# If-then syllogisms

We have a sentence like this:

If you are right above 85/100 then you can enter a university.

Does this sentence presuppose that a university exists in order for it to be true?

• It depends on context and conventions. One could in principle make a counterfactual statement that it would take 85/100 to enter a university even if there were no universities around. – Conifold Jul 10 '18 at 20:54
• I made an edit to clarify the question. You may roll this back or continue editing. – Frank Hubeny Jul 10 '18 at 22:54

The following is from John Nolt's article, "Free Logic", in the Stanford Encyclopedia of Philosophy:

Classical logic requires each singular term to denote an object in the domain of quantification—which is usually understood as the set of “existing” objects. Free logic does not.

For classical logic the domain of universities referenced by the sentence in the question is not empty. In free logic, the domain of universities may be empty.

Reference

Nolt, John, "Free Logic", The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/win2014/entries/logic-free/.

Does this sentence presuppose that a university exists in order for it to be true?

This answer is the best I can offer. The sentence is an A statement, All S are P. Here, it means, "All people who are right above 85/100 are people who can enter a university."

The hypothetical viewpoint does not assume that any X exist. The existential viewpoint assumes that at least one X exists. Fifteen valid forms of the syllogism require only the hypothetical viewpoint. These fifteen would not require a university (the predicate) to exist.

Using the existential viewpoint, nine additional forms are valid, depending on whether one assumes the existence of the subject, middle term, or predicate.

Here, "university" is the predicate. Only one syllogism, AAI in the fourth figure, requires the predicate to exist in order to be valid.

Source: Barker, Stephen. The elements of logic (McGraw-Hill 1965), pg. 48, 49, 68.

This question hinges on how can is interpreted, and as there are multiple distinct modal senses of can, there are multiple answers.

If can is interpreted as a deontic modal then this statement is defining the regulations of university entrance; such regulations can exist without there being any universities.

If can is interpreted as an epistemic modal then this statement is explaining what is possible, and I think would most naturally be taken as implying that at least one university does exist, though it would not be infelicitous for it to be used when universities don't exist as a direct reflection on someone else's deontic regulation. The very similar (for this sentence) dynamic modal interpretation would, I think, only make sense if a university does exist.

The consequent "you can enter university" cannot be true if no university exists. So if no university exists, the if-then statement reduces to the negation of the antecedent condition ("you are right above 85/100") is true. So if no university exists, and it is also true that you are right above 85/100, then the if-then statement is false.