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This question is meant for a bit of fun as a comedic corollary to JDH's top-voted question, "What would it take in a book to convince a rational person that it had been written by or directly inspired by a god?"

I would suggest that there is not something that any (all) rational persons agree on, and therefore not something that can convince any rational person of any particular thing. What's funny to me is that this also demonstrates a contradiction with the word "rational" in the premise, which in turn implies we aren't even communicating with 100% efficiency, even with formal systems. Or stated otherwise, disagreement and misunderstanding can always be confused for one another.

Some references for qualitative support:

  • "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." - Bertrand Russell
  • "The purpose of philosophy is not to prove everything from nothing, but to assume as given, all." - Kurt Gödel
  • Wittgenstein/Kripke's Rule-Following Paradox
  • "The Tao that can be spoken is not the true Tao." - Tao Te Ching

If you believe there is something all rational people agree on, what is it? 1+1=2? X is X? I think therefore I am?

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    Yes, if you insist on "all" you'll come up empty. Yes, apparent disagreement can be due to miscommunication. But where is the contradiction? Rationality isn't about agreeing on things, it is about agreeing on getting from premises to conclusions. How one gets their premises is a different matter. Still, many rational people agree on many practical matters, and that is often enough. – Conifold Oct 10 '20 at 20:39
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    If you limit "all rational persons" to "all rational persons with common priors," you get to contend with Aumann's agreement theorem, which basically says that they cannot agree to disagree, even if they have reviewed different evidence. – Kevin Oct 10 '20 at 20:57
  • @Conifold I'm suggesting that we can't ever even agree on the premises. – TCP Oct 10 '20 at 21:04
  • Why "even"? That's the hardest part. Logic tells us where to go from there. And while we can not all agree all of the time, most of us agree most of the time where it matters, in practice. – Conifold Oct 10 '20 at 21:56
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    @TCP- What you've hit on in your 'little bit of fun' is in fact the inescapable conundrum for today's academic regime in philosophy. By insisting that any and all propositions can be made sense of in some imaginary parallel world, and reduced to some type of statistically probable outcome, the analytic methodology removes all attempts for any meaningful agreement on; language, epistemology, ontology, metaphysics and all else in philosophy. Stand your ground, Don't back down! Regards, – user37981 Oct 16 '20 at 17:18
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This is really a question about the definition of "rational person." Rationality can be subdivided into a number of different types or categories of reasoning, which include:

  • Deductive reasoning (drawing logical inferences from rigorous application of the rules of classical logic).
  • Inductive reasoning (inferring that a general statement is "probably" true from seeing a large number of specific examples).
  • Abductive reasoning (inferring that a statement is "probably" true because it is the simplest explanation which is compatible with available evidence).

The word "rational" could ambiguously refer to any of these forms of reasoning. However, I think it is fairly uncontroversial to require that a "rational person," without further qualification, is at least rational with respect to deductive reasoning. That is, a rational person should accept a sound deductive argument, once it has been presented to them.

If we take that definition as given, then any rational person, in general, will accept statements of the following form, when accompanied by a proof which the rational person can understand:

The axioms of [mathematical subfield], specifically [list of axioms], logically entail [any theorem of that subfield].

For example:

The axioms of arithmetic, specifically the Peano axioms, logically entail 1 + 1 = 2.

This does not mean that any rational person will accept that 1 + 1 = 2. But they will accept the entailment from the Peano axioms to 1 + 1 = 2, because the latter is a theorem of Peano Arithmetic (strictly, we also need to offer definitions of the symbols "1", "+", and "2", as these appear nowhere in the axioms, but such clarification doesn't change the meaning of the statement, it just makes it more verbose). The entailment itself requires no premises, and so if it is logically valid, it must be logically sound as well.

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  • Thanks Kevin, I think entailment is a good example. Curious if you would accept the summary that "all rational people believe modus ponens"? – TCP Oct 11 '20 at 18:49
  • And how might you respond to someone who says that we in fact don't agree on entailment as demonstrated by its numerous forms and interpretations in classical logic, intuitionistic logic, model theoretic logic, paraconsistent logic, etc.? – TCP Oct 11 '20 at 19:09
  • @TCP: As I explained, this is contingent on your definition of rationality. If you want to define rationality in terms of classical logic (perhaps allowing some other forms of reasoning as well), then modus ponens is part of classical logic and so this is true by definition. If you want to define rationality in terms of some other form of logic, then you get analogous statements which are tautological in that logic. If you don't want to define rationality at all, then your question is ill-posed. – Kevin Oct 12 '20 at 20:20
  • So you're saying that 1) all entailment would be accepted by a rational person and 2) all entailment is tautological. Does that mean you would agree that all tautologies would be accepted by a rational person? – TCP Oct 13 '20 at 21:19
  • @TCP: Based on my understanding of what most people mean by "rational," yes, all rational people would accept tautologies. But if you want to argue about whether this is true or not, you really do need to pick a definition. – Kevin Oct 13 '20 at 23:18
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Short Answer

This question goes to the heart of human nature, experience, and justification as a product of the human genome. If we slightly soften the ask, then there are plenty of examples of ideas that are near-universal, reasonable propositions, such as 'one and one makes two', 'up is the opposite of down', 'ants are smaller than elephants', and 'fructose and sucrose are sweet'.

Long Answer

Technically speaking, the quantifier ALL is very strong, meaning that somewhere on earth, if 1 of more than 7 billion people disagrees, there is no universal agreement. You then complicate by predicating with "rational people", whatever that may be. Even clinically insane people can use logic, no? But let's just tighten the proposition a bit by saying anyone who seems reasonably integrated into their society which allows us to use the lens of cognitive science and philosophy of mind within the context of a naturalized epistemology to examine cultures for universals and particulars.

First, if you accept psychologism as a thesis, then you are in good company, and can take note of the proposition that genes among humans are nearly identical. In fact, you share 70% of your DNA with marine worms, and with chimps, closer to 98%. From a statistical, genomic picture, it is defensible to claim that you are almost genetically identical to your closest relative. Should it be a surprise then, that since you share so many genes with your fellow Homo sapiens, that you should have the same rational ideas? This is a fundamental thesis of a philosophy of mind that undergirds embodied cognition and is seemingly displacing other theories of mind among cognitive scientists.

Steven Pinker, the internationally famous psycholinguist, in his The Blank Slate, devotes an entire book outlining exactly how similar and different we are and has a wonderful appendix devoted to Donald E. Brown's anthropological work on human universals. The appendix contains a list of over 250 universals of human state and behavior and gives a legitimate characterization of the human condition.

But you are more interested in ideas than in behavior, and to that, it is possible to draw your attention to the metaphysical presuppositions of cognitive semantics which embraces a wider vision of human meaning allowing to theorize (somewhat pre-scientifically) all human thought as emerging from a similar foundation. One of the seminal works of the field is Women, Fire, and Dangerous Things: What Categories Reveal about the Mind by George Lakoff who in conjunction with other linguistics from the same faction of the linguistics wars has argued a metaphysical position called embodied realism.

Ultimately, why "rational people" agree on "one and one makes two" is a function of the idea that the brain as we understand it has universal anato-physiological function, and thus supports a variety of functionalism in philosophy of mind.

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    Thanks J D. Lakoff's paper and history is new to me, so happily digesting all that. – TCP Oct 20 '20 at 3:56

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