Saturday, May 03, 2008

Boole on Identity, Noncontradiction, and Excluded Middle

As the principles of identity and excluded middle...are true principles and are moreover either first principles or as consciousness informs us lie close to the very ground of the possibility of thought (it matters not here that they have been regarded by some as metaphysical and not logical and by others have been considered frivolous and trifling). A theory of Logic which does not both recognise them and give to them a very important place must be a very imperfect theory. It does not suffice that their existence should be casually noticed.

On the other hand it is very evident that the principles of identity, contradiction and excluded middle are rather principles which relate to conception and to judgment -- to the power by which [we] conceive of things as existing and as existing in relation expressible by propositions -- than to reasoning. To the latter they seem to belong only or chiefly in an implicit manner inasmuch as reasoning presupposes conception and judgment as the sources form which the materials upon which it operates are derived.

George Boole, Prolegomena, sects. 4 & 5, Selected Manuscripts on Logic and its Philosophy, Grattan-Guinness and Bornet, eds. Birkhäuser Verlag (Boston: 1997) 51-52.

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