Both quantification functions, ∃ and ∀, only specify how many values of the variable they quantify make the statement that follows true, — Pfhorrest
and the statement doesn't necessarily have to be asserting the existence of anything, — Pfhorrest
The word "exists" has a metaphysical meaning — TheMadFool
Statement 3 makes an existential claim i.e. unlike statement 2, statement 3 asserts that unicorns exist but that's not true — TheMadFool
Clearly, ∃x translated as "there exists..." is an issue. — TheMadFool
But, the million dollar question is, Does the existential quantifier, ∃, need to make a distinction between fact and fiction? — TheMadFool
No. — bongo fury
If I write "This Dodo is brown" it's logical equivalent is ∃x(Dx & Bx) but we know Dodos are extinct and the logical translation of that is ~∃x(Dx) — TheMadFool
Both quantification functions, ∃ and ∀, only specify how many values of the variable they quantify make the statement that follows true, and the statement doesn't necessarily have to be asserting the existence of anything, so saying that there exists some thing goes beyond what this function really does. — Pfhorrest
Meinongian quantifiers — Srap Tasmaner
Right... were you unsure whether these would turn out to be compatible or not? — bongo fury
Well, as it turns out, if the logical equivalent of "some Dodos are brown" is Ex(Dx & Bx) then, — TheMadFool
The "for all", universal quantifier never makes an existential assertion. — TheMadFool
why does the particular statement, "some A are B", ∃x(Ax & Bx) have to be translated as "there exists something that is an A and a B"? — TheMadFool
But the configuration of prefixes '~∀x~' figures so prominently in subsequent developments that it is convenient to adopt a condensed notation for it; the customary one is '∃x', which we may read 'there is something that'. — Quine, Mathematical Logic
But does anyone think that, in saying "A dog is barking", you are asserting the existence of dogs? — Srap Tasmaner
You're assuming or presupposing there are dogs, and so far as that goes you are committed to the existence of dogs, in Quine's sense. — Srap Tasmaner
(Math doesn't suffer from this weirdness — Srap Tasmaner
It's not like when you conclude that there is a point within this interval such that ..., you are asserting the existence of points, whatever that would even mean.) — Srap Tasmaner
Not so. — bongo fury
In the 19th century, George Boole argued for requiring existential import on both terms in particular claims (I and O), but allowing all terms of universal claims (A and E) to lack existential import. — Wikipedia
It doesn't. ~(∀x(~(Ax & Bx))) — bongo fury
An existential statement is one which expresses the existence of at least one object (in a particular universe of discourse) which has a particular property. That is, a statement of the form: ∃x:P(x) — Google
I argue you have a translation problem, at least in part created by your "if." Boiled, peeled, reduced, it amounts to saying, if something that isn't is, then it doesn't make sense because it isn't. I think we all share the experience one time or another of turning out into this Holtzwege; the trick is not to get lost in it, and then to recognize them without having to traverse them. — tim wood
If I recall correctly, the modern interpretation of universal statements don't make an existential claim for some reason I forgot. Aristotelian universal statements do make existential claims. — TheMadFool
That's right, although in everyday day speech universal statements still tend to carry existential import: from 'Everyone on the ship got sick' you may conclude 'Some people on the ship got sick'.
You can see in the SEP article how this leads to trouble with empty terms, but Parsons also makes the intriguing point there that weakenings, deriving a "some" from an "all", were not traditionally of much interest, much as empty terms were ignored. Indeed, what is the point of concluding that some people got sick if you know everyone did?
Still the modern version preserves our ability to say that if everyone on the ship got sick and so-and-so was on the ship then they got sick, which is all math needs. It saddles us with all the Martians on the ship having gotten sick too, though, but in fairness that's not just an issue with universal quantification but with the material conditional. — Srap Tasmaner
Ex should also be neutral on the matter of existence like its companion Ax. — TheMadFool
Yes, i.e. they specify how many (actual, existent) things in the domain of discourse the predicate or open sentence is true of. So no call for the "only". — bongo fury
Do you mean in something like the way talking about numbers (or fictional characters) leaves it open whether they actually exist? — bongo fury
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