I had a few questions about the handout. The issue is whether an argument like (L)-(W) on Heller (pp. 199-200) can avoid the charge of equivocation, given that the premise (L) and the conclusion (W) have different world-parameters. You admit:
Yes, the premise has RL as its parameter but the conclusion has RW, and the two are distinct. In this technical sense the point is correct; the inference of (W) from (L) is, very strictly speaking, not an instance of Antecedent-Strengthening.Nevertheless, you argue:
But that very strict sense of "instance" is neither specified nor intended in logic textbooks that present Antecedent-Strengthening as a valid form of inference. What students and professional philosophers have always been told is that barring equivocation or overt indexicals, arguments of the sentential surface formI wanted to ask whether, among philosophers and in logic textbooks, it is the sentential surface form by which we identify instances of valid arguments. I had been told that arguments are not individuated by their grammatical form but (not to sound flippant) their logical form. Put differently, arguments are not sets of sentences, but sets of propositions. This is so we can say that the following two sets of sentences express qualitatively the same argument:
A > B / \ (A & C) > B are valid arguments, period. And that is what is refuted by Heller's example.
(P1) I am carrying an umbrella
(P2) If I am carrying an
umbrella, it is raining.
(C) Therefore, it is raining.
(P1) An umbrella is being
carried by me.
(P2) If an umbrella is being
carried by me, it is raining.
(C) Therefore, it is raining.
Even though the first set of sentences is not qualitatively the same as the second set of sentences, the two sets express qualitatively the same argument.
We might look at this as a mere convention, however, and so we might ask why we should individuate arguments by their logical form. I think it would be precisely to side-step problems with indexicals and the like. But as you suggested, we may individuate arguments by their grammatical form, if there are no occurrences of indexicals and friends. Yet what if there are indexicals? In other words, how would we show that the "she is a boat" argument is not a valid argument (on Heller p. 197)? I suspect we'd want to point to the fact that the referent of 'she' is switched between the two premises. But that's just to individuate the premises by their logical form, not their grammatical form. So why don't we just say that, in general, arguments (and thus the statements that compose them) are individuated by logical form? If we individuate by grammatical form, then the exceptions to that rule seem somewhat ad hoc--since the only motivation to go this more complex grammatical route, it seems, would be to make the convenient distinction between "strict" instances and "loose" instances of argument forms.
You consider the following objection to your view:
One can continue to insist that Antecedent-Strengthening is valid for the strict sense of "instance," but at the price of keeping us from telling easily and uncontroversially when a set of ordinary English sentences is an "instance" of an argument form. So I think it is better to use "instance" in the [loose sense].In other words, when we individuate by grammatical form, we have the benefit of easily and uncontroversially telling when an argument is an example of modus pollens, modus tollens, etc. Of course this is true only if we are conveniently ignoring arguments that use indexicals, homonyms, proper names, etc. Considering those cases, then, the idea might be that individuation by grammatical form (plus the exception clause )is better because (a) in cases without indexicals and the like,
However, we may be considering a straw-person version of "individuation by logical form alone" view in the foregoing comparison. A better version would use the following two rules:
(A) Individuate all arguments
by logical form.
(B) In cases without indexicals
and the like, individuate arguments by logical form via grammatical form.
[I.e. when there's no indexicals et al., use the following rule of thumb:
whenever you have the same grammatical form, you have the same logical
form.] In all other cases, individuate arguments by considering their
logical form "directly" (whatever that may mean).
The first thing to note is that, like your rule,
this is a rule that we may stipulate, and so do not need to justify (at
least, not until we we're wanting justification for stipulation in logic
generally). But what's more, if I'm right about philosophers and logicians,
this is a rule we have stipulated, albeit perhaps implicitly. And
in addition, like your view, this revised view also allows us to individuate
instances of arguments easily and uncontroversially (where there are no
indexicals or friends of indexicals). And in cases where there are indexicals,
the view does the same thing as your view, viz., individuate by logical
form. But besides having the virtue of reflecting actual practices of logicians
(as far as I understand them), the view is
uniform in demanding that logical form be the ultimate arbiter in the
individuation of arguments.
We might wonder, however, if your view and the view sketched in (A) and (B) are really two different ways of saying the same thing. The difference I suppose arises in cases like Heller's argument (L)-(W): Your view would say that the argument is a "loose" instance of argument strengthening (since you individuate the argument by grammatical form), whereas the view (A)-(B) would not make the distinction between "loose" and "strict" instances--it would just say that the argument is not an instance of antecedent strengthening (since it considers logical form in individuating that argument).
But we might ask further why your view should individuate (L)-(W) by grammatical form, even by your own lights. Why not see the parameter shift between (L) and (W) as akin to a shift in index? Accordingly, why wouldn't you make an exception of (L)-(W), in the way that the "she's a boat" argument is an exception to the rule of individuating by grammatical form? In other words, why do you individuate (L)-(W) by grammatical form, but not the "she's a boat" argument? You could of course individuate the "she's a boat" argument by grammatical form, and therefore call it a "loose" instance of conjunction introduction. But surely this "loose" instance is not the sort of "instance" which interests philosophers and logicians. On the other hand, to be uniform, you could individuate (L)-(W) and the "she's a boat" argument by logical form--which is exactly what I'm inclined to do.
Here you might appeal to the fact we can stipulate what to do in logic, without giving a justification. Accordingly, you might just say "I hereby stipulate that parameter shifts do not matter in the individuation of arguments." But then, the burden would be to show that this stipulation accords with our actual practices in logic. And there is some reason to think that stipulation does not accord with our practices. Consider the following argument:
(P1') Everyone made it to
the party.
(C') Therefore, every person
from every nation made it to the party.
This argument is equivocal only in the sense that there is a parameter
shift. But by your rules, it seems like this is a "loose" instance of a
valid argument--and moreover, that it is an instance of validity that philosophers
and logicians normally care about. But that can't be the case, since the
argument would be counted as invalid by philosophers and logicians, precisely
because of the parameter shift. It can be true that everyone made
it to the party, but false that every human being in the
world made it to the party.