# Causality vs. implication

Implication is said to be more general than causality since, for example, being a dog implies being a mammal but it doesn't cause it. Is there a formalization of the difference between implication and causality (in the field of metaphysics or philosophy of logic)? What criteria could one use?

Implication and causation are relations between different kinds of terms. Implication is a logical relation, holding between propositions, or declarative sentences. Fido is a dog (proposition), all dogs are mammals (proposition), therefore Fido is a mammal (proposition).

Causation is a real relation, holding in the world, outside language. Causation is a time-related relation, because it is relates changes. Causation is relevant only where there is change (so, for example, there is no causation in mathematics). I throw the switch, subsequently the light goes on. One change (switch off -> switch on) caused a subsequent change (light off -> light on).

Implication is explained by laws of logic (e.g. modus ponens). Causation is explained by laws of nature (e.g. laws of electricity).

• Propositions aren't terms. Jun 1 '15 at 17:02
• @Atamiri Yes, they are. The thing is that I used here the word 'term' in a different sense than the one you seem to think about (the linguistic). One of the senses of 'term' is "end point", as in "bus terminal". There is an old philosophical sense of 'term' according to which the "terms" of a relation are the things that are related by the relation. A relation is compared to a line connecting two points. These two end-points, the terms, are what the relation relates. And since in my answer I talk of a (logical) relation between propositions, these propositions are its (the relation's) terms. Jun 2 '15 at 8:38
• My context was formal logic, where propositions aren't terms. Jun 2 '15 at 11:43
• @At Doesn't matter. Just understand what I meant by the word 'term'. Jun 2 '15 at 12:13

Implication is a relation on statements. Causality is a relation among facts in a world (perhaps the real world, perhaps a possible or hypothetical one).

Causality is notoriously tricky to define and pin down. (For example, in a deterministic world, does it make sense to even talk about causality, since given an initial condition there is no other way any event could possibly have been?)

Implication, on the other hand, is really easy to define: statement A implies statement B in all cases except when A is true and B is false.

But this is emotionally unsatisfying because it doesn't match up with our intuitive sense of implication ("I want to know that B is true because A is true"). Well, I can't help you there. That's just what the word means. Totally unrelated statements imply each other. False statements imply everything. I'm really glad that false statements don't cause everything.

• Ok, so generally in the case of causality the predications have to be related somehow. Makes sense. Material implication is indeed a bit weird from the standpoint of common sense reasoning. Jun 1 '15 at 15:53
• @Atamiri Even if we restrict both implication and causation to real events, and make implication semantic (e.g. undefined when the premise is false) there is still a difference. It is often said that even perfect correlation does not imply causation, and Romans had a quip post hoc, non propter hoc (after it, not because of it). Two events can be perfectly correlated without causing each other, e.g. if they have a common cause that always forces both. Relationship between correlation and causation is explored in the theory of scientific inference. www3.nd.edu/~rwilliam/stats2/l32.pdf Jun 2 '15 at 4:14
• @Conifold But then it's not implication either. Correlation means departure from independence, which raises an additional question: What does it mean that two eventualities are (in)dependent? Jun 2 '15 at 18:56
• @FreeMind Facts are statements. And there are implications between facts that are not causes. Jun 2 '15 at 19:00
• The best answer I heard so far by a member of a working group on evidence and causation in medical sciences was: Causation has at least two components, i.e. correlation and a reasonable mechanism that explains how one event implies the upcoming of the second one. Correlation without an explanation why they should be linked through laws of nature does not qualify for causation. Feb 25 '18 at 2:56

The following proposition:

A and B then C

Can be expressed (not always) as

A + B = C

In the second form, A is implicated in C. There's no sequence in time. The system A is part of C, or it has a relationship with C. That's the meaning of implication.

In the first form, A is causal of C, meaning that when A happens, C could follow. The word follow expresses a time sequence. Causality always is a time-based sequence. Time is essential to causality.

Consider that causality is only a mental construct. Most philosophers reject causality as an attribute of nature. It is our brain that works using a causal fashion. Probably because time is nothing more that a mental construct (Kant).