Necessary conditionhood is a notion I employ all over the place, and I've only just noticed that I'm not really sure what it amounts to.
Suppose P is a necessary condition for Q. Here are some of the things I've probably taken that to mean on various occasions:
1. Q materially implies P
2. Q strictly implies P
3. ~P materially implies ~Q
4. ~P strictly implies ~Q
5. If Q then P
6. If ~P then ~Q
7. Necessarily, if Q then P
8. Necessarily, if ~P then ~Q
9. If Q were the case then P would be the case
10. If ~P were the case then ~Q would be the case
On other occasions I've taken necessary conditionhood to involve some more substantial kind of dependence, so that if P is a necessary condition for Q, then Q's obtaining depends causally, explanatorily, or in some other interesting way, on P's obtaining. So for instance another thing I've taken it to mean is:
11. If ~P were the case then ~Q would be the case *because* of ~P
All this goes for sufficient conditions too, mutatis mutandis.
Some questions this raises: is one of these understandings right and the others wrong? Or do we in fact have a wide range of notions of necessary conditionhood? If the latter, is that a good state of affairs? Should we take more care to spell out what we mean each time we use the phrase 'necessary condition'?
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8 comments:
Hi Carrie,
Hope you're enjoying the great down-under.
"is one of these understandings right and the others wrong? Or do we in fact have a wide range of notions of necessary conditionhood?"
The first question seems to be ambiguous between two readings: First, it might be taken to ask whether one (or more) of 1-11 correctly describes a notion of necessary conditionhood figuring in our actual processes of inferences.
But secondly, however, it might be taken to ask whether one (or more) of 1-11 states a correct normative condition C such that we ought to reason in accordance with C.
The second question you ask seems also to be compatible with either interpretation. Whether one is engaging with the descriptive or the normative project, it seems indeed to be a separate question whether one is after a singel notion or not.
... yeah, that should have been 'single' of course...
Hi Andreas,
I was intending to ask the descriptive question, though the normative one is also interetsing!
I would say first define necessary and you will answer the question in a
satisfying way.
Excuse my ignorance, guys, but can anyone explain what's the difference between 2/4 and 7/8 in Carrie's list?
As far as I know, C.I. Lewis defined 'Q strictly implies P' as 'Necessarily, If Q then P'...
Thanks,
Ignoramus Anonymous
Hi anonymous,
I was using 'P strictly implies Q' to mean the same as 'necessarily, P materially implies Q'. If you think the natural language conditional 'if ... then' is different from the material conditional, as most people do, then 2/4 won't be the same as 7/8.
Hi Mark,
Relevant implication's an interesting suggestion - I'll add it to my list!
Carrie wrote:
"If you think the natural language conditional 'if ... then' is different from the material conditional, as most people do, then 2/4 won't be the same as 7/8."
I see. It's just that it sounds a little odd to embed the natural language conditional (which many people think it's *not* truth-conditional at all) in the scope of a modal operator---what would the truth conditions of `Necessarily, If Q then P' be if the `if...then' is taken as the natural language conditional? I'm not saying it can't be done. It's just going to look a bit messy, that's all.
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