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Ch. 1 - Why are people?

#71: Sept. - Oct. 2009 (Non-Fiction)
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Interbane

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I ran across this while browsing (Perhaps Neitszche was on to something):

Another popular spin on this fallacy involves referencing the so-called laws of logic and suggesting that these "laws" have to be dictated by somebody or something, ergo God exists. In reality, there are no "laws of logic". Logic is a name given to describe the function of how your brain processes information. Your stomach's function involves digestion. Is there a "law of digestion?" No. Another intellectually bankrupt semantical run-around.
http://www.freethoughtpedia.com/wiki/To ... nce_of_God
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Interbane wrote:
We cannot conceive a real space in which pi does not apply.
Pi's relationship to a circle is analytic; within the definition of a perfect circle. When you conceptualize an abstract perfect circle, Pi is necessarily part of the definition. This does not make Pi any more eternal than a perfect circle. Also, to say that we can't conceive of a real space in which Pi does not apply does not mean there isn't one. Pythagoras theorem as a relationship to a triangle was discovered to not apply to some geometries.
Pi is equally eternal as a perfect circle. Both, like all mathematical concepts, are outside time. The hypothetical existence of a space in which Pi does not apply is not really relevant to actual mathematics.
Interbane wrote:I ran across this while browsing (Perhaps Neitszche was on to something):

Another popular spin on this fallacy involves referencing the so-called laws of logic and suggesting that these "laws" have to be dictated by somebody or something, ergo God exists. In reality, there are no "laws of logic". Logic is a name given to describe the function of how your brain processes information. Your stomach's function involves digestion. Is there a "law of digestion?" No. Another intellectually bankrupt semantical run-around.
http://www.freethoughtpedia.com/wiki/To ... nce_of_God
This argument is weak. Logic is not a 'brain process' but how that brain process links to the external reality. For example Jupiter is five times as far as the earth from the sun. This is a material relation between Jupiter and the earth which is independent of human cognition.
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The hypothetical existence of a space in which Pi does not apply is not really relevant to actual mathematics.
Why not?
Logic is not a 'brain process' but how that brain process links to the external reality.
Wouldn't it be better to say that logic is a brain process, and also links to the real world? I've come to disagree with this understanding after doing some studying. It seems logic is a tool we have for understanding the world, and there is no such thing as an objective instance of logic. For every web site I've found, they all state logic as the study of principles of correct reasoning.
For example Jupiter is five times as far as the earth from the sun. This is a material relation between Jupiter and the earth which is independent of human cognition.
I understand, but how do you go from this instance to the abstraction of whatever math you've gained from it being eternal?
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Interbane wrote:
The hypothetical existence of a space in which Pi does not apply is not really relevant to actual mathematics.
Why not?
We are trying to understand reality. The beauty of the mathematics in The Selfish Gene is that it shows how intrinsically number is integrated into evolutionary reality. I am extending this principle (per the Platonic axiom that number is discovered not created by thought) to say perfect circles are real concepts, with clear application to the world. A hypothetical alternative universe in which Pi does not apply is not real.
Logic is not a 'brain process' but how that brain process links to the external reality.
Wouldn't it be better to say that logic is a brain process, and also links to the real world? I've come to disagree with this understanding after doing some studying. It seems logic is a tool we have for understanding the world, and there is no such thing as an objective instance of logic. For every web site I've found, they all state logic as the study of principles of correct reasoning.
The 'correct reasoning' definition of logic has been questioned, for example in Heidegger's definition of truth as disclosure rather than representation. Of course there is objective logic. We use it to say, for example, that Jupiter is five times as far as the earth from the sun.
For example Jupiter is five times as far as the earth from the sun. This is a material relation between Jupiter and the earth which is independent of human cognition.
I understand, but how do you go from this instance to the abstraction of whatever math you've gained from it being eternal?
The number five is embedded in this relation. This number only has ideal existence as concept, but would equally apply in a successor universe in which one thing was five times as big as another.
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The number five is embedded in this relation. This number only has ideal existence as concept, but would equally apply in a successor universe in which one thing was five times as big as another.
The number isn't embedded. We make a neural connection. Orbits are elliptical and Jupiter will most likely never be exactly 5 times as far from the sun as the Earth is. Even if it every happens to be within an inch or two of that exact length at any point in time, that will not be the case for every spacetime vector.
I am extending this principle (per the Platonic axiom that number is discovered not created by thought) to say perfect circles are real concepts, with clear application to the world. A hypothetical alternative universe in which Pi does not apply is not real.
Show me an instance of a perfect circle. You can't, because there is no such thing. The concept as an abstraction of the category circular is able to be combined with the concept "perfect" in our heads. Just because we can imagine such a thing doesn't make this abstraction real. It's a method of understanding, a necessary neural segway into making sense of reality.

What is still a grey area for me is why nature obeys mathematical rules. Why does math necessarily apply? These processes and relationships are different than the idealist category of geometric shapes, so if you have insight in this area that is how you'll get through to me.
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Robert Tulip wrote:
Interbane wrote:You say that pi is the same for all eternity, but you don't support this claim with any reasoning.
We cannot conceive a real space in which pi does not apply. Pi is part of the structure of space, in so far as circles exist. Pi is an eternal logical condition for the existence of circles.
Just because we can't conceive it, can we know it doesn't exist? (Interbane already pointed this out.)

However, we *can* conceive it. Pi depends on Euclidean geometry, that is, geometry in a flat plane subject to Euclid's five axioms. Consider a circle inscribed on a sphere C(s). The radius of C(s) will be longer than the radius of the same sized circle on a plane C(p) because the center of C(s) is not in the same plane as the circumference. Thus the ratio of circumference to radius will be different for the two circles, i.e., in geometries on the surface of a sphere, pi has a different value than it does in plane geometry. Actually, on a sphere, pi would not have any fixed value. The ratio of circumference to radius would not be the same for the equator of the sphere as it would be for a much smaller circle inscribed on the sphere.
Interbane wrote:What is still a grey area for me is why nature obeys mathematical rules. Why does math necessarily apply? These processes and relationships are different than the idealist category of geometric shapes, so if you have insight in this area that is how you'll get through to me.
I don't think nature obeys anything. Nature does what it does. It looks to me like math is a conceptual framework humans invented to describe observed consistencies in nature's behavior over a very short period of time. All we can say is that for the moment or two out of the history of the universe that human brains have been looking, some aspects of nature have been consistent. Cosmologists theorize that the rate of change in the universe has not been constant in the past. I see no reason to expect it to remain constant in the future.

I would guess that thinking that nature "obeys" mathematics comes from using the "law" metaphor to talk about our descriptions of nature. Humans obey laws (sometimes), so talking about Newton's laws of thermodynamics or Boyle's laws of pressure and volume leads by analogy to thinking of nature "obeying" our descriptions rather than the other way around.

This is the sort of pitfall I believe one is likely to fall into along the Platonic path.
Robert Tulip wrote:A number such as pi, derived from the ratio between diameter and circumference of a set of planar points equidistant from one point, is indeed the same for all eternity, because it does not depend on anything temporal for its existence.
I would say that the temporal thing it depends on for its existence is a consciousness sufficiently developed to form the concept.
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I don't think nature obeys anything. Nature does what it does.
Well, contrast 'something' against complete random behavior. That something, the way nature behaves, corresponds to mathematics for whatever reason. Math is able to discover new ways in which nature behaves by manipulating nothing but the mathematical abstractions themselves, so in total it is not an unrelated set of abstractions. It is the reason why nature corresponds to math that I would like to understand better.

Thanks for jumping in the conversation, I've had not experience in this area, it's all new territory to me.
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Heh. I've been trying to stay out of it cause I don't think I can keep up with Robert. :hmm:

But sometimes my thoughts and fingers get the better of me and I find myself in the middle of it again.

I had a conversation with my parents (Southern Baptist missionaries) a while back where I was trying to communicate my worldview to them. At some point, my father exclaimed something like, "Nonsense! That doesn't make any sense at all! It's just all made up!"

Which was more or less exactly how I feel about his worldview. So I've stopped trying to explain how I see things to them. There doesn't seem to be much way or hope of bridging the gap since they don't seem to be willing to set aside their point of view long enough to try mine on. Of course, I think I've looked through theirs before and don't want to go back there, thank you very much, so I imagine they're feeling similarly about me -- that I'm unwilling to set aside my obviously foolish notions and come back to the Way That Works... for them.

I have the sense that there's a similar divide between Robert and me. He seems pretty sure that information has its own existence, independent of any physical representation (at least that's my understanding of his position). It seems pretty obvious to me that such is not the case. I'm sure Robert's position seems just as obvious to him as mine does to me. But I tend to feel a mite pessimistic about the possibility of fruitful discussion when we're so clearly on opposite sides of the argument and how things are seems so clear and obvious to each of us.

And, the same kind of thing seems to be going on between Stahrwe and everyone else on the board. I have no doubt that he is sincere in his beliefs and that they provide him comfort and peace and happiness. I imagine that his desire to share his beliefs come from the most generous of motives -- he wants others to experience the same joy and sense of closeness to god that he does.

But yelling past each other doesn't seem very productive to me. So I try not to. Until somebody says something that I can't resist responding to. :)

So, anyway, you were saying that nature's consistency and isomorphism to some mathematical structures was what you were pointing at. I agree that it's amazing. I have no idea why it's like that and I wonder, too. Do you have any ideas about how to push the inquiry forward? One question I would ask is, "Is nature's correspondence to math simply due to math being designed as a description of nature?"
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tbarron wrote:
Robert Tulip wrote:
Interbane wrote:You say that pi is the same for all eternity, but you don't support this claim with any reasoning.
We cannot conceive a real space in which pi does not apply. Pi is part of the structure of space, in so far as circles exist. Pi is an eternal logical condition for the existence of circles.
Just because we can't conceive it, can we know it doesn't exist? (Interbane already pointed this out.)
Hey Tom, thanks for joining this abstruse thread. The mathematics of eternity is not everyone's cup of tea, but it does emerge as a logical question from Dawkins metaphysics in the first chapter of The Selfish Gene.

We don't know that there are no parallel universes in which the laws of mathematics are somehow different, hard as that may be to conceive. However, this hypothetical conjecture - saying maybe our universe is not the whole or only universe - is entirely unproductive as a way of understanding our own universe. Here, mathematics is consistent and logic is eternal.
However, we *can* conceive it. Pi depends on Euclidean geometry, that is, geometry in a flat plane subject to Euclid's five axioms. Consider a circle inscribed on a sphere C(s). The radius of C(s) will be longer than the radius of the same sized circle on a plane C(p) because the center of C(s) is not in the same plane as the circumference. Thus the ratio of circumference to radius will be different for the two circles, i.e., in geometries on the surface of a sphere, pi has a different value than it does in plane geometry. Actually, on a sphere, pi would not have any fixed value. The ratio of circumference to radius would not be the same for the equator of the sphere as it would be for a much smaller circle inscribed on the sphere.
Pi applies in solid geometry. The surface area of a sphere is 4Pi R squared, and the volume of a sphere is 4/3 Pi R cubed. Pi is embedded in the concept of the sphere. Just because actual space bends in the presence of gravity does not mean that ideal space should not be imagined as Euclidean. Your example of the comparison between a spherical section and a circle depends entirely on pi to calculate its shape. Victory again to the eternal pi.
Interbane wrote:What is still a grey area for me is why nature obeys mathematical rules. Why does math necessarily apply? These processes and relationships are different than the idealist category of geometric shapes, so if you have insight in this area that is how you'll get through to me.
I don't think nature obeys anything. Nature does what it does. It looks to me like math is a conceptual framework humans invented to describe observed consistencies in nature's behavior over a very short period of time. All we can say is that for the moment or two out of the history of the universe that human brains have been looking, some aspects of nature have been consistent. Cosmologists theorize that the rate of change in the universe has not been constant in the past. I see no reason to expect it to remain constant in the future.

I would guess that thinking that nature "obeys" mathematics comes from using the "law" metaphor to talk about our descriptions of nature. Humans obey laws (sometimes), so talking about Newton's laws of thermodynamics or Boyle's laws of pressure and volume leads by analogy to thinking of nature "obeying" our descriptions rather than the other way around.

This is the sort of pitfall I believe one is likely to fall into along the Platonic path.
Ah, the pitfalls of Plato! So, you suggest the laws of gravity, relativity and thermodynamics will not apply forever, even though they are highly consistent and predictive? Admittedly, physics has not cracked the TOE, the theory of everything which would unify the four forces, but it has made some rather eternal discoveries. For example, Newton's claim "the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve" once adjusted for relativity, exactly predicts the location of the planets. Nature obeys this description, which is why the law of gravity is a law.
Robert Tulip wrote:A number such as pi, derived from the ratio between diameter and circumference of a set of planar points equidistant from one point, is indeed the same for all eternity, because it does not depend on anything temporal for its existence.
I would say that the temporal thing it depends on for its existence is a consciousness sufficiently developed to form the concept.
So in far unknown galaxies, pi is not embedded in any circles? Pi is a natural relationship, discovered by thought but not created by thought.
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tbarron wrote:Heh. I've been trying to stay out of it cause I don't think I can keep up with Robert. :hmm:
I am not hard to keep up with. If you don't understand something I said please pipe up.
But sometimes my thoughts and fingers get the better of me and I find myself in the middle of it again.
Thanks Tom, the aim is just to have a conversation.
I had a conversation with my parents (Southern Baptist missionaries) a while back where I was trying to communicate my worldview to them. At some point, my father exclaimed something like, "Nonsense! That doesn't make any sense at all! It's just all made up!"
Science and logic are, in principle, not 'made up' but discovered. Mythology is made up. However, actual science and logic have a mythic component, for example when scientists believe that the values they infer from their methods are universal. This is why Christians often don't like scientists. Scientists claim to be oh-so-logical, but actually have assumptions that they do not understand. Hence Edmund Burke's famous reflection that revolting reason produces terror. Much of the 'Enlightenment' worldview is 'all made up' in your father's phrase.
Which was more or less exactly how I feel about his worldview. So I've stopped trying to explain how I see things to them. There doesn't seem to be much way or hope of bridging the gap since they don't seem to be willing to set aside their point of view long enough to try mine on. Of course, I think I've looked through theirs before and don't want to go back there, thank you very much, so I imagine they're feeling similarly about me -- that I'm unwilling to set aside my obviously foolish notions and come back to the Way That Works... for them.
Speaking of worldviews is an important starting point for dialogue about philosophy. The memetic power of worldviews, whether religious or scientific or other, derives in large part from the viral method of convincing their adherents that they are absolute and universal. You describe the polarity between religion and science (I assume) as two separate worldviews. Each is encompassing, and finds it difficult to establish points of dialogue with the other. My view is that faith and reason must be reconciled, and that both social camps need to change for such a union of thought.
I have the sense that there's a similar divide between Robert and me. He seems pretty sure that information has its own existence, independent of any physical representation (at least that's my understanding of his position). It seems pretty obvious to me that such is not the case. I'm sure Robert's position seems just as obvious to him as mine does to me. But I tend to feel a mite pessimistic about the possibility of fruitful discussion when we're so clearly on opposite sides of the argument and how things are seems so clear and obvious to each of us.
Information has its own existence. Genes are the best example. Trait information is encoded in genes, irrespective of human observation of this fact. When the human genome was 'represented' by sequencing, the information in it did not suddenly spring into existence. This information had been causing protein chemistry since the dawn of life. Your position reminds me of Bishop Berkeley's famous belief that 'to be is to be perceived'. This is a modern empirical version of idealism which is completely out of kilter with Plato, and serves as a crude empiricist myth to deflect understanding of the nature of ideas and information.
And, the same kind of thing seems to be going on between Stahrwe and everyone else on the board. I have no doubt that he is sincere in his beliefs and that they provide him comfort and peace and happiness. I imagine that his desire to share his beliefs come from the most generous of motives -- he wants others to experience the same joy and sense of closeness to god that he does.
At least my claim that logic is eternal is logical :). Cognitive dissonance has a range of causes, as Dawkins shows in his mind-bending use of the Necker Cube. (cf The Extended Phenotype).
But yelling past each other doesn't seem very productive to me. So I try not to. Until somebody says something that I can't resist responding to. :)
I hope I haven't yelled past you Tom. Pull me up if you think so.
So, anyway, you were saying that nature's consistency and isomorphism to some mathematical structures was what you were pointing at. I agree that it's amazing. I have no idea why it's like that and I wonder, too. Do you have any ideas about how to push the inquiry forward? One question I would ask is, "Is nature's correspondence to math simply due to math being designed as a description of nature?"
Again, math (or as we say in the British Empire, maths) is discovered not designed. The self-consistency of mathematics is its main feature. Physics is also self-consistent because there is one universe given for us to know. A non-isomorphic universe, in which there were no mathematical laws of physics, could not work, let alone evolve intelligence. Our existence is proof of the isomorphism of the universe.

This anthropic method was used by Fred Hoyle to discover the origin of carbon in the stars. Carbon exists, observed Hoyle, therefore the question arises how must the universe be structured to bring carbon into existence from primeval hydrogen? Similarly, we may observe, we exist, so what does this say about how mathematics governs our universe?
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