# Is there a logical system that accounts for cause and effect relationship?

The reason I ask is because of the ambiguity of some statements when the conditionals of a condition are not referenced by tense i.e time. For example, in the Cognito Ergo Sum 'I think therefore I am', it could be read as saying that thinking causing existence, which is obviously not the case.

Let my elucidate the problem, as you'll be well aware, this is an instance of Modus Ponens, which can broken down as such:

``````p
q

p > q
p
______
q
``````

This is usually thought of as p being a sufficient cause, which necessitates an effect, in the case of the Cogito Ergo Sum, this would mean thinking causes existence. However, it could also mean that p is sufficient evidence of a necessary cause, in the case of the Cogito Ergo Sum, this would mean that thinking is sufficient evidence for the necessity of one's existence, which of course is Descartes intent in his assertion. So it's not that a given cause (thinking) is sufficient for the necessary outcome for one's existence (the effect), but that thinking (the outcome) is a sufficient effect which can be adduced to a necessary cause – existence.

It's not just grand assertions like the Cogito Ergo Sum, however, that is prone to such ambiguity. Afterall, one may consider that given such a fundamental assertion, it may not be the best example. Consider then the assertion: 'if there is rain, then there are clouds'. Certainly one has never seen the pour of rain from a cloudless sky, so we can say this is true with great confidence. However, if a blind man was told that 'if it is raining, then there are clouds' (and was never taught the cause-effect relationship of clouds and rain) he would be as justified to presume (though wrong) in saying that rain causes clouds.

• Modal logics with necessity could be used to model causal relations...? Commented Feb 10, 2017 at 20:28
• you say "This is usually thought of as p being a sufficient cause, ...". can you offer a citation? i am not aware of any logician who would treat modus ponens as involving causality in any way.
– user20153
Commented Feb 11, 2017 at 19:56
• @mobileink why would I need a citation? It's tacit. If A, then B. B isn't just happening by coincidence, it's caused by A. If you really wanted a reference, you could ask any scientist out there, for the heart of science lies in causal relationships. Commented Feb 15, 2017 at 20:55
• @user108262: you would need a citation because i asked you for one. but let's not quibble. you seem to be confusing logic and empirical science. nothing "happens" in logic. there is no concept of causality in logic. A -> B does not mean that A causes B.
– user20153
Commented Feb 15, 2017 at 21:00
• e.g. note that A -> B is in no way a conditional. It does not mean that B depends on A or that A is a condition of B. It just means that you cannot have A without also having B. But you can have B without A, so A is not a condition or requirement fot B.
– user20153
Commented Feb 15, 2017 at 21:06

Assuming for the sake of discussion the fact that clouds are the cause of rain, this does not mean that "if there are clouds, then there is rain" is correct.

From the fact that clouds are the cause of rain we have:

"if there is rain, then there are clouds".

A good exercise is to replace the "if..., then___" construction with a different one using "when".

We can rephrase the above assertion as : "when there is rain, there are clouds" and also with : "there is rain, only when there are clouds".

The last version is more perspicuous : we cannot have rain without clouds.

But nothing is said about the converse : we cannot have clouds without rain.

Thus, if we cannot have rain without clouds, but we may have clouds without rain, it is quite clear that clouds are the necessary condition for rain : no clouds, no rain.

We have also that rain is the sufficient condition for clouds; but this must not be read as "rain causes clouds".

Again, if we cannot have rain without clouds, this means that from the evidence of rain, we are licensed to infer the presence of clouds: this is the "sufficiency".

Regarding "logical" analysis of causation, see Counterfactual Theories of Causation as well as Probabilistic Causation.

• clouds are the cause of rain??,
– user20153
Commented Feb 11, 2017 at 19:57
• Yes, it is true that if we cannot have rain without clouds, but we may have clouds without rain, then it is true that clouds are the necessary condition for there being rain, and thus part of the cause. However, my concerns lied not here, for it lied not in the content of the argument, but its form, which turns out to be the form a conditional. The reason for such concerns was due to the double meaning of the conditional, as to whether a conditional is stating that a cause necessitates an effect, or whether it is effect arising out of necessary conditions. Commented Feb 15, 2017 at 21:04

no. the topic of logic is (logical?) consequence. causality is a completely different topic. the latter is an empirical matter, and there are prominent philosophers who argue that there is no causality in nature (and i do not mean just Hume, but contemporary philosophers). there is no inherent connection between logic and causality.

p.s. to see that modus ponens does not involve causality just look at it's formal definition. p -> q can be true even if p is false. it's a common misconception that p -> q means that p and q are some how connected. not true. the -> operator is not even primitive, p -> q just means that p AND ~q is false. just consider e.g. birds have wings -> Paris is the capitol of France. if birds happen to have wings, that does not cause Paris to be the capitol of France.

• If we can do without the conditional, why then do we use it. Don't get my wrong, I know that P > Q does equal to ~P + Q, but surely given this, there's something else that's implied given P > Q, because if there's not, it's literally useless (and am one of the few who actually use the term accurately). Commented Feb 15, 2017 at 21:07
• @user108262: this is actually a well-known problem in logic. the material implication A -> B does not match our intuitions. the branch of logic that tries to address is usually called sth like "Relevance logic", the idea being that we normally only say "if A then B" is there is some connection between A and B. But in formal logic that is not the case. "Today is Wed., therefore Paris is the capital of France" is logically impeccable, but intuitively nutty.
– user20153
Commented Feb 15, 2017 at 21:13
• Ah, so am not alone in this! :') Maybe we cannot lay claims to a perfect system of logic... yet, though at least we may be able to claim to have developed a pretty decent one. Our work in incomplete, then. Commented Feb 15, 2017 at 21:18
• don't get me wrong, the relation between logic and causality is hyuuge, and has been addresses by many great philosophers. but it remains an open question afaik, since it takes you into the weeds of "what is causality, really?", and thst is a very hard problem. Huw Price, for example, argues that it's really just the way we talk about stuff.
– user20153
Commented Feb 15, 2017 at 21:19
• oh gosh no, you're not alone or nutty! it's a excellent and fascinating topic with lots of unanswered questions.
– user20153
Commented Feb 15, 2017 at 21:21

Your question seems to stem from the fact many student take away that conditionals are necessary or sufficient. I am not sure if instructors are telling that to students but you see there is a problem. The context of a conditional can vary. It is not always the case the relationship is relevant in a conditional. I will list several context of a conditional.

If the Yankees make it to the 2017 World Series, I am a monkey's uncle.

Surely there is no connection between the antecedent and the consequent in the above example. One thing has nothing to do with the other but the expression is meant to be doubtful the Yankees will make it to the World Series this year. One can claim this conditional is for rhetorical effect.

If you combine 2 hydrogen with one oxygen then the mixture will yield H2O (water).

This seems to be necessary. I am not a scientist but the conclusion seems to be unavoidable of getting water when two hydrogen combine with oxygen. It also suggest if I alter the left hand side the right hand side will be effected. This is not so in the above example. Clearly this has a relationship the above conditional did not have. So this case seems to indicate there are no other alternatives for a conclusion. This is scienctific.

If a number is divisible by two, then that number is an even number.

This example is also necessary. It is impossible to have a number divisible by two and have a non even number. Also one can note that this could be linguistic. That is by definition of an even number we can say this is so. This is different from above. We don't need science to verify this as the one above.

If I die then I am hit by a bus.

In this case the antecedent is limiting all of the available options. The consequent is not necessary at all. I can die a number of ways: old age, cancer, get murdered, a serious fall injury like jumping out of a plane without a parachute, accidental death of jumping out of a plane and the chute malfunctions, etc.

If I get hit by a bus then I will die.

Neither the antecedent nor the consequent must happen. There is sufficient cause perhaps as a serious injury from a bus hitting me can cause death. I am not required to get hit by a bus. Getting hit by a bus alone still does not guarantee my death. There is a possibility I survive.

If Floyd Mayweather fought Sugar Ray Leonard in his prime, Mayweather would lose.

This may seem to be a value judgement. In a form alone context the antecedent and consequent are clearly impossible to achieve. There is no sufficient or necessary cause present. This is a hypothetical. That is the conditions are not in reality but we want to make a prediction anyway. This use is clearly distinct from all the examples above.

If you are born in this world after Christ then you are a sinner.

Here we have a case of a conditional whose requirement makes the claim true even if you swap positions of the terms. I can also say if you are sinner then you were born in this world after Christ. Either way I say this example the truth value does not change. This is a bi-conditional. Surely this is distinct from all the above examples as well. You can't just swap terms in conditionals and maintain truth values. This is a special relation that is true in some conditionals.