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
self-contradictory It contradicts itself.  Its truth entails its falsity and its falsity
entails its truth.

Logical paradoxes are fatal to any logical system  because one requirement
of a logical system is that it is self-consistent, contains no contradictions.  Arithmetic, for example, would collapse if it contained a contradiction.

Russell showed that any logical system could be shown to contain paradoxes.
When Frege sent him a draft of his turning arithmetic into a logical system, Russell devastated him by showing that the system contained a paradox.  All of logic is threatened if we cannot eliminate 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
statements about statements, etc., each of which was a different Type (of statement).  The theory was to the effect that every statement must fall into one
type or another, so that it was not allowed that there be a statement which was of more than one type.  "I am lying" is both a statement and about my statement and therefore is not to be allowed into a system.  Thus the system will not contain that paradox.  It is saved from paradox by The Theory of Types.

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
does not, the statement may seem to us "off the wall," crazy.