# Can something indubitable be inferred from something dubitable?

I’m trying to respond to an argument. But I need this principle:

Consider a set of propositions P1, P2,...Pn that entails Q, where n>1. If

(1) any one of the Pk alone does not entail Q, and

(2) at least one of the P’s is dubitable,

then Q is not indubitable.

Is this principle correct? Intuitively, I think if p is dubitable and q is indubitable, I would be very surprised if p&q is indubitable.

• Your (1) should be strengthened to: Q is not entailed if any one of Pk is dropped. You also need to say something about the type of inferences involved in the derivation of Q. Most substantive inferences are not "indubitable", they are only plausible, so the conclusion is open to doubt even if the premises are not. If you restrict to formal inferences this principle can be defended, but there isn't much that can be formally inferred outside of mathematics. Feb 12, 2020 at 8:46
• It is hard to believe that there is "something that is indubitable": philosophers and scientist in the past have doubted about everything. Feb 12, 2020 at 10:40
• In principle: YES. See Ex falso: if P is false, we can validly infer anything from it, and thus also Q Feb 12, 2020 at 11:02
• Couldn't Q be entailed by the 'indubitable' P_{n+1}, not in the original set? Would that be a counterexample to your principle? Feb 12, 2020 at 16:13
• One cannot infer anything at all from a flawed set of Ps. Or, to put it another way, one can infer anything at all, including direct contradictions. This is a classic technique for proving that the set of Ps is flawed. One cannot say anything at all about Q. Feb 12, 2020 at 19:33