Quantifier (logic)

A quantifier is a fancy word in logic to describe how we talk about things. Just like when we talk about things in our everyday lives, we use words like "some," "all," "none," or "there exists." These words help us describe how much or how many of something there is.

For example, if I ask you, "Do you have any siblings?", you could answer with "Some" or "None" depending on if you have siblings or not. These words are called quantifiers in logic.

In logic, we use symbols to represent these words. The symbol for "all" looks like this: ∀ and the symbol for "there exists" looks like this: ∃.

So, if I want to say "All dogs have fur," I would write it like this: ∀x(Dx → Fx), which means "for all x (where x is a dog), if x has D (dogness) then x has F (fur)."

And if I want to say "There exists a dog who likes to run," I would write it like this: ∃x(Dx ∧ Lx), which means "there exists an x (where x is a dog) that has D (dogness) and has L (likes to run)."

In short, quantifiers help us talk about how much or how many of something there is using special words and symbols in logic.