网范文：“Category theory applied to description of time and space ” 麦克塔加特的想法通过在虚幻的时间进行阐述，自然学者多年来保持极大的兴趣。在这篇哲学范文中,有一个简短的讨论，对于提到的一些重点，对哲学的兴趣,并继续他的思想运用到现代物理学和神经科学。事实上，英语论文题目，用动态系统模型进行了描述,说明了这个事实。许多泡沫的解释,也来源于麦克塔加特的观点,讨论了各种例子和有效性，英语毕业论文，量子效应可判断。
在十九年代末期,我开始与教授在曼彻斯特,试图描述完全融入一个数学系统,物理定律。我和教授发现了一个实用的解决方案,不过非常抽象,太困难。我相信我们需要一些新的数学理论。下面的这篇范文将进行详述。
Abstract
McTaggart's ideas on the unreality of time as expressed in "The Nature of Existence" have retained great interest for many years for scholars, academics and other philosophers. In this , there is a brief discussion which mentions some of the high points of this philosophical interest, and goes on to apply his ideas to modern physics and neuroscience. It does not discuss McTaggart's C and D series, but does emphasise how the use of derived versions of both his A and B series can be of great virtue in discussing both the abstract physics of time, and the present and future importance of McTaggart's ideas to the subject of time. Indeed an experiment using human volunteers and dynamic systems modelling which was carried out is described, which illustrates this fact. The Many Bubble Interpretation, which also derives from McTaggart's ideas, is discussed and various examples of its use and effectiveness are referred to. The Schrodinger Cat paradox is essentially resolved in principle, the quantum Zeno effect interpretable, Kwiat's recent result referred to, and the newly discovered reverse Stickgold effect described.
Introduction
I began in the late nineteen sixties , with Professor R.O. Gandy in Manchester, England, by trying to describe and attempting to completely incorporate into a mathematical system, the laws of physics. I used basic methods, such as those of Gentzen, Heyting Brouwer etc., etc. But both I and Professor Gandy found a practical solution, even in the very abstract, to be too difficult at the time. I believe we both thought that we needed some new mathematics, which either did not seem to exist or which we simply had not located ! Now the work of Turing, and later Chaitin and Connes, for example, should have helped but somehow it seemed to me necessary to go even deeper down and more basic. In fact the philosophy of approach with which I began was that of the early formal system theory of Smullyan (1961). Clearly on the face of it, it looked as if strange mathematical constructs like that of Godel universes as well, could be included in such an approach. But at that point, the pieces did not seem to fit. For example, pursuing the Turing path, which has been trod by so many workers by now, like for example Juergen Schmidhuber, was not going to be enough.
There was more to it than simple computability problems, we needed to go in a sense to a higher level. Even using the physically peculiar looking results of quantum theory which have by now been incorporated into modern methods of quantum computing, and some of the early results of which, for example, were first published in a journal which I founded and of which I was Editor in Chief for many years (Feynman, 1982) could certainly enlighten us and might well have to be included in some more complete description of the universe which more finally became of use to us, were probably too intellectually ad hoc and thus too flimsy to effectively suppress or even mollify the deep angst of our lack of basic understanding.
It was almost like trying to understand modern number theory in a position where transfinite numbers had not been invented. There almost had to be "another dimension or dimensions", or even another "kind of dimension". Early string theory was around at the time, but at this very basic level, the explanation was unlikely to have that kind of simplicity. It was likely to be much more basic, deep and profound. In sum we were looking for fundamental mathematics, not just the simple technical physics that string theory, even today, would seem to amount to. I felt in the early nineteen sixties, and still feel now, that the great Emmy Noether, who has since been described flamboyantly but possibly realistically as the greatest mathematician who ever lived, in making a comment on the equality of numbers outlined a more basically sensible approach and that comment should be able to enlighten our understanding. "
If one proves the equality of two numbers a and b by showing first that "a is less than or equal to b" and then "a is greater than or equal to b", it is unfair, one should instead show that they are really equal by disclosing the inner ground for their equality". The same idea applies of course if, for example, a does not equal b but the formulation of our problem here is thornier. And although I end up here talking about the A and the B series, it is not with the idea of using a simple logical, physical, or mathematical proof but a striving for something closer to the absolute.
McTaggart and Angst
Referring now back to space and time, Buber (1959) pointed out 'A necessity I could not understand swept over me: I had to try again and again to imagine the edge of space, or its edgelessness, time with a beginning and an end or a time without beginning or end, and both were equally impossible, equally hopeless – yet there seemed to be only the choice between the one or the other absurdity'. The problem here is that when Buber tried to get down to philosophical details he just had not got the right stuff and relativity theory shows us that. There is really no certain reason, using relativity, why time or space would have a beginning or an end - philosophical problem solved.
Now we could say that Buber's confusion was caused by his acceptance of Newton's concept of space rather than Leibniz's. In Newton's world-view physical objects could exist by being in space, but space could exist even if devoid of any physical objects. In Leibniz's view, objects existed anyway and could touch one another, be separated by various distances and so on but space, per se, did not exist. This immediately resolved Buber's problem. One can solve such a problem by showing that it contains an untenable proposition. In this case the problem was not with space itself, but with Newton's conception of space.
The answer was to accept Leibniz's more economical view, or simply to look for a consistent definition of space, which without relativity was hard to find. McTaggart (1927) reasonably showed that in his context time showed a contradiction and he was right and logical to suggest that time did not exist, or is unreal. That was a sensible and economic view but slightly harder to develop than in Leibniz's case, where Leibniz had effectively inferred that space, per se, did not exist and was able to get quite a good theory for his era. But McTaggart's concern with time is in many ways very analogous with Buber's concern with space. Buber knew more or less what space was, but when he thought about it, it looked somehow spooky and unreal. Maybe we could say that that is "Angst". It is certainly a clear indicator that something needed to be done.. Anyway, the same thing happened to McTaggart with time, and as we will pointed out here, just as Einstein resolved Buber's philosophical worry about space, so too category theory can up to a point resolve McTaggart's problem with time. But that of course does not give us the right to ignore McTaggart's problem just as relativity has shown we should not certainly not have ignored Buber's problem. Just as in a way we have all been ersatz Leibnizians, prior to Einstein, let us importantly try to avoid continuing the same line of error with McTaggart, whether or not a resolution of his problems is more of a serious mathematical and philosophical challenge than Einstein's resolution of Newton's problem was.
Acknowledgements
I would like to thank Deepak Dhar and Navin Singhi, both of the Tata Institute of Fundamental Research, Mumbai for their helpful advice, encouragement and discussions, and Deepak Dhar for the chance of having a fine lunch at the Tata Institute of Fundamental Research, Mumbai. I would also like to thank David Chalmers, Professor of Philosophy at the Australian National University, for his helpful advice and encouragement .()
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