“the possibility of unicorns”

Question

https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://philarchive.org/archive/WALTPO-31&ved=2ahUKEwjs1YOos6qAAxWrLEQIHfvKCy8QFnoECBYQAQ&usg=AOvVaw3i_OU52wSjloqNi8WznGF1

I’ve been trying to wrap my head around this one, but I can’t even get past the summary:

“He then claims that this possibility shows that the logic of metaphysical modality is not S5, and, in particular, that the B axiom is false. Dummett’s argument against B, however, is invalid.”

What is a B axiom?

I’ve found articles attempting to explain but alas, they remain beyond me.

Any help would be very appreciated

In: 0

Answer 1

>I’ve found articles attempting to explain but alas, they remain beyond me.

I’m not surprised. The only online information I’ve found that indicates an education level is that it’s for students taking a PhD in Computer Science.

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Logic deals with *propositions,* which are statements, or ideas. “London is the capital of England” is a proposition, as is “Berlin is the capital of France”. “Lucy is asleep” is another.

A proposition can be true or false; we know the first is true, the second is false and we don’t know what Lucy is up to.

Modal logic adds on a must be, cannot be, might be, might not be. London must be the capital of England, Berlin can’t be the capital of France, Lucy might be asleep / might not be asleep.

So already we can see that if one mode is true then others can’t be so. You can’t say London might be the capital of France.

Now it gets tricky when we add “not”.

“Must be true” is the same as “isn’t might be not true”. 1+1=2 is true so it’s not possible that 1+1 is not 2.

“could be” is the same as “can’t not be”, so “John could be tall” because he doesn’t have to be short.

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And you can combine a couple of these to “prove” a third. Such a statement is an axiom. S5 is a collection of five axioms, such that if 1, 2 and 3, or 1, 2, 4 and 5 are true, then you can prove unicorns exist if you have the right propositions. These axioms have their own letter, and B is the fifth.

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I’m going for a lie down.