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Source: 2 minutes 30 seconds juncture; Lecture 2, Video 4 (transcription);
MITx: 24.00x Introduction to Philosophy; by MIT Associate Prof Caspar Hare PhD (Princeton)

So good, interesting arguments have a further virtue in addition to soundness. That is they're potentially convincing. Now, this depends on where you start. Potential convincingness depends in part on who is in a position to be convinced. We'll define it like this:

An argument is potentially convincing for a person when, prior to being confronted with the argument, the person believes the premises but doesn't believe the conclusion, and the person is in a position to see that the argument is valid.

So if the argument is potentially convincing for you, then because you believe the premises before being confronted with the argument, you'll be inclined to accept all of those premises. And because you're in a position to see that the argument is valid, you'll be in a position to see that, given that the premises are true, the conclusion, too, must be true. So you're in a position to be persuaded that the conclusion is true.

Strangely, none of my 3 books on logic, or this Coursera course Think Again: How to Reason and Argue, introduced the bolded terms above. They only discussed 'validity' and 'soundness' for arguments. A Google search cites uses only from the lecture above.

So are there other names for the bolded? If not, why is this 3rd key quality of arguments omitted?

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    That is because "convincingness" is irrelevant to logic. Soundness and validity (truth of premises, propriety of inferences) are properties that describe how arguments function logically, not what kind of effects they have on the audience. The latter are the subject of rhetoric, not logic. en.wikipedia.org/?title=Rhetoric
    – Conifold
    Commented Jun 18, 2015 at 1:02
  • I think "potential" is a fitting name for this further virtue.
    – Ronnie Royston
    Commented Jun 18, 2015 at 18:56

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Georg Polya calls this 'plausiblity', and attempts to lay out rules for keeping arguments plausible in his book "Patterns of Plausible Reasoning".

Mathematics, science and logic would, each in its own way, like to think they are about facts, but they are in fact about psychological models of the world at different levels of abstraction. And there are therefore psychological observations that identify patterns that encourage the discovery of good proofs, convincing theories and of plausible arguments.

I would take Polya's lead and refrain from combining scientific and plausible reasoning into rhetoric because their goal is still ultimately logical, if only statistically so. A poorly presented plausible or scientific argument is often no less effective, upon adequate reflection, due to its presentation. But a rhetorical one is. (Otherwise computer people and every-day scientists would have to learn to write in a convincing, and therefore an easily read, manner.)

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  • Its not plausibility but potential, no? In other words, it amounts to the difference between what the person believes (the premises) but doesn't believe (the conclusion). The greater that amount the more disruptive the argument. Potential.
    – Ronnie Royston
    Commented Jun 18, 2015 at 18:51
  • No one uses the word that way, i.e. in reference to the audience. A potential argument is equally possible to give anyone. But an argument is plausible to an audience, one who can find a common base of premises, and who can follow it.
    – user9166
    Commented Jun 18, 2015 at 19:24
  • The book is Mathematics and Plausible Reasoning, volume 2 is Patterns of Plausible Inference. But Polya is talking about heuristics, and his plausibility is not "convincingness", the point is not to convince, but to discover. If anything, heuristic arguments are designed to be less convincing than logical ones, their purpose is to generate conjectures, which can later be verified by other means. One loosens the screws to let more in. en.wikipedia.org/wiki/Mathematics_and_plausible_reasoning
    – Conifold
    Commented Jun 18, 2015 at 20:24
  • The case where the argument is actually valid is a subcase, but it is still an instance of plausibility. It is all one thing, making something seem likely to be true is the same whether you are seeking something or communicating something you have already found.
    – user9166
    Commented Jun 19, 2015 at 1:22

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