Necessary Conditions

MichaelJYoo

Can someone help precisely define a necessary condition? In a conditional X→Y, Y is supposed to be a necessary condition of X. Now, I usually see a necessary condition defined as something (in this case Y) that must occur if X is to occur; in other words, something without which it is impossible for X to occur. When we say this--that it is impossible for X to occur without Y--however, do we mean that the necessary condition (Y) must be antecedent in time and occurrence to X? Or only that if X is the case, that Y must also be the case? Because it seems, from the way it is most commonly described, that the former is intended. But surely this seems false. Take, for example, the following conditional:

If it is raining, then the grass outside is wet.

In what tolerable sense can it be said that the grass outside must be wet (Y) before it can rain? Yes, if it is raining, it is necessarily true that the grass outside is wet. But is it necessary that the grass be wet before it can rain or is raining?

Is my confusion here due to my failure to rightly understand the true nature of a necessary condition? Sorry if this is a dumb question.

Pfhorrest

Time is not a factor in logical necessity. If it can't both be the case that "it is raining" and the "ground is not wet", then the ground being wet is a necessary condition for it to be raining. That doesn't mean the ground has to be wet first; just that it can't be raining without the ground also being wet.

Michael

When we say this--that it is impossible for X to occur without Y--however, do we mean that the necessary condition (Y) must be antecedent in time and occurrence to X? Or only that if X is the case, that Y must also be the case? Because it seems, from the way it is most commonly described, that the former is intended. But surely this seems false. — MichaelJYoo

It's the latter, not the former.

Harry Hindu

If it is raining, then the grass outside is wet.

In what tolerable sense can it be said that the grass outside must be wet (Y) before it can rain? Yes, if it is raining, it is necessarily true that the grass outside is wet. But is it necessary that the grass be wet before it can rain or is raining? — MichaelJYoo

I don't see how the statement implies that the wet grass occurred before the rain, so I'm failing to see the problem you are posing.

There is also the problem of rain not necessarily being the cause of wet grass. Condensation can cause the grass to be wet, not just rain.

Time is not a factor in logical necessity. If it can't both be the case that "it is raining" and the "ground is not wet", then the ground being wet is a necessary condition for it to be raining. That doesn't mean the ground has to be wet first; just that it can't be raining without the ground also being wet. — Pfhorrest

I guess it depends on where we drawn the boundary between raining and not raining. Is it raining when the water drops are condensing and falling from the sky before the water drops hit the ground, and how much water on the grass qualifies it as being wet? This isn't an instantaneous process.

As usual, most philosophical problems are the result of how we use language.

Maybe we should say that once the density of water in the atmosphere reaches a certain point, grass becomes wet.

3017amen

↪MichaelJYoo

Consider using the words 'only if' in order to identify it as a necessary condition. Otherwise, for example in contrast, you'd be using the rules of inference or Modus Tollens.

Examples of Modus Tollens:

If the cake is made with sugar, then the cake is sweet.
The cake is not sweet.
Therefore, the cake is not made with sugar.

If the dog detects an intruder, the watchdog will bark.
The dog did not bark.
Therefore, no intruder was detected by the dog.

We can infer those to be true, but not necessarily true, since the cake can be made with artificial sweetener, and there may have been an intruder that the dog did not detect. And so, similarly, (as HH pointed out) there could have been dew on the grass prior to it raining which made it wet.

And Harry is right, it is how we use language that presents these kinds of difficulties (the liars paradox/self referential statements, etc.).

Are you trying to make some sort of distinction between necessary conditions (from nature) and logical necessity (from a priori reasoning)?

Pfhorrest

I don't see how the statement implies that the wet grass occurred before the rain, so I'm failing to see the problem you are posing. — Harry Hindu

The apparent problem is that “the grass being wet is a necessary condition for it to be raining”, which is supposed to mean the same thing as “if it is raining then the grass is wet”, sounds superficially like the grass has to be wet first.

I guess it depends on where we drawn the boundary between raining and not raining. Is it raining when the water drops are condensing and falling from the sky before the water drops hit the ground, and how much water on the grass qualifies it as being wet? This isn't an instantaneous process. — Harry Hindu

That’s why I said “IF it can’t be true...”. For the reasons you mention, it could be true that it is raining and the grass is not wet, so the grass being wet is not in fact a necessary condition of it being raining. But IF it were...

MichaelJYoo

↪Pfhorrest

I think your answer here clarifies things for me the most. As does Michael's answer. Thank you.

MichaelJYoo

↪Michael

Your short answer here helped tremendously. It really is the heart of what my question was getting at.

MichaelJYoo

↪3017amen

What I meant to ask was whether in the conditional, X→Y, when we say that Y is a necessary condition of X, if this means that Y is a prerequisite condition of X; that is, that it must be true before X can occur; or only whether it cannot fail to be true if X is true. Hope that helps clarify what I was trying to ask.

3017amen

↪MichaelJYoo

MY!

Maybe try re-writing the conditional statement... .

Harry Hindu

↪Pfhorrest

It seems to me that you are agreeing that how we use language is the problem.

The apparent problem is that “the grass being wet is a necessary condition for it to be raining”, which is supposed to mean the same thing as “if it is raining then the grass is wet”, sounds superficially like the grass has to be wet first. — Pfhorrest

In a deterministic universe effects are just as necessary of a condition of their causes as causes are a necessary condition of their effects. The difference between them is spatial-temporal.

Sounds like wet grass (the effect) is dependent upon the initial condition of it's raining (the cause) - and that wet grass will come after the fact that it is raining.

That’s why I said “IF it can’t be true...”. For the reasons you mention, it could be true that it is raining and the grass is not wet, so the grass being wet is not in fact a necessary condition of it being raining. But IF it were... — Pfhorrest

Sure. I could put a tarp over my lawn and then it would be raining but the grass wouldn't be wet. Sounds causal to me. If I can insert some element into the process to prevent what we claimed was a necessary condition for something else, or show that the effect (wet grass) isn't necessarily the result of it raining (it could be condensation, or someone is watering their grass), then obviously rain isn't a necessary condition of wet grass. It would simply be a matter of misusing/misinterpreting words.

Necessary Conditions

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