- #36
PFanalog57
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Hurkyl said:This is not "self-identity"; this is the "fallacy of composition". In general, the whole does not have the properties of its parts.
"self-identity" says that the set of all sets that contain themselves must be the set of all sets that contain themselves.
The correct logic is:
If A then B
A
therefore B
Yet the fallacy of composition is equivalent to:
If A then B
B
therefore A
which is incorrect logic.
The set of natural numbers has the identity "natural number" that distributes over all members of the "set"[the whole distributes over the parts].
The most fundamental identity distributes over all elements of the "Universal Set". True, one specific aspect is not a universal property but the universal property can be the first step in the logical deduction that eventually leads to the specific aspect.
U[X[Y[Z...{ }]]]
Russell's paradox is a form of the liars paradox:
This statement is false
Which leads to Goedel's incompleteness theorem.