True and False - in Other Theories

In Other Theories

Intuitionistic type theory uses types in the place of truth values.

Topos theory uses truth values in a special sense: the truth values of a topos are the global elements of the subobject classifier. Having truth values in this sense does not make a logic truth valuational.

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    The wise man regulates his conduct by the theories both of religion and science. But he regards these theories not as statements of ultimate fact but as art-forms.
    —J.B.S. (John Burdon Sanderson)