What does possibly necessary mean in modal logic [crazy question actually]

In summary, the conversation discusses the concept of X being not necessarily not Y and how if X is Y, then it necessarily cannot be Z. The question is raised as to whether this means X cannot be Z. The conversation then clarifies that the first statement is a solipsistic statement and the second statement suggests that if X is all there is, it cannot imagine being annihilated. The conclusion is drawn that X cannot imagine its own annihilation, although this does not necessarily mean living forever in oblivion.
  • #1
klqc_
2
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Suppose the following

X is not necessarily not Y.
If X is Y then X necessarily cannot be Z.
Does that mean X cannot be Z?

I probably screwed up stating that...

To clarify
The first line is meant to be a solipsistic statement - I may be all there is.
The second line is meant to state that if I am all there is then I cannot imagine being annihilated.
In the third line I conclude that I cannot imagine my annihilation.


I'm not concluding that we must "live" forever in oblivion but it's kinda the idea.
 
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What does "possibly necessary" mean in modal logic?

In modal logic, the term "possibly necessary" refers to a proposition that is possible and also necessary. This means that the proposition is true in some possible worlds and also true in all possible worlds. In other words, the proposition cannot be false in any possible world.

Can a proposition be both possibly necessary and possibly contingent?

No, a proposition cannot be both possibly necessary and possibly contingent at the same time. If a proposition is possibly necessary, it means that it must be true in all possible worlds, while a possibly contingent proposition is only true in some possible worlds and false in others.

How is "possibly necessary" different from "necessarily possible" in modal logic?

The terms "possibly necessary" and "necessarily possible" may seem similar, but they have different meanings in modal logic. "Possibly necessary" means that a proposition is true in some possible worlds and also true in all possible worlds, while "necessarily possible" means that a proposition is true in all possible worlds but may not be true in every possible world.

What is the symbol used to represent "possibly necessary" in modal logic?

In modal logic, the symbol ◊ is used to represent "possibly necessary." This symbol is read as "possibly" or "possibly true." It is often used in conjunction with the symbol □, which represents "necessarily" or "necessarily true."

Can a proposition be both "possibly necessary" and "possibly impossible" in modal logic?

No, a proposition cannot be both "possibly necessary" and "possibly impossible" in modal logic. If a proposition is possibly necessary, it means that it must be true in all possible worlds, while a possibly impossible proposition is only true in some possible worlds and false in others.

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