Lexicon of Arguments

 

I 116
Tautologies/Mates: Tautologies depend on the meaning of "and", "not", " if .... then ", etc. , but not the meaning of " all ", " some ", " people ", " mortal" , etc. -
((s) I.e. only from the logical constants, not from the quantifiers).
>Logical constants, >Quantifiers, >Quantification.
On the other hand: analyticity of a syllogism depends on the meaning of "all" , "some".
>Analyticity/Syntheticity, >Synthetic, >Syllogisms.
I 117
Tautology/Mates : can not be an atomic statement - because this also may not be valid.
I 119
There are valid statements that are not to be tautological:
E.g. "(x ) Fx > Fa "
There are inferences that are not tautological. - In inferences only tautological inferences are needed.
>Derivation, >Derivability.
Def tautology: valid statement whose validity does not depend on the quantifiers.
>Validity.
I 119
Tautology/propositional calculus/Mates : since all statements of p.c. (propositional calculus) are quantifier-free, they are tautological, if they are valid.
>Propositional calculus.
That carries over to their inserting results. - There is still no decision procedure, if there is tautology.
I 127
A tautology is the same as a consequence of any set of propositions.
>Consequences.