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Ch. 1 - Why are people? 
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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.



Sun Oct 25, 2009 8:32 am
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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.



Sun Oct 25, 2009 12:57 pm
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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?"



Sun Oct 25, 2009 4:40 pm
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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.

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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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).
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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.
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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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Robert Tulip wrote:
tbarron wrote:
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.
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.

Robert, what would be wrong with saying that genes do what they do, while we create information regarding what they do? Proof of this could be that a gene cannot possibly 'get it wrong'. What it does is alway 'right,' even in those rare cases when it doesn't copy perfectly. We, however are surely not always right about the information that genes encode. We try to represent what they do through information, but it is only an attempt and as Tom believes, it does not have real existence.

Hey Robert, I don't suppose it would do any good to petition you not to litter your good prose with jargon like 'viral' and 'memetic'? I just had to ask it :!: :smile:
Bill



Mon Oct 26, 2009 9:51 am
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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.


But Robert, that's simply not the case. I was hoping you'd respond to my examples of where even the most simple of our logics do not apply. Logic seems to apply universally because we have shed what doesn't work over thousands of years. What could be more simple than the rule of identity(A=A)? Yet, modern science shows that we can't rely on this rule empirically. The only place it still applies is to our abstractions. That point alone makes it clear that logic is developed by us as our best system at this time of reasoning. We will need to continually advance it and modify it to incorporate new discoveries.

What you're referring to when you mention mathematic being eternal is not our abstractions of real world instances. You're instead referring to whatever underlying reason there is for nature to be explained by mathematics. Mathematics is merely an abstraction of that underlying reason. We do not know what that reason is, but this doesn't give us the elbow room to elevate our mathematical abstractions to be real things.

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Science and logic are, in principle, not 'made up' but discovered.


Science and logic are most certainly made up. What is not made up is why objective reality behaves in such a predictable manner that our constructions of logic and science are able to apply. This can be thought of similar to Plato's forms, as the distinction between category and instance. Science is made up, but the instances it discovers, the objectively real laws of nature, are not made up. It is vital to maintain this distinction to gain the proper perspective.

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Just because actual space bends in the presence of gravity does not mean that ideal space should not be imagined as Euclidean.


There is no such thing as ideal space, almost all of our universe is warped by mass to some extent. What you refer to as ideal space is nothing but an idea in your head, it doesn't equate to the real world. This is where idealism becomes absurd, that inferences gained by our understanding of our world are somehow more truthful than objective reality.



Mon Oct 26, 2009 1:34 pm
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DWill wrote:
what would be wrong with saying that genes do what they do, while we create information regarding what they do? Proof of this could be that a gene cannot possibly 'get it wrong'. What it does is alway 'right,' even in those rare cases when it doesn't copy perfectly. We, however are surely not always right about the information that genes encode. We try to represent what they do through information, but it is only an attempt and as Tom believes, it does not have real existence.
There is an established scientific usage, expressed in The Selfish Gene, that genes provide information to activate traits. This occurs directly within the body, regardless of human knowledge of it. It depends though, on your definition of information. If you choose to say that any transmission of data that is not mediated by a human brain is not information, I think that ignores the actual data transfer operating in genetics.

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Hey Robert, I don't suppose it would do any good to petition you not to litter your good prose with jargon like 'viral' and 'memetic'? I just had to ask it :!: :smile:
Bill
Bill, you are objecting to my statement "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."

This comment derives from Dawkins' observation that in the arms races between germs and their victims, germs are continually evolving new and novel ways to get around defences, as there is big genetic paydirt for such successes - testing Murphy's Law to work out just what can go wrong.

In the case of human religion, the God meme has 'hit on' a fantastic viral trick. Convincing the adherent that you are the only possible meme is a superb way to improve memetic fecundity, fidelity and longevity. My comment was just that this is a big part of the power of religion.



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Interbane wrote:
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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.
But Robert, that's simply not the case. I was hoping you'd respond to my examples of where even the most simple of our logics do not apply. Logic seems to apply universally because we have shed what doesn't work over thousands of years. What could be more simple than the rule of identity(A=A)? Yet, modern science shows that we can't rely on this rule empirically. The only place it still applies is to our abstractions. That point alone makes it clear that logic is developed by us as our best system at this time of reasoning. We will need to continually advance it and modify it to incorporate new discoveries.
Interbane, you are entirely twisting the findings of science in service of a misguided agenda with your strange assertion here that a thing can be something else. Common sense says a thing is what it is and not something else. Logic supports this common sense. The fact that a thing (eg a quark) may appear to human perception in different ways is entirely irrelevant to the basic premise of deductive logic that as an existing thing it is what it is. You are confusing the limits of perception with the verities of eternal logic.
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What you're referring to when you mention mathematic being eternal is not our abstractions of real world instances. You're instead referring to whatever underlying reason there is for nature to be explained by mathematics. Mathematics is merely an abstraction of that underlying reason. We do not know what that reason is, but this doesn't give us the elbow room to elevate our mathematical abstractions to be real things.
Your concept of ‘underlying reason’ is right to some extent, and something to work with. It seems we agree the ratios of proportional relations are real. However, your admission that nature follows an underlying reason explained by mathematics directly contradicts your claim that ideas of number are not real. The reality of the ideas of mathematical logic is in their reflection of the reason inherent in the universe.
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Science and logic are, in principle, not 'made up' but discovered.
Science and logic are most certainly made up. What is not made up is why objective reality behaves in such a predictable manner that our constructions of logic and science are able to apply. This can be thought of similar to Plato's forms, as the distinction between category and instance. Science is made up, but the instances it discovers, the objectively real laws of nature, are not made up. It is vital to maintain this distinction to gain the proper perspective.
Again, you twist the terms. “Made up” as introduced by TBarron, has connotations of fictional fantasy without objective reference. “Making up” science or logic would give false claims equal weight to true ones. With truth as the criterion, the greatness of rational investigation is the focus on discovering what is actually there, rather than imputing to reality something imposed by the mind (although this latter path has some validity in the construction of myth).
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Just because actual space bends in the presence of gravity does not mean that ideal space should not be imagined as Euclidean.
There is no such thing as ideal space, almost all of our universe is warped by mass to some extent. What you refer to as ideal space is nothing but an idea in your head, it doesn't equate to the real world. This is where idealism becomes absurd, that inferences gained by our understanding of our world are somehow more truthful than objective reality.
It is not absurd to postulate ideal space. For example, in asking how far between two points, we can legitimately consider the distance relativistically, ie influenced by the gravity of nearby masses, or non-relativistically, correcting for gravity. It’s like if there is a black hole one mile across, then you would define its “actual” width in terms of the path of light around it, even though this figure could be markedly different from the observed diameter. Both methods of measuring have their applications. If “ideal space” is an abstraction, then so is distance itself.



Tue Oct 27, 2009 9:28 pm
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Interbane, you are entirely twisting the findings of science in service of a misguided agenda with your strange assertion here that a thing can be something else. Common sense says a thing is what it is and not something else. Logic supports this common sense.


Read a book on quantum physics Robert, you'll find regardless of author a common theme repeating itself; common sense does not apply. Much of quantum physics is counterintuitive, and this isn't merely a limitation of observation. The mathematics that describe what is actually happening shows that it's counterintuitive. Logic and common sense have in common a macro worldview, which fits with them being nothing more than methods of understanding the world. Cavemen and Aristotle did not have quantum physics around which to develop their logic.

I will piggyback on your mentioning me having an agenda. You're right, but you must understand that my agenda has one directive; the truth. I have no other motive. If I'm wrong or if I'm biased, I will home in on that. However, I understand that others do not have the truth as their primary objective. There are other parallel motives, such as supporting some idea or another. Attempts to find a valid hypothesis for god is the most ubiquitous usurper of motive. I understand this, and naturally take the opposing stance. This isn't because I'm opposed to the idea, it's because I understand the other person has a motive which isn't only 'the truth'. Where there is parallel motive, there is almost always a deviation from the truth, thus my agenda. As a disclaimer, I doubt we can ever achieve absolute objective truth, but it is an ideal we should strive for.

Quote:
However, your admission that nature follows an underlying reason explained by mathematics directly contradicts your claim that ideas of number are not real. The reality of the ideas of mathematical logic is in their reflection of the reason inherent in the universe.


As I said before, I hold somewhat of a pantheistic perspective regarding math and it's ability to describe the universe. I'm ambivalent on the subject without having a better understanding. I plan to read some books on the philosophy of mathematics here in the near future. I will say that after discussing this with you I'm leaning in the direction of math and logic being human creations, no matter how accurately they reflect reality. What they reflect, the actual physical processes and relationship, those are real. The methods we develop to describe them must necessarily accurately reflect them, but that doesn't mean these abstractions of ours exist outside our heads.

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“Made up” as introduced by TBarron, has connotations of fictional fantasy without objective reference. “Making up” science or logic would give false claims equal weight to true ones.


Yet, science relies on us to make up our theories. We don't 'discover' them, as strange as that sounds. Some scientists, at some point in time, hypothesizes something, then tests that hypothesis against reality. While hypothesizing, inside the scientists head, he must weigh some potential hypotheses against others and what he currently knows about how nature works. The hypotheses that he judges will best survive experimentation are the ones he tests. It is in this way that theories aren't only 'made up', with stress on the word only. They are made up, but at the same time weighed against current scientific understandings. It is during repeated experimentation that verisimillitude can be assessed.

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It’s like if there is a black hole one mile across, then you would define its “actual” width in terms of the path of light around it, even though this figure could be markedly different from the observed diameter.


Are you trying to validate the idea of ideal space by contrasting the observed diameter with actual diameter? One of the two is correct, the other isn't. Even though the observed diameter has it's applications(whatever they may be), the observed diameter is not necessarily the actual diameter. An example is Newton's equation for gravity. It is still very useful, but at the same time we understand that it isn't objectively true. By objectively true, I mean to express that it perfectly reflects reality, versus a mere approximation. We realize that it is an approximation, just as Einstein's theory may very well be an even more accurate approximation.

I don't think 'ideal space' is even a valid abstraction. It may be useful in the same way that Newton's laws are useful, but that does not mean it's an accurate reflection of reality. There is no 'ideal space' out there in objective reality from which to abstract the notion. Here, we must distinguish usefulness from truthfulness. They aren't the same. If you're hoping to show that logic is an eternal perfect reflection of reality, you must weight current logic against what is real. The more formal logic of Aristotle's time is shown to not apply to quantum physics. There is, of course, quantum logic that is being developed. Also, logic is meant to apply to reasoning rather than real things. The distinction is a difficult one, since that reasoning to which logic applies deals with real things.



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I would recommend the work of John Barrow, especially The Constants of Nature: The Numbers that Encode the Deepest Secrets of the Universe.



Wed Oct 28, 2009 12:35 am
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