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. — Mww

So we are not really in conflict - just talking about different things. Fair enough. As it happens, I regard the history, origin and purpose of ideas as of interest, even importance, in understanding their meaning. However, if your quotation is indeed from Kant, I'm not equipped to do more than try to follow the conversation. For the record, I think I'm talking about what it is to act rationally in the context of probability, an issue that puzzles me greatly.

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

It is indeed a test that is often proposed in real life. So it is relevant to say, not that a bet is no test of confidence, but that interpretation of a given decison is complicated by the fact that a bet is the result of weighing risk (disutility) against reward (utility) in the context of one's confidence. Confidence alone does not determine a (rational) decision.

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. — Mww

I sort of understand this and don't disagree with it.

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. — Mww

I'm not sure I quite get this. Mind you, my grasp of what people mean by metaphysics is, let us say, weak. I don't quite see why what I am saying about betting degrades anything that you are doing. After all, you know it all already and don't seem to have any problem putting it aside for the purposes of your conversation.

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

Well, your reaction is not unhelpful to me, so thank you for that. I won't bore you any further on the subject.

So it is relevant to say, not that a bet is no test of confidence, but that interpretation of a given decison is complicated by the fact that a bet is the result of weighing risk (disutility) against reward (utility) in the context of one's confidence. Confidence alone does not determine a (rational) decision. — Ludwig V

You may be groping your way towards Bayesian statistical decision theory. As I have said before, there are 4 components: model, data, prior, utility. That is enough to make a 'rational' decision. I'd prefer to say it provides a principled or formalized decision-making process. It doesn't stop you having an unreasonable model, prior or utility.

Thanks - there's a lot here. I'm not closing the book on probability, but opening it.

That our deliberations rarely fit propositional or predicate logic clearly and unambiguously does not undermine the use of propositional or predicate logic. It may still provide a model for our reasoning. That same goes for the various examples of the use of probability here. You don't need a confidence of 100% in order to go to your fridge with the expectation of retrieving a beer. Indeed, it makes little difference if there are six or five, if what you are after is one. Your confidence that there is more than one beer is what is at issue. Your confidence in that is shown through action.

Ramsey's contribution is to show the interaction of belief, preference and action, and what must apply if these are to remain consistent despite being partial, fallible, and changing - his axioms.

Ramsey doesn't guarantee that we will always bet rationally. He sets out (or better, begins to set out) how we can understand being rational in circumstances of partial belief. He shifts the question from “Is this belief true?” to “Is this belief coherent with my other beliefs and actions?”

So will you go to the fridge or keep watching the game? Your choice shows your preferences and what you think is so.

You may be groping your way towards Bayesian statistical decision theory. As I have said before, there are 4 components: model, data, prior, utility. That is enough to make a 'rational' decision. I'd prefer to say it provides a principled or formalized decision-making process. It doesn't stop you having an unreasonable model, prior or utility. — GrahamJ

I'm not sure what the model is, but the other components are pretty obvious. Perhaps the Bayesian theory works - I wouldn't know how to assess it. Can we run the process in a lab and assess whether it gets the answer right - or what?
The thing is, it runs decision to action. The question here is whether you can run it backwards to read from action to decision. The difficulty is that most readings will be underdetermined, I suppose.

That our deliberations rarely fit propositional or predicate logic clearly and unambiguously does not undermine the use of propositional or predicate logic. It may still provide a model for our reasoning. — Banno

I didn't know I was challenging it - though one might have thought that a two-valued logic would have a problem - not with the probability of a coin toss, but with degrees of confidence.
I don't quite understand the concept of a model for our reasoning.

He shifts the question from “Is this belief true?” to “Is this belief coherent with my other beliefs and actions?” — Banno

I see. Do we care whether the two are the same thing?

So will you go to the fridge or keep watching the game? Your choice showsyour preferences and what you think is so. — Banno

Only if you can read it correctly.

Only if you can read it correctly. — Ludwig V

What could it be to "read it correctly"? The presumption here seems to be that there is a seperate and "correct" belief, perhaps a piece of mental furniture, apart from the choice to go to the fridge or not.

But neither of us want to say that.

But neither of us want to say that. — Banno

Perhaps "correctly" is over-stating it. But it is also possible to revise my interpretation in the light of more and better information or even to actually misinterpret my action

One can go to the fridge for many reasons apart from taking out a beer. One can take a beer out of the fridge for many reasons apart from feeling thirsty.

I'm not saying that there is not a range of equally acceptable answers, though my report is helpful in narrowing down the field. But there are also answers that may look right and turn out to be wrong.

I assure you, my mind is completely unfurnished.

I assure you, my mind is completely unfurnished. — Ludwig V

As is mine.

But it is also possible to revise my interpretation in the light of more and better information or even to actually misinterpret my action — Ludwig V

Yes, indeed. But if we are to do so consistently, we might do well to presume a few things. Ramsey doesn't tell us how to be certain. He tells us what it means to be coherently uncertain — to reason, act, and believe in a way that fits together, even when the world is incomplete, and we are fallible.

Your preferences reveal what matters to you, that your beliefs are not binary but admit of degree, that you would do well to choose those acts that maximise expected utility, given your beliefs, and that you can update your beliefs, given new information. And perhaps most originally, that you would do well to value your beliefs so as to be internally consistent; so as to avoid a dutch book.

That this is not the whole explanation for your possible actions does not retract from the usefulness of these suggestions.

I assure you, my mind is completely unfurnished.
— Ludwig V
As is mine. — Banno

I have a replica of Versailles in mine. You're missing out.

I got a ton of unreal stuff in mine, bordering on a chaotic rhapsody if I’m being honest, all of which I’m somehow persuaded I can’t do without.

Language games. Put unreal stuff in an unreal place, then call it by real names. Sure. Why not.

In Bayesian probability, Frank P. Ramsey and Bruno de Finetti required personal degrees of belief to be coherent so that a Dutch book could not be made against them, whichever way bets were made.

Well, I can see that a Dutch book would be a bad idea. On the other hand, there is the possibility of a "Czech book", in which the probabilities add up to less than 1. Wikipedia, which is never wrong, tells me that always pays out to the gambler.

He tells us what it means to be coherently uncertain — to reason, act, and believe in a way that fits together, even when the world is incomplete, and we are fallible. — Banno

That sounds wonderful, and better than the sceptical bewailing of our failure to match the traditional expectations.
I can see that conforming to the requirements will avoid some nasty traps, so that's good. But I can't see that it will do more than that.

I'm not sure what the model is, but the other components are pretty obvious. Perhaps the Bayesian theory works - I wouldn't know how to assess it. Can we run the process in a lab and assess whether it gets the answer right - or what?
The thing is, it runs decision to action. The question here is whether you can run it backwards to read from action to decision. The difficulty is that most readings will be underdetermined, I suppose. — Ludwig V

You have talked quite a bit about making decisions under uncertainty - about medical treatments, weather forecasts, coin-tossing, and beer in fridges. I was replying to all of that and I may have confused things by quoting a particular paragraph. I wasn't trying to 'run it backwards' to interpret a decision.

The model is your idea of how some aspect of the world works. It provides the probabilities of various outcomes.

The model is your idea of how some aspect of the world works. It provides the probabilities of various outcomes. — GrahamJ

OK. That makes sense.

You have talked quite a bit about making decisions under uncertainty - about medical treatments, weather forecasts, coin-tossing, and beer in fridges. I was replying to all of that and I may have confused things by quoting a particular paragraph. I wasn't trying to 'run it backwards' to interpret a decision. — GrahamJ

I'm trying to keep the enthusiasm for Bayes in proportion by anchoring our conversation in how we do things, or how we think we do things, when we aren't relying on Bayes. I'm trying to work out whether we can rely on Bayes or not. At present, the assumption is that we can. My mind is not made up.
As for running the Bayesian process backwards, I didn't think you were trying to. The idea came from me alone. It may seem a bit crazy, but we have two questions to ask about these situations. There are two question. One is forward-looking - what shall I do? The other is backward-looking - why did that person do that? So far as I can see, Bayes helps with forward-looking. My question is whether it can help with backward-looking. I don't see why we couldn't use Bayes to reconstruct a decision after the event. That would be an analytic process that could clarify what was going on.

I want to go back to this:

Instead of seeking justification for induction, (Ramsey) explains how we act as if inductive reasoning were valid. — Banno

I hope it's clear that I am not advocating doing induction using probability. Better to drop induction all together and instead look at how a bit of maths can help show us if our beliefs - held for whatever reason, or no reason at all - are consistent.

Better to drop induction all together and instead look at how a bit of maths can help show us if our beliefs - held for whatever reason, or no reason at all - are consistent. — Banno

Help with consistency is always a good idea. Dropping induction, I fear, may be more difficult. Pavlovian conditioning works at levels beyond the reach of voluntary control.

Instead of seeking justification for induction, he explains how we act as if inductive reasoning were valid. — Banno

I prefer this Humean explanation. But I thought that since the fifties and sixties, we had all given up worrying about the deductive invalidity of induction. Why are we revisiting the past? I'm sure the Bayes process has its place, but I don't really see why induction needs to be replaced or even can be replaced. There is one thing the Bayes process can do that cannot be done any other way - it can give us some help in dealing with one-off probabilities. (Not even induction can do that!)

I'm unable to work out where we disagree - if at all.

I gather we agree that induction - the conclusion that a general rule is true, on the basis of specific instances - is problematic.

We have it from Hume, Wittgenstein et al. the despite this, it is not unreasonable to believe in some general rule, given specific instances.

We have it from Ramsey and others that there are solid statistical methods for comparing and revising various beliefs, and we agree that these are A Good Thing.

Do we have a disagreement?

Do we have a disagreement? — Banno

I think I may be a bit more sceptical than you. But I agree that you have outlined the context in which we need to think about this technique.

The distinctive feature of Bayes is that it enables us to articulate a single case. So it will always be an good place to start.

I keep recalling a slogan I remember from the days when computers were new. Maybe you also remember GIGO - garbage in, garbage out. I don't see how that doesn't apply to this process as well. This is why an algorithm cannot improve on the data it start from. What it can do is to articulate intuitions suspicions and prejudices and reveal where they are wrong and where they are right. That's not nothing.

We have it from Ramsey and others that there are solid statistical methods for comparing and revising various beliefs, and we agree that these are A Good Thing. — Banno

The key word there is "revising".

Repeated applications of the Bayesian process, in which the first run uses whatever starting-points we have and subsequent runs feed back the outcomes from that. Perhaps in the context of an scientific investigation of some problem or project - which I understand was the context that Bayes had in mind. Wouldn't that develop more accurate predictions - not necessarily to the point of developing a universal law, as simple induction does, but it could develop a more complex collection of laws and it could certainly develop more accurate probabilities?

It's a more formalized and accurate process of trial and error.

That's just a sketch on the back of an envelope.

Ok.

Bayesian analysis takes a prior and updates it given further information. Ramsey is different, more fundamental. His stuff is setting out what rationality looks like in a situation in which we have only partial belief - no certainty. The betting structure shows gives us a way of understanding what a belief and preference amount to, using just behaviour.

I wasn't thinking of Bayesian analysis in my comments, until that was raised by your good self.

So not so much about laws.

This needs a good example. I'll work on it.

The betting structure shows gives us a way of understanding what a belief and preference amount to, using just behaviour. — Banno

Well, gambling was important in the development of probability theory from the beginning. So it's no surprise that it crops up here. More than that, it's true that people do sometimes challenge a claim that they disagree with by suggesting the proposer puts their money where their mouth is. But I'm irritated that, in this context, people talk as if the size of the bet is somehow an index of the strength of the belief. Outside of artificial situations in labs, that's just not the case. A bet is a balance between risk and reward assessed in the context of the degree of confidence and in the wider context of the bet.
Of course, if you use a bet as a model for all behaviour under uncertainty, the scope of the theory is extended. But it seems at least possible that there are limits to that scope. Insurance is like a bet in some ways, but quite different in other ways. Is it helpful to think of a decision to buy a particular car or house as a bet? And so on.

This needs a good example. I'll work on it. — Banno

I'll look forward to that.

The two accounts are of very different things.

You have a plant. You water it every day. This is not a symptom of a hidden, private belief, on Ramsey's account - it is your belief. Notice the similarity to Ryle.

A Bayesian account presumes some level of belief and modifies it, without saying what that belief is. You think 150ml is enough for the plant, it starts to wither, so you adjust the watering up to 200ml, and so on, adjusting your belief according to the outcome.

Ramsey offers a minimal account of the nature of belief, while the Bayesian account assigns a value to a belief without specifying what that belief might be. Ramsey gives an account of belief’s nature; Bayesianism gives a rule for belief’s revision.

So your criticism that Bayesianism assigns a value to belief without saying what belief is, is quite fair. But does not apply to Ramsey.

Got it: https://www.gutenberg.org/cache/epub/4280/pg4280-images.html#chap105

A few paragraphs into that section.

To be fair I didn't know the passage I just guessed it was Kant, and had some help.

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. It frequently happens that a man delivers his opinions with so much boldness and assurance, that he appears to be under no apprehension as to the possibility of his being in error. The offer of a bet startles him, and makes him pause. Sometimes it turns out that his persuasion may be valued at a ducat, but not at ten. For he does not hesitate, perhaps, to venture a ducat, but if it is proposed to stake ten, he immediately becomes aware of the possibility of his being mistaken—a possibility which has hitherto escaped his observation. 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.

Who will take my bet, and at what odds? Should I be prepared to trust anyone who did take it? — Ludwig V

I'll bet the same against you, on the odds that it doesn't -- given I have nothing and I could win on the bluff I might as well.

That's what I meant to imply by the 1 million dollar buy in before. Maybe it's stupid. I ought read Ramsey that @Banno linked to judge either way.

I distrust betting on the whole. It's a test of who is right and who is wrong -- so I can persuade a person to bet against that the LNC* is false in at least one circumstance, and then provide the argument from the liar's sentence (which will certainly not persuade), and we'd be right back doing philosophy again rather than betting.

*EDIT: I think going for the LEM is much easier but that'd undermine my point: that at a certain spot we'd stop betting and start talking philosophy

The bet is just a portrayal of any act. The philosophical move is from the action representing the belief to the action constituting the belief.

The bet is just a portrayal of any act. The philosophical move is from the action representing the belief to the action constituting the belief. — Banno

OK, fair.

So, bets, promises, posts on one hand and paying up, following through, and reading on the other.

Ramsey offers a minimal account of the nature of belief, while the Bayesian account assigns a value to a belief without specifying what that belief might be. Ramsey gives an account of belief’s nature; Bayesianism gives a rule for belief’s revision. — Banno

You put the difference very neatly. Only, I didn't intend it as a criticism, but as an analysis.
BTW, yes, I had thought of Ryle when Ramsey first came up. I shall take the opportunity to say, because it needs to be said as often as possible, that Ryle is not a behaviourists the sense that Watson and Skinner are. (I can't say whether that's true for Ramsey, since I haven't read the texts). He has a "thick" conception of what action is, whereas Watson and Skinner have a "thin" conception. To put it another way, where Watson and Skinner think of the brain as a telepone exchange - a switching mechanism - Ryle and (I guess) Ramsey think of the mind as what enables us to act rationally.

Got it: — Moliere

Well done! I found a copy of the chapter on some obscure web-site, but couldn't find any attribution - which was a little frustrating.

You notice, I hope, that Kant's account of the incident is entirely true to life. But he considers his "victim" as a person like him. He doesn't consider how much a peasant would stake, given that they have virtually no money.

I'll bet the same against you, on the odds that it doesn't -- given I have nothing and I could win on the bluff I might as well. — Moliere

Yes. You see how your thinking is conditioned by risk and reward in relation to your resources. Yes, of course, it is a non-standard, even contrarian, decision, but nonetheless, the amount you will bet is not an index of your belief, but the result of several interacting factors. To fnd the strength of belief, you have to work through all those factors.

I distrust betting on the whole. It's a test of who is right and who is wrong -- so I can persuade a person to bet against that the LNC* is false in at least one circumstance, and then provide the argument from the liar's sentence (which will certainly not persuade), and we'd be right back doing philosophy again rather than betting. — Moliere

I like the twist that events will take you back to philosophy, because there has to be agreement on the outcome.

That's what I meant to imply by the 1 million dollar buy in before. — Moliere

I'm sorry. I don't remember what the buy-in was.

The philosophical move is from the action representing the belief to the action constituting the belief. — Banno

I'm sorry. I don't see what you are getting at.

So, bets, promises, posts on one hand and paying up, following through, and reading on the other. — Moliere

I can see the link between the two. But I don't see how that fits with what @Banno says.

I can see the link between the two. But I don't see how that fits with what Banno says. — Ludwig V

On the left hand side I have three examples of representing belief, and on the right hand side I have each corresponding constituting actions of belief. At least, that's what I was thinking in offering the examples: Also to get a better idea of this wider sense than the bet, to see what other species of representing/constituting belief there may be.

Banno, J,
I know you have moved to some interesting discussion here, but the issues below still seem live to me, and related to where you are now.

And related to post on the Bernard Williams thread.

To call something misleading is to say it leads somewhere—but crucially, somewhere we didn’t intend, or that doesn’t fulfill the function we took ourselves to be engaging in. That’s not the same as saying there is a metaphysical end-point we ought to be led to; rather, it’s to say that a particular use diverts us from how the practice normally works or what it aims at internally. — Banno

So your last word “internally” seems to frame the whole position. Because phrases like “somewhere we didn’t intend” or “somewhere that …doesn’t fulfill the function we took ourselves to be engaging in” or “how the practice normally works or what it aims at..” seem to confuse the issue of whether “there is a metaphysical end-point” or not (since they all sound like euphemisms for metaphysical end-points or causes).

You appear to be saying that a philosopher’s best (or better) use of skills is to take models and language games and rigorously determine their consistencies and inconsistencies, confirm coherence, and root out incoherence. Philosophic language ought to be aiming at coherent and consistent models, internally, and can side-step judgments regarding correspondence type analyses that endeavor only to point externally to the world or “metaphysical end-points we ought to be led to.”

Are philosophers to frame their questions tightly focused on internal consistency, and build standards that are most uniquely philosophic when those standards are based on coherence, not correspondence?

You seem to be saying that all correspondence usages of “truth” or “facts about the world” should be left to physics models and agreed upon stipulated languages like biology, or mythology, or good literature. But philosophy remains best (or ‘better’ I should say to avoid reference to some ‘metaphysical end-point’) when it aims to weed out inconsistencies and incoherence from any language, from any logic.

To frame this another way, the better philosophical discussions are about whether a belief may be true because it is consistent internally with what it purports to say and actually does say as a model. Less rigorous philosophy unwittingly or carelessly falls back into discussing what is actually true, in the world, regardless of how things may have been worded (and regardless of the well-established epistemic and metaphysical problems correspondence entails).

Is that what you think, and somewhat what Williamson was getting at? Doing better means clarifying the coherent, not discovering the correspondent?

The reason for reading the canon is to improve on it. But in order to "improve" on it, one does not need already to have an idea of the perfect or ultimate item.
— Banno

Yes. In the arts, "improve" might better be thought of as "develop" or "enrich" or, of course, "react wildly against"! — J

I do agree that one “does not need already to have an idea of the perfect or ultimate item.” I agree because the subject of this sentence is an “item”. There is no ultimate item. At least not necessarily.

But then, how are we to ever mean “ultimate” - how is the word ever a valid part of a useful model? How, for instance, did I know there is no such thing as the ultimate item? How can we measure “improve” or “better” and apply them?

The point I was trying to make that for some reason seems to only interest me was that you in fact DO have the “ultimate” or “best” in mind whenever you say “enrich” or “progress” or “improve” - ultimate is your metaphysical measuring stick, or metaphysical end, or cause. It’s not an item, but a clear enough concept to tell you “that item over there ain’t the ultimate item.”

I suggested an example -- the battle of the bands -- in which we don't appear to need a constitutive idea of "best" in order to choose a winner. (Remember, we're both agreeing to reject that other reading of "best" which simply defines it as "top choice." That's not constitutive. That would be like saying that piety is what the gods love. It provides no content.) — J

I’ll get back to a constitutive example, but, I don’t think I rejected “top choice” as “best” - an idea like “top” will always be found near the idea of “best”. My point is that an idea like “best” will always be found near an idea like “better”.

You raise a good example of what I’m trying to point out. You said, “…’piety is what the gods love’… provides no content.”

So while I see that “piety is what the gods love” is a good example of circular reasoning or possible tautology between “piety” and “gods love”, which provides no content to “piety” internally and adds no measure of consistency to using “pious”; however, I also see that, for some other reason, you aren’t talking about say “brown” or “honey”.

“What is piety?” Piety is a sweet flavor, like honey. Or wait, piety is a brownish color, like mud. Or wait, “piety is what the gods love.”

So ‘what gods love” actually does provide some content, because I’m sure you know that, at the very least, piety is not like honey and brown. Piety is about the gods - that gets some work done. An idea like “piety” will only be found near an idea like “god”. This doesn’t ultimately define either, but the idea of “brown honey” is useless, that is for certain (somehow).

I think what I am trying to point to is indirectly reflected in this: just like it is hard to give a good constitutive example of a superlative ideal such as “best”, it is hard to give a good example of something wholly non-constitutive such “piety is what gods like” is not wholly non-consitutive. Speaking at all requires coherence AND a corresponding world for us communicate at all, for us to agree and disagree through language. (I think this needs to be developed, and its development would make distinctions between speaking and communicating where communicating requires a mind independent world in between two communicants, but I think I digress …)

But to finish my more general (but I think necessary for rigor) point. You and Banno seem to want to be able to develop content using words like “better” and “enrich” while avoiding inherent references to the ‘best’ and the ‘richest’. That to me is using words like “piety” without any orientation or end in site, in which case maybe piety is really green and smells funny. There needs to exist something upon which we both can agree, apart from us both, external to our language, about which we are speaking and possibly agreeing; not simply language. To use “better”, we need to see: 1) two things 2) being compared by some standard, to then form 3) agreement on which makes sense to call the “better” or not.

Analyzing 2) only, the standard, we are talking about a shoe-horning into the picture of a metaphysical measuring stick of worst-better-best. That is what “better” means in itself; it means that which is in between the worst and the best, but leaning towards the best (or something like that). Better entails worst and best, in itself, by definition, in every appropriate use. We need that to be the case, to use “better” at all.

But applying/using/testing this ideal laden measuring stick also requires items in the world, appraised by some standard (ie ‘music that is able to be danced to’ - which is ‘better’, x or y style of music). Marry the measuring stick of some specific standard, apply it to two or more items and you can debate and communicate which is “better”.

If we remove the metaphysical, we can’t have this debate.

And if we are always only looking for coherence and consistency, the content can always remain hypothetical and progress always means “yes, that’s coherent” or “no, that’s incoherent”. (Better becomes a weak judgement of something more plainly good or not good.)

Consider this: it is coherent and internally consistent to say this: ‘when comparing only two items, the one that is better is also the one this is best.’ This is a coherent understanding of “worst-better-best” in a context of two items, without any need to actually consider two actual objects in the world. I believe you are saying analyzing statements like this is philosophy’s best use, correct? So objects in the world are hypothetical, if needed at all, to do philosophy.

So now I ask you, must the best philosophy relegate itself to identifying and clarifying consistent/inconsistent and coherent/incoherent relations internal to systems/models? Or is there more to it that can still be rigorous and ought to be the work of philosophers?

So now I ask you, must may the best good philosophy relegate devote itself to identifying and clarifying consistent/inconsistent and coherent/incoherent relations internal to systems/models? — Fire Ologist

Yes. Though it needn't.

Or is there more to it that can still be rigorous and ought to can be the work of philosophers? — Fire Ologist

Yes.

I almost left the word "internally" off that paragraph, yet you see it as pivotal. So something is adrift.

The simple point is that we can deal with our present situation without positing some absolute.

I don't have much more to say on the issue.

It seems to me that you do not have an argument, so much as an intuition - something like that we can only have consistency if there is a "metaphysical endpoint", whatever that might be.

But that's not right. It's as if you were to notice that (locally) every number has a higher number, and conclude that therefore there must be a highest number. It ain't so.

The simple point is that we can deal with our present situation without positing some absolute. — Banno

Ok. Did you argue that somewhere without positing some absolute?

What is an "absolute"?

I juxtaposed "relative" and "absolute" measurements, in the example of hot and cold - I hope that is clear.

We can instead play with "local", as in the example of cardinal numbers. Locally, given any cardinal, we can add one, producing another cardinal. That doesn't lead to the "absolutist" conclusion that there must be a highest cardinal.

So can we set out an argument that making any comparison requires some sort of "absolute"? I don't think so.