In that case I have problems thinking about it as a model of rationality for reasons so far said.

It's just a game. A good inference involves conversation and dialogue and time -- a bet thrives on forcing someone to make a choice with what they have.

Yes, it's just a game, in much the same way as predicate calculus is just a game.

Can it be used to model some of the things we do? Can it show us how we can act more coherently?

Well, yes. It shows us how a Dutch Book reveals an inconsistency, for example.

You are right that there is a lot going on here, and plenty more to be said. People do not act rationally. Leaving aside the question of whether they ought act rationally, Ramsey has given us a part of the way to understanding what it is to act rationally. Not a theory of how people actually think, not a theory of what beliefs are true, but a framework for what it would be to act coherently, given one’s own beliefs and preferences.

but a framework for what it would be to act coherently, given one’s own beliefs and preferences. — Banno

I suppose I'm a still skeptical of the framework, but I have little else to say as to why.

I'm fine with going along with the framework.

Is it possible to tie it into Williamson's concerns?

Ask Dummett to join a betting circle?

:lol: OK, fair enough.

I'll admit I didn't expect that answer.

In the most literal sense I suppose we'd have to ask ourselves here in the conversation what we're willing to bet on anything we say. (I bet 1 million dollars as a buy in)

You are right that there is a lot going on here, and plenty more to be said. People do not act rationally. Leaving aside the question of whether they ought act rationally, Ramsey has given us a part of the way to understanding what it is to act rationally. Not a theory of how people actually think, not a theory of what beliefs are true, but a framework for what it would be to act coherently, given one’s own beliefs and preferences. — Banno

I don't understand your enthusiasm for Ramsey. (Not that I've actually read him!). But the idea that induction is really just about probability is not that uncommon.

For two reasons
First, if you would bet more on f(e) given f(a), f(b), f(c), f(d) than you would on (f)c given f(a), f(b), then aren't you just betting on induction?
Second, if we need to find some sort of account of how we behave, what's wrong with Hume's custom or habit, based on our general heuristic of association? Or Wittgenstein's "This is what I do."

Or we could just stop treating induction as a poor man's deduction. We've given deduction this hugely special status as the only form of rationality. Given how limited deduction really is, it seems a bit irrational.
In practice, induction is more complicated than "the future will resemble the past". We know darn well that it won't - what we're trying to do here is to get a grip on how things will change as well as how they won't. I'm sure you know about J.S. Mill's much more complicated, and realistic, account of the methods of induction.

My "enthusiasm" stems from my reading Davidson's Truth and Predication, where Ramsey is mentioned. I'm not advocating Ramsey so much as exploring some ideas I haven't given much attention too until now.

It's not what I expected. He's not claiming that "induction is really just about probability" so much as dropping induction as a justification and instead considering degrees of belief. So while we might not know what is true and what isn't, we can have degrees of belief, and deal with them in a rational fashion.

...you would bet more on f(e) given f(a), f(b), f(c), f(d) than you would on (f)c given f(a), f(b)... — Ludwig V

...isn't the sort of thing that Ramsey is claiming, from what I can work out. He's not necessarily basing the bet on some series of accepted truths but on degree of belief, measured through betting behaviour, and arguing in favour of follow the axioms of probability to avoid incoherence.

...what's wrong with Hume's custom or habit, based on our general heuristic of association? Or Wittgenstein's "This is what I do." — Ludwig V

It's more that this is an implementation of "what we do" that is coherent; or perhaps better, shows is what coherence might look like.

Or we could just stop treating induction as a poor man's deduction. — Ludwig V

I think that's pretty close to what Ramsey is doing - moving past the problem of induction, getting to the point of how it is we behave.

He presents us with a tool that allows us to navigate uncertainty.



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Added: Yeah, I said

Ramsey instead says given f(a) and f(b), how much would you bet that f(c)? and develops a logic around this. — Banno

but that's not quite right. He's not saying that f(a) and f(b) implies f(e) is a better bet than just f(a). He;s not saying anything about f(a)'s truth or falsity at all. He's instead talking about the degree to which you and I believe f(a).

Thanks for the question - working out the answers is a great help in working out what Ramsey was doing.