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Question 1

This mentions "...belief in the existence of members of the subject class". Is this necessarily true ?

Consider "Some pizza has pepperoni on it".

You get the following. Which is one is an existential import ?

  1. Pizza exists
  2. Non-pizza exists
  3. pepperoni exists
  4. Non-pepperoni exist
  5. Cross on Sentence 1 through 4

Now,

 Question 2

This claims existential import is rejected per Boole. So why are texts teaching it still ? Is it because Aristotle had it but Boole rejected it so the mention it for legacy reasons ?

New Student
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1 Answers1

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The so-called "problem of existential import" arises in the context of traditional, i.e. Aristotelian interpretation of the Square of Opposition.

According to it, an A proposition : "All swans are white", and an I proposition : "Some swan is white", are in a subalternation relation, i.e. the subaltern (I) must be True if the superaltern (A) is.

This means that the inference from A to I is - according to Aristotle - valid.

The standard translation of the categorical proposition A:

"All S are P" ("all swans are white")

is: $(\forall x)(Sx → Px)$, while the corresponding I :

"Some S is P" ("some swan is white")

is: $(\exists x) (Sx \land Px)$.

In modern terms, the conditional corresponding to A is true also when there are no swans at all, while the I is not.

This is the gist of

"the truth of the proposition requires a belief in the existence of members of the subject class".

The traditional interpretation of Syllogism assumes that the class corresponding to the term in subject position is not empty.

There is no issue with "Some pizza has pepperoni on it"; it will be symbolized with $\exists x (Pizza(x) \land WithPep(x))$.

Obviously, the statement will be true only if there are pizzas.

Mauro ALLEGRANZA
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