Logical if (â†’) and iff (â†”) are doing my head in.

â†’ is if, the “conditional connective”. A â†’ B means that A can be true **only if** B is true.

So â†’ is false when A is true despite B being false. But otherwise it’s true. Because we don’t care about those scenarios. I don’t know why. I suppose otherwise it would just be âˆ§ . I’m going to have to just accept this like the dot product, which also doesn’t fit into my mathematical worldview, which is based on cakes.

â†” is iff, the “biconditional connective”. A â†” B is equivalent to [(A â†’ B) âˆ§ (B â†’ A)].

See? It’s **bi**-conditional. So â†” is false when A â†’ B âˆ§ (B â†’ A), or B â†’ A âˆ§ (A â†’ B) . Possibly I can come to terms with â†’ as half of â†” .

Next: the Axiom Schema Of Separation and how you can’t model that using cakes either.

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