Greetings Ignoro

Not sure that I understand you correctly, but it looks like you are searching for the wrong word. Logic in general works with strict systems, so there is no way to pop up arguments from the middle of nowhere. You are describing correlation, not causation... The contribution itself means just that you don't have enough information about the system.

If you don't have enough information about the system, the only thing you can do is estimation, so it's closer to probability and fuzzy logic, not a classic one. In a simplest form you need something like a probability with a confidence interval

I'll give it my best shot.

So one of the things about logic is it is irrelevant to time. The premises state the facts as they are at a particular moment. If the facts change, then that is a different argument.

So lets start with your first premise. We know it is unnecessary to consider time, just a "slice of time". So lets examine your slices.

So our first premise is that Q exists.
Our second premise is that P can exist while Q exists, but it is not necessary that P exists, for Q to exist.
In logic it would be
1. Q
2. P
So far, you have indicated no casual relation between the two.

Now your third premise is a little trickier to break down. You are establishing a relationship, but it is indirect. If I understand this correctly, it means there is no causal relationship between the two, but perhaps there is a consequent interaction. Maybe P and Q bump into one another. Maybe P bumps into R, which bumps into Q, changing the state of Q into something else like W.

In logic, P, Q, and all the letters represent a sliced state of being. Meaning if Q is altered, it is no longer Q anymore. We make a new letter at this point. If we say things rely on Q, we would say, "Q causes R", which is represented by Q -> R.

So I would say at this point you'll need to clarify what you mean by an indirect relationship. The best way to do that is invent states of relation, creating a new letter for each one.

As for a contributory cause, I believe that means that Q's existence or state is part of the necessary requirement for R to exist. As it is a contribution, it implies that more than one states are necessary for R to exist.

So for example, (P and Q) -> R

P and Q do not rely on each other for their existence, but together, they create a new state. Just remember that P and Q should be careful translations of the words you are using. I hope this is a useful start, but I think we'll need some greater clarification of the idea before we can really examine it in detail.

P and Q are temporal facts.... Is there logical proof that if P ceases existing there can still be the possibility of Q existing? — Ignoro

And,

If we have the premise that a certain fact P is not a necessary neither a sufficient cause for Q. — Ignoro

Already QED.

((P v ~P) ^ Q) => Q

It seems to me you're not actually looking for a proof in logic, but perhaps a negative proof that Q can exist absent P in fact. If in fact Q does exist absent P, then that's all you need. If it's the result of an experiment, then you may also need to replicate the experiment and get the same result.

As to definitions of cause, that's actually a difficult and complicated word. If there's a special context, then likely it's a term of art within that context.

Very nice Tim Wood! I think he's got you covered Ignoro.

Also, what is the formal definition of contributory cause? I can't find this anywhere. — Ignoro

Maybe there isn't one? I'd understand a contributory cause in one of two ways depending on context.

One of them is: a contributory cause of X is a member of a set of causes which are jointly a sufficient cause for X to occur. EG, if all of the set happens, then X happens. But if at least one of the elements of the set does not happen, then X does not have to happen (but it still might for other reasons).

One of them is: a contributory cause of an event X is a member v of a set of random variables V such that the probability of X happening given that v has happened is higher than if v did not happen and v has a causal relationship with X. In other words, when v is a risk factor for X that has a causal relationship with X.

I'm adding the causal relationship bit to the second because, well, no one's gonna say that being poor causes people to die in the same way that shooting someone in the head causes them to die.

That's consistent (I think) with the account given here.

Is there logical proof that if P ceases existing there can still be the possibility of Q existing? — Ignoro

I guess one way of approaching that would be to find a counter model. I read your assumptions as:

(1) P is not a necessary cause of Q. (Q happens only when P)
(2) P is not a sufficient cause of Q. (Q is forced by P)
(3) P is causally related to Q somehow.

Is there logical proof that if P ceases existing there can still be the possibility of Q existing? — Ignoro

I don't know precisely what you mean by "existing" there, but I'm going to interpret it in context as either:

(4a) P demonstrably having an effect on Q in some circumstance.
or
(4b) If P never existed regardless of its causal status and other relationships with Q, then Q would never occur.

Since (4a) is already implied by P (I think) being a contributory cause of Q (add the other contributing causes as part of the circumstance?), I'll deal with (4b) exclusively.

Which makes the whole argument of the form:

(1) P is not a necessary cause of Q. (Q happens only when P)
(2) P is not a sufficient cause of Q. (Q is forced by P)
(3) P is causally related to Q somehow.
to conclude
(4b) If P never existed regardless of its causal status and other relationships with Q, then Q could not occur.

So one plausible counter example is P=whether someone is a smoker and Q = whether someone has lung cancer. You can have lung cancer ( Q ) without being a smoker ( P ), so P is not necessary for Q. So that satisfies ( 1 ), similarly you can be a smoker without ever developing lung cancer, so that satisfies ( 2 ). ( 3 ) is obviously true too. But what about (4b)? This amounts to the claim that if there were no smokers, there would be no lung cancer - and surely that is false, cancer caused by anything can metastasise around the body, so Q can occur, so (4b) is false.

All the assumptions true, conclusion false. So yes, I think there is the possibility that Q "exists" if you somehow deleted P from existence.

leaving what counts as a causal relationship vague intentionally — fdrake

A wise man ... (Yes, I always read your inline notes.)

You did a very nice job lining up simple material conditionals to necessity and sufficiency. You avoided counterfactuals and you avoided the word "because", both of which take some fancy footwork.

It often seems to me that when talking about proximate vs distal causes, people implicitly recognize that the last member of the set to show up has the role of completing the set -- like a "tipping point" state in an election -- so that it's not just necessary like all the others but, when it's the only one we're waiting on, it takes on the sufficiency of the whole set. That means what people mean by "cause" is often expressed by a conditional that is backwards from what "if ___, then ___" suggests. (And this tends to lead straight to counterfactuals.)

And this shows up in a phenomenon known as "perfecting the conditional". There's evidence (at least I think there is!) that English speakers tend to hear statements like "I'll give you $10 if you cut my grass" as "I'll give you $10 if and only if you cut my grass".

(( I was planning on doing this one, when I could get a moment, but I'm glad you got to it before me because you did it better than I would have! ))

(( I was planning on doing this one, when I could get a moment, but I'm glad you got to it before me because you did it better than I would have! )) — Srap Tasmaner

Thank you!



Though in context I am left with the impression that my response will raise the probability of @Ignoro ignoring medical advice. Which should only be done carefully.

I will respond to you when I have the time to carefully read all of the responses, but I want to advance that the definition of contributory cause can be found in some articles, and it seems relevant for some sciences.

In a Wikipedia article about causation, there's a citation about an author that does formalize it. I found his book (The Cement of the Universe: a Study of Causation, Mackie), but reading it takes some time.

Causality in general is an informal concept. We have intuitions and practices related to causality; theories (plural) of causality attempt to capture some or most of those informal causal notions. You won't find the definition of contributing cause, because, depending on the theory of causality and what it seeks to highlight, it can be defined differently, if at all. Some philosophers are even skeptical that causality is a real thing, like Hume or early Russell ("The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.")

I feel that in putting formalism first you are approaching the problem from the wrong end. One needs to understand the problem before deciding which, if any, formalism is the most appropriate. With most situations with which we deal in our everyday life formalism is unhelpful: at best, it is just a long-winded way of stating what we already understand, and at worst, it can provide a false sense of certainty by cutting out genuine doubt through oversimplification and distortion.

You mentioned that you wanted to answer some real-life question. If you can paraphrase it without revealing personal details that you wish to keep private, it would be helpful to the discussion. But state it in your own words; formalism should come last in the analysis.

Very well, I will attempt to describe the situation.

After suffering a (mental) illness, I ended with fear of certain things. The doctor still consider I have the illness because I have this fear. However I see no sense in that, as the relationship between the illness (P) and the fear (Q) is 1. indirect (that I informally inferred from the word he used, that I will translate as "unchained", or as an "indirect consequence of a series of events") and, as a matter of fact (I didn't ask this, and as it a fact of the world, believe is the case), the illness is not necessary nor sufficient for the existence of the fear.

That is, as I see, the illness led to a state "similar to trauma" (paraphrasing my therapist), and the trauma itself is enough for the endured fear, and I see to logical need for the fear to be a sign of the illness (whose commonly listed symptoms don't include fear, and it may not even be present in some cases of this illness). Yet the specialist considers that the "parcial" part about the remission is the existence of the fear (I actually asked this).

Thus I seek to understand what kind of arguments the empirical sciences may have to stabillish a causation and existence chain in this kind of problem. The best bet I have is to ask and have a conversation, but nothing says I can't try to at least put my perspective in a better way than "it doesn't make sense". It is admitedly confusing, being a case where I have limited information.

See, fdrake, you was kind of right, but in a different way. I don't intend to just dismiss what he says, however.

In the way you put, I think that P is a risk factor to Q

(4b) If P never existed regardless of its causal status and other relationships with Q, then Q could not occur. — fdrake

But that I would say (4c) instead: that even if is not the case that P anymore (one is not anymore a smoker), Q can still be the case (one can have lung cancer).

The actual problem muddies this belief, because even if it seems a sure thing for me, it is not for the doctor. The actual example of lung cancer may not be ideal, as it is something we already have a belief regarding (4c). (Am I incorrect in is this last affirmation?)

So one of the things about logic is it is irrelevant to time. The premises state the facts as they are at a particular moment. If the facts change, then that is a different argument. — Philosophim

There is such a thing as temporal logic, though. Even if in this situation it doesn't apply, it considers time.

Oversimplifying it, I see as P -> R; R -> Q; but I still can't formalize it properly. I could try, and this is what I have come up with, but it could be wrong:

1. This illness (P) lead to some symptoms S1, S2... Sn.
2. S1 and external factor (E) lead to the initial fear (Qi)
3. Somehow all of this lead to "trauma" (T)
4. And T is a source of enduring fear (Q)

But it is just a guess, and may be more in the way than helping to understand it. I was on the assumption that limiting to the essencial premises would be more helpful. 2 and 3 are an extrapolation of the belief that Q can exist without P (whose symptom S1 doesn't exist anymore). It appears to be circular logic. I could complement it in this way:

1a. It not the case that S1 anymore
1b. It is the case that Q
1c. Thus, there is some factor causing Q that does not need S1 to be true in this moment. I attempted to write it as 2 and 3. I could also say "S1 ^ E -> T", which is simpler.

Already QED.

((P v ~P) ^ Q) => Q

It seems to me you're not actually looking for a proof in logic, but perhaps a negative proof that Q can exist absent P in fact. If in fact Q does exist absent P, then that's all you need. — tim wood

I'm under the impression that this is not sufficient as an argument for the doctor... It is a fact of the world that fear of "things" can exist without an illness, and that this illness does not always lead to fear. I could present this just to see his response.

-

Thank you misters, for the discussion, and forgive me for my confusion, I'm trying my best to understand this.

Edit: And I must mention. I don't want to burden members with a particular issue. Just to understand in a more abstract and generalist way a given problem.

Thanks for your candid explanation. As I suspected, what is at issue here is not the original question, which is easy enough to answer, but how you frame the question in the first place. The key contention here is empirical, not logical. The therapist thinks that the illness is the main reason for the persisting symptoms, with the implication that treating the illness would alleviate the symptoms. Your position is that the symptoms would likely persist with or without the illness, with the implication that the proposed treatment probably would not address the problem. (On a personal note, this situation is familiar to me, and probably to many others as well; even now I am in a similar situation of having to decide on a course of treatment, having consulted with a specialist.)

Unfortunately, this contention is not something that a formal logical analysis could resolve. Everything hinges on the two contrary judgements regarding "the facts about the world," as you put it.