Peirce’s 1903 Lowell Lectures • Comment 1

Cf: Laws Of Form DiscussionJA

A question arose concerning one of Peirce’s ways of explaining logical negation.

Re: Peirce List DiscussionGF

I commented as follows.

One way of saying “not x” or “x is false” is to say “x implies α” where “α” is taken to mean “any proposition whatever”.  This is the hoary old rule of ex falso quodlibet, more lately going under the name explosion principle.  It is related to the definition of an inconsistent logical system as one in which every formula is a theorem, and thus in which no line of distinction can be drawn between true and false.

One place where Peirce makes use of this style of negation is in his comments on a logical formula we now call Peirce’s Law.

This entry was posted in C.S. Peirce, Diagrammatic Reasoning, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce List, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization and tagged , , , , , , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.