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If person A gives an argument to person B in order to convince them about the truth of claim X, how can B determine how compelling A's argument is in a way that is as objective as possible (i.e. in a way that anyone should be able to verify and agree)? The only types of arguments that exemplify by excellence that idea in my opinion are proofs of mathematical theorems or mathematical claims in general, since if everyone agrees upon the initial axioms and follows the deductive argument step by step, everyone should be able to arrive at the same conclusion, and even an automated theorem proving system should be able to do it as well. Although, to be fair, it's still technically possible to question the truth of a mathematical proof by questioning the initial premises (e.g. why should I accept Zermelo-Fraenkel Axioms?, etc.).

But not all arguments are formal, logical and deductive like mathematical proofs. In Physics for example there are "proofs" that make use of approximations, such as the small-angle approximation. Or in domains that lack a formal mathematical syntax, such as philosophy, philosophical "proofs" rely heavily on the use of everyday natural language to express arguments, which unavoidably introduces a greater degree of ambiguity due to the imprecise meaning of certain words, which leaves room for subjective interpretation, questioning the logical implications, etc. (For example, I'm not sure if a "philosophical proof" can ever be restated in a way that can be verified by an automated theorem prover.)

And beyond deductive reasoning, there are other kinds of reasoning paradigms as well, such as inductive reasoning and abductive reasoning, in which the nature of the arguments made is different.

If B wants to verify how compelling the case is that A is attempting to make to convince them that X is true, how can B go about it in a way that is as objective as possible? Should B give more credence to deductive arguments, abductive arguments or inductive arguments? Should B question and inspect every single premise? How can B determine when a premise is worth being accepted instead of questioned? Can B consider A's case more compelling if A presents multiple, independent arguments?

In sum: are there objective ways to determine how compelling an argument (or a case made by multiple arguments) is?

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  • I've removed the "proof theory" tag. Proof theory usually means analysis of [deductive, formal] proofs of precisely the kind you don't inquire (are not skeptical) about here. Also, I'm a bit skeptical this q isn't too broad; one can write entire articles just about inductive arguments e.g. plato.stanford.edu/entries/logic-inductive
    – got trolled too much this week
    Commented Mar 28, 2021 at 15:42
  • @Fizz - good point, thanks for the edit. I added the 'logic' tag instead.
    – user48437
    Commented Mar 28, 2021 at 15:53
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    @SpiritRealmInvestigator, one thing that can be done is to break down the argument so that we can see which steps involve deductive reasoning, which steps involve abductive reasoning etc. I think natural language can be very deceptive which is why debates go back and forth without resolution. Objections to an argument should be pinned down to the questionable step or steps. If a step is questionable, then perhaps the person making the argument can break that step even further etc. I think there is too much use of essay writing, discussions etc to try and resolve scientific disputes.
    – Ameet Sharma
    Commented Mar 28, 2021 at 19:00
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    It seems like you're looking for a list of all the ways in which an argument can be flawed or invalid, because that corresponds to how "compelling” it is. There is no single overarching way to verify arguments, there are many ways that depends on the argument.
    – NotThatGuy
    Commented Mar 28, 2021 at 23:55
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    Outside of deductive validity and soundness, arguments are judged on plausibility of premises and inferences. Such judgments depend on personal backgrounds and biases, which influence what is psychologically "compelling". Keeping those out leaves evaluation on cognitive values, like precision, unification, explanatory power, simplicity and coherence. But judgments on those still vary, and do not apply well to individual arguments. They rather apply to entire frameworks within which arguments are made.
    – Conifold
    Commented Mar 29, 2021 at 5:29

2 Answers 2

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When you say "from A and B we can conclude (informally) C," there is a great deal of variation in whether a listener accepts it. People have background assumptions and methods of thinking - often not stated or known in words - which lead them to either conclude C or deny C to varying degrees of confidence.

  • Does the listener accept A and B? If not, they will not accept the argument.
  • Does the listener accept A and B, but not accept the argument? There are possibilities:
    • (a) The argument involves unstated implicit premises D, E, ... , some of which the listener does not accept.
    • (b) The "inference rule" or method of thinking used to conclude C from A and B (and also maybe from D, E, ...), is held by the speaker but not by the listener.
    • (c) The listener may accept A and B and would under normal circumstances conclude C from A and B, but the listener holds an additional belief F, which he considers to defeat the premises A and B. "Well, normally C would follow, but in this case it does not because of F." See non-monotonic logic.
    • (d) As in case (b), F may be an "inference rule" or method of thinking rather than an explicit belief.
    • (e) The listener may simply not understand the argument. This is not necessarily a separate case from (a)-(d), because it tends to be the result of the listener lacking some method of thinking or implicit premise that is necessary to follow the argument.
    • (f) The listener may be dishonest and refuse to admit C if doing so would damage his self-esteem, tribal allegiance, finances, or other personal interests. This is rather different from (a)-(e) because the listener may perfectly understand and privately agree, but simply not be willing to say so. "It is difficult to get a man to understand something when his salary depends on his not understanding it." - Upton Sinclair

So at first glance this looks like bad news for being able to say arguments can be "objectively" compelling.

However, if someone doesn't understand an argument at first, they may come to understand it through further arguments. They may refuse to accept A, but they do accept X and Y, and they would accept that X and Y imply A, if only someone pointed it out to them. Then one only needs to point out X and Y to them, and they will agree with A and then with C. After this process, the person, if they are "rational," would be happy that they have achieved greater consistency in their beliefs.

We might take a step and say that a person ought to believe a proposition, if they would be persuaded of it eventually after thinking and talking it over and looking at relevant evidence. A person should not willfully remain in ignorance.

So this gets close to your idea of arguments being "objectively" compelling, if it's not exactly the same. We may rephrase it: an argument "objectively" ought to convince a person, if they would be convinced of it had they known more about the premises and background information.

See also Bayesian inference which is in many ways a decent normative model of humans updating their beliefs based on informal evidence. The biggest flaw in the model is that exact Bayesian inference is computationally intractable, so humans can't possibly be doing it. But they may be doing something that approximates it.

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    Well, the other problem with Bayesian inference is that people often engage in cognitive biases which are obviously inconsistent with the Kolmogorov axioms. See for example the conjunction fallacy (non-monotonic probabilities), confirmation bias (seeking "evidence" which is of low probative value under classical Bayesian assumptions, and then regarding it as having high value), and all the other nonsense that comes in under the representativeness heuristic.
    – Kevin
    Commented Mar 29, 2021 at 0:10
  • @Kevin yes, but this does not present a challenge for Bayesian inference as a normative model of human inference; in the instances you mention, normatively, humans should make the Bayesian judgments, although they do not.
    – causative
    Commented Mar 29, 2021 at 4:01
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    In recent years, proponents of Bayesian learning have begun describing the theory-theory - a popular folk psychology, in a mathematical way (en.wikipedia.org/wiki/Theory-theory). But since you admitted Bayesian inference is not applied in reality due to above several difficulties, then how can it have any real life applications in argument persuasion except its appearance in some academic decision theory papers? Do you know any mainstream app leveraging it?
    – Double Knot
    Commented Mar 29, 2021 at 5:49
  • @DoubleKnot I mentioned Bayesian inference as a normative model, i.e. not what people actually do, but an ideal that a rational person ought to approximate. Do I know of a "mainstream app" leveraging it? Approximate Bayesian inference is behind many models in machine learning, e.g. restricted Boltzmann machines are trained that way.
    – causative
    Commented Mar 29, 2021 at 11:20
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Ideally for any dispute between two parties or you want to convince others some propositional argument, we should translate and plug into some formal logic system, and then let's just calculate, and hopefully a definitive answer will emerge after a short while. And historically some audacious philosophers took such daunting project, such as Leibniz. Leibniz recurrently thought about such project using his so-called Characteristica Universalis of human ideas, much more ambitious than Frege's Begriffsschrift.

Frege's motivation for developing his formal approach to logic resembled Leibniz's motivation for his calculus ratiocinator (despite that, in the foreword Frege clearly denies that he achieved this aim, and also that his main aim would be constructing an ideal language like Leibniz's, which Frege declares to be a quite hard and idealistic—though not impossible—task). Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter century.

The later famed logician Kurt Gödel, on the other hand, believed that the characteristica universalis was feasible, and that its development would revolutionize mathematical practice. The computer-aided formal proof of the famous Four color theorem seems fulfilled his vision in math realm.

So far seems only in the domain of logic, math and science we can successfully convince others objectively. For me a major practical issue to apply to real life situations is due to epistemic Contextualism. In real life situations, background context is much more complicated than pure scientific or logic realm since it's essentially a nearly infinite network with too many parameters. Even in economics, any realistic useful predictive model may easily require hundreds of parameters. So to achieve your goal of convincing others objectively, you need to focus on context clarification and parameters filtering in theory. Even after doing so, due to modern society's numerous kinds of relativism, your carefully constructed persuasion will still get misunderstood inevitably by many holding different views than yours....

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