Math Forum / Mathematics / Mathematical Logic / October 2008

PROPOSAL
Statements can play no substantive role in logic. The logical statement
is an oxymoron, entailing the inappropriate physical positioning of
meaning.

ARGUMENT
Statements are identifiable but they do not have truth values or
meanings, despite Russell's advice to the contrary. Statements are
identified, of course, as ink marks on paper or as illuminated pixels.
This identification is made on the basis of an implicit physicalism.
However, we then, mistakenly, extend the application of the physical
model by physically placing 'meaning' itself. This application suggests
a merger of incommensurable categories - physical position and meaning.
It is a category error, in Ryle's terminology, and the logical statement
is an oxymoron, entailing the inappropriate physical positioning of
meaning.

So, what is, or ought to be, a statement? We identify a place to read
when we are given a statement. For this reason it is not appropriate to
consider truth values and meanings in the context of statements or
propositions. A similar argument can be made for 'strings'. Strings
cannot be identified by their elements, but only by their spatiotemporal
location which no more than offers us a place to read.

CONCLUDING DISCUSSION
Statements and strings have no place in logic or mathematics as their
identification is made through a physical category that cannot
substantively link them to the category in which meanings are conveyed.
While "this statement is false" is both a great resource and a popular
plaything for logicians - bringing the greatest of minds to bear on
ideas of paradox and completeness - I have suggested that, really
speaking, such statements and the endeavours associated with them, died
before they were born.