Monday, February 15, 2010

Logical Obverse

There was a flap recently about Cherie Booth, the wife of Tony Blair, who had given a lenient sentence to a man, saying, "I am going to suspend this sentence for the period of two years based on the fact you are a religious person and have not been in trouble before. You caused a mild fracture to the jaw of a member of the public standing in a queue at Lloyds Bank. You are a religious man and you know this is not acceptable behaviour." I hadn't paid much attention to it, but wandering about I happened to come upon an essay and discovered that A.C. Grayling needs a little assistance with the application of logic.

Grayling argues in response to Booth's claim:

As a barrister Mrs. Blair should be able to see the inadmissible corollary of passing lenient sentences on believers because they are believers; namely, that non-believers should receive less lenient sentences. If she had said – and said twice – in passing judgment on a person she knew to be non-religions, ‘I am going to apply the full penalty of the law based on the fact that you are not a religious person,’ she would not have merited any less of an outcry than she has caused, for the very good reason that this is the logical obverse of what she in fact said, and would be as unacceptable.


Unfortunately, this is not the logical obverse of what she in fact said. What she in fact said (and Grayling had just quoted her as saying it a few sentences before) was that she was giving a lenient sentence because Shamso Miah was a religious man and had not been in trouble before. From this it does not follow that not being a religious person is a reason for not being lenient: there is a conjunctive term here, and one conjunct of it has wandered out of Grayling's analysis. Moreover, Grayling clearly gets the whole thing backwards. We can see this by simplifying a bit and recognizing that to get the 'logical obverse' Grayling wants, we have to interpret Booth as assuming something like

All people who should get lenient sentences are religious people.

The logical obverse of this is that no people who should get lenient sentences are non-religious people; which is equivalent by conversion to the claim that no non-religious people should get lenient sentences, which Grayling seems to have in mind. But even if we ignored the conjunction, and even if we take Booth to be making a strong assumption, the actual assumption attributed to Booth to make her comment make any sense would have to be something more like:

All religious people should get lenient sentences.

And the logical obverse of this is that no religious people are not people who should get lenient sentences; if we also contrapose, then we can get the claim that all people who should not get lenient sentences are non-religious people, but it does not follow from this that if you are non-religious you don't get a lenient sentence; the assumption is consistent with some people who are non-religious getting a lenient sentence. You can only get to something like Grayling's 'logical obverse' by an illicit conversion.

Such an assumption is too strong in any case; it is consistent with the claim that being religious is sometimes a reason for leniency, and that only some religious people should get leniency because of being religious -- due to the way in which they are religious. And, indeed, the conjunctive term requires a weaker assumption. The strongest assumption Booth can be possibly committed to on the basis of her words is the following:

All religious people who have not been in trouble before should get lenient sentences.

This just tells us that some religious people should get lenient sentences. (The logical obverse of this, in case you are wondering is, with the conjunctive term, that no religious people who have not been in trouble before are not people who should get lenient sentences; and in the I-form without the conjunctive term, it just tells us that some religious people are not people who should not get lenient sentences.) There is no way to get from this to anything like Grayling's 'logical obverse'.

But one could also plausibly suggest that the claim is consistent with an even weaker assumption, because she doesn't have to be making a universal assumption; her assumption can be particular:

Some religious people who have not been in trouble before should get lenient sentences.

All that is required to apply such an assumption in this case is to hold that there is reason to think that this is in fact one of those cases. And this indeed is much closer to the claim that Booth seems to be making, namely, that some people who should get lenient sentences should get them because they are religious people who have not been in trouble before.

From all this we can see that pretty much nothing follows about non-religious people from Booth's claim. From the fact that religion, even all religion, is a reason for leniency we cannot conclude that lacking a religion is a reason for non-leniency; it may not be a reason one way or another. This is true a fortiori if we only admit that some things that are called religion -- for instance, things relevant as a testimony to character, which I take it is why Booth brought it up in the first place -- are reasons for leniency. For instance, the fact that someone is a philosophy professor is a reason for concluding that they can handle the logic of an argument; but it does not follow from this that we are therefore saying that the fact that someone is not a philosophy professor is a reason for concluding that they can't handle the logic of an argument. There is no way to get the one from the other.

I suspect that Grayling has confused himself with the word 'because'. In this context it works as reduplicative that qualifies how the term in the predicate applies to the subject. Saying that X should get Y because X is Z, this is the same as to say that X should get Y on account of being Z. If I say that religious people are people who should get lenient sentences on account of being religious, this has as its corollary that non-religious are not people who should get lenient sentences on account of being religious. This is not only obviously true, it is not the same as the corollary claimed by Grayling, that non-religious people should not get lenient sentences on account of being non-religious. That would involve an illicit shift in the reduplicative: since the reduplicative limits what about the term is being applied to the subject, changing the reduplicative changes the whole predicate and introduces an equivocation.

There are any number of other problems with Grayling's argument that follow from his failures here. For instance, he says,

So she must be assuming – leaving all history and the contemporary world aside as providing too many troubling counter-examples – that there is a tendency for religious people to be of good character because they are religious (and not, say, that they have a tendency to be of good character because they are people).


But this can only be the conclusion if you leave out the fact that the reason given by Booth was conjunctive: it was the conjunction of the fact that he was a religious person and that he hadn't been in trouble before. So all Booth must be assuming is that people who are religious and have not been in trouble before tend to be of the sort of good character that makes it reasonable to be lenient in the context of a court. It does not require the assumption that all religious people tend to be of good character; it is consistent, for instance, with religion being thrown out as a legitimate reason for thinking a person of good character if they have been in trouble before. Moreover, it does not even require (contrary to the course Grayling's argument later takes) that the 'good character' involved be fully moral good character rather than good character in the limited sense that they are social enough that they can be expected to behave themselves better in the future. But it's clear that when courts in considering leniency look at whether a person has good character they are really only doing the latter: they are simply looking for indications that a person is not a complete social misfit, but someone who participates in the community, who has shown that they are capable of participating in the community without misbehaving, and who has been shown to have social incentive to be more careful in the future.

It is very extraordinary how much of a tempest in a teapot this whole thing is: so much sleight of hand to make the whole thing seem more severe than it is. One can reasonably argue that religion should not be a reason considered when determining whether to be lenient or not. However, one cannot reasonably argue that considering religion as one reason for leniency commits anyone to the claim that people who are non-religious should not be treated leniently on account of the fact that they are non-religious.

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