In this post I may simply show myself to be confused and nothing more (in which case I would be pleased to be enlightened); but I rather suspect that I am confused for the reason that the things confusing me are in a muddled state. I was recently trying to find a good defense of the standard contemporary view of existential import, and failed miserably, because, it would seem, no one has done anything but parrot the same (very bad) arguments for the past fifty years at least. All of the discussions I have been able to find make three major mistakes.
(1) They confuse implicature and implication. When we say "Some X are Y" (with something plugged for X and something else for Y), we usually take this as implying (in a broad, colloquial sense) that X's of some sort exist. But a natural way to understand this is to say that we wouldn't usually have any reason for saying "Some X are Y" if no X's existed at all. And that makes it a matter of implicature, not 'import'. So any appeal to common usage has to make the distinction.
And you can indeed have a good discussion of existential import that distinguishes between the claim that "Some X are Y" implies that X's exist and the claim that "Some X are Y" implicates X's existence. John Venn does it, and he manages to do it more than thirty years before Grice was even born. He doesn't, of course, use the term 'implicature'; instead he talks about "understandings" and "implications" (the latter being used in quotations to indicate that it is being taken in a broad sense). If Venn can distinguish between implication and implicature before anyone had even done serious work on implicature, contemporary logicians have no excuse.
(2) They confuse existence in a particular sense and existence taken generally. Copi and Cohen, for instance, take 'existence' to mean actual existence, and even go so far as to try to wave away existence claims about literary and mythological characters as rare and not really existence claims at all. Because of this, several of their arguments trade on the assumption that the existence indicated by a proposition with existential import must be physical existence in the real world. But as Venn, Carroll, and Keynes recognized in the nineteenth century, this is an assumption that is both implausible and needless; the existence that is relevant here is membership in the domain of discourse established by the terms of the proposition, and that could include dreams or Wonderland. [Of course, this raises an interesting question, since domains of discourse are usually ignored in contemporary logic: Are modern logicians like Copi and Cohen even talking about the same problem as the nineteenth-century logicians?]
(3) They confuse I propositions with existential propositions. I mentioned this in the previous post. As far as I can tell, there have been no good arguments for taking I propositions to have existential import since the nineteenth century. In the twentieth century it is taken as unassailable dogma, which is remarkable. Why must we assume that I propositions have existential import? If I say, "Some impossible things are geometrical impossibilities," am I really implying the existence of impossible things? Perhaps, although it raises the question of how 'existence' would be understood in such a case (it's not a problem if impossible things can be members of the universe of discourse; but this requires that we not confuse 'existence' here with actual existence in the real world). The closest anyone seems to come to doing so appeals to common usage -- and not only does this virtually always commit error (1), it ignores the salutary distinction noted by Carroll between what is logically required and what is convenient for practical purposes. At least when Keynes, the nineteenth century logician who perhaps has the view on existential import closest to the contemporary view (he gets it by generalizing comments made by Venn with regard to symbolic logic to all of logic), appeals to common usage, he doesn't leave it at that, but argues that taking particular propositions to have existential import has a number of logical advantages.
So on this point, at least, logic in the twentieth century seems to have degenerated: points that were once taken as a matter for serious debate are now taken as undeniable, and the arguments put forward are merely cases of uncritical repitition. The nineteenth century logicians seem to do a much better job of handling the matter than anything more recent. In any case, if anyone's come across a better recent defense, let me know.
Here's a puzzle, too. The contemporary view of existential import is usually understood to cause problems for subalternation and conversion per accidens. In Copi and Cohen we find the following argument put forward as an example of the 'existential fallacy':
(1) No mathematician is one who has squared the circle.
(2) No one who has squared the circle is a mathematician.
(3) All who have squared the circle are nonmathematicians.
(4) Some nonmathematician is one who has squared the circle.
We get (2) from (1) by conversion; (3) from (2) by obversion; and (4) from (3) by conversion per accidens. The move from (3) to (4), says Copi (and Cohen), commits the fallacy of assuming that there is someone who has squared the circle. Of course, as already noted, this assumes that (4) is an existential proposition, which should be open to discussion. One could just as easily argue two other positions:
(A) That the real fallacy is committed only if we move from (4) to the claim "Some nonmathematician who has squared the circle exists." But as (4) is obtained from (3) by means of a conversion by limitation, we should really read (4) as simply a more limited (3), telling us that some nonmathematicians (in this case those who are nonmathematicians in the sense that, unlike real mathematicians, they don't exist) are circle-squarers. That is, it doesn't assume existence, but merely that we can take the terms partwise, so to speak.
(B) For that matter, if we went so far as to defend common usage, we might well begin to think if there is an existential fallacy it has to be attributed to the obversion rather than the conversion per accidens. If there is any proposition in the above argument that would suggest to most people in most circumstances that there are people who have squared the circle, it's (3), because we would naturally take it as saying that, Of those who have squared the circle, all are nonmathematicians. And that really would usually suggest that there exist some people who have squared the circle.
I hold to the first, although I think students are owed a non-question-begging explanation why the move from (2) to (3) doesn't commit the existential fallacy.
In any case, that wasn't my puzzle. My puzzle is this. How can people straightfacedly reject subalternation as committing the 'existential fallacy' and yet accept universal instantiation, given that the two are logically very similar? (Certainly from a term logic standpoint there is very little difference, and free logics often treat UI as doing more or less what subalternation is accused of doing -- Karel Lambert, for instance, seems to be very explicit that this inconsistency with regard to the treatment of UI and subalternation was one of the motivations for his work in free logic, although certainly not the only one. And it is worth pointing out as a side note, since people forget, that (x)(Fx) is in term logics an A proposition even though it is not in the hypothetical form into which most A propositions are recast when translated into the predicate calculus, and thus yields no hypothetical form when instantiated.) And yet we find this done all the time. At the very least textbooks that criticize subalternation for violating existential import should give reasons why universal instantiation (esp. in combination with existential generalization) should not be treated the same way, but I have found none that do so, despite there being obvious reasons why such a point would need to be addressed. (If you look carefully in more advanced works you find that the reason for distinguishing the two has to do in part with a particular theory of interpretation, one in which a great many propositions apparently of the form "Some x is F" are not really I propositions at all, and many propositions apparently of the form "a is F" are not really singular at all. This is the only reason why "Some things are impossible" can be held to be intelligible if I propositions have existential import, for instance: we have to say that it is not an I proposition at all. We get mired in a great deal of controversial theory if we look at why universal instantiation and subalternation are supposed to be treated differently; and we begin to wonder whether we are dealing with a legitimate logical need (as some say) or a set of epicycles designed to save the phenomena for an approach that has serious weaknesses.)
And, of course, it seems slightly absurd in a broader sense, too. As Venn noted, no one takes the possibility that in a particular case you might divide by zero to be a good argument for never dividing by variables. One might well ask, even if the standard contemporary view is entirely correct, why we would talk as if we should reject subalternation and conversion per accidens altogether rather than recognize them under some set of conditions. (We certainly do that with existential generalization anyway.)
So I find the whole mess to be obscure and puzzling; even if the standard contemporary view is correct, it certainly doesn't seem to be taught properly.
