Re: Peirce on Definition and Determination

Note 7.  http://inquiryintoinquiry.com/2012/06/11/definition-and-determination-7/

Peircers,

Peirce clearly set great store by his 1902 definition of logic as formal semiotic, whose principles he proposed to
deduce by evident and rigorous mathematical reasoning from his triadic relational definition of a sign.

     It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of
logic. (NEM 4, 21).

     It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical
reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. (NEM 4, 54).

By “criticism of Weierstrassian severity”, Peirce refers to the reconstitution of mathematical analysis precipitated by
Karl Weierstrass during the last half of the 19th Century, replacing many intuitive but problematic concepts with
exacting enough definitions to support the development of coherent and powerful theories.

• http://www-history.mcs.st-andrews.ac.uk/Biographies/Weierstrass.html

That bit of history teaches an important lesson.  Not every form of words that might be cast about an intuitive object 
or used to express an intuitive concept will exhibit the strength of a formal definition, one that supports mathematical 
reasoning and allows the evident deduction of a coherent and comprehensive theory of its object domain, for example, in
our present instance, “the principles of logic”.

The moral of the story so far is to recognize the qualifications of these “industrial strength” definitions, and to
realize what it means for Peirce to be advertizing these very virtues for his 1902 brand of sign definition.

Regards,

Jon

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