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Frege holds that existence cannot be said to be a first-order predicate for the following reasons. If existence is to be considered to be a first-order predicate, it follows that in statements denying the existence of certain objects, the absurdity ensues of stating something along the following lines: there is an A such that A doesn't exist. The question is simply left to be asked, "how can there be an 'A' such that it doesn't exist?" This led Frege to believe that the 'A' which is being spoken about is itself only a concept, and existence is only a second-order predicate, as speaking of concepts rather than actual objects. This analysis thus is taken to defeat the traditional doctrine of the real distinction between essence and existence, which asserted that existence is said of objects.

But does Frege's anaylsis not assume that the objects in an existential context exist already? For example, Frege holds that there is a contradiction in saying 'there is an A such that A doesn't exist'. But this is only because Frege assumes that what is meant by 'there is an A' is existentially biased, so as to preemptively assert the actual existence of the object that's actual existence is the very thing in question. Could one instead hold that the object in question is itself existentially neutral? It could be argued that A being a concept or being actually existent is thus not evident in the simple thought of A itself, but rather determined in complcated thoughts about A, which is comprised of predicates therein, of which it seems existence must be said to a predicate to the object in question. The statement could thus be amended as follows: 'there is an A, such that A is existentially neutral, which in fact does not exist'. This would seem to avoid the criticism of Frege, so long as I understand Frege correctly.

  • I don't understand the sentence "But does Frege's anaylsis not assume that the objects in an existential context exist already? " – virmaior Dec 4 '15 at 1:30
  • @virmaior I go on to explain what is meant by this later on. Frege seems to believe that an object that has a predicate of any kind, even in a context that is attempting to determine the existence of the said object, already exists, as is seen in his main criticism about the supposed contradiction in stating that an object fails to instantiate existence as a first-level predicate. The only reason this could be a contradiction is if Frege assumes that the objects already exist. – Chosen One Dec 4 '15 at 1:43
  • To me, the English doesn't really make sense there... I'm also a little confused by the format. Is the first paragraph your interpretation of Frege's project or from a source? – virmaior Dec 4 '15 at 5:11
  • Regarding the second paragraph, I may not be understanding you correctly but when I read it I feel like you're misunderstanding predication for Frege. Predication is Xa. (a has property X). and thus it makes no sense to predicate of things that don't exist ... – virmaior Dec 4 '15 at 5:11
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    "There is an A such that A doesn't exist" is simply : ∃xAx ∧ ¬∃xAx and thus is plainly contradictory; not only "according to Frege". We have no "logical" issues with sentences of form : ¬∃xAx; the point of view of Frege is exactly : "exitsence" is not a predicate but a quantifier. – Mauro ALLEGRANZA Dec 4 '15 at 7:36
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I think you are correct in what you say about Frege. In his logic, you can only quantify over things that exist, and all and only those things that exist have names. Therefore one cannot correctly predicate anything about things that do not exist.

Your idea about existentially neutral objects that may or may not exist sounds like the ontology of Meinong. He held that it was OK to speak of objects that subsist, because we can imagine them, and that existence is a first order property of such objects.

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