02-14-2008, 01:12 AM
B"H
Please let me comment, very quickly and without much ado, on where I differ from mathematical Platonism. Ancient and medieval mathematical realism was far less pragmatic and scientifically oriented than modern realism/Platonism. By contrast, on the other end of the spectrum, Nominalism is another thing altogether. Actually, in some strange way, ancient Platonism had one familiarity with Nominalism, its opposite on the spectrum. That commonality was the belief that Reality could not be separated from Mind.
Modern philosophy divorced reality from Mind. You remember from college; Descartes, Locke, Hume, Kant, most of the "modern philosophers" divorced Reality from Mind. A few mavericks like Schopenhauer, Emerson, and the Romantics refused to go along with this divorce, but most of science did until the twentieth century. Subject-object dichotomy arose from the great divorce.
Ancient and medieval philosophy did not divorce Mind and Reality so easily. And, strangely enough, nominalism and post-modernism have thrown the divorce between Reality and mind out, except that these recent philosophies seem to have concluded that there is no Reality apart from the human mind. yet, the equation of the human mind with Mind itself is an assumption made by atheists of both the modern and post-modern schools, with no valid proof.
In contrast to modernism and its divorce we have Martin Buber's "I-Thou" relationship. Buber restored an ancient understanding of holistic Reality, but in a way that can appeal to the egalitarianism of modern man, the need for holism and not hierarchies or chains of being. And, I believe that Buber's emphasis on relationship is exactly how I would address Mathematical Platonism. It also touches on where I do not exactly agree with Mathematical Platonism. Modern Mathematical Platonists err in divorcing numerical reality from mind. They share a common error with nominalists, in that "mind" is assumed to be dichotomous with natural reality. This dichotomy is false and unproven.
Nominalists have to broker absurd objections to modern science, objections that Fundamentalists of all stripes, or even New Age mystics, would blush at making. One nominalist objection to mathematical realism posited that we cannot empirically know that science relies on mathematics because we do not have a science that does not rely on mathematics to compare.
Honestly, the reason that we do not have a form of science not relying upon Mathematics is because, well, frankly, such a form of science would not describe physical reality at all. In short, it would fall flat. The objection is utterly absurd, and yet I found it in a Stanford publication!
However, I must admit that the nominalists have a point. Mathematical Platonists who are atheists and agnostics have to grapple with the question of how symmetries and organizations that are patterns rife with intelligence and design could be divorced from Mind. Most believe that mind evolved intelligence because it is in a Universe of intelligence and design. However, a primitive Homo Habilus did not need to know Calculus and Quantum Mechanics. Clearly there is something else at work in the development of the human brain from its earlier models than mere adaptation and survival.
One can accept evolution while not accepting Darwinianism as a crude form of reduction. A minority of religious people, myself included, fall in to this camp. The majority of ultra-Orthodox Jews deny evolution completely. However, I never follow majorities if I can avoid it. Yet, my sense is that the Darwinist form of evolution falls in to a tautology. "A species survives because it adapts. And, we know that a species adapted because it survived." To me, that is a circular argument.
I agree with speciation and the basic mechanics involved with life's changes over the last 3.9 billion years, but remember that Darwin lived before Mendel, before modern genetics, and before the DNA molecule was discovered. In fact, Darwin himself never abandoned a kind of Deism that upheld intelligent design at the beginning of life's journey.
What I cannot accept is a purely biological explanation of number sense. It is too coincidental that humans would develop the means by which we would understand galaxies and nebulae by adapting to the bush. Now, modernist Mathematical Platonists would argue that the same physical laws that apply to the bush also apply to the Andromeda galaxy, some 2.5 million light-years away. However, they cannot really give an adequate explanation as to why this would be so, leaving them open to some of the objections that the nominalists might level at them. The weak Anthropic principle could be one such objection.
Thus, I agree with Mathematical Platonists strongly, but I disagree with them weakly. There is some validity to the nominalist argument in one sense. We cannot really prove the Mind-Reality divorce that so many realists posit. Sorry, but we can't. It might fit what you learned in a philosophy of science class, but we can't really prove it. I also do not believe in it. I believe that Mind and Reality are very much joined. And, I believe that the I-Thou relationship upheld by the Chassidics, by mystics of other religions, and described by Martin Buber gives us an important insight in to how to transcend the I-It dichotomy that modernism posited toward a more relational understanding of reality.
I will leave this thread to the debaters. I have said my piece on the subject. As to how I reconcile the Big Bang and Genesis? Well, remember Einstein's greatest blunder? Do you know why he made it? He assumed that the old-fashioned Book of Genesis was out of date and irrational. Thus, he could not accept the new cosmology as it was emerging. There is a lesson in that somewhere.
I also do not want to debate Creationism, Darwin, Intelligent Design or anything like that. Feel free to do so if you wish. This reality is not the ultimate reality anyway, so, although I love science and physical Nature, I look ever upwards. For Creationists of the Jewish, Christian or Islamic faiths who look askance at this post, I say that if belief in the Big Bang or evolution gets in the way of your Walk with G-d, then go with your Walk with G-d as that is the most important thing. I don't agree with you, but don't let me stop you. For the rest of you, enjoy the debate and yes, I'd better duck now.
All the best,
Please let me comment, very quickly and without much ado, on where I differ from mathematical Platonism. Ancient and medieval mathematical realism was far less pragmatic and scientifically oriented than modern realism/Platonism. By contrast, on the other end of the spectrum, Nominalism is another thing altogether. Actually, in some strange way, ancient Platonism had one familiarity with Nominalism, its opposite on the spectrum. That commonality was the belief that Reality could not be separated from Mind.
Modern philosophy divorced reality from Mind. You remember from college; Descartes, Locke, Hume, Kant, most of the "modern philosophers" divorced Reality from Mind. A few mavericks like Schopenhauer, Emerson, and the Romantics refused to go along with this divorce, but most of science did until the twentieth century. Subject-object dichotomy arose from the great divorce.
Ancient and medieval philosophy did not divorce Mind and Reality so easily. And, strangely enough, nominalism and post-modernism have thrown the divorce between Reality and mind out, except that these recent philosophies seem to have concluded that there is no Reality apart from the human mind. yet, the equation of the human mind with Mind itself is an assumption made by atheists of both the modern and post-modern schools, with no valid proof.
In contrast to modernism and its divorce we have Martin Buber's "I-Thou" relationship. Buber restored an ancient understanding of holistic Reality, but in a way that can appeal to the egalitarianism of modern man, the need for holism and not hierarchies or chains of being. And, I believe that Buber's emphasis on relationship is exactly how I would address Mathematical Platonism. It also touches on where I do not exactly agree with Mathematical Platonism. Modern Mathematical Platonists err in divorcing numerical reality from mind. They share a common error with nominalists, in that "mind" is assumed to be dichotomous with natural reality. This dichotomy is false and unproven.
Nominalists have to broker absurd objections to modern science, objections that Fundamentalists of all stripes, or even New Age mystics, would blush at making. One nominalist objection to mathematical realism posited that we cannot empirically know that science relies on mathematics because we do not have a science that does not rely on mathematics to compare.
Honestly, the reason that we do not have a form of science not relying upon Mathematics is because, well, frankly, such a form of science would not describe physical reality at all. In short, it would fall flat. The objection is utterly absurd, and yet I found it in a Stanford publication!However, I must admit that the nominalists have a point. Mathematical Platonists who are atheists and agnostics have to grapple with the question of how symmetries and organizations that are patterns rife with intelligence and design could be divorced from Mind. Most believe that mind evolved intelligence because it is in a Universe of intelligence and design. However, a primitive Homo Habilus did not need to know Calculus and Quantum Mechanics. Clearly there is something else at work in the development of the human brain from its earlier models than mere adaptation and survival.
One can accept evolution while not accepting Darwinianism as a crude form of reduction. A minority of religious people, myself included, fall in to this camp. The majority of ultra-Orthodox Jews deny evolution completely. However, I never follow majorities if I can avoid it. Yet, my sense is that the Darwinist form of evolution falls in to a tautology. "A species survives because it adapts. And, we know that a species adapted because it survived." To me, that is a circular argument.
I agree with speciation and the basic mechanics involved with life's changes over the last 3.9 billion years, but remember that Darwin lived before Mendel, before modern genetics, and before the DNA molecule was discovered. In fact, Darwin himself never abandoned a kind of Deism that upheld intelligent design at the beginning of life's journey.
What I cannot accept is a purely biological explanation of number sense. It is too coincidental that humans would develop the means by which we would understand galaxies and nebulae by adapting to the bush. Now, modernist Mathematical Platonists would argue that the same physical laws that apply to the bush also apply to the Andromeda galaxy, some 2.5 million light-years away. However, they cannot really give an adequate explanation as to why this would be so, leaving them open to some of the objections that the nominalists might level at them. The weak Anthropic principle could be one such objection.
Thus, I agree with Mathematical Platonists strongly, but I disagree with them weakly. There is some validity to the nominalist argument in one sense. We cannot really prove the Mind-Reality divorce that so many realists posit. Sorry, but we can't. It might fit what you learned in a philosophy of science class, but we can't really prove it. I also do not believe in it. I believe that Mind and Reality are very much joined. And, I believe that the I-Thou relationship upheld by the Chassidics, by mystics of other religions, and described by Martin Buber gives us an important insight in to how to transcend the I-It dichotomy that modernism posited toward a more relational understanding of reality.
I will leave this thread to the debaters. I have said my piece on the subject. As to how I reconcile the Big Bang and Genesis? Well, remember Einstein's greatest blunder? Do you know why he made it? He assumed that the old-fashioned Book of Genesis was out of date and irrational. Thus, he could not accept the new cosmology as it was emerging. There is a lesson in that somewhere.
I also do not want to debate Creationism, Darwin, Intelligent Design or anything like that. Feel free to do so if you wish. This reality is not the ultimate reality anyway, so, although I love science and physical Nature, I look ever upwards. For Creationists of the Jewish, Christian or Islamic faiths who look askance at this post, I say that if belief in the Big Bang or evolution gets in the way of your Walk with G-d, then go with your Walk with G-d as that is the most important thing. I don't agree with you, but don't let me stop you. For the rest of you, enjoy the debate and yes, I'd better duck now.
All the best,