Saturday, August 20, 2022

Intention and entailment

Suppose Alice intends to hit Bob with a stick. There are two ways that the stick could be involved in Alice’s intentions. First, Alice might not care that it is a stick she hits Bob with, but a stick happens to be ready to hand. In that case, her hitting Bob with a stick is a means to her hitting Bob.

Second, Alice might care about hitting Bob with a stick—perhaps she is punishing him for hitting a defenseless person with a stick and wants the punishment to match the crime. In that case, hitting Bob with a stick is not a means to her hitting Bob, as her hitting Bob does not figure in her intentions apart from the stick. But even in that case it seems right to say that Alice intends to hit Bob. For while it is false to say in general that

  1. if p entails q and Alice intends p then Alice intends q

(even if one adds that Alice knows about the entailment, or makes the entailment relevant in the sense of relevance logic), it seems that the following special case is true:

  1. if q is a specification of p and Alice intends q then Alice intends p.

Alice’s hitting Bob with a stick is a specification of Alice’s hitting Bob.

A similar point applies to conjunctions. If Alice intends to hit Bob with a stick and to insult him, she intends to hit Bob with a stick and she intends to insult him. But sometimes at least, hitting Bob with a stick and insulting him do not figure as independent intentions. Yet they are intended nonetheless. So we have another special case of (1):

  1. if p is a conjunct of q and Alice intends q then Alice intends p.

It is an unhappy situation that some special cases of (1) are true, but (1) is not true in general, and I do not know how to specify which special cases are true.


Harrison Lee said...

This is very interesting, Alex. Maybe the difference is that if p partly consists of q then anything which might count as a reason to pursue p also counts as a reason to pursue q (for a fully informed agent, anyway--that is, for an agent who understands that p partly consists of q). This explanation leaves room for 1 to be false since p might entail q without partly consisting of q--as when p will certainly cause q. But if q is a specification of p then p partly (or wholly) consists of q--at least if I understand what you mean by specification.

But if this is the right explanation then it is hard to see how Sam could intend to kill the mammal without intending to kill the human, since killing the mammal consists of killing the human.

Philippe Bélanger said...

What if Alice has strange beliefs such that she believes q but doesn't believe p, even if p is a conjunct of q? Does she still intend p if she intends q?

Alexander R Pruss said...

I doubt this is possible. It seems to me that one way to believe p is to believe a conjunction of which p is a conjunct. It's not like our beliefs are stored as separate sentences in the brain. They are, I expect, often encoded in a kind of bundle. And conjunction is one way for them to be bundled.

Philippe Bélanger said...

In general I would be reluctant to ascribe such beliefs to someone but I can imagine situations where I would. For example, if Alice earnestly said q, denied p and explicitly said that she does not believe that a conjunction entails its conjuncts.

Alexander R Pruss said...

If someone said she did not believe that a conjunction entails the conjuncts, it would take a lot of work to convince me that they know what "conjunction" means.

Notice that normally when you believe a conjunction, you don't need to take any extra steps to believe the conjuncts. You automatically count as believing the conjuncts by believing the conjunction. If you then deny a conjunct, then it may well be that you are simply contradicting yourself: you both believe and don't believe that conjunct.

Alexander R Pruss said...


That's a valiant attempt at generalizing, but I don't think it works. Suppose Alice doesn't know that pigs are mammals. Then she can easily intend to eat a pig without intending to eat a mammal, even though pig eatings are a subset of mammal eatings. In fact, I think even if she does know, mammality may not be in her intentions at all even if pigness is.

Alexander R Pruss said...

But even if she knows, she may not care, and hence she may not intend. I know that 6 is the smallest perfect number ( ). But if I intend to eat six dumplings, I need not be intending to eat a perfect number of dumplings, because I may not care about the number theoretic properties of the dumpling count.

Alexander R Pruss said...


You have a history of posts written in a style far from the polite, calm and intellectual style of academic debate. I have given you several warnings, deleted a number of comments, but the unacceptable emotional tone has continued. Consequently, I have set up a script to automatically delete new comments from you. There are some glitches in the script, so the above comment of your may stay up or not.

Note that Blogger's policy is about Blogger censoring posts. As far as I can tell, blog owners are free to moderate comments as they see fit.