Refusing to assign numerical probabilities because you don't have a rigorous way to derive them is like refusing to choose whether or not to buy things because you don't have a rigorous way to decide how much they're worth to you.

Explicitly assigning a probability isn't always (perhaps isn't usually) worth the trouble it takes, and rushing to assign numerical probabilities can certainly lead you astray -- but that doesn't mean it can't be done or that it shouldn't be done (carefully!) in cases where making a good decision matters most.

When you haven't taken the trouble to decide a numerical probability, then indeed vague expressions are all you've got, but unless you have a big repertoire of carefully graded vague expressions (which would, in fact, not be so very different from assigning probabilities) you'll find that sometimes there are two propositions for both of which you'd say "it could be true, but I doubt it" -- but you definitely find one more credible than the other. If you can make that distinction mentally, why shouldn't you make it verbally?