I know that universal quantifiers are written in terms of conditionals, while existential quantifiers are written in terms of conjunctions. However, what does it mean when an existential quantifier uses a conditional?

For example, how would you translate the following into English?

$$\exists x \left( \text{Cube} (x) \to \text{Small} (x) \right)$$

• I don't know what "universal quantifiers are written in terms of conditionals, while existential quantifiers are written in terms of conjunctions" means. Could you clarify what you mean by that, please? – Arthur Aug 14 at 4:45
• @Arthur The OP is referring to how the statements "Every A is B" and "There is some A which is B" are expressed. – Noah Schweber Aug 14 at 6:36

(That is, "$$p\rightarrow q$$" is just "$$(\neg p)\vee q$$." Note that $$\neg$$ binds more tightly than $$\vee$$, so this can be written unambiguously as just "$$\neg p\vee q$$.")