Introduction to Logic and to the Methodology of Deductive Sciences by Alfred Tarski, Olaf Helmer-Hirschberg

Introduction to Logic and to the Methodology of Deductive Sciences

Read/Write Review

Search Inside This Book

View Checked Search Results

Shared Notes On This Item

Table of Contents

VII
CONSTRUCTION OF A MATHEMATICAL
THEORY:
LAWS OF ORDER FOR NUMBERS

43. Primitive terms of the theory under construction; axioms
concerning fundamental relations among numbers

With a certain amount of knowledge of the fields of logic and
methodology at our disposal, we shall now undertake to lay the
foundations of a particular and, incidentally, very elementary
mathematical theory. This will be a good opportunity for us
to assimilate better our previously acquired knowledge, and
even to expand it to some extent.The theory with which we shall concern ourselves constitutes a
fragment of the arithmetic of real numbers. It contains funda-
mental theorems concerning the basic relations less than and
greater than among numbers, as well as the basic operations on
numbers, namely of addition and subtraction. It presupposes
nothing but logic.The primitive terms which we shall adopt in this theory are the
following:

	real number,
	is less than,
	is greater than,
	sum.

Instead of "real number" we shall, as before, simply say "number".
Also, it is slightly more convenient to consider, instead of the
term "number", the expression "the set of all numbers" as a primitive

-155-

Questia, a part of Gale, Cengage Learning. www.questia.com

Publication Information: Book Title: Introduction to Logic and to the Methodology of Deductive Sciences. Contributors: Alfred Tarski - author, Olaf Helmer-Hirschberg - transltr. Publisher: Oxford University Press. Place of Publication: New York. Publication Year: 1941. Page Number: 155.