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:
“Nature’s law says that the strong must prevent the weak from living, but only in a newspaper article or textbook can this be packaged into a comprehensible thought. In the soup of everyday life, in the mixture of minutia from which human relations are woven, it is not a law. It is a logical incongruity when both strong and weak fall victim to their mutual relations, unconsciously subservient to some unknown guiding power that stands outside of life, irrelevant to man.”
—Anton Pavlovich Chekhov (1860–1904)
“The reason for the sadness of this modern age and the men who live in it is that it looks for the truth in everything and finds it.”
—Edmond De Goncourt (1822–1896)