Non-Euclidean geometry and God.

Great Debates
101

Because they’re two separate claims, and both important to my general argumentation: faiths, generally, cannot be logically told apart (based on one being more correct), and even every single one faith cannot be logically proven correct, hence it is much less possible to assess their correctness than it is to tell them apart, the issue of their correctness being the more fundamental statement than their distinctiveness.

So, do you mean anything with that? If you’re intimately familiar with such arguments, could you point me to some general discussion of them (I am aware of logical positivism, should that be what you’re thinking about)?

102

Much less than “no way”? What is that: negative way?

I just meant “thanks for the discussion”, and I added a “Cool” smilie.

I’m not intimately familiar with similar arguments about atheism, but it seems to me that your argument is (kind of) the opposite of the Transcendental Argument for the Existence of God, which argues that human knowledge and experience is not meaningful without a belief in God.

Of course, there are counterarguments, and there’s the Transcendental Argument for the Non-existence of God.

Perhaps there’s something useful there for you.

103

Half you’ve lost me as well. If reality changes then reality changes and that matters not if it’s because God does it or because the laws of the universe sponteously morph. By some theistic systems those are the same thing anyway. I can know what was by observation and I can know what is by observation in either case.

As far as the argument goes, I of course disagree about whether or not I’ve established that there are areas of knowledge inquiry for which empiricism is ill-equipped and for which accepting some god postulate sets up a different sort of inquiry and a potentially more adaptive worldview. I think we’ll have to just accept that we see that differently.

You are also apparently joining the ranks of those who confuse this to be a discussion about organized religious views rather than the broad idea of god(s). I again am not defending as rational the god of the bible or of any other specific text. That god concept was something I rejected, oh I think I was 9, about four decades ago. Class atheist in my religious school and interestingly enough one of the Rabbi’s favorite students because I was thinking about it and engaging in the discussion. My soft pantheism is something I have come to not as a means to maintain a theism but having grown into some doubts of my atheism as I have intellectually matured (mind you, not necessarily grown :)). It is an appreciation for the theism expressed by Einstein and others of that ilk and a wish to at least believe that there actually are some things that are Good and Evil rather than just good and evil, if you get that distinction. I also leave open the possibility that just as my mind is a nonmaterial entiy emergent of the material of my body - an epiphenomenon - so to is it possible that there is something self-similar on a larger universal scale, as incomprehensible to me as I am to one of my neurons. Of course that speculation is also not scientific or falsifiable and of little difference in how we live our lives other than by way of potentially providing some perspective to our places in the universe. Arguing here as if you are arguing against the Biblical God, or god of any mythic narrative, is shadowboxing.

Duhkecco - I have heard the essence of Half’s thesis before but what of it? If he came up with it independently or if he had somehow heard it before remembering that or not, has nothing to do with the validity or invalidity of the argument does it?

104

I was just curious, that’s all. I had never heard it before.
I didn’t present a counterargument based on whether it was original or not.

105

'kay.

106

Oh, here is one place making an argument simliar to yours Half, not exactly the same mind you.

107

If the laws of the universe change without a supernatural intervention, that merely means you didn’t know the full set of laws beforehand. I really don’t know how to make myself any more clear, I’m sorry.

Let’s look at a grossly simplified world, in which all knowledge – absolute knowledge! – is contained in the statement ‘proposition A is true’. Now, the supernatural comes in, snaps its fingers, and suddenly, proposition A isn’t true any more. That’s fundamentally different from any natural change, since if there were such a thing, ‘proposition A is true’ obviously wasn’t absolute knowledge in the first place, because there would have to be a mechanism by which proposition A can fail to be true in some circumstances, and knowledge of that mechanism is obviously not contained in the statement ‘proposition A is true’, which I had defined as absolute knowledge!
Thus, in a system without the possibility of supernatural intervention, if ‘proposition A is true’ is the complete knowledge, it stays that way; in a system where supernatural intervention can happen, proposition A can fail to be true at any given time.

Does my argument make sense to anybody, or does it only work in my head?

That’s not what I’m doing, and I don’t see how you could think that. I’m not particularly concerned with any specific religion, even though I may use some as examples now and then, because it’s more convenient to use something known to all participants rather than cooking up something new every time.

108

I think I get what you are saying but …

You presume the possibility of complete knowledge. I presume the impossibility of the same.

You exclude my personal favorite -theism, pantheism, in which God is the natural world itself and knowledge of God is therefore also necessarily contained within that all inclusive Proposition A. Perhaps you could even also think of it as God changing God’s mind along the same way I change mine - a function of my mind but also reducible to more basic material things. To that way of thinking the mind of god is revealed by studying the natural world, even if totally understanding it is forever beyond our grasp.

109

I don’t think I need that for my argument to work, it’s just easier to illustrate; I think I’d need objective existence and a finite set of laws to govern whatever it is that exists objectively, but I don’t actually need any knowledge about any of that – because in those cases, you can always create a truth, and have it be incontrovertible, by, say, storing any statement in such a way that there is no (known) natural influence that could alter it, say, by writing some number on a piece of paper and putting that into a safe. If there is some unknown natural influence that can alter what you have put into the safe, you’re essentially conducting an experiment to detect this influence, which you can subsequently eliminate from your setup and start over; there’s at most a finite number of natural influences, so at some point, there won’t be any more unknown influences (even though you obviously don’t know this and have to assume there still might be). And once every natural influence has been ruled out, whatever you wrote on that scrap of paper in the safe (or whatever setup you may like) will stay the same forever. However, if there’s a god, he can always change it, no matter how often you do this experiment, and that’s a fundamental difference in such a way that the statement ‘the number I wrote on the piece of paper in the safe will always stay the same’ can never be strictly true in a faith-based world view (even if it does end up being true by god choosing not to give a hoot about scraps of paper you put into a metal box for some reason).

About pantheism, I don’t know very much about that, and frankly what little I know has always seemed like ‘lets just call the laws of nature god’, more or less in the way Einstein used the term.

110

It isn’t a “tool for understanding the material world”; it’s a tool for denying it. The intellectual equivalent of hiding under your desk, eyes closed and hands over your ears. “Revealed truth” that is held as “true by definition” is another way of saying that your worldview is fictional and you refuse to pay attention to the facts that contradict it. It’s sheer delusion, not a way of understanding the material world or anything else.

Now that’s just silly. A lack of adaptability is a central feature of religion. It’s based on faith, not reason or facts; since it does not acknowledge reality it’s hardly “adaptive”. It’s to a large degree about AVOIDING adaptation; about avoiding uncomfortable or inconvenient truths.

Garbage. Those myths are the one and only reason the whole idea of God exists. What’s really happening is that you are proposing a minimalist God carefully designed without handles; without any way to connect it to the real world and without any history. Your position is fundamentally untenable, but rather than admit that you set up a God whose main feature is that it has the fewest points of vulnerability in an argument. And in some fashion you refuse to discuss, you appear to think this is some defense of “absolute morality”.

111

I was speaking as a matter of the current mode of thought of athiests, not how they managed to get there.

God is a meme, and so it is passed to children quite readily because it is a simple meme… as is santa claus.

I’m glad you said “A child” instead of children… because many children are not exposed to the santa claus meme (in other cultures, in the tribal amazon) and other children can be taught standards of evidence that allow them to infer that santa claus is imaginary (as in my household.) Part of the reasons that these (fallacious) beliefs are so prevalent is that our society fails to teach critical thinking skills until well into high school and beyond.

So, while I agree with the bulk of your argument, I disagree with the reasoning behind it.

:slight_smile: … i suppose i shouldn’t point out that Einstein’s metaphysical beliefs were highly reminiscent of pandeism.

Just sayin’

112

I would prefer a more generic statement as the heading of this thread:

Listen closely, people: parallel planes NEVER intersect.

From this it can then be derived that no line contained in a plane can EVER intersect with any line contained in another plane parallel to this plane, whether the respective lines be straight or curved.

To restrict this axiom to straight lines, you have to define a straight line as the intersection line of two planes, and parallel straight lines as the respective intersections of a plane with two parallel planes.

Spherical geometry, as far as I got it from this thread (I left school at 16), is confined to the planisphere, and I don’t know if it can be extended to concentric spheres. If yes, the same postulate as with two parallel plans would apply, i.e. two concentric planispheres NEVER intersect.

You may have noticed that parallel has been replaced by concentric. Are these planispheres parallel? No, only two infinitely small areas as defined by the respective intersection points of a radius line are parallel. Really parallel? As far as I can understand, infinitely small areas or infinitely small segments cannot be parallel because they have no orientation, only their tangents can be parallel.

The problem under discussion is purely semantic, as in the statement
“parallel lines never intersect” the term “line” is (linguistically speaking) an ellipse.

(For the non linguists, here is my own personal explanation of what a linguistic ellipse is: when you look at a circle from a point not situated on its generation axis, the circle appears as an ellipse. Therefore, if you present an ellipse to somebody, you may assume that if he is familiar with spatial geometry he may as well perceive the ellipse as a a potentially perfect circle).

Hence, in the said statement the term “line” will be interpreted as “straight line”.

Whereas in the statement: “parallel lines MAY intersect”, the elliptic term “line” will be interpreted as “curved line”.

Let’s try an analogy:

Listen closely, people: The LHC will NEVER generate a black hole.

Those who infer that “LHC” and “black hole” are elliptic expressions, may then object:

Listen closely, people: The next LHC MAY generate a financial black hole.

113

Went of on a bit of a tangent there, huh?

Anyway, I guess pretty much everyone is tired of the subject an my continued posting on it by now, but indulge me one last time, I’ll try to be brief.

So, it occurred to me today that my proposition is probably better stated the other way round – in both atheistic and theistic systems, the highest degree of certainty you can have about anything is something like ‘as far as I know, proposition A is true’. That’s sorta at the end-user level, not much of a difference there. However, I do think there is one at the system side, and it’s one that does have some consequences I think are rather important. Now, proposition A can, in fact, be true, or it may not be, or it may be true now and not be true sometime later, or the other way around. That’s again in both systems. But, the difference is – only in the atheistic system does the case that proposition A is true and always will incontrovertibly remain true exist; in the theistic system, the proposition can well be true and always remain true, but there can be no proposition that’s guaranteed to remain true, since there’s always the possibility of supernatural interference. Right?

Now, what does this mean? Well, if I’m not mistaken, it means that only in the atheistic system, a series of ever-improving assumptions about the world, derived from empiricism, will necessarily converge onto a true description of the world – i.e. the scientific method works in such a system. Call that the completeness of the system, since it’s somewhat reminiscent of the completeness of a metric space as derived from the convergence of Cauchy sequences. In this sense, the theistic system is ‘incomplete’, since that sort of convergence can’t be guaranteed.

114

Sorry, I got this wrong, it should read as follows:

Listen closely, people: The LHC will NEVER:D lead to a fatal BLACK HOLE.

Those who – in a discussion about the risks inherent to the LHC in terms of potentially dangerous black holes – would perceive both “NEVER” and “BLACK HOLE” as elliptic expressions (with NEVER seen as a merely provocative joke), would then complete the statement to read:

Listen closely, people: The LHC will NEVERTHELESS lead to a fatal FINANCIAL BLACK HOLE.

Half Man Half Wit wrote about the above analogy: Went off on a bit of a tangent there, huh?

Now you see, man+wit/2, I bent the tangent to help you round-off the thread…