# If A causes B and B causes C

1. Apr 12, 2010

### jaketodd

I know this is very basic but it has been awhile since my logic course in college. If A causes B and B causes C, does A cause C? And if the answer is "sometimes," then what requirements are there for A to cause C?

I did some research on Google and most of what I found agrees that A causes C, but then I ran into some gray area.

Thanks,

Jake

2. Apr 12, 2010

### sutupidmath

The property where : If A 'causes' B, and B 'causes' C, then A 'causes' C, is known as transitivity.

In this case it really depends what do you mean by 'cause'.

Many relations are transitive. Indeed, all equivalence relations are transitive..so are simple order relations as well.

3. Apr 12, 2010

### SW VandeCarr

Causality is an empirical concept, not a logical relation. There are a number logical (or formal) relations which are transitive such as (>)where if a>b>c, then a>c. However this would apply to causality only in specific situations, and only as observations from which certain empirical relations might be inferred as opposed to proved.

Last edited: Apr 12, 2010
4. Apr 13, 2010

### jaketodd

If A causes B through an equation and B causes C using the same equation, then does A cause C?

Thanks for the help,

Jake

5. Apr 13, 2010

### SW VandeCarr

Show me an equation where A causes B and B causes C.

6. Apr 13, 2010

### jaketodd

b=ax
c=bx

7. Apr 13, 2010

### SW VandeCarr

That's two different equations. You've just shown that:
x=b/a; and x=c/b

How does this show transitivity and what's it got to do with causality?

First: Causality is sometimes incorrectly confused logical implication. For example P -> Q and Q -> R. than you can conclude that P ->R where -> means 'implies'.

Now lets say c is the relation of causation. Then what does A c B; B c C mean?
Does it mean A is the sole cause of B?
Does it mean A always causes B?
Does it mean A can be the sole cause of C as well?
Does it mean A always causes C?
Does it mean that A will cause C only by causing B which causes C?

Discussions of causality really belong in the philosophy forum. It's much more complicated than I indicated here. For example, it involves the notion of necessary and sufficient conditions.

Last edited: Apr 13, 2010
8. Apr 13, 2010

### jaketodd

So if A causes B and B causes C, then A is not causally connected to C?

9. Apr 13, 2010

### SW VandeCarr

A lighted match lights a fuse which detonates some dynamite. The dynamite detonation causes the old bridge to collapse. Did the lighted match cause the old bridge to collapse?

Last edited: Apr 13, 2010
10. Apr 16, 2010

### joxnas

I believe that by "causes" you mean "implicates".

well, in fact
((A => B) ∧ (B => C)) => (A=>C)

Is always true

11. Apr 16, 2010

### SW VandeCarr

Of course. So? jaketodd continued to use the word "cause". Do you know the difference between empirical relations and logical relations? In post 7 I gave an example of logical implication and questions related to empirical causal reasoning.

How would you answer my previous example of a lighted match causing a bridge to collapse? This obviously only applies to a specific set of circumstances.

Last edited: Apr 16, 2010
12. Apr 19, 2010

### joxnas

Sir, please stand calm and dont be hostile. by "you" I was refering to the person who started this topic. Besides I only wanted to give my good-willed contribute so the eventual doubty thoughts of jaketodd could be cleared.

And yes, I know the difference betwen logical and empirical relations.

Don't let the 8 hundred posts of difference betwen you and me be an argument for making any kind of assumptions about who I am or what I know. Because.... A doesn't cause B

Last edited: Apr 19, 2010
13. Apr 19, 2010

### SW VandeCarr

Sorry. jaketodd seemed to have difficulty understanding this despite my efforts, and you seemed to be following suit. My response wasn't hostile. Just a bit exasperated. If you post here frequently, you will get hostile responses sooner or later, regardless of what you post (although PF is better than most such forums in this regard).