Thursday, September 07, 2006

What Is A Necessary Condition?

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'?

9 comments:

Andreas said...

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.

Andreas said...

... yeah, that should have been 'single' of course...

Carrie Jenkins said...

Hi Andreas,

I was intending to ask the descriptive question, though the normative one is also interetsing!

Anonymous said...

I would say first define necessary and you will answer the question in a
satisfying way.

Mark Jago said...

Hi Carrie, it's a good question! Given the 'paradoxes' of material and strict implication, could this be a job for relevant implication? Adding *because of* (or *in virtue of*) clauses could be tricky, not least because such clauses themselves stand in need of explanation (we can ask, what is a necessary condition for something holding *in virtue of* something else?)
Mark

Anonymous said...

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

Carrie Jenkins said...

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.

Carrie Jenkins said...

Hi Mark,

Relevant implication's an interesting suggestion - I'll add it to my list!

Anonymous said...

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.