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Karlen Karapetyan
4Does correlation imply causation?
The questions below regard the main source material discussed in this paper and available on wikimili.com, titled "correlation does not imply causation": This paper borrows from the source material and is in part a summary of what I learned from the source material:
https://wikimili.com/en/Correlation_does_not_imply_causation
Consider the following questions that I have come up with from reading the source material. I am still learning this material, and so I would appreciate informed responses, since I need help understanding these questions too, and I humbly seek to share my knowledge and gain knowledge. I would appreciate your answers.
Questions
- What are the sufficient conditions for causation?
- What are the necessary conditions for causation?
- What types of causes exist? Necessary? Sufficient? Both? Neither?
- Is correlation sufficient to establish that X causes Y?
- Is correlation necessary to establish that X causes Y?
- If correlation is not sufficient, then what is a sufficient condition for causation?
- If correlation is a necessary condition for causation, then what else is necessary?
- Is a perfect correlation between X and Y ever sufficient to demonstrate causation? What if the coefficient of determination is a 100%? Note: coefficient of determination is a measure of the best fit of correlated data (i.e., the strength of the correlation)?
- Does a perfect correlation prove causation?
- Does a perfect correlation even count as evidence towards establishing causation?
Types of Causes for 'X is the cause of its effect Y':
A cause (X) can be either of the following four options:
- Necessary Cause
- Sufficient Cause
- Both a Necessary and a Sufficient Cause
- Neither a Necessary nor a Sufficient Cause
A cause can be either of the following types:
(1). Necessary Cause:
If X is a necessary cause of Y, then the presence of Y necessarily implies the prior occurrence of X. Note, the presence of X does not imply that Y will occur.
(2). Sufficient Cause:
If X is a sufficient cause of Y, then the presence of X necessarily implies the subsequent occurrence of Y.
(3). Necessary & Sufficient Cause:
The cause X and the effect Y can only either occur together or fail to occur together.
(4). Neither Necessary Nor Sufficient Cause: Contributory Cause (Factor)
A contributory cause is not implied to be necessary, though it may be so. A factor being a mere contributory cause implies that it cannot be sufficient; if it were sufficient it would not be considered a mere contributory cause.
The following approaches to analyzing causality exist in contemporary philosophy:
- Empirical Regularity: constant conjunctions of events.
- Probabilistic: changes in conditional probability.
- Counterfactual: counterfactual conditions (conditionals with a false if-clause)
- Mechanistic: mechanisms underlying causal relations
- Manipulationist: invariance under intervention.
According to the counterfactual view of causality, X causes Y iff without X, Y cannot be. It can be stated that X causes Y iff the two events (X,Y) are spatiotemporally conjoined, and X precedes Y.
How can one demonstrate a cause and effect relationship between X and Y; such that X causes Y, where X is the cause (event), and Y is the effect (event)? Demonstrating causation is proving the existence of a cause (X) and effect (Y) relationship: demonstrating a causative link and its direction.
"Correlation does not imply causation" means there is no way to legitimately deduce (i.e., derive) a cause and effect relationship between two variables X and Y solely on the basis of an observed association or correlation between them, no matter the strength of the correlation. Correlation alone cannot be sufficient to establish a cause and effect relationship (i.e., to demonstrate causation); more is required to determine which of X and Y is the cause and which the effect (i.e., the direction of causation). Correlation furthermore cannot imply causation because what are thought to be the cause X and the effect Y are actually effects both caused by another variable Z.
Correlation cannot possibly materially 'imply' causation because 'material implication' is necessarily a deductive process that sets up a sufficient condition: P -> Q: ("If P then Q"): 'P materially implies Q' logically implies that P is a sufficient condition for Q and that, likewise, Q is a necessary condition for P.
A demonstration of causality seems to require synthetic-empirical knowledge; meaning: knowledge that is not true merely by virtue of its meaning and is a-posteriori (i.e. empirical).
What is Causality? How can one demonstrate that 'X causes Y'?
Correlation is a necessary condition for causality, not a sufficient condition! Correlation is not sufficient to demonstrate causality, no matter how strong the correlation between X and Y, because just because X and Y co-occur does not excluded the possibility that both X and Y are caused by a third variable Z.
Moreover, from the mere fact that X and Y co-occur one cannot deduce (deductively derive) the direction of causation from X to Y or in reverse; that is, correlation can never be sufficient to determine which one of the variables X and Y is the actual cause and which the effect.
The following causal relations exist between two events (X, Y), some such that exactly one of X and Y is the cause, and the other the effect called direct and reverse causation. Furthermore, there is a relation between X and Y such that neither X nor Y is the cause (in the case where both X and Y are the effects of a common cause Z), and the option in which both X is the cause of Y and (simultaneously) Y is the cause of X, where both X and Y are individually both the cause of the other and the effect of the other.
- H0: The Null Hypothesis: There is no connection between X and Y, called: coincidental correlation.
- H1: Direct Causation: "X causes Y"; let this direction of causation be henceforth 'forward'.
- H2: Reverse Causation: "Y causes X"; the reverse of 'forward' (i.e. the "converse").
- H3: "X and Y are both caused by a third variable Z".
- H4: Bidirectional Causation: "X causes Y" and "Y causes X". When X and Y cause one another, simultaneously, at the same time, in the same sense, it is referred to as bidirectional causation. Otherwise, if 'X causes Y' and then 'Y causes X' and so forth, then this type of causation is called cyclic causation.
What is the difference between "X implies Y" and "X causes Y"?
(What is the difference between implication and causality?)
A material implication holds between X and Y iff X materially implies Y. Therefore, "If X, then Y" is a material conditional ("if-then") statement that only fails to hold true for a true 'if-clause' (X) and a false 'then-clause': that is, a true antecedent X cannot materially imply a false consequent Y. It is an implication of the material conditional 'X -> Y' that X is a sufficient condition for Y.
This is in essence the most important things that I have studied regarding whether correlation implies causation, a topic of philosophy of science, and comes up in statistics too. My positions are not proclamations of absolute knowledge or certainty, nor are they proclamations of truth, but rather my tentative, provisional. subject to revision conclusions that I have arrived at (thus far). I have posted this paper to probe my understanding of the subject matter. I would appreciate if people were kind enough to identify mistakes and offer corrections. My aim is the impartial quest for truth. -
tim wood
9.3kAh, now please complete your post with a short paragraph telling us what (a) cause is. Back when we all had paper dictionaries, cause took up a lot of column inches because it's not-so-simple. For present purpose, that you or I might agree with or subsequently adjust or refine, what do you say it is? -
invizzy
149I was previously using sufficient / insufficient and words to frame causation, but now I wonder if it is better framed in terms of specific and general.
It seems that a lot of words have a specific and also a general use. ‘A spark’ can refer to a specific spark and a spark more generally, for instance.
I think an (efficient) 'cause’ is simply when something specific is necessary for something else specific. I know this sounds far too simple but have a think about it.
If we want to say that a specific spark is necessary for a specific fire to exist we say: ‘a spark caused a fire’. This distinguishes from the claim that ‘a spark’ in general is necessary for ‘a fire’ in general (which appears not to be true).
The fuel and the oxygen are also necessary for the fire, so why aren't they causes? Well fuel in GENERAL is necessary for fire in GENERAL (you don't need any particular fuel, any will do, same for oxygen, and both these are needed for any fire).
We know smoking causes cancer - but here not just any smoking is necessary for any cancer. ‘Causes’ is simply the plural of the case where specific smoking (from one person) triggers specific cancer (in the person smoking).
So 'cause' is really performing a grammar role here rather than talking about a relationship between two things. -
invizzy
149
I'm actually well versed on these as it happens.
The fact is it is still an open question about what causation is. My ideas are closest to Mackie's INUS conditions, but I think this improves on them. He thought the conditions didn't work for general cases, but I'm saying 'cigarettes cause cancer' is NOT a general case (in some sense). -
Gnomon
3.8k
Your well defined, but complex, post goes over my philosophically untrained head. But I will comment on one facet of the Causation question that I am somewhat familiar with. In the pre-scientific era : the implication that an object in motion could cause another object to move was intuitive (e.g experience with billiard balls). But the the observers had no idea how to explain mechanical transfer of motion between objects. An ancient word for invisible causes was "Spirit" (wind or breath). So, the implication was that some invisible "ooomph" was transmitted from the moving object to the stationary object, forcing it to move in the same direction. Today, we use the words "Energy" and "Force" to explain the transmission of unseen "momentum" from the kinetic object to the static object. But all of those "ooomph" words describe a mathematical relationship, not a material substance that can be off-loaded from one carrier to another.(What is the difference between implication and causality?) — Karlen Karapetyan
The causal relationship between Kinetic & Static is so reliable, that we would be surprised if the cue ball struck the eight ball, and suddenly stopped dead, with no corresponding acceleration of the the struck ball. Where did the "oomph" go? Due to our intuition of cause & effect we have come to expect Action & Reaction to be joined at the hip (Necessity is implicit). That is the ancient belief we call "Causality". But scientists have since explained the causal mystery in terms of Mathematical ratios instead of Material substances. Momentum is not a load of stuff carried by moving objects, but a dominant/submissive relation between primary Action and secondary Reaction. However, we can now explain Causation in terms of Information Theory.
Metaphorically, the active partner in this exchange issues a coded command (kinetic energy) and the passive partner (static Mass) obeys, by shouldering the original Power Load (momentum) and transporting it in a direction & velocity that is proportional to the relative powers of Dominant & Submissive agents. In this case, the Load (or Charge) is not material stuff, but immaterial (mathematical) Information about the relative interrelationship. To view Causation in terms of Information Theory is a novel concept, but has been demonstrated experimentally. :smile:
Causal Force :
As we experience enough cases of a particular constant conjunction, our minds begin to pass a natural determination from cause to effect, adding a little more “oomph” to the prediction of the effect every time, a growing certitude that the effect will follow again. It is the internal impression of this “oomph” that gives rise to our idea of necessity,
https://iep.utm.edu/hume-causation/
Information transfer is the way information is turned into a code and transferred from one place to another.
https://www.generationgenius.com/information-transfer-lesson-for-kids/
Energy transformation, also known as energy conversion, is the process of changing energy from one form to another. In physics, energy is a quantity that provides the capacity to perform work or moving, or provides heat. ___Wikipedia
Information to Energy conversion :
We briefly review the first experimental demonstration of Maxwell's demon of Szilard's engine type that converts information to free energy.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4629685/
EnFormAction : the power to cause change of form, or motion
Form : a pattern by which we recognize & define objects in the world. -
invizzy
149I still haven’t seen a convincing argument against my idea of causation!
A cause is necessity between particular things.
We need, though, to explain what I am referring to by ‘particular’ things.
A lot of words can have both a general and a particular ense. ‘A spark’ can refer to a bit of flammable material at a particular time and place. But ‘a spark’ can also refer to ANY thing that is a spark, not just a particular one.
When we say ‘a spark causes a fire’ we mean that a particular spark is necessary for a particular fire.
The classic argument against necessity as causation is that things like oxygen and fuel are necessary for the fire too, yet we wouldn’t say oxygen caused the fire, or fuel caused the fire.
Yet we have a handy answer for this: no particular oxygen is necessary for the fire (it can be any oxygen), and no particular fuel is necessary for the fire (it can be any fuel).
Note that the question of ‘what sorts of things are causes’ leaves us with a broad conception: events, actions, things can all be actions. It is necessity that is the common factor. -
Banno
25.3kI still haven’t seen a convincing argument against my idea of causation!
A cause is necessity between particular things. — invizzy
:wink:
Really?
There is no necessity for you to reply to my post - this post. There are possible worlds in which you choose not to reply.
Yet should you reply, your reply is caused by this post.
Therefore there are causes that are not necessitated. -
Banno
25.3kI suspect its more that causation has no specific sense of the sort posited - it's rather a family resemblance, sometimes necessity, sometimes implication, sometimes mere correlation.
Counterfactual accounts become overly complex very readily, but regularity and inference seem inadequate. I sometimes puzzle over whether cause is a mere attribution under a description rather than something physical. , neat OP. But I suspect it will reach aporia. -
invizzy
149
Sorry, perhaps I was unclear. I don’t mean necessary in the sense that things necessarily happen (as you say possible worlds seems to imply that very few things necessarily happen).
I mean necessary in the sense that the cause is necessary for the effect, with the added condition that both cause and effect are particular things rather than general things.
Your particular post was necessary for my particular reply therefore the post caused the reply. -
invizzy
149
No sorry, I meant to correct myself. I would like to retract the ‘necessity between particular things’ bit.
Think I misspoke.
The claim is simply that a cause is a particular thing that is necessary for another particular thing.
It seems to me any counter example can be explained by the fact that either the proposed cause is not necessary for the effect, or that the proposed cause or effect are general things rather than particular things. -
invizzy
149Is it that in any possible world, if event A happens then even B also happens - we say A causes B? — Banno
No that’s not my claim.
It’s actually more simple than that. There can be all sorts of reasons that one thing is necessary for another. In the case of the reply your post is necessary so that I can know how and when to reply.
A spark might be necessary for a fire because fires require heat to start. The dropping of a vase might be necessary for a vase to break because it needs momentum when it hits the ground, that sort of thing.
But to be clear, it’s not being necessary that makes something a cause, it’s the fact that one thing is necessary for another and that they are both particular things. -
Gnomon
3.8k
I'm not an Aristotle scholar. But, I assume you are using "necessity" in the Aristotelian sense of a lawful relationship (metaphysical connection) between objects that results in physical change. This seems to be a specific case of Ari's notion of a natural "place" for everything --- perhaps a primitive notion of gravity/mass. Some things are naturally superior (gravitas) to others, and possess more inherent force or power, to rule subordinate things. This concept was later applied to the divine (natural) right of Kings & Nobles to govern lesser beings. The "necessary" ruler/ruled relationship was inherently metaphysical, even though it was sometimes enforced by physical compulsion. So, is your "necessity" a metaphysical concept or a physical law -- which are historically related*1?I still haven’t seen a convincing argument against my idea of causation!
A cause is necessity between particular things. — invizzy
In a post above, you seem to imply that Causation itself is "a thing". If so, is it a physical object or a mathematical (metaphysical) ratio between Cause & Effect, mover & moved, ruler & ruled? In physics, the necessity of Cause & Effect is limited by the Space-Time "light cone", which is set by the speed of Light (photons ; particular things), which are particles or waves that propagate causal Energy from one place-time to another. In which case, the speed limit of Light is essentially a Natural Law governing Causation, and Necessity Relations.
As I understand it, in the Aristotelian model of Necessity, the First Cause (Prime Mover) of Nature is also the Final Cause of all natural events. And any intermediate Effective causes (energy ; force : momentum) are essentially agents of the ultimate cause. This is a teleological notion, which indicates that causal events are Necessary due to their subordinate relationship to the Ultimate Authority of the Prime Cause. But Hume denied that human induction (from objective observation) could logically infer an unbroken (necessary) chain of causation from First to Final causes. Is that an argument against your idea of causation, or merely missing the metaphysical point? :smile:
*1. Divine Natural Law :
While our main focus will be on the status of the natural law as constituting the principles of practical rationality, we should consider for a moment at least the importance within Aquinas’s view of the claim that the natural law is an aspect of divine providence.
https://plato.stanford.edu/entries/natural-law-ethics/
*2. Causal Agent :
Aristotle defines the agent or efficient "cause" (κινοῦν, kinoûn) of an object as that which causes change and drives transient motion (such as a painter painting a house) (see Aristotle, Physics II 3, 194b29). In many cases, this is simply the thing that brings something about.
https://en.wikipedia.org/wiki/Four_causes
-
Cuthbert
1.1kIs a perfect correlation between X and Y ever sufficient to demonstrate causation? — Karlen Karapetyan
No: at least, not of X by Y; nor of Y by X. X and Y might each be caused by Z. If an animal has a heart then it has a liver and if an animal has a liver then it has a heart. But the liver is not caused by the heart and the heart is not caused by the liver. -
Bartricks
6kCorrelation does imply causation.
I flick the switch. The light comes on. That keeps happening. The reasonable conclusion is that there is a causal relation between my flicking the switch and the light coming on.
Objection: but there are cases of correlation without causation.
Reply: yes, but 'imply' does not mean 'entail'. if one thing is correlated to another, then it is reasonable to suppose there is an explanation of this and that explanation will cite causes. -
god must be atheist
5.1kKarlen and invizzy: are you one and the same person, with two identitties on this site?
It does not matter to me if you are, but to the organizars and the owner of this site it does.
Since I also have to say something about the topic: causation is inseparable by logical means from coincidental repetitions. Your choice to believe either. Nobody will ever prove it one way or another.
The best we can do is assume (not know!) that all repetitives are caused, until one or more exceptions occur. This is Topper's (?) test of scientific fallibility.
If you can't accept my proposition, so be it; I can't prove it. -
god must be atheist
5.1k
Correlation does imply causation. — Bartricks
To A. Smith: if you think you can get Bartricks to agree with anything, then you set yourself up to a Gargantuan task. Moses could get water out of a rock for his people in the desert by simply asking, and rather convincingly. Moses himself could not squeeze an agreement out of Bartricks, in my opinion.Correlation ?→?→ causation. Would you agree? — Agent Smith
Karlen: please ignore Bartricks. In my opinion he or she is nothing on this site but an angry, cantencerous, and hugely illogically thinking naysayer. His biggest and only quality contributions on this site is the word choices and phrases he uses to berate and dery his conversations partners.
Of course you don't have to believe me. Please check Bartrick's history of posted material on this site, which will be more amusing than enlightening, but certainly informative.
P.s. I harbour no more ill feelings for Bartricks; I did have some difficulty dealing with him in the early days of my existence here. I do warn new users, however, and that is the only purpose of this post, to make you to be wary of his antics. -
Bartricks
6kTo A. Smith: if you think you can get Bartricks to agree with anything, then you set yourself up to a Gargantuan task. Moses could get water out of a rock for his people in the desert by simply asking, and rather convincingly. Moses himself could not squeeze an agreement out of Bartricks, in my opinion. — god must be atheist
You think a random collection of claims constitutes an argument!
Karlen: please ignore Bartricks. In my opinion he or she is nothing on this site but an angry, cantencerous, and hugely illogically thinking naysayer. His biggest and only quality contributions on this site is the word choices and phrases he uses to berate and dery his conversations partners. — god must be atheist
HOw condescending. Who do you think you are? Let other people make their own decisions. Christ.
P.s. I harbour no more ill feelings for Bartricks; I did have some difficulty dealing with him in the early days of my existence here. I do warn new users, however, and that is the only purpose of this post, to be wary of his antics. — god must be atheist
Oh yeah? SO that post was what, then? That was an expression of ill feelings. You really are a very confused person. Confident, condescending and confused. The four cs. -
Agent Smith
9.5kCorrelation ?→?→ causation. Would you agree?
— Agent Smith
To A. Smith: if you think you can get Bartricks to agree with anything, then you set yourself up to a Gargantuan task. Moses could get water out of a rock for his people in the desert by simply asking, and rather convincingly. Moses himself could not squeeze an agreement out of Bartricks, in my opinion. — god must be atheist
Thanks for the warning! I'm optimistic that Bartricks will home in on the point he's making. -
Agent Smith
9.5kI don't know what that means - what do the arrows mean? — Bartricks
They're from symbolic logic where = implies/entails. -
Bartricks
6kDo you think implies means the same as entails?
And why did you use symbols and not words? -
invizzy
149
Nope I don’t think I know Karlen, but if he’s been mistaken for me he must be very handsome ;)
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