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could you give a brief explanation about quantifiers in

Luckily… I love talking logic.

Your questions hit, for the most part, hit on the many confusions that white people seem to have about their logic.

The most basic confusion is basically conflating to entirely distinct kinds of logic and operating in this space of deep misunderstanding. Even though whites are the most logical 4ever.

The two kinds being confused are inductive and deductive logic. Generalizations are the realm of inductive logic.

(okay, it is tedious to write the statement over and over again so we are gonna use symbolic logic.

x ≡ white people
W ≡ understand logic)

When you make a generalization based on your observation of the world, say ~Wx this is an *inductive* statement. It is not logically inconsistent to assert ∃Wx and ~Wx at the same time, at least in the realm of generalizations. Nor does ∃Wx act as a sufficient counter-example for ~Wx. This is the basis of scientific reasoning (and why studies can make claims even though, in the same study, there are individuals who contravene the general claim).

Now, a common reply to ~Wx is ~∀~Wx. Which, seems like an appropriate reply, however it relies on the equivocation of ~Wx and ∀~Wx, which is a false equivocation. They are not identical propositions and they imply different things. Particularly, statements like ∀~Wx are universal statements are usually covered in syllogistic (or predicate) *deductive* logic, rather than inductive logic (existential statements likewise properly belong in this realm but don’t create the same errors when mixed with inductive logic, as shown above).

Your last question relates to if (and this never happens) someone asserts both ∀~Wx and ∃Wx, which would be contradictory… But the criterion of consistency only applies to white people. This is *your* logic, not mine. So. I’ll leave it to you to work out how to resolve this contradiction (this can be homework). My human brain has no problems asserting two contraditory statements at the same time. *shrug*

But, in concerning the truth of these statements… how about we use a different example.

Let R ≡ is racist.

This contradictory statement usually comes up when a PoC asserts Rx. And then someone replies ∃~Rx (although, I’m not sure I see any PoC ever asserting both Rx and ∃~Rx). Anyway, the problem is that ~∃~Rx. So there is no contradiction to be had.