Peirce’s 1903 Lowell Lectures • Comment 10

Re: Peirce List DiscussionJohn Sowa

In the Lowell Lectures [1903] Peirce defined the Sheet of Assertion as the representation of a universe that was constructed during a discourse between Graphist and Grapheus.

But that is just one of many ways of using logic.  In 1911 he wrote about “whatever universe” and “the whole sheet”:

Every word makes an assertion.  Thus  ──man  means “There is a man” in whatever universe the whole sheet refers to.

This is less restrictive than the definition in the Lowell lectures.  For example, it would allow a logician to use a sheet of paper to write a proof by contradiction.  In that case, there would be no universe about which the statements on the paper could be true.

In that case we may say that a sign’s set of denoted objects is empty.  I think this tactic probably goes back to my earliest algebra courses, where our teachers cautioned us to remember that the “solution set” of a formula could be the empty set.  By apt analogy, then, we may well call “a sign’s set of denoted objects” its “denotation set”.  Of course an empty set is a subset of every set, but nothing about this requires the universe of discourse to be empty, much less not to exist.


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.

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