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Hi,
A logically fallacious argument, as far as I understand should always be invalid - in every possible world.
But take a kid's argument : This is true, because my father said so. On one hand it seems obviously invalid. Such an attitude is never smart (of course, I do not imply a case in which the father is known to be an expert in something, and therefore is a valid authority, but a kid's childish attitude).
However, there is a possible world in which the father of the kid is omniscient and always telling the truth. It seems a logical possibility. But, if it is a logical possibility, then one cannot argue the argument is _logically_ invalid.
Sincerely, Sam

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Do all things exist?
Nonexistence is the absence of existence, by definition. So, nonexistence does not exist. Therefore there is no such thing as nonexistence. To say that something does not exist thus seems to be a fallacy, since NOTHING does not exist. Everything, therefore, must exist.
Is this right? If not, what is wrong with the argument?

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Do false statements imply contradictions?
Consider the truth table for logical implication.
P...........Q.............P-> Q
T...........T.............. T
T...........F...............F
F...........T...............T
F...........F...............T
Notice that for a false statement P, the last two rows of the truth table, both Q and ~Q follow. No matter what Q is, it's truth follows from false statement P, as the third row shows. We can therefore take Q to be "P is true." From here it follows that a false statement P implies it's own truth, as the third row shows.
Do false statements really imply their own truth? Do they really imply contradictions? Are false statements also true?

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Is every statement true?
Consider the following argument:
If a statement is true, then it is a member of the set of true statements.
If a statement is false, then it implies a contradiction. Since anything follows from a contradiction, it follows that the statement is true. Thus the statement is a member of the set of true statements.
Since a statement is true or false, all statements therefore belong in the set of true statements. All statements are true, with the set of false statements being a subset of the set of true statements. A statement thus is either true and true only, or both true and false.
Does this mean that all statements are true?

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