very, very, very, very, very plausible, perhaps.
well, by your definition, i would argue that "aleph0 = aleph1" is not indeterminate for nothing in reality thus far, as far as we know, is different from itself. i too think it's not indeterminate. however, the claim that there is a cardinal number x such that aleph0 < x < aleph1 has been shown to be indeterminate in the mathematical sense.
by your definition of tangible, God is tangible for it interacts with the whole universe. i agree with the "detected" part but the "implicates behavior" part i don't. the warppage of space-time changes the behavior of light rays but that doesn't mean the warpage is tangible, to me, at least.
don't patronize me. it's not that i don't understand you. it's that i disagree. I'm not chalking up your disagreeance of me as a lack of understanding...
i don't think mathematics is one network of tautolgies. it may consist of several collections of consitencies... but i guess you could call that whole collection one body if you would also call twin brothers one body.
you seem to have contradicted yourself. you said this:
False = Is contradicted by reality.
Falsifiable = Can be tested for contradiction by reality.
but you also said this:
Falsification has nothing to do with falsehood!
well, i see two words starting with contradict and two instances of reality. it seems that they have SOMETHING to do with each other. i retract my "supercalifragilisticalization" comment for they do have something to do with each other.
String(or M) theory is a theory that is consistent as far as we know with past true theories, tangible in what it claims will happen, and is increasingly falsifiable. String (or M) theory is incomplete.
In terms of science, because of the element of falsifiablility, it is impossible to "prove" a theory in an absolute way.
since we have different view on what "tangible" means, we cannot agree on whether "11 dimensions" are tangible. i simply don't see how you could say that they're tangible until we have a new kind of telescope to "see" into them. but i guess that's where we'll have to agree to disagree.
you say it's "increasingly falsifiable," but isn't it really the case that string theory has a long way to go before it will be accepted by the experimentalists (people like feynman, who i know is dead)? I've heard that we won't have the technology to test some major predictions for a LONG time...
"it is impossible to "prove" a theory in an absolute way." that's mainly what I'm trying to argue. that's essentially what i think you think about religion. but when you say that about religion, you say that, "faced with this indeterminancy (where by that i mean an inability to prove it in an absolute way), it is simply impossible to have a meaningful conversation." if that is the case, it shoudl apply to science as well. i think meaningful conversations are to be had in both fields even though no theory in either field will ever be proven "absolutely."
in his [nash's] autobiographical essay, written after he won the nobel, nash writes that “rational thought imposes a limit on a person’s concept of his relation to the cosmos.” he refers to remissions not as joyful returns to a healthy state but as “interludes, as it were, of enforced rationality.”
it is my deep suspician that removing such limitations is exactly what will lead us to be able to prove a theory absolutely.
cheers,
phoenix