How does symbolic logic distinguish different meanings of the word ā€œisā€?

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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 B(t).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 c=s.13
  • Existence: Used to assert that an entity exists (e.g., "Zeus is"), it is expressed using the existential quantifier, such as (∃x)(x=z).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 (∀x)(W(x)⊃M(x)).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