So it seems to you that my argument proves too much, eh?

[Cross-posted at Think: Just Do It!]

Philosophers often make the following complaint:

It seems to me that, if the author were right, then s/he would prove too much.

For example, some have complained that Moore's open question argument proves too much. I take it that those who make this sort of complaint mean that the conclusion argued for seems too strong. For example, in the case of Moore's open question argument, which can be reconstructed as follows:

1. Suppose that 'x is good' is equivalent to 'x is pleasure'.
2. If 'x is good' is equivalent to 'x is pleasure', then 'pleasure is good' is equivalent to 'pleasure is pleasure'.
3. But 'pleasure is pleasure' is an uninformative tautology.
4. If those who assert 'good is pleasure' mean to express more than a mere tautology, then the question whether pleasure is good remains "open."
5. Those who assert 'good is pleasure' mean to express more than an uninformative tautology.
6. Therefore, the question whether pleasure is good remains "open."

the conclusion strikes some as too strong, since it means that, for any definition of 'good' in terms of some natural property, such as pleasure, it remains an open question whether that natural property itself is good.

But so what? If Moore's argument is sound, so what if the conclusion strikes us as too strong?

[Please don't get hung up on the example. If you don't like it, pick your own example. I have no interest in defending Moorean non-naturalism. I am interested in the meta-philosophical question of whether an intuition that an argument's conclusion is too strong should outweigh a sound argument supporting that conclusion. In other words, should the "author proves too much" objection be taken seriously?]

If the choice is between a sound argument and an intuition that the argument's conclusion is too strong, I would go with the sound argument. Which would you go with, fellow pupae?

Update:

I've tried to sum up the different readings of the "proving too much" charge we have discussed in this diagram. What do you guys think?

Comments

[Clayton]

Hi Moti,

I agree that the objection would be obscure if the objection was really just that the conclusion seems intuitively to be too strong, say, prior to any consideration of the argument offered in its support. I always took the "proves too much charge" to be something like this: the argument offered supports conclusions that are false and so cannot be a sound argument for the conclusion offered. If _that_ is what the "proves too much" charge comes to, it would have force.

(Full disclosure: I'm guilty of leveling the charge that an argument proves too much. I recently responded to an argument that was supposed to show that motivating reasons consist of mental states on the grounds that reasons have to be causes and that causes have causal powers by saying that the argument proved too much. In that case, I meant that the argument proved too much because the argument supported views that were clearly false (e.g., that only substances can be reasons).)

[Moti Mizrahi]

Hi Clayton,

Thanks very much for your comment.

I agree with you that your interpretation of the “proving too much” charge is legitimate. If an author argues that p, and there are indeed independent reasons to believe that p is false, then the objection has force. But then the objection is not really that the argument for p “proves too much,” but rather that the author who argues for p should take into consideration those reasons to believe that p is false.

I grant that there are philosophers who use the “proving too much” objection in this way. But I suspect that there are also philosophers who use the “proving too much” charge in the way I have described in the post. That is, such philosophers object that an argument for p must be unsound, since p strikes them as too strong. This use of the “proving too much” charge has very little force.

[Marcus Arvan]

Moti,

I've always understood the "proving too much" move as being something like this. A great deal of the time, when one is making an argument, one doesn't *know* that its premises are all true. Rather, they strike one as "plausible", and one makes a *case* for the truth of each premise to oneself, and to one's readers. But then, in some cases, a valid argument containing premises that strike one as "plausible" is found to lead to a conclusion that strikes one as entirely *implausible*. In that case, what is the epistemically reasonable thing to do? It's not obvious that it's more reasonable to accept the argument than it is to reject the argument by way one big modus tollens (i.e. by rejecting the conclusion).

Notice that this seems perfectly legitimate. Arguments can be thought of as one giant conditional (viz. IF these premises are true, then THAT conclusion is true). If one's epistemic confidence that the consequence (i.e. the conclusion) is false is greater than one's confidence that the antecedent (i.e. the argument's premises) is true, it's perfectly reasonable to reject the argument on the basis of one's beliefs about the likely truth of the conclusion.

In short: it all depends on what one has more epistemic confidence in -- the falsity of the conclusion or the truth of all the premises.

[David Morrow]

Interesting. I've always interpreted the "proves too much" objection differently -- something along these lines: "The author argues from x&y&z to p. But if that argument works, then x&y&z (or some suitably similar equivalent) entails q. And, for reason R, this should make us reluctant to accept the author's argument." Reason R might be any of several things: Maybe q is false, or the conjunction p&q can't be true, or x&y&z clearly doesn't entail q, or whatever.

Some examples:

Pascal's Wager "proves too much" because a parallel argument could also be used to prove that we should believe in a sadistic deity who will reward us for being horrible people.

Anselm's ontological argument "proves too much" because a parallel argument proves that Gaunilo's Lost Island exists.

The Open Question Argument "proves too much" because a parallel argument proves that water is not identical to H2O.

[David Morrow]

Incidentally, I'm not necessarily endorsing my three examples of the "proves too much" objection. They're just examples that I've seen people use.

[Moti Mizrahi]

Hi Marcus,

Thanks for your comment.

Like Clayton’s, your take on the “proving too much” charge seems different from the one I had in mind. So we have three interpretations already (I suspect there are more) of the “proving too much” charge:

(1) The author’s argument for p must be unsound because p strikes me as too strong.
(2) The author’s argument for p must be unsound because there is an independent reason r to believe that p is false.
(3) The author’s argument for p must be unsound because p strikes me as implausible.

I am suggesting that (1) is an illegitimate charge, although (2) and (3) may be legitimate.
Perhaps all of this goes to show that people should be careful when they level the “proves too much” charge against others.

[Marcus Arvan]

Moti (and David),

I guess I'm just not sure there's a difference between (1) and (3). Offhand, I want to say, when people object to a conclusion being too strong, they are really objecting to the plausibility of the conclusion. Consider your own example. I take it that people who worry about the open question argument want to say something like this: "That conclusion is too strong. It's implausible to think that *no* natural property could itself be good." That is, they want to reject the argument because they are more certain that the conclusion must be (is probably?) false than they are that all of the premises are true. This is, at any rate, what *I* mean when I say a conclusion is "too strong." I mean: the conclusion is so strong that I find it *less* plausible than the premises that (jointly) entailed it.

[Moti Mizrahi]

Thanks for your comment, David.

I think that your take on the “proves too much” charge is different from the ones we’ve discussed so far and that it can be understood in two ways:

(a) Assuming that an argument for p is valid, by saying that the argument “proves too much” one might mean that one of the premises must be false, since an argument with the same form can be used to prove that q, and q is false. (Since a valid argument cannot have true premises and a false conclusion, if the conclusion is false, one of the premises has to be false as well.)

(b) Assuming that the premises in an argument for p are true, by saying that an argument for p “proves too much” one might mean that the argument is invalid, since an argument with the same form can be used to prove that q, and q is false. (Since a valid argument with true premises must have a true conclusion, if the conclusion is false, and the premises are true, the argument must be invalid.)

Does that sound right?

[Moti Mizrahi]

Marcus,

Perhaps you are right that to say that p is too strong is just to say that p is implausible.

I think of ‘p is too strong’ as a sort of subcategory of ‘p is implausible’. When one says that p is too strong, I take it, one means to say that p is implausible in a particular way. The way in which p is implausible, in this sense, is that p would encroach on other domains, as it were. For example, the conclusion of Moore’s open question argument would apply not only to meta-ethics but also philosophy of language (as David pointed out). And so it might strike some as implausible that Moore’s open question argument has such far-reaching implications.

[David Morrow]

Moti,

I think you're right. My version of the objection would amount to saying, "Your argument is either invalid or valid but unsound," without committing oneself to identifying which premise is false or explaining exactly why it is invalid. It's a useful argumentative device for showing that an argument is flawed when you can't say exactly why it's flawed.

To be honest, I've never interpreted a "proves too much" objection in the way that you all seem to interpret it--viz., as implying that the stated conclusion is somehow "too much."

[Clayton]

Hi Moti,

I think that you're right that there's not some single thing someone has in mind when she says that an argument proves too much. I should add that the charge will often convey the speaker's judgment that there's an undercutting defeater that defeats the justification for the conclusion rather than a rebutting defeater. On the 4th reading, the idea is this: p might be true, it might be false. The argument offered for p doesn't just support p, it also supports q and we know independently that q is implausible/false. The fact that the argument for p supports q isn't evidence that ~p, it's evidence that the purported justification for believing p doesn't give us any (undefeated) reason to believe p.

[Moti Mizrahi]

Thanks, Clayton.

I've tried to sum up the different readings of the "proving too much" charge we have discussed in a diagram (please see the updated post). Does it seem right to you?

[David Morrow]

Your diagram seems right to me, Moti, except that I wonder whether you might be able to use a "proves too much" objection without knowing exactly what's going on in the second and third layer of your diagram. To adapt an analogy from Reid, a "proves too much" objection shows that the target argument "leads us to a coal pit" (which wasn't where we wanted to go), but it can do so without showing us exactly where or how we went wrong. So, if you use such an objection, you might not even be able to say whether you're attacking the form or the premises of the argument. You might just know that there's *something* wrong with the argument.

Or will the relationship between the target argument and the parallel argument reveal what's going on in the objection?

[Moti Mizrahi]

Thanks, David.

I'm inclined to think that the relationship between the target argument and the parallel argument can reveal what kind of "proving too much" objection one has in mind.

For example:

(1) Suppose that the argument for p is valid.
(2) The argument for q has the same form as the argument for p.
(3) So the argument for q is also valid.
(4) But q is false.
(5) So one of the premises of the argument for q must be false.
(6) So one of the premises of the argument for p must be false as well.

Or

(1) Suppose that the premises of the argument for p are true.
(2) The argument for q also has true premises.
(3) But q is false.
(5) So the argument for q must be invalid.
(6) So the argument for p must be invalid as well.

[David Morrow]

I think the Supreme Court's refusal to uphold the individual mandate under the Commerce Clause rests on a "proves too much objection." From Roberts' opinion:

"People, for reasons of their own, often fail to do things [e.g., purchase health insurance] that would be good for them or good for society. Those failures--joined with similar failures of others--can readily have a substantial effect on interstate commerce. Under the Government's logic, that authorizes Congress to use its commerce powers to compel citizens to act as the Government would have them act." But clearly, Congress is not so authorized in all such cases. Therefore, the Government's logic is flawed.

[Moti Mizrahi]

This is an interesting example, David.

The court’s interpretation of the government’s argument seems to be something like this:

1. People often fail to do things that would be good for society as a whole.
2. When people fail to do things that would be good for society as a whole, Congress can use its power to make people to do those things that would be good for society.
3. Therefore, Congress can use its power to make people to do those things that would be good for society.

If this is the government’s argument, then one could make the charge that it “proves too much,” if one thinks that there are certain things that the government cannot (i.e., has no authority to) make people do.