contraposition and 'most'

Is this odd, or am I just under-caffeinated at the moment?

The principle of contraposition (= the equivalence of 'If P then Q' and 'If not-Q then not-P') doesn't hold when the quantifier is 'most'. That is, 'Most As are Bs' is not equivalent to 'Most non-Bs are non-As'.

I take 'Most As are Bs' to mean: the number of things that are both A and B is greater than the number of things that are A but not B.

A minute or two of drawing (unless I've messed up somewhere) will get you a picture where
(1) the number of ABs > the number of A non-Bs
is true, but
(2) the number of non-A non-Bs > the number of A non-Bs
is false.

Again, maybe this point is as obvious as 2+3=5. But I am covering simple inductive arguments in my critical thinking class at the moment, trying to figure out which ones are good, and I had never thought about this case before, but it means the inductive analogue of quantified modus tollens (Most As are Bs, x is not B, Thus x is not A) is no good. And that surprised me, since the analogue of modus ponens is perfectly fine.


Galen Strawson on moral responsibility

As many readers will know, Galen Strawson recently published a brief piece on his views about free will and moral responsibility in the New York Times. Now I am very late to the discussion on this, and even more out of my professional depth, but we are reading this piece for my freshman seminar, along with Strawson's interview in Tamler Sommers' A Very Bad Wizard, and I wanted to post a thought about the basic argument. I'm sure someone must have said this before; any references to the relevant literature would be greatly appreciated.

Here's Strawson's argument (quoting from the NYT piece):

(1) You do what you do ... because of the way you then are.

(2) So if you’re going to be ultimately responsible for what you do, you’re going to have to be ultimately responsible for the way you are ... .

(3) But you can’t be ultimately responsible for the way you are ... .

(4) So you can’t be ultimately responsible for what you do.

I take it that (2) is supposed to follow from (1) (since there's a 'So' at the beginning of (2)). Now, what implicit premise does Strawson need to make that inference valid? Something like the following:

(*) If X because of Y, then if you are ultimately [morally] responsible for X, then you are ultimately [morally] responsible for Y.

In other words, you can only be morally responsible for the effect if you are also morally responsible for the cause (=you can't be morally responsible for an effect unless you are also morally responsible for the cause).

I think this principle (*) may have counter-examples; I'm curious to hear about other people's reactions. Here's one such example: A person is driving along a very infrequently traveled mountain road, when some giant falling rocks hit him and his car. His car careens off the road, and he is badly injured by the rocks and subsequent crash. If he does not get to a hospital soon (and there's one 30 minutes away by car), he will die.

Now suppose someone drives by a few minutes later, and she sees that the first person is badly injured and will probably die soon if he doesn't make it to the hospital (imagine the second driver is a physician). She decides that picking him up, putting him in the car, and taking him to the hospital would be an annoyance, and she leaves him there (let's assume that taking him to the hospital wouldn't really be any significant cost/ burden for her).

Now, I think this may be a counterexample to Strawson's argument. Why? Let X be the first driver's death, and Y be the falling rocks hitting the car. It seems reasonable to say that (i) the first driver died because of the avalanche of falling rocks, but (ii) the second driver is at least partially morally responsible for the guy's death, even though (iii) she is certainly not morally responsible for the rocks hitting his car (she wasn't standing at the top of the mountain, pushing down rocks to harm passersby). If (i)-(iii) are correct, then we've got a counter-example to (*).

Someone who wanted to defend Strawson has at least one reasonable response to this: the second driver's leaving the first one to die is (at least part of) the cause of the guy's death; at the very least, we have the right sort of counterfactual dependence that is a necessary condition for causation (If she had not driven right past, then he would not have died). But now we are in the difficult and murky issue of causation by omission -- a contentious and vexed topic, since if we allow omissions to be causes in general, then a LOT of things become causes that we do not ordinarily think of as causes. (Sarah McGrath's "Causation by Omission" is an excellent treatment of this issue.)

So I guess my final conclusion is that, in order to accept (*), you have to accept a contentious metaphysical thesis about omissions being causes as well. This is of course not a refutation, but it certainly provides a respectable 'way out' of Strawson's basic argument.


The power of Carnap

Yes, this is awesome.