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.



_____________
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.

Although we arrived at Ramsey from critique of Kant and induction, it has another place in the discussion, since it provides us with a model for comparing constraints of the sort discuss at around p.17 of the Must Do Better article.

Ramsey doesn’t start with an absolute scale of belief or value. Instead, he begins with cases of indifference — where outcomes or propositions are treated as equally preferable or equally likely — and uses these as anchor points to infer a system of degrees of belief and utility that is coherent, even if it is partial, subjective, and shifting.

Now a point of indifference in a philosophical debate is a point of agreement.

An alternative method might be, rather than demanding an absolute resolution, begin with points of indifference or agreement — shared constraints, overlapping commitments, common ground. From these, construct a framework of reasoning that remains coherent, though incomplete or evolving.

Ramsey shows the formal consistency of such a method, given the axioms of his system.

Some fairly vague thoughts, prompted by

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

we can have degrees of belief, and deal with them in a rational fashion. — Banno

There's an intricate relationship between degrees of belief and belief in probabilities, which I find confusing. It looks to me as if "S has a x degree of belief in p and S believes that p has a probability x. Are they equivalent? If there's a difference, what is it?

What makes you say that Bayes is rational? If you are prepared to call Bayesian epistemology rational, how is induction any less rational?

You've probably seen customer satisfaction surveys that ask people to assign a number to their degree of satisfaction with a service or product. Once you have a number, you can do all sorts of interesting things with the statistics. But if the number is little better than arbitrary, what is the significance of the statistics? Well, there's an empirical test. If predictions based on those statistics are accurate, then the methdology does have at least some validity (meaning). But what outcome confirms or refutes a Bayesian prediction about a single case?

I'm torn about Bayes. Intuitively, there's at least some justification for assigning a probability to a single case. We do it all the time. So Bayesian epistemology seems to me to work on the same sort of basis that one can assign a number to my degree of satisfaction. But it is very hard to know how to factor any probability in to decisions about individual cases. If there's a 10% chance of some side-effect from a medical treatment, 1 in 10 patients will suffer that side-effect. How do I rationally factor that in to my decision about whether I accept the treatment, bearing in mind that accepting the treatment is all or nothing? Making a bet is one thing, because if one loses a bet, one can just make another bet. But getting ill from a medication is not necessarily like that. (yes, that's from the heart and live experience).

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. — Banno

Do you mean "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 as a justification." or "induction is really just about probability" so much as dropping induction as a justification and instead considering degrees of belief as a datum even though it is arbitrary from a rational point of view".

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). — Banno

Shouldn't that sentence end with f(e)?
But he might find that people do in fact bet more on propositions that are backed by inductive evidence. (And, yes, he might not.)

“…. The usual test, whether that which any one maintains is merely his persuasion, or his subjective conviction at least, that is, his firm belief, is a bet. (…) If we imagine to ourselves that we have to stake the happiness of our whole life on the truth of any proposition, our judgement drops its air of triumph, we take the alarm, and discover the actual strength of our belief. Thus pragmatical belief has degrees, varying in proportion to the interests at stake.…” (1787)

I'm sorry but who wrote that - I can't work it out.

My response is to point out that betting £1000 on the truth of a given proposition is a very different matter if your annual income is £10,000 or £100,000. It is also a different matter if you are single or have a family to support. And so on.

I am willing to bet a very large amount of money indeed (everything that I own or can beg, borrow or steal). that the sun will rise tomorrow morning. Who will take my bet, and at what odds? Should I be prepared to trust anyone who did take it?

“…. Thus we find in purely theoretical judgements an analogon of practical judgements, to which the word belief may properly be applied, and which we may term doctrinal belief. I should not hesitate to stake my all on the truth of the proposition—if there were any possibility of bringing it to the test of experience—that, at least, some one of the planets, which we see, is inhabited. Hence I say that I have not merely the opinion, but the strong belief, on the correctness of which I would stake even many of the advantages of life, that there are inhabitants in other worlds….” (ibid)

The nature of and how much the bet, and by whom the validity of the ground of the bet is judged, is irrelevant, with respect to its occurrence. Hence the implied correspondence to induction, which serves a subject as sufficient rational justification a priori for the construction of his empirical beliefs, while not being sufficient for their proofs.

The point being, of course, all of this has been done before, in which case should be found, if not the congruent thesis, then at least a conceptually similar initial condition, merely clothed in new words.

I would very much like to know who wrote the passage you are quoting. Just curious.

The nature of and how much the bet, and by whom the validity of the ground of the bet is judged, is irrelevant, with respect to its occurrence. — Mww

Yes. But those details are what give you the evidence of the degree of belief, or confidence.

Hence the implied correspondence to induction, which serves a subject as sufficient rational justification a priori for the construction of his empirical beliefs, while not being sufficient for their proofs. — Mww

Yes, I can see that - roughly. But Ramsey, apparently is not doing that. Ramsey is by-passing induction

altogether.

The point being, of course, all of this has been done before, in which case should be found, if not the congruent thesis, then at least a conceptually similar initial condition, merely clothed in new words. — Mww

Well, given that it was written in 1787 and Ramsey was writing in the 1920's, it would seem to follow. Which would be interesting, but I don't think it would change any of the arguments.

Thanks. I felt we were diverging far, and so I appreciate the tie-in back. (though I ought say I'm responsible for that divergence, too)

Also, your general description here:

Now a point of indifference in a philosophical debate is a point of agreement.

An alternative method might be, rather than demanding an absolute resolution, begin with points of indifference or agreement — shared constraints, overlapping commitments, common ground. From these, construct a framework of reasoning that remains coherent, though incomplete or evolving.

Ramsey shows the formal consistency of such a method, given the axioms of his system. — Banno

I get along with. The social reality of betting is what caused doubt in me, which is why I asked how literal you meant.

Any thoughts on this @Srap Tasmaner?

I'm mostly relying on you to get an understanding of Williamson, while attempting to put in enough work to make sure I'm not just missing something obvious.

But those details are what give you the evidence of the degree of belief, or confidence. — Ludwig V

A bet was intended to represent the subjective validity of a belief, for which the quality of the evidence just is the degree, both of which are presupposed in the construction of it.

That which evidences my degree of belief, and that by which I am confident of its truth….and indeed whether or not I’m inclined to bet on it at all…..is determined by the possibility of my experience of its object.

Those conditions incorporated in a bet I make, what kind and how much, or even the one I wouldn’t, give YOU the evidence of the degree of my belief, and the confidence in it. This becomes quite apparent, when I admit you are more justified in betting greater on the sun rising tomorrow, than I am betting there is life on other planets we can see.

But enough of this, yes? I was only pointing out the peripheral notion of bets in historical metaphysical investigations.

But enough of this, yes? I was only pointing out the peripheral notion of bets in historical metaphysical investigations. — Mww

As you wish.

Do you have more? Didn’t mean to shut you off.

I'm sorry but who wrote that - I can't work it out. — Ludwig V

I am wondering too. ?

Ehhhhh….dialectical precedent has it that responses to a quote are subjectively more honest without the influence of the author’s name, which is often detrimental to the message on the one hand, or tautologically affirms it on the other.

That, and my clandestine supposition that 1787 would be a sufficient clue.

Easy enough guess in the case of Mww, but one can also quote and Google "The usual test, whether that which any one maintains is merely his persuasion, or his subjective conviction at least, that is, his firm belief, is a bet."

I Can't figure it out.

(Tho I did the google, and wouldn't mind a A/B reference)

- I assumed Kant, but affirmation would be nice. Unsourced quotations seem like a funny animal to me.

Funny animal it may seem, yet still be nonetheless relevant to the topic at hand. Or, I guess, now, the sub-topic.

.

Kant, Critique of Pure reason, A825 / B852.

Kant is not measuring degrees of belief but critiquing overconfidence and metaphysical presumption. It's not to do with explaining belief so much as measuring it. The belief remains for Kant a piece of mental furniture.

Ramsey is closer to saying that the belief just is the disposition to act. The disposition to act is the degree of the belief. His axioms are then used to build a model of rational action.

You might see the difference between Kant and Ramsey if you consider this:

One way to highlight the difference between this view and representationalism is this: Imagine that we discover an alien being, of unknown constitution and origin, whose behavior and overall behavioral dispositions are perfectly normal by human standards. “Rudolfo”, say, emerges from a spacecraft and integrates seamlessly into U.S. society, becoming a tax lawyer, football fan, and Democratic Party activist. Even if we know next to nothing about what is going on inside his head, it may seem natural to say that Rudolfo has beliefs much like ours—for example, that the 1040 is normally due April 15, that a field goal is worth 3 points, and that labor unions tend to support Democratic candidates. Perhaps we can coherently imagine that Rudolfo does not manipulate sentences in a language of thought or possess internal representational structures of the right sort. Perhaps it is conceptually, even if not physically, possible that he has no complex, internal, cognitive organ, no real brain. But even if it is granted that a creature must have human-like representations in order to behave thoroughly like a human being, one might still think that it is the pattern of actual and potential behavior that is fundamental in belief—that representations are essential to belief only because, and to the extent to, they ground such a pattern. Dispositionalists and interpretationists are drawn to this way of thinking. — SEP Article on Belief

Gilbert Ryle might have more in common with Ramsey than with Kant.

There's an intricate relationship between degrees of belief and belief in probabilities, which I find confusing. It looks to me as if "S has a x degree of belief in p and S believes that p has a probability x. Are they equivalent? If there's a difference, what is it? — Ludwig V

It seems that for Ramsey the degree that one is willing to bet constitutes the partial belief. A belief is not "private" or "subjective", but measurable, and comparable with other beliefs.

The relationship, then, is not between "degrees of belief and belief in probabilities", but between degree of belief and willingness to act. Consider willingness to act as an extensional substitute for degree of belief.

There need be no inner fact about belief that can diverge from one’s consistent actions.

Oh yes, those. You say it (a proposition) is only a description (of a state of affairs) until asserted of reality? Until then, proposed but not yet carried, I suppose? — bongo fury

There's a difference between understanding what it would take for "the cat is on the mat" to be true, and asserting that the cat is on the mat.

Between "p" and ⊢p".

One might, somewhat redundantly, further assert that one asserts that the cat is on the mat. If the need arose.

moved his post.

Do you have more? Didn’t mean to shut you off. — Mww

Thank you. But it is better not to bore on about something to someone who is not interested. But since you've opened the door.... Even if you are not interested, there may be others who are.

Those conditions incorporated in a bet I make, what kind and how much, or even the one I wouldn’t, give YOU the evidence of the degree of my belief, and the confidence in it. This becomes quite apparent, when I admit you are more justified in betting greater on the sun rising tomorrow, than I am betting there is life on other planets we can see. — Mww

I don't have a problem with the general idea. But I do have a problem with the skimpy version of the idea that we have here. It is a fragment of the practice of betting - a gesture towards something that could be much more illuminating if it were taken out of the arm-chair and into real life.
1. The measure is not a measure of confidence alone. A bet is a combination of risk and reward and a decision to bet is the result of balancing, one might say, the disutility of one outcome against the utility of the other outcome in the context of the likelihood of each outcome. Confidence in the outcome is only one factor. The one virtue of this idea is that it takes a step to articulating what it means to act rationally in the context of probabilities.
2. Utility and disutility are the result of a wider context. For example, if you have 20 units of currency, the utility of 1 unit is one thing, but if you have 100 units, it is quite different. That can work in artificial situations, such as a laboratory experiment (or an armchair or seminar room), but in real life the context is much more complicated.
3. It is one thing to explore probability or confidence in the context of a decision about a single specific action, but there are subtler effects on rational action that also deserve to be taken into account. If the probability of rain is 80%, you may well decide to go to the gym rather than your walk/run/bike ride. If it is 50%, you may well decide to go out, but take an umbrella or wet weather gear in your back-pack. The most prominent example of this is the practice of insurance. Here, one bets on an outcome that is unlikely, but has high disutility, not because one wants to win, but to provide for that eventuality.

Ehhhhh….dialectical precedent has it that responses to a quote are subjectively more honest without the influence of the author’s name, which is often detrimental to the message on the one hand, or tautologically affirms it on the other. — Mww

I can see that. On the other hand, it can help to know the context....

That, and my clandestine supposition that 1787 would be a sufficient clue. — Mww

Not enough for me. But I can manage without that information.

There need be no inner fact about belief that can diverge from one’s consistent actions. — Banno

Believe me, there is no chance that I am going to knowingly posit anything "inner" or "private" in the sense that Wittgenstein was talking about.

It seems that for Ramsey the degree that one is willing to bet constitutes the partial belief. A belief is not "private" or "subjective", but measurable, and comparable with other beliefs. — Banno

In one way, that's fair enough. But if you think it through, you find a world of complication and illumination. At least, I do, because I keep returning to the puzzle what probability actually means. (I'm particularly interested in what probability actually means in a single case.) The betting issue brings that out. Hower, Ramsey is only taking a first step. See above.

The relationship, then, is not between "degrees of belief and belief in probabilities", but between degree of belief and willingness to act. Consider willingness to act as an extensional substitute for degree of belief. — Banno

Yes. I was talking about something else. I think I can be a little clearer.
It seems crystal clear to me that we know, for sure, that a toss of a coin has a 50% chance of coming down heads. It's not even empirical knowledge, but an "analytic" result of the rules. We also know that the empirical probability will be only roughly, and not exactly, the same. I think that we also know that various empirical probabilities (I think the mathematicians call them estimates) based on past experience. The proportion of smokers who get lung cancer is higher than the proportion of non-smokers, etc. etc.
All this is quite different from my confidence in, for example, that I have 6 cans of beer in my fridge. It is a binary question, and perhaps I remember that I bought a pack on my way home. But I also know, perhaps, that my memory is not what it used to be, so my confidence is less than 100%.
Of course, there is a relationship between the two. Insofar as I am rational, I will adjust my confidence to conform with objective probabilities and also to conform with my evidence for my beliefs. All I'm saying is that the two are not necessarily co-ordinated and are, let me say, different states of affairs. Ramsey is presupposing a perfectly rational being with access to all relevant information.

But I do have a problem with the skimpy version of the idea that we have here. It is a fragment of the practice of betting — Ludwig V

I agree it is a skimpy version of the idea, and it is a fragment of the practice itself. I was thinking to highlight the history, the origin and purpose the idea represents, rather than its manifestation as a practice.

When push comes to shove, it seems to me elaboration of the idea into a practice degrades the dialectic regarding it, to a psychologically-bounded exhibition, when it started as a metaphysical idea. In other words, we’re at the ends of a thing without the means by which the thing occurs, from which arises the legitimate right to ask, not about what or how much the bet, which presupposes no more than the belief related to it, but rather, the composition of the belief itself such that a bet relative to it represents defense of that composition. So we have what looks like belief in a belief, which is absurd.
—————-

“The usual test, whether that which any one maintains is (…) his firm belief, is a bet.”

From a subjective point of view, isn’t it possible for one to bet on his firm belief, shown subsequently some conditions by which his construction of it is flawed, yet still firmly maintains it? Furthermore, in Kant, there are those beliefs in the purely empirical domain of which maintaining the firmness of them is irrational in which case some tests are failed, but there are others in the purely moral domain, the firm maintenance of them is necessary, in which case every test is passed.

And this is what happens when skimpy versions are filled out. Or….bloated, as some might say (grin)