brokenhead: Any part of a logically true statement about something, such as a premise, belongs to set B.
Kevin Solway: I have no idea what you are on about here.
It is very simple. A logical truth is something that is necessarily based on something that is a truth but ultimately rests on something that is not a logical truth as such.
For instance, to say a thing cannot be other than itself is not a logically true statement, for it requires definitions, which are not themselves logical truths. A=A presupposes AdefA, where the symbol "def" stands for "is defined as." Therefore, a logically true statement would be: "If AdefA, then A=A." This is
required in order to make this logically true statement: "If A=A, then A
notequA cannot be true." Here, "
notequ" means "does not equal" or "is not the same as."
This is a crucial point. Another premise, which in itself is not a logical statement but enables us to construct logical statements, is the statement "Let every portion of the Totality be a 'thing.'" Yet another is : "Let any such 'thing' be representable by the symbol A." To say "A thing cannot be other than itself" is therefore not a logical truth in and of itself. A logically true statement would take the form: "If the previous two statements are true (premises), then a thing cannot be other than itself."
Kevin, my point is simply that a logical truth cannot be debated. Yet debates do and shall always exist. What we debate are premises and therefore conclusions.
It [the earth before life began] is imagined to have existed, but there's no way for us to tell with certainty that it did.
If the earth existed before life appeared on it, then it falls within the category of things we do not know, and exists as such.
Therefore, any proposition about the origin of life is equally valid, as long as it seems to account for what we are able to observe now.
The only limitation of logic is that it can never be what it is not.
Logic can never be illogic.
But it is limited by the statement A=A, to which all logic must ultimately appeal, and which is, itself, not a logical statement, nor is it an illogical statement, but rather, simply, a definition.
For instance, X+Y is decidedly not the same "thing" as Y+X. In many algebras, called
noncommutative algebras, (X+Y)
notequ(Y+X). This is a general rule in a noncommutative algebra, yet the following (logically) true statement holds: "Iff X+Y=A AND Y+X=A, then X+Y=Y+X." Note that this also, as every logically true statement
must,
assumes the logical premise A=A. (For those readers who may not have seen it before, "Iff A, then B" means "A implies B" AND "B implies A." "Iff" is read "If and only if.")
Let "A" be something. Thing "A" is itself and not other than itself. And that is a logically true statement about "A". Why on earth you would want to think that a part of that statement is not a logically true statement, is beyond me.
I think you need to completely reformulate your argument.
Because to say "Thing 'A' is itself and not other than itself" is not a logically true statement as it is given. Rather, it is a definition used as a proposition and can be part of a logical truth. Remember, a logical truth cannot be debated. We have said that any portion of the Totality is a thing. Let a crossing guard be a thing, as, being part of the Totality, it must be. Let us call it thing "A." Let a dentist be a thing. Let us call it thing "B." Let Mrs. Jones be thing "C." Crossing guard A can be the dentist B, Mrs. Jones C, working in her spare time. That is, unless we define thing "A" differently. I have debated the clause above
"... and not other than itself."
In short, a statement is a logically true if there is no possibility of it being false.
Yes! Exactly my point! A logical truth cannot be debated.
This was my rationale behind laboriously defining sets
A and
B. Definitons belong to set
B, as they are not logically true statements. Notice that both
A and
B contain true statements.