and you refuse to provide any logical basis for it.
The logical basis for it was already given at the end of
http://www.internationalskeptics.com/forums/showpost.php?p=11704139&postcount=2363 and
http://www.internationalskeptics.com/forums/showpost.php?p=11704251&postcount=2364.
Here are more details:
Question:
Are tautologies and contradictions analogous to universal sets and empty sets, respectively? (
http://math.stackexchange.com/quest...-analogous-to-universal-sets-and-empty-sets-r)
Visual AND symbolic reasoning answer:
It is well established that given any logical framework, it is bounded by contradiction and tautology, no matter how many distinct logical states that are ~contradiction AND ~tautology are logically addressed between them.
By the current accepted notion of set, a given set must be marked by some symbol(s) in order to formally air our view about it.
The simplest marked set is the empty set, marked as {}.
This set has no members, where the notion of no members is not marked by any symbol, yet this set is marked as {}.
By this fundamental reasoning, even before using axioms, we logically address the void between {} as contradiction, and the outer braces as tautology,
where such reasoning is derived from simultaneously using both our visual AND symbolic brain skills.
Exactly as contradiction and tautology are logically distinct of each other, so is the case of any amount of distinct marked members between contradiction (the unmarked) and tautology (the outer braces).
So, logically no amount of marked members is reducible into contradiction (the unmarked) or extendible into tautology (the outer braces).
Now let's inductively construct a given set by two different construction methods that are logically equivalent, as follows (I use only braces for "pure sets" construction):
Here is an example of Von-neumann inductive construction:
{ 0,1,2,3,4,...
} =
{ {}, {{}}, {{},{{}}}, {{},{{}},{{},{{}}}}, {{},{{}},{{},{{}}},{{},{{}},{{},{{}}}}}, ...
}
Here is an example of Zeremelo inductive construction:
{ 0,1,2,3,4,...
} =
{ {}, {{}}, {{{}}}, {{{{}}}}, {{{{{}}}}}, ...
}
Please be aware that in both constructions the outer braces of any given set are not taken as parts of any amount of members (in both cases order is insignificant).
So by logically observe the concept of set, one actually discovers that no non-empty set is logically complete, since its members are logically irreducible into contradiction (the unmarked) or extendible into tautology (the [bold] outer braces).
From this fundamental logical point of view there is no complete finite or infinite set, yet given any set (empty or non-empty) it is logically bounded by contradiction and tautology.
Moreover the marked "level" of being a set (the bold braces) is logically not any one of its members (Russell's paradox is logically avoided without the need of any axiomatic framework like
ZF(C), etc.).
So as for your question, tautology is logically analogous to the "level" of being a set (logically inaccessible to any amount of its members), and contraction is logically analogous to the "level" of no members of the given set.
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Also maybe you will find
https://drive.google.com/file/d/0B3hcPBRBCzClakdJZjNNOW5RSTQ/view?usp=sharing helpful.
But remember this, no one but you can take you to the next step.
