existence is not treated as a predicate in logic. That is, there is no simple way to parse. "Xtrix exists".
— Banno
∃ Xtrix = there exists Xtrix
∄ Xtrix = there does not exist Xtrix — Olivier5
:up:Like any logical formalism, there's no question of it being right or wrong, just apt to certain purposes. — Snakes Alive
Free logic
Existence is a first order predicate, and hence
Singular terms can refer to things which are not members of the domain
The domain is not empty — Banno
So it turns out that existence is (or can be, amongst other things) a logical predicate after all... — Olivier5
In classical logic, to make the inference you would have to presume the predicate "... is a leprechaun". How you understand that predicate remains moot; and one can play on that ambiguity.
This is the ambiguity ↪bongo fury apparently traded on in the Being thread.
If one supposes that all ∃(x)(Lx) says is that something is a leprechaun, one need not conclude that one might meet a leprechaun walking down the street. That there are leprechauns says nothing more in this context than that we can predicate being a leprechaun to something - fictional or otherwise.
Some folk see this as problematic. Seems to me to be just an ambiguity in the use of "is". That Shamus is a leprechaun does not imply that you might meet him in the pub. — Banno
And we are left in much the same position as I have pointed out in the thread on Being: things that exist because they are the presumed individuals in the domain, and things that exist because they are the subject of a predicate. — Banno
You've made leprechauns part of the domain by presupposing the predicate "...is a leprechaun".
That is, fictional species are part of the conversation, so you can talk about them in your scheme.
In free logic leprechauns would not be members of the domain of things that exist - E!. But you could still make inferences about them.
However as noted above, you could not infer their existence, even in free logic.
In classical logic, to make the inference you would have to presume the predicate "... is a leprechaun". How you understand that predicate remains moot; and one can play on that ambiguity. — Banno
...sentences found in fiction are literally false — Srap Tasmaner
Free logic would, in my humble opinion, open up the world of fiction - Tolkein's works, Doyle's works, etc. - to logical analysis. — TheMadFool
It seems that you're under the impression that with free logic we can begin an analysis of a given domain of objects and then, almost miraculously, switch the topic to something outside that domain. — TheMadFool
Treated in ordinary logic this statement would be false, since Gollum does not refer to anything. But we can make use of Free logic, since here Gollum is fictional, but not Gödel, hence E!(Gödel) but ~E!(Gollum). In a positive free logic Gollum is more famous than Gödel.Gollum is more famous than Gödel.
Holmes lived at 221b Baker Street. Why shouldn't we consider this to be true, within the context of the writings of Doyle and their derivatives? Is there an argument against this? — Banno
More aptly referred to as being stipulated or written, rather than being true. no? We have good reason to believe it is true that it is written that Holmes lived at 221b Baker Street. — Janus
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