| view 👀:9 |
🙍 oneddl |
redaktor: book24h | Rating👍:
The Logic of Number (True PDF) [#473862]
English | 2022 | ISBN: 978-0192846679 | 376 pages | True PDF | 6.77 MB
In The Logic of Number , Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable 'single-barreled' abstraction, in contrast with the 'double-barreled' abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle.
Natural Logicism imposes upon its account of the numbers four conditions of adequacy: First, one must show how it is that the various kinds of number are applicable in our wider thought and talk about the world. This is achieved by deriving all instances of three respective schemas: Schema N for the naturals, Schema Q for the rationals, and Schema R for the reals. These provide truth-conditions for statements deploying terms referring to numbers of the kind in question. Second, one must show how it is that the naturals sit among the rationals as themselves again, and the rationals likewise among the reals. Third, one should reveal enough of the metaphysical nature of the numbers to be able to derive the mathematician's basic laws governing them. Fourth, one should be able to demonstrate that there are uncountably many reals.
Natural Logicism is realistic about the limits of logicism when it comes to treating the real numbers, for which, Tennant argues, one needs recourse to geometric intuition for deeper starting-points, beyond which logic alone will then deliver the sought results, with absolute formal rigor. The resulting program enables one to delimit, in a principled way, those parts of number theory that are produced by the Kantian understanding alone, and those parts that depend on recourse to (very simple) a priori geometric intuitions.
https://rapidgator.net/file/143cae3bc78d39dbe09d2acb56f4296c/cvhin.T.L.o.N.T.P.rar.html
Please Help Me Click Connect Icon Below Here and Share News to Social Network | Thanks you !
⚠️ Dead Link ?
You may submit a re-upload request using the search feature.
All requests are reviewed in accordance with our Content Policy.
Significant surge in the popularity of free ebook download platforms. These virtual repositories offer an unparalleled range, covering genres that span from classic literature to contemporary non-fiction, and everything in between. Enthusiasts of reading can easily indulge in their passion by accessing free books download online services, which provide instant access to a wealth of knowledge and stories without the physical constraints of space or the financial burden of purchasing hardcover editions.
Comments (0)
Users of Guests are not allowed to comment this publication.