TheTemperature paradox orPartee's paradox is a classic puzzle informal semantics andphilosophical logic. Formulated byBarbara Partee in the 1970s, it consists of the following argument, which speakers ofEnglish judge as wildlyinvalid.
Despite its obvious invalidity, this argument would be valid in most formalizations based on traditionalextensional systems of logic. For instance, the following formalization infirst order predicate logic would be valid viaLeibniz's law:
To correctly predict the invalidity of the argument without abandoning Leibniz's Law, a formalization must capture the fact that the first premise makes a claim about the temperature at a particular point in time, while the second makes an assertion about how it changes over time. One way of doing so, proposed byRichard Montague, is to adopt anintensional logic for natural language, thus allowing "the temperature" to denote itsextension in the first premise and itsintension in the second.
Thus, Montague took the paradox as evidence that nominals denoteindividual concepts, defined as functions from aworld-time pair to an individual. Later analyses build on this general idea, but differ in the specifics of the formalization.[1][2][3][4]
