# Constant conjunction of events and probability

Hume argued that it's impossible to say that event A causes event B. For all we know, everytime event B is directly followed by event A, we could be witnessing the "constant conjunction of events." Therefore, although we regularly rely on what we perceive to be causation in order to predict outcomes, those predictions do not stand on the same ground as things that are necessarily true by definition (e.g., 1+1=2).

However, would Hume concede that certain events have a higher probability of occurring based on past events? Is it much more likely that a rock will break a window when thrown with a certain force than not? Or is that a fallacious argument grounded in confusing the "constant conjunction of events" (of always seeing rocks break windows) with causality?

• doesn't 'constant conjunction' make for belief some things are more likely but it can't be "justified" rather than habitually held to? – user35983 Jan 2 '19 at 0:58
• Why would Hume have to "concede" it? It is his point that we assign the label of causality to conjunctions of events that are particularly common, but that this label has no self-standing referent in reality. In contrast, the traditional belief is that causality (as in natural laws) is objectively grounded in some form. – Conifold Jan 2 '19 at 23:41
• My question is simply whether or not saying certain events have a higher probability is compatible with the problem of induction. I can't say A causes B, but can I say the occurrence of A means there is a higher probability that B will follow? Based on the answer below, this is still consistent with Hume's argument. – user27343 Jan 3 '19 at 1:58
• Yeah, the standard terminology (along with a lengthy discussion) nowadays is en.wikipedia.org/wiki/Correlation_does_not_imply_causation (For the past thousand+ years, the monsoon season in India has occured several weeks after the flowers bloom in upstate NY. But that doesn't mean blooming flowers cause monsoons.) – user19423 Jan 3 '19 at 5:40
• Hume would concede nothing. But his thinking ultimately led to the notion that induction is a red herring. Consider Karl Popper (qv) and the notion that we should just go for systematically maximizing the probability of guessing right, instead of establishing facts at all. – user9166 Jan 3 '19 at 11:07

William Edward Morris and Charlotte R. Brown present a view of Hume's idea of causation that may help resolve the OP's question whether probability could justify causal inference through reason or understanding.

As the OP notes, effects are not necessarily true given past events believed to be causes of those effects. So, one cannot justify causal inference through relations of ideas, that is, there is no necessary connection between past events and future events.

To consider probability is to consider matters of fact rather than relations of ideas as a rational justification for causality. According to Morris and Brown, Hume also rejects matters of fact, that is, probability, as a rational justification for causal inference: (Section 5.1)

Hume argues that there is no probable reasoning that can provide a just inference from past to future. Any attempt to infer [a future prediction] from [a past experience] by a probable inference will be viciously circular—it will involve supposing what we are trying to prove.

Hume spells out the circularity this way. Any reasoning that takes us from [a past experience] to [a future prediction] must employ some connecting principle that connects the past with the future. Since one thing that keeps us from moving directly from past to future is the possibility that the course of nature might change, it seems plausible to think that the connecting principle we need will assure us that nature is uniform—that the course of nature won't change—something like the uniformity principle:

Establishing this uniformity principle is what prevents both relations of ideas (necessary truths) and matters of fact (probability) from providing a justification of causal inference using reason or understanding.

Hume offers "custom or habit" as alternatives to reason and understanding to explain why we make causal inferences: (Section 5.2):

Since we're determined—caused —to make causal inferences, then if they aren't “determin'd by reason”, there must be “some principle of equal weight and authority” that leads us to make them. Hume maintains that this principle is custom or habit:

They quote Hume:

whenever the repetition of any particular act or operation produces a propensity to renew the same act or operation … we always say, that this propensity is the effect of Custom. (EHU 5.1.5/43)

Here are the questions:

However, would Hume concede that certain events have a higher probability of occurring based on past events? Is it much more likely that a rock will break a window when thrown with a certain force than not? Or is that a fallacious argument grounded in confusing the "constant conjunction of events" (of always seeing rocks break windows) with causality?

Hume accepts "custom or habit". He does not accept probability through reason or understanding. That is, neither relations of ideas nor matters of fact (probability) provide a rational justification for causal inferences.

Morris, William Edward and Brown, Charlotte R., "David Hume", The Stanford Encyclopedia of Philosophy (Spring 2017 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/spr2017/entries/hume/.

• Thank you for this thorough response. The first answer disagrees with yours, but I believe this is correct. I'm a little confused on the uniformity principle. If nature is uniform – and the course of nature won't change – does that mean the past is identical to the future? But then it says that "establishing the uniformity principle" is what prevents necessary truths and probability from providing a justification for causality. I thought it would be the opposite. In other words, supposing nature is uniform is necessary to establish causaliity. – user27343 Jan 3 '19 at 21:42
• @user27343 I think Hume is claiming he needs to derive the uniformity principle from either relations of ideas (necessity) or matters of fact (probability), but he can't and so he claims it comes from causal determinism through custom. I don't think he is right here. The uniformity principle is questionable given the big bang and so is causal determinism given quantum physics, but his criticism of causal inference seems correct coming from Aristotle's distinction of knowledge and belief. – Frank Hubeny Jan 4 '19 at 4:43
• I looked up the uniformity principle and think I understand it now. Induction relies on the uniformity principle being true, and the uniformity principle relies on induction to be sound (circular argument). However, what do you mean about the uniformity principle and the big bang? As far as quantum mechanics, my understanding is that although uncertainty is inherent in nature, we can still predict the location of an electron from "statistical laws based on probability." Don't those laws still rely on induction? Doesn't all of science rely on induction? – user27343 Jan 4 '19 at 6:43
• @user27343 The big bang suggests there may be a beginning to this uniformity which would undermine the uniformity. The only thing that quantum mechanics would potentially undermine is the causal determinism that Hume also supports. I think he would be called a compatibilist with regards to free will. We can still make predictions as you mention. I may ask a question of my own about Hume's determinism. He doesn't want to accept the uniformity principle, but seems justified in accepting causal determinism. But that's for later. – Frank Hubeny Jan 4 '19 at 17:13

According tor David Hume :

our awareness of causation (or power, force, efficacy, necessity, and so forth - he holds all such terms to be equivalent) is a product of experience [...]

what this awareness consists in ? What is meant when some event is judged as cause and effect? Strictly speaking, for Hume, our only external impression of causation is a mere constant conjunction of phenomena, that B always follows A, and Hume sometimes seems to imply that this is all that causation amounts to. (And this notion of causation as constant conjunction is required for Hume to generate the Problem of induction .) Nevertheless, ‘causation’ carries a stronger connotation than this, for constant conjunction can be accidental and therefore doesn’t get us the necessary connection that gives the relation of cause and effect its predictive ability. We may therefore now say that, on Hume’s account, to invoke causality is to invoke a constant conjunction of relata whose conjunction carries with it a necessary connection.

For Hume human reasoning involves only relations of ideas and matters of fact. Matters of fact can be either particular specific observation or

Claims about states of affairs not directly observed.

[These ones] would include both predictions and the laws of nature upon which predictions rest. We cannot claim direct experience of predictions or of general laws, but knowledge of them must still be classified as matters of fact [i.e. empirical].

All predictions must involve causality and must therefore be of [the above] category. But what justifies them?

This is the gist of so-called Humean Problem of induction.

The probabilistic approach is for sure one of the candidate answer to the problem.

• Thank you. Just to make sure I understand that article correctly. I can't say A causes B, but I can say the occurrence of A means there is a higher probability that B will follow if based on previous observations B has consistently followed A? – user27343 Jan 3 '19 at 2:06
• @user27343 - Exactly. The issue is that we think to causality in terms of "necessity", while an empirical established correlation may be contingent. – Mauro ALLEGRANZA Jan 3 '19 at 9:10