## Peirce’s 1903 Lowell Lectures • Comment 10

JFS:
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.

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