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How does symbolic logic distinguish different meanings of the word āisā?
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Plato (center left) and Aristotle, detail from School of Athens, fresco by Raphael, 1508ā11; in the Stanza della Segnatura, the Vatican. Plato is shown pointing to the heavens and the realm of forms, Aristotle to the earth and the realm of things.
In symbolic logic, particularly within the tradition established by 20th-century logicians like Gottlob Frege and Bertrand Russell, the natural-language verb "is" is considered multiply ambiguous. To eliminate this ambiguity, symbolic logic assigns distinct logical forms to its various uses:123
- Predication: Used to attribute a property to a subject (e.g., "Tarzan is blond"), it is represented as a predicate applied to an argument, such as .13
- Identity: Used to express that two terms refer to the same entity (e.g., "Clark Kent is Superman"), it is symbolized using the identity sign, as in .13
- Existence: Used to assert that an entity exists (e.g., "Zeus is"), it is expressed using the existential quantifier, such as .13
- Class-inclusion: Used to state that one class is a subset of another (e.g., "The whale is a mammal"), it is represented using the universal quantifier and the conditional, such as .13
While this "Frege-Russell ambiguity" claim is a hallmark of modern formal logic, some philosophers argue that "is" may not be genuinely ambiguous, but rather context-dependent.23