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Models to Illustrate the Foundations of Mathematics
Excerpt from Models to Illustrate the Foundations of Mathematics
In that work it will be found that pure mathematics is regarded as consisting of attempts to deduce propositions by the methods Of Formal Logic from postulates, or axioms, about terms of which the meaning is intentionally left undefined. These postulates or axioms are not looked upon as truths necessarily self-evident to the mind, nor as experimental facts, but merely as assumptions (p. Calling such a series of logically connected propositions an abstract mathematical system, then mathematics as a whole is defined as consisting of all such systems together with all their concrete applications (p.
In that work it will be found that pure mathematics is regarded as consisting of attempts to deduce propositions by the methods Of Formal Logic from postulates, or axioms, about terms of which the meaning is intentionally left undefined. These postulates or axioms are not looked upon as truths necessarily self-evident to the mind, nor as experimental facts, but merely as assumptions (p. Calling such a series of logically connected propositions an abstract mathematical system, then mathematics as a whole is defined as consisting of all such systems together with all their concrete applications (p.
132 pages, Paperback
First published September 27, 2015
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