But the argument itself is insufficient for drawing conclusions.

This seems like it would be true only if you'd already propagated all logical consequences of all observations you've made. But an argument can help me to propagate. Which means it can make me update my beliefs.

For example, is 3339799 a prime number?

One ought to assign some prior probability to it being a prime. A naive estimate might say, well, there are two options, so let's assign it 50% probability.

You could also make a more sophisticated argument about the distribution of prime numbers spreading out as you go towards infinity, and given that only 25 of the first 100 numbers are prime, the chance that a randomly selected number in the millions should be prime is less than 25% and probably much lower.

I claim that in a case like this it is totally valid to update your beliefs on the basis of an argument. No additional empirical test required before updating.

Do you agree?