A Structural Account of Mathematics - download pdf or read online

By Charles S. Chihara

ISBN-10: 0191533106

ISBN-13: 9780191533105

ISBN-10: 0199228078

ISBN-13: 9780199228072

ISBN-10: 0199267537

ISBN-13: 9780199267538

Charles Chihara's new ebook develops and defends a structural view of the character of arithmetic, and makes use of it to give an explanation for a few extraordinary positive aspects of arithmetic that experience questioned philosophers for hundreds of years. The view is used to teach that, with a view to know how mathematical structures are utilized in technological know-how and daily life, it's not essential to suppose that its theorems both presuppose mathematical gadgets or are even precise. Chihara builds upon his past paintings, within which he offered a brand new approach of arithmetic, the constructibility concept, which failed to make connection with, or resuppose, mathematical gadgets. Now he develops the venture additional by way of interpreting mathematical platforms at the moment utilized by scientists to teach how such platforms fit with this nominalistic outlook. He advances a number of new methods of undermining the seriously mentioned indispensability argument for the life of mathematical items made well-known via Willard Quine and Hilary Putnam. And Chihara provides a motive for the nominalistic outlook that's relatively assorted from these quite often recommend, which he continues have resulted in severe misunderstandings.A Structural Account of arithmetic should be required examining for a person operating during this box.

Show description

Read or Download A Structural Account of Mathematics PDF

Best logic & language books

Download PDF by George Englebretsen: Something to reckon with: The logic of terms

By means of delving into the background and envelopment of good judgment from its beginnings to the trendy period, George Englebretsen rehabilitates time period common sense and demonstrates that an more desirable conventional good judgment continues to be a manageable risk. Taking suggestion from Fred Sommers' paintings, he creates an up to date and engaging model of time period common sense; one he believes to be simply as valid as, and in methods improved to, the at the moment main mathematical good judgment.

Read e-book online Enciclopedia iberoamericana de filosofia, Vol. 7. Logica PDF

Desde Aristoteles hasta Wittgenstein, todas las corrientes filosoficas se han ocupado de un modo u otro de l. a. logica, pero ha sido el espectacular desarrollo de l. a. logica durante este siglo el que ha incidido de modo irreversible sobre l. a. filosofia y el filosofar actuales, de tal modo que se ha llegado a afirmar que sin logica no se puede filosofar.

The complete Lojban language by John W Cowan PDF

The whole Lojban Language is an entire description of the synthetic language Lojban. It serves as a reference grammar for the language, providing an summary of the language, in addition to linguistic info on each point of the language. This booklet serves because the ordinary defining the language layout.

Karin de Boer's On Hegel: The Sway of the Negative PDF

Concentrating on the technology of good judgment , this wide-ranging and cutting edge examining exposes the strength in addition to the restrict of Hegel's philosophy. Drawing on Hegel's early account of tragic conflicts, De Boer brings into play a kind of negativity that demanding situations the optimism inherent in modernity and Hegelian dialectics alike.

Additional resources for A Structural Account of Mathematics

Example text

Then, what properties of Bill Clinton and this singleton determine that it is Bill Clinton and nothing else that is in the membership relation to this unit set? Who knows? Set theory does not tell us. Perhaps membership is not that sort of relation. Perhaps membership is like the relation of being married. Perhaps it is in virtue of some things Bill Clinton, the singleton, and some third being have done that brings it about that Clinton is in the membership relation to the set in question. Again, we haven't the vaguest notion of what actions, if any, are required for the relation to obtain.

But would such a proof establish the propositional consistency of this theory? Clearly not. 16 Hilbert's criterion of truth and existence Let us now consider Frege's objection to Hilbert's doctrine that, if a set of axioms is consistent, then the axioms are "true" and the things defined by the axioms exist. Frege submitted to Hilbert the following example of a set of axioms: (Al) A is an intelligent being (A2) A is omnipresent (A3) A is omnipotent, suggesting that if this set is consistent, then it should follow by Hilbert's doctrine that the axioms are true and that there exists a thing that is intelligent, omnipresent, and omnipotent (Frege, 1980: 47).

Geometry has become pure mathematics. Axioms are not evident truths. They are not truths at all in the usual sense" (Freudenthal, 1962: 618). Hilbert never gave an adequate reply to the above objection of Frege's and he continued to provide confusing and conflicting characterizations of his axioms. No doubt, he felt that Frege's objections were mere quibbles and that, mathematically, he was on firm ground in claiming that his axioms were definitions. When Frege found that Hilbert had not altered his 10 Mueller, 1981: 9.

Download PDF sample

A Structural Account of Mathematics by Charles S. Chihara


by Richard
4.4

Rated 4.56 of 5 – based on 24 votes