Download e-book for iPad: A Profile of Mathematical Logic (Dover Books on Mathematics) by Howard DeLong

By Howard DeLong

ISBN-10: 0486139158

ISBN-13: 9780486139159

Publish 12 months note: First released in 1971
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This textual content explores the historic purposes for the formation of Aristotelian good judgment, the increase of mathematical common sense, the character of the formal axiomatic technique and its use, and the most result of metatheory and their import.

From 1971 edition

Includes 22 figures and 19 tables. Appendixes. Bibliography. Indexes.

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Additional resources for A Profile of Mathematical Logic (Dover Books on Mathematics)

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This allows mathematics to be seen as the study of regularities, within regularities, within…, within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers’ essay [1] and comments that were made on the FQXi website [2]. The Unreasonable Effectiveness of Mathematics in the Physical Sciences The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve—Eugene Wigner [3].

Even if it turns out that our universe sprang from a tiny fluctuation in some primordial “false vacuum” quantum field, you still need to get some false vacuum from the store! On the other hand, if the basic level of reality is an abstract mathematical structure, and mathematical structures exist by themselves, in a “timeless” and “eternal” way, there is no longer any issue. So, if you can get over the initial shock and disbelief that physics can be the same thing as mathematics “seen from the inside”, cosmic structuralism as expressed by the MUH explains in a simple way why our universe exists.

Thus, the search for a theory of everything is not fruitless; I just do not expect it to ever terminate. Secondly, my theory predicts that the mathematical representation of fundamental physical theories will continue to become increasingly abstract. The more phenomena we try to encompass in our fundamental theories, the further the resulting hubs will be from the nodes representing our direct sensory experience. Thus, we should not expect future theories of physics to become less mathematical, as they are generated by the same process of generalization and abstraction as mathematics itself.

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A Profile of Mathematical Logic (Dover Books on Mathematics) by Howard DeLong


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