Logical Truth and Logical Constants
Logical constants, including logical connectives and quantifiers, can all be reduced conceptually to logical truth. For instance, two statements or more are logically incompatible just in case their conjunction is logically false. One statement logically implies another when it is logically incompatible with the negation of the other. A statement is logically false just in case its negation is logically true, etc. In this way all logical connectives can be expressed in terms of preserving logical truth.
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Famous quotes containing the words logical and/or truth:
“The contention that a standing army and navy is the best security of peace is about as logical as the claim that the most peaceful citizen is he who goes about heavily armed. The experience of every-day life fully proves that the armed individual is invariably anxious to try his strength. The same is historically true of governments. Really peaceful countries do not waste life and energy in war preparations, with the result that peace is maintained.”
—Emma Goldman (1869–1940)
“An idea is a putting truth in check-mate.”
—José Ortega Y Gasset (1883–1955)