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For example, if people used to believe the Earth was the center of the universe, and we discover it is not, we now say, "people used to falsely believe that the Earth was the center of the universe", we say they were wrong before we attained knowledge which disproved them.

However, say in the case of the name of a place, take for example Istanbul, which used to be called Constantinople. We do not say "people used to falsely believe that Istanbul was called Constantinople", instead we realize that this was just a decision made by people, but we recognize it as real nonetheless.

However, we still say "Istanbul exists" with the exact same authority as we say "The Earth is a sphere" and therefore, "The Earth as a sphere exists", but we somehow assert this with more authority than we do with the name of Istanbul and Constantinople. Sure we might arrive at some other name for it, it isn't necessary to call it a 'sphere', but we assert there is some real property that Earth has that we have knowledge over; whereas in the Istanbul-Constantinople case, we are referring to something which is unnecessary, but nonetheless real. Wittgenstein says this on the word is.

"hus the word ‘is’ appears as the copula, as the sign of equality, and as the expression of existence; ‘to exist’ as an intransitive verb like ‘to go’; "

(In the proposition ‘Green is green’ – where the first word is a proper name and the last an adjective – these words have not merely different meanings but they are different symbols.) (§3.323) It is perhaps worth elaborating how Wittgenstein’s example in the last paragraph of §3.323 illustrates the point of the first paragraph of §3.323. The propositional sign ‘Green is green’ can be understood to symbolize in three different ways18 – and hence can be understood as an expression for any one of three different thoughts. One way of noticing how the same sign symbolizes differently in each of these three cases is to focus on the word ‘is’. In each of the propositions which expresses each of these three different thoughts, the sign ‘is’ symbolizes a different logical relation. In one, the sign ‘is’ symbolizes the copula (a relation between a concept and an object); in another, we have the ‘is’ of identity (a relation between objects); in the third, we have the ‘is’ of co-extensionality (a relation between concepts)

Whereas then we say, spiderman or a cyclops does not exist at all, only as "figments of our mind". We do not simply say "spiderman is", as to refer to its existence.

I guess what I'm getting at is, in the first place, more of what is occurring seems to be necessarily true qua the nature of the universe, while the second category of cases seem to be more imposed on the world by us--like in the naming of a person. If someone changes their name, we treat it the same way. However, with gender, it gets different(we say the person falsely believed they were the wrong sex quite often, at least in some circles of language).

What is going on here? Is there any philosophical literature on this? This seems related to Kripke's idea that the categories of existence(mind, epistemology, and metaphysics) don't need to follow each other, but I'm having a hard time breaking it down. I feel like this is something that has certainly been talked about in philosophy, going back to the Greeks, but I would love to see a nice historical article laying out the various ways to respond to this basic question of existence.

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    This is called the analytic/synthetic distinction. What is analytic is roughly "true in virtue of meanings", conventional, and what is synthetic is imposed by facts. It was once believed to be sharp, but now is recognized to come in shades of grey, when it can be made at all, see truth by convention. – Conifold Feb 1 at 22:50
  • So the location of the Earth in space would be considered analytic, but the name of a person or the name of a place is synthetic? – Matthew Feb 1 at 22:55
  • "Your name is Matthew" is analytic and "Earth is the third planet in the Solar system" synthetic. – Conifold Feb 1 at 23:05
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Maybe I'm oversimplifying this, but take your Constantinople vs Istanbul example. The people who once called that place Constantinople were not wrong when they called it that. The name of said place changed from Constantinople to Istanbul, as did people's belief about the name of the place. So, at no point was there a mismatch between belief and reality.

I think that there is understood temporal component to truth statements. For another example, "it is the 31st of January" was true yesterday, but not today.

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