Why Correlation Does Not Imply Causation
Does 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
Types of Causes for 'X is the cause of its effect Y':
A cause (X) can be either of the following four options:
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:
etc.
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.
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.
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.
etc.
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.
Comments (77)
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.
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).
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.
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.
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.
: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.
Perhaps I mean necessity in a special sense, where x is necessary for y.
In that sense your post is necessary for me to to reply to it!
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.
I wonder if we need the rather unsatisfying and untidy family resemblance idea when my idea works perfectly well and appears more parsimonious?
Can you think of a case where my idea doesn’t hold?
I did.
My post cause your reply, without necessitating it.
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.
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.
Is it that in any possible world, if event A happens then even B also happens - we say A causes B?
But there are possible worlds in which you did not reply to my post, and yet we say that my post caused your reply.
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.
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?
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" (??????, 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
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.
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.
Correlation [math]?\to[/math] causation. Would you agree?
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.
Quoting Bartricks
Quoting 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.
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.
You think a random collection of claims constitutes an argument!
Quoting god must be atheist
HOw condescending. Who do you think you are? Let other people make their own decisions. Christ.
Quoting 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.
Thanks for the warning! I'm optimistic that Bartricks will home in on the point he's making.
They're from symbolic logic where [math]\to[/math] = implies/entails.
And why did you use symbols and not words?
Not anymore! Danke!
Nope I don’t think I know Karlen, but if he’s been mistaken for me he must be very handsome ;)
I was tryin' ta make sense of your claim that correlation [s]entail[/s] implies causation. That be all to it mate!
Correlation does not entail causation. But it does imply it.
Just my two cents: correlation does not imply causation, but it doesn’t imply NO causation either.
I always jump into conclusions, 75 percent of the times too early and without enough warrant... my apologies.
I surmise now that you were referring in the third post here to another script somewhere on the site that had been written by you.
Surely it implies causation, though does not entail it. On what other basis does one infer causation's presence?
Note, I am not saying that we always infer causation - we are, in our own case, directly aware of it (I am directly aware that I am causing my intentions, for example). But when it comes to the external world, we posit causal relations to explain correlations.
Well now I’m not sure if either it is you or I that has a non-standard understanding of ‘implies’.
I am using ‘implies’ to mean that something necessarily follows from something else. But I think you are using ‘entails’ to say the same.
You seem to be using ‘implies’ to mean something like ‘gives some evidence for’ which doesn’t seem strong enough.
Do you have a source for this? I would use entails and implies as synonyms.
I ask because a cursory search appears to confirm my intuition.
Imply does not mean entail.
Infer does not mean imply
Refute does not mean deny
Raise the question does not mean beg the question
Disinterested does not mean uninterested
And so on.
Now, why would you want me to provide you with a source, when you can't even perform a simple google search? You're dishonest, no? You want me to take the time to provide you with a source for something that you could discover by a simple search (or by simply taking down the dictionary), and that you are then going to check out that source and read it, yes? That's what you want me to do - to provide you with a source that you're then going to hunt down and read, yes? You're going to do that. You can't do a google search. But you want me to provide you with a source that you're then definitely going to go away and read?
Paris is the capital of France. "Can you provide a source on that, because I think Canberra is".
Do a google search or, you know, go back to school and pay attention this time around.
I’ve obviously upset you but when I google I am not bringing up the same information that you are. I’m not trying to be difficult I’m just curious where you’re getting your information. I suspect it might be wrong.
Bartricks is using the everyday, unwashed-man-in-the-street definition of "implies". From Oxford Languages ,
Invizzy is using the definition of "implies" from logic, also called the conditional. It is a much stronger relationship. In logic, if A implies B, then the truth of A guarantees the truth of B.
Since philosophy tends to favor logic, I think the stricter definition must win out, unless specified otherwise.
Oh that makes so much sense when you put it like that. I don’t know why I missed that version of implication in my internet search though. Sorry @Bartricks!
I have to say that those who say ‘correlation doesn’t imply causation’ are using the formal sense as far as I can tell!
Yeah, this also happens every time a non-math person starts a math thread on TPF. As much as you try to clarify the mathematical definitions for them, they keep insisting on their own folk-wisdom interpretations. So you go round and round and get nowhere.
What am I implying about you? Or, to put it another way, what am I entailing about you? That makes sense, doesn't it?
What do you say when you want to express the idea that something is suggested, but not entailed? What word?
Careful. Nailing Bartricks to see his own contradiction is like trying to nail a bit of liquid quicksilver to the wall.
Like I said, Bartricks is illogical, and has a tendency to make no sense, but in such a provokative way, that people will be drawn into arguing with him.
One of the tricks Bartricks uses is "So you are saying that (x)?" where you never said x, but maybe something similar, but sufficiently different from what Barticks claims you said so you feel compelled to clarify it for Bartricks. Then the cycle repeats. Please do NOT believe me on face value, just because I said so. But do remember later down the road that I warned you, Real Gone Cat and invizzy.
Er, no. Just to be clear - you're someone who thinks this -
1. God is not evil.
2. God did not create evility.
3. Humans have free will and they created evility with their moral displestitude.
4. The devil exists.
is an argument! Presumably you think shopping lists are arguments. And windows. And tuesday.
It does not entail it. But it does imply it.
If, when you say "correlation does not imply causation' you mean 'correlation does not entail causation' then you are a) misusing the language and b) saying something incredibly banal that isn't worth saying.
Speaking for myself, I've made it clear that there are two uses, or meanings, for "implies". One meaning is "suggests" (Those dark clouds imply rain.). The second meaning is "necessitates". The second meaning is a stronger relationship. This second meaning is also known as Logical Implication
Since we use logic to construct our arguments (or should), logical implication is always meant when using "implies" in an argument. Otherwise, modus ponens would have been abandoned millenia ago.
Now, if you so desire, you can reserve "implies" for the looser definition (suggests) and employ "entails" for the stronger definition (logical implication), but none of your listeners will know you are doing this until you tell them.
The problem for the OP has to do with another word. The OP confuses the reader by using "cause" as a noun and "cause" as a verb without distinguishing between the two. As a noun, it is true that there are necessary causes and sufficient causes. But as a verb, "cause" indicates logical implication, i.e., the antecedent is sufficient for the consequent.
Have you ever said "what are you entailing?" When someone says something that implies you are full of something?
Now, when someone says 'correlation does not imply causation'what do you think they mean?
Do tell.
And do you agree that the claim that correlation doesn't entail causation is so mindnumbingly banal that no one in their right mind would make it?
I’m pretty sure that the strong ‘entail’ version is PRECISELY what people mean when they say correlation doesn’t imply causation.
Now it’s said so often because it is true. Unarguably true. But I don’t think it’s quite ‘banal’. It’s a point about not being able to draw causation purely from statistics. You need causal models or something else to do thst.
I don't think I've ever used the word "entail" in my life.
Have you? [Hint : review this topic before you answer]
I'm sure there's a Logic for Dummies out there. Please find it.
Imply does not mean entail. It means suggests. Whereas if something is entailed there is no suggestion at all - it occurs or follows. And that is how you use it. Yes?
And when someone says correlation does not imply causation that is how they are using it.
And that is also how you used it, because you are continuing to thing that statistical correlations do not imply causal links, even though they do. They just don't entail them, that's all.
Correlation DOES imply causation.
Correlation does not ENTAIL causation
The latter is not worth saying. By contrast, if correlation doesn't imply causation that would certainly be worth saying as if true as then we would have to deny the presence of all causation apart from that which we directly experience in the form of our own willings.
"Implication" as in "material conditional" corresponds to a certain type of truth-functional relation between the antecedent and the consequent:
Accordingly "Correlation Does Not Imply Causation" simply means that one can have "correlation" (A="E1 is correlated to E2" is true ) but not "causation" (B="E1 is causing E2" or "E2 is causing E1" are false). Here some examples: https://wikimili.com/en/Correlation_does_not_imply_causation#Examples_of_illogically_inferring_causation_from_correlation
Are you entailing that invizzy was wrong or that I was wrong? Which one - which one are you entailing?
Tell me, Neomac, when someone says "correlation does not imply causation" what do you think they mean? Do you think they mean that it does not entail it, or that it does not imply it?
Psst: it's the latter. And it is false. Yes? It's false. It DOES imply it.
It doesn't ENTAIL it.
It does IMPLY it.
Such a statement about causation would be the formal ‘entail’ sense of the word. One would only really use imply as a synonym for‘suggest’ if a PERSON was doing the implying, not when state of affairs implies something.
You know as well as I do that you meant by imply, imply - that is, suggest. And that's what everyone else means when they say 'correlation does not imply causation'. And they're wrong. It does imply it.
I'm not sure which of my uses of 'imply' you're referring to, but it doesn't matter as I've been very consistent in using it as a synonym for 'entails'. That's because I / we are talking about correlation implying something. Correlation isn't a person so it can't be said to imply something in the 'suggest' sense of the word, it implies in the formal 'entails' sense.
I can absolutely tell you that correlation does not imply causation because a standard reading of that claim would tell us all correlations are instances of causation. I know you don't believe that, so I must insist you switch to a standard use of the words: suggest for when people imply and entails for when states of affairs imply.
@Bartricks's having a lend of you all. Stop feeding him.
implies[sup]2[/sup] = entails (to use the terminology being used in the thread so far)
It is precisely because correlation implies[sup]1[/sup] causation that it's important to keep in mind that correlation does not imply[sup]2[/sup] causation. It's not banal, as Bartricks has claimed.
By the way, and roughly speaking, I think implication in logic is something that happens within statements (if then), whereas entailment happens within arguments, that is, between sets of statements and a conclusion.
Don't waste your time with Bartricks.
I'd agree (except that "implies2" != "entails" see below)
Quoting Jamal
I agree on that too, but I would elaborate further as follows. The notion of "entailment" has broadly to do with semantics, while "implication" in formal logic is just a certain type of truth-functional operator (namely expressing a certain combination of truth conditions as in the "material conditional"). So when we deduce a conclusion from some premises (like in propositional logic by using logical connectors like "if/then", "and", "not", "or", etc.), one can claim the conclusion is "entailed" by the premises, when the truth-functional meaning of the logical connectors (independently from the actual/full meaning of the terms they combine) ensures the truth of the conclusion. In conclusion, while the "entailment" expresses a semantic link between terms, "implication" doesn't express any such link.
Yup. Been making the same point, difference being I ...
Pretty much in agreement, but I think you're splitting hairs a bit finely here. The statement [math]A\Rightarrow B[/math] carries within it the modus ponens argument. [Isn't modus ponens just one row of its truth table?]
Unless you're reserving "implies" for the form of the argument, and "entails" for an instantiation. (Still too delicate for my tastes.)
Why say many words when a few will do just fine
Alas, 'tis the power of condensing information with big impact into a little box".
Hahaha. Almost missed this one.
This cat person has feelings, you know. Your callous dismissal wounds me. Cannot cat people bleed?
From now on, I would prefer if you referred to me as Mr. Real Gone Cat. We are not friends, sir. Good day.
And you can refer to me as Dr Bartricks.
Correlation, let's remember, does imply causation.
It doesn't entail it.
It does imply it.