By Charles S. Chihara

Charles Chihara's new booklet develops a structural view of the character of arithmetic, and makes use of it to give an explanation for a couple of amazing good points of arithmetic that experience wondered philosophers for hundreds of years. particularly, this attitude permits Chihara to teach that, so as to know the way mathematical structures are utilized in technological know-how, it's not essential to imagine that its theorems both presuppose mathematical gadgets or are even real. He additionally advances a number of new methods of undermining the Platonic view of arithmetic. an individual operating within the box will locate a lot to present and stimulate them right here.

**Read Online or Download A Structural Account of Mathematics PDF**

**Similar logic & language books**

Whilst this booklet used to be initially released in 2006, Epistemetrics was once now not as but a scholarly self-discipline. with reference to clinical details there has been the self-discipline of scientometrics, represented by means of a magazine of that very identify. technological know-how, although, had a monopoly on wisdom. even though it is one among our most vital cognitive assets, it isn't our just one.

**The Paradox of Self-Amendment: A Study of Logic, Law, Omnipotence, and Change**

The 1st full-length research of self-reference and paradox in legislation, this e-book will intrigue and teach somebody attracted to legislations, good judgment, philosophy, or political thought. heritage exhibits that self-amendment - for instance, using a constitution's amending clause to amend itself - is general; felony research indicates it to be lawful, whether (as a few logicians have alleged) it's self-contradictory; and philosophical research indicates it to be foundational for legality.

**Against the Current: Selected Philosophical Papers**

The current selection of seventeen papers, such a lot of them already released in foreign philosophical journals, bargains either with matters within the philosophy of common sense, the philosophy of arithmetic, the philosophy of language and epistemology. the 1st half comprises serious exams and slightly deviant renderings of the paintings of 2 seminal philosophers, Frege and Husserl, in addition to of the younger Carnap and Kripke.

**Symbolic Logic An Introduction**

This booklet is meant either as a textbook in symbolic common sense for

undergraduate and graduate scholars and as a treatise on the founda-

tions of common sense. a lot of the cloth was once constructed in an under-

graduate path given for a few years in Yale collage. The

course used to be basically a primary direction in common sense for college students interested

in technological know-how. Many substitute units and strategies of presentation

were attempted. these incorporated listed here are the ones that appeared most

successful.

**Additional info for A Structural Account of Mathematics**

**Example text**

18 / FIVE PUZZLES exist mathematically. But if it can be proved that the attributes assigned to the concept can never lead to a contradiction by the application of a finite number of logical inferences, I say that the mathematical existence of the concept (for example, of a number or a function which satisfies certain conditions) is thereby proved. 11 A third outstanding mathematician seems to have maintained a view that is very similar to the above. According to the historian of mathematics Joseph Dauben, Logical consistency was the touchstone which Cantor applied to any new theory before declaring it existent and a legitimate part of mathematics....

According to the historian of mathematics Joseph Dauben, Logical consistency was the touchstone which Cantor applied to any new theory before declaring it existent and a legitimate part of mathematics.... Since he took his transfinite numbers to be consistently defined, ... there were no grounds to deny his new theory. This kind of formalism, stressing the internal conceptual consistency of his new numbers, was all mathematicians needed to consider before accepting the validity of the transfinite numbers.

The relation is not internal because its holding does not depend solely on the intrinsic properties of the person and the piece of property. It is not external because its holding does not depend purely on the intrinsic properties of the composite consisting of the person and the piece of property. The unsatisfactory nature of the typosynthesis theory A question now arises: is it possible for us to place the relation of typosynthesis within this classification? In other words, can we classify typosynthesis as internal, external, or extrinsic?