The Quantitative Mean: Saved or Abolished?

Giles Pearson thinks that my defense of a 'quantitative' version has perhaps served to abolish it. He writes as follows:

Many thanks for this discussion.

Here’s an attempt at a reply:

First, just so we are not misunderstood, it was the squeak of mice that was not to be feared (see NE 7.5.1149a7-8), not mice in general. (And if the reader does not like this either, they should substitute something that they do not think one should fear at all (Aristotle certainly believes this is not an empty set, see NE 3.7.1115b34-35)).

Second, of course the fearless phobic is a contrived example, but its function is simply to point to a general flaw in the quantitative analysis. Having said that, I don’t see why we can’t generate numerous parallel cases to the fearless phobic that are reasonably common. Take the example I gave in my paper with respect to sphere of temperance. Suppose someone takes pleasure in adultery (something he should not), but does not take pleasure in eating healthy food (something he should). With respect to these objects, this person takes pleasure in the right number of objects (i.e. 1), but the wrong objects. Yet, I imagine there are quite a few people like this, and that such a character does not contravene any of the distribution points you were canvassing.

Finally, let me turn to your response to my argument.

Your idea is that we can rephrase

(1): ‘He fears mice too much’

with

(2): ‘He shows too much fear in fearing mice’

I presume that (2) is to be read as:

(3): ‘In fearing mice, he shows too much fear’,

(rather than e.g. ‘He shows too much fear of mice’, which would imply that there was a right amount to fear mice and so my problem would arise directly.)

Your idea is that (3) does not cause the problem, because it does not imply that there is a right amount to fear mice.

My reply is twofold:

(i) Part of the reason the rephrase does not have the unwanted implication is because it is not actually a rephrase. This is because whereas (1) was referring to how much someone feared something, (3) instead refers to the fact that in fearing a certain thing, an agent manifests (the separate property of experiencing) too much fear. (Cf. ‘the courageous agent fears death the right amount’, which you would rephrase: ‘in fearing death, the courageous agent shows the right amount of fear’. But that was not what the first sentence was saying.)

(ii) More crucially, your (3) seems in effect to do away with a quantitative analysis altogether.

To see this, consider the following. Why does the fact that an agent fears mice mean that he manifests too much fear? Of course, it is because he should not fear mice at all. But then what does ‘he shows too much fear’ mean here? Presumably: ‘he exhibits fear when he shouldn’t exhibit it’, or: ‘he exhibits fear in front of an object he shouldn’t’, or some such?

But, if so, has not the quantitative dimension that you were trying to preserve, upon analysis, disappeared? Exhibiting fear too much, just right, or too little, in effect seems to have reduced to fearing the right or wrong objects.

To see this further, consider:

(4) ‘In fearing death, he exhibits just the right amount of fear’

Why does the agent in (4) exhibit the right amount of fear? Well, in saying this we are not really trying to specify how much he fears death; we are only really referring to the simple fact that he fears this object in the first place. After all, the whole point of your rephrase was to avoid a quantitative dimension in the first clause of the rephrase (‘in fearing death’, ‘in fearing mice’). Hence, (4) simply means: ‘in fearing death, the agent fears what he ought to’. Likewise, I suggest, (3) means: ‘in fearing mice, the agent fears something he should not’.

This rephrase bypasses the problem I set, but only because it in effect does away with the quantitative dimension of the mean altogether.