I'm having trouble with this argument:

Everything has a cause --- premise 1
If God exists, then something isn't caused --- premise 2

Therefore, God does not exist --- conclusion

I can see intuitively that the argument is valid, but how to prove it? The problem seems to be that premise 2 is a combination of a hypothetical and a particular categorical proposition. Is there some way of converting it so it's completely categorical or completely hypothetical? I'm stumped.

Hi James.

See in this regard the following page: http://www.thelogician.net/3b_buddhist_illogic/3b_chapter_10.htm

To answer your question:

Everything has a cause --- premise 1
If God exists, then something isn't caused --- premise 2
Therefore, God does not exist --- conclusion

Premises 1 and 2 seem incompatible. Thus, one of them must be wrong. Either "NOT everything has a cause, e.g. God does not have a cause" or "if God exists, it does NOT follow that something isn't caused" (but the common view of God is of course that He is not caused - so I would maintain your premise 2). Thus your putative conclusion "God does not exist" is not the only possible outcome of the premises - we could also say that your premise 1 is wrong.

Now, in this regard - what is this alleged "law of causation" based on? There is no FORMAL basis for it - it is just a generalization, which is quite open to debate.

To study this issue more deeply see:
http://www.thelogician.net/4_logic_of_causation/4_chapter_19.htm
http://www.thelogician.net/4_logic_of_causation/4_chapter_10.htm
http://www.thelogician.net/4_logic_of_causation/4_chapter_16.htm#2.%20%20%20%20On%20Laws%20of%20Causation.

Something about you (optional) logician

I should add regarding the form of yor argument, it is like this:

If A, then B (premise 2)
but not B (premise 1)
therefore, not A (your conclusion).

So the argument is formally valid - it is just a standard apodosis, denying the consequent (B = some things are uncaused).
The connection between A (God) and B (uncaused) is not in doubt (granting that we are talking about the God of monotheism).
The issue is therefore only the truth of the minor premise (i.e. "not B"). If the minor premise is true, then the conclusion (viz. "not A") is unavoidable. If, however, the minor premise is open to doubt, then the conclusion is not proved by this argument (nor, of course, disproved).

Something about you (optional) logician

Hello Avi and thanks for that. I was actually more interested in the form of the argument rather than whether it was sound or not (is that the right term - "sound"?), but thanks for the links, I will look at them but at the moment I'm still trying to learn the basics. I'm enjoying logic but it does make your head hurt at times!

It's so obvious now, I think my problem was not seeing the wood for the trees. Of course, premise 1 is of the form "All X is Y" which is the contradictory of "Some X is not Y" and the conclusion then follows. I was getting confused because I was seeing premise 2 as a combination of an If-Then statement and a categorical statement. I've read that it's possible to express an If-Then statement as a universal affirmative categorical statement "All X is Y", but not sure whether this is possible for all If-Then statements.

I think this argument can be seen more clearly if we obvert premise 1 then transpose the premises -

If God exists, then something is uncaused
Nothing is uncaused (denial of the consequent)
Therefore, God does not exist. (denial of the antecedent)

Or -

If God exists, then Some things are not caused (an O proposition)
All things are caused. (An A proposition/denial of the O proposition consequent)
Therefore God does not exist (denial of the antecedent)


These ways it is more clearly seen as the modus tollens form.