When should we accept an argument's conclusion?

Philosopher William Lane Craig has often stated, as one of the conditions of a good argument, that the premises must be more plausible than their negations. I disagree with this, on the grounds that it does not always apply - there are counterexamples. Consider this:

1. My neighbor's dog is outside.
2. It is raining.
C. My neighbor's dog is outside and it is raining.

This argument is valid - the conclusion follows from the inference rule known as "conjunction introduction": if p is true, and q is true, then the conjunction p and q is true.

Now, it might be quite plausible, when considered alone, that my neighbor's dog is outside; after all, his dog is almost always outside. It might also be very plausible that it is raining; perhaps I have looked outside and seen that it is raining. However, I might not be very certain at all that the conclusion is true - who would leave their dog outside in the rain? Should I think it's plausible to accept this conclusion, just because both 1 and 2 are plausible? Surely not.

One might object by saying that 1 is not plausible because it is raining. This, however, is erroneous; and even supports my point. To say such is not to consider the plausibility of 1 at all; rather, one is instead actually commenting on the plausibility of the conclusion.

So, when should we accept the conclusion of an argument? I employ a modification of Craig's method. First, I check the argument's validity. If the argument is valid, I put all of the premises on the "left", and the negation of the conclusion on the "right". I then ask myself which is more plausible (or, which "side" I am more certain of. If it is the left, I accept the conclusion of the argument. If the right, I do not. For example:

Left:
1. My neighbor's dog is outside.
2. It is raining.

Right:
C/N. Not (My neighbor's dog is outside and it is raining).

If I am more certain of the conclusion's negation (perhaps because I believe that my neighbor is home, and cares for his dog), then I do not accept the argument.

Let's run through another example, with an argument often proffered by Dr. Craig:

Left:
1. Whatever begins to exist has a cause.
2. The universe began to exist.

Right:
C/N. not (The universe has a cause).

Of course, different people will have many different views on the plausibility of these premises and conclusion. Most people will not be certain at all that "the universe does not have a cause". However, one may in fact be even less certain of 1. Depending on rough probabilities, one may be justified in rejecting this argument based on the uncertainty of 1 alone. In any case, these subjective probabilities, combined with this analysis of what makes an argument "good", serve very well to explain why certain arguments are convincing to some but not to others.

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