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Notes on Bertrand Russell's The Theory of Types by Jerry Shaffer Bertrand Russell developed
what he called The Theory of Types to deal with logical paradoxes.
A logical paradox consists of a statement which if true is false and if
false is true. Thus consider "I am lying." If it is true and
I am lying, then I am saying something false (that is what a lie is) and
if it is false and I am saying something false, then it is true that I
am lying. Such a statement is
Logical paradoxes are fatal to any logical system because one
requirement
Russell showed that any logical system could be shown to contain paradoxes.
Russell's solution, which he sent to Frege and also included in his
own Principia Mathematica, was his Theory of Types. He made a distinction
among statements:statements, statements about statements, statements
about
Gregory Bateson was influenced by Russell's theory of logical types. He distinguished statements from statements about statements. If I say "I love you," that is a statement. If I say "Don't believe me when I say, 'I love you,'", that is a statement about a statement. No problem there. Each is allowable. But if I combine the two, say "I love you" in a tone which indicates you shouldn't believe me, then I am combining two communications in one, both saying something and saying you should not believe what I am saying. It violates The Theory of Types. It may also screw up the listener. (Remember the infamous "schizophreno- genic mother"). If I make a statement but leave it totally ambiguous as to how that
statement is to be taken, e.g., as a statement of belief, as a question,
as a line in a play, as a poetic conceit, as a deliberate lie, etc., then
I have omitted a statement about the statement. Ordinarily context
supplies the content of the statement about the statement, tells us how
the statement is to be taken. But if the context
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