We cannot justify it by deductive reasoning, but we can by inductive reasoning — Janus

I still do not understand this. "We can by inductive reasoning" just is "the future will resemble the past". It's re-stating, not explaining.


Added:

To put it another way, it is rational in a practical sense to assume that the future will resemble the past, because to our knowledge it always has. — Janus

That says that the future resembles the past, because the future resembles the past...?

Valid, I suppose, but I find it unsatisfactory.

"We can by inductive reasoning" just is "the future will resemble the past". It's re-stating, not explaining. — Banno

:up:

We can move on from the nineteenth century. — Banno

Welcome to the 1960s? Anglophone logic choppers wake up to realise something or other might be slightly amiss. They begin shift in their armchairs and chat among themselves quietly.

Perhaps we all can reach some agreement that Bayesian calculus of one sort or another is a rational response to Hume's problem?

The “normative” aspect here does not consist in a choice among alternatives, but in adherence to what follows from the model itself. — Banno

If conforming to a model solves the problem, then simply infer a model on the basis of the constant conjunction of the empirical evidence. Under the framework of the model, the (otherwise) inductive inference s necessitated by the model.

I alluded to this earlier.

Perhaps we all can reach some agreement that Bayesian calculus of one sort or another is a rational response to Hume's problem? — Banno

Sure. The problem that remains is do we aim to eliminate every wrong hypothesis or magically leap to the only correct one? This appears to be how you are framing things.

And clearly, neither is computationally efficient. But Bayesianism is more efficient if there are general priors to rapidly constrain the search space to discover some particular best answer.

It is like the old game of animal, vegetable, mineral. A dichotomising algorithm that can eliminate half the possibilities at each turn will zip through the alternatives at exponential speed.

So the problem is finding the needle in the haystack. But then you can divide the stack in half and stick it through a metal detector. Pretty quick, you arrive at your destination.

Thus we are being asked to believe in some false dilemma. Abduction doesn’t have to discover the needle in one inspired leap, nor sift the stack forever. Being organised as a hierarchy of dichotomising constraint gets the job done. And we get to shortcut the process still further by a smart choice of priors. We can already launch into the search from some “paradigm” that reduces the search space in a generally reliable fashion.

Bayesianism reduces the abductive arc of reason to an algorithm. Something a neural network could do. Once it has been suitably trained on some pragmatic task and formed a hierarchy of weighted priors. And it has some way of learning from its errors.

That is a closing of the loop as a maximisation of self-information via the minimisation of entropic surprise. The rational process that results in a stable sense of self within its generally ignorable world.

So Bayesianism sounds the opposite of abduction. One laboriously eliminates all hypotheses but one. The other supposedly leaps to just the one and ignores all the others.

However, in reality, pragmatism results in a hierarchical organisation of knowledge habits that can parse the world efficiently with built in priors. And also had the feedback loop that is the flip to attentional processing. Pausing to stop and think. Coming to a halt at surprise or error. Learning what needs to learnt to rewrite the hierarchy of priors and move on.

So it is not simply the fact of a Bayesian algorithm. It is the ability to grow an organised hierarchy of priors in a scalefree way. Bayesianism applied over every scale of the challenge that is being a thinking organism within a world that is itself becoming increasingly transformed by that thinking which is taking place. The world as the organism wishes to “improve” it.

That’s a lot to unpack, Apo. You’ve got Bayes, neural nets, and pragmatism all packed into one explanatory hierarchy. Impressive, but maybe overengineered? Bayesianism gives us a model for updating beliefs, that can be implemented in brains, machines, or whatever. But it's not a replacement for abduction but an elaboration. Bayes doesn’t eliminate the guesswork, it formalises it. We still need to choose priors, and those priors depend on the very same customs, habits, and shared practices that Hume, Wittgenstein, and Davidson were talking about.

So yes, it closes the loop, because we’re already inside it. The Bayesian calculus doesn’t tell us why we ought to weight one hypothesis over another; it just tells us how to do so consistently, given a prior. The “hierarchy of priors” you describe isn’t an algorithmic miracle — it’s the social, linguistic, and biological history of our talk about causes.

Rationality isn’t something we add on top of experience, but what emerges from doing what we do - talking, testing, correcting, and learning together. In that sense, Bayesianism is one more way of describing Hume’s “custom and habit,” not a transcendence of it.

If conforming to a model solves the problem, then simply infer a model on the basis of the constant conjunction of the empirical evidence. — Relativist

So you would use model theory to explain induction? An interesting idea. What do you have in mind? There'd need to be a move from the preservation of truth to a preference between model, I presume?

Bayes doesn’t eliminate the guesswork, it formalises it. We still need to choose priors, and those priors depend on the very same customs, habits, and shared practices that Hume, Wittgenstein, and Davidson were talking about. — Banno

But then these "customs, habits, and shared practices" are what are left vague. Half-baked. Contingencies treated as obligations.

So I prefer the Bayesianism that is properly biosemiotic. A story about life and mind and why it exists in the way it does within world that is the way it is.

So sure, there is this layer of sociology mediating between the neurobiology and the metaophysical levels of human semiosis. We are socially-constructed by language in a fashion that equips us to create a social level of organismic purpose and function.

Yet that sociology just likes to leave so much out. It doesn't want to root itself in physics – the thermodynamic imperative that entrains its structure. It doesn't want to believe in the metaphysics that might draw that essential connection to its attention.

Sociology wants its own little world which is closed off and free just to be itself. Some agreeable collection of priors in the form of "customs, habits, and shared practices". Humans doing their human thing in a pluralist, civilised and non-totalising fashion. The world as it should be for the incurable romantic.

Here you frame my approach as "surely a little too much work; a risk to the easy life of cosy presuppositions that the 'philosopher' would choose to socially-construct". And I agree. Yet also I enjoy the work.

The “hierarchy of priors” you describe isn’t an algorithmic miracle — it’s the social, linguistic, and biological history of our talk about causes. — Banno

Yep. That was my point. Same algorithm repeated at different levels of topological order.

And if sociology is the cosy talk level that self-confirms our status as civilised humans, then that is why I emphasise the need to switch things up to an investigation of causality itself. Not just merely a bit of loose chatter that describes things that have been said rather than targets an explanation of the phenomenon.

You just pointed to a mathematical view of induction as a Bayesian calculus. I then pointed to the issue left hanging – the how and the why of the priors. You say that is just sociology. I say descriptively that may be so, but I says we want to cash that out at the mathematical level too. Which is what for instance the Bayesian Brain approach to life and mind is trying to do. The self arising inside the loop as a hierarchy of priors, a hierarchy of Peircean habits of interpretance.

Rationality isn’t something we add on top of experience, but what emerges from doing what we do - talking, testing, correcting, and learning together. In that sense, Bayesianism is one more way of describing Hume’s “custom and habit,” not a transcendence of it. — Banno

Well I've just argued the case for "nope". Yet again.

Of course you will protest that you employ logic too in your armchair approach. But there is a big difference between learning to count and do a little algebra and learning to think in terms of the mathematical architecture that stands behind symmetries and their breaking.

This is the reason Peirce stressed his approach was architectonic. The holism of a systems approach. The logic that gives you the irreducible triad of vagueness, dichotomies and hierarchies.

So yes, rationality can evolve from a linguistic level to a mathematical level. From a social syntax that aims to tell us "who did what to whom" – the subject-verb-object structure appropriate for coordinating the behaviour of a band of chatty hominid foragers – to a logical and abstract syntax that can organise a metaphysical story of hierarchies composed of their global constraints and their local freedoms.

The way a Cosmos itself self-organises. And the way life and mind could arise within that cosmos by stumbling on the self-making power of biosemiosis.

So of course you will again object to the grandeur of this vision. Wittgenstein fell flat on his face, along with Whitehead and other heroes of the logical atomic age, by trying to be a totaliser. If those dudes couldn't do it, we should as just stop trying.

And yet Peirce had already whipped up a robust logic of reality. And systems science was chipping away in the background. Science and maths really began to catch up after WW2. A theory of complexity could become the new research goal.

Much more is happening every year than you seem to even imagine. You just have to have the itch to get out an explore.

No, not to explain induction. Rather, I'm suggesting that the development of a model is rooted in induction.

I see a 2 step process: 1) infer elements of a model from induction, based on the conjunction of empirical evidence; 2) cast a specific inference (eg "all swans are white") from this element of a model.

This seems consistent with science. When an innovator proposes a hypothesis at odds with the current conventional wisdom, he is setting aside that conventional model and presenting an element of an alternative model.

The grand edifice.

But there's a difference in our methodological dispositions that may be irreconcilable. I have an allergy to explanations of everything. I think complete explanations are completely wrong. So I'll leave you to your mythologising, and muddle along. — Banno

I’ll stick with the patch I can walk on, the language I can play with, the practices I can follow. That’s enough to get things done, and more than enough to keep me honest. Your cathedrals are impressive, but I’m happier muddling in the workshop.

In model theory, a model is a structure that makes a formal system’s sentences true.

I think we are at cross purposes.

In model theory, a model is a structure that makes a formal system’s sentences true — Banno

But they don't, really- unless you embrace a "relativist" theory of truth.

Might leave this were it is. Check out the SEP link. The Model Theory to which I referred is a branch of mathematics.

I still do not understand this. "We can by inductive reasoning" just is "the future will resemble the past". It's re-stating, not explaining. — Banno

I don't take it as being "the future will resemble the past", but "the future will most likely resemble the past". This is practical, not "pure" or deductive, reasoning based on what has been experienced in the past— as far as we know the future has always resembled the past. We don't know of any exceptions— "exceptions" denoting 'breaches of the common set of regularities and invariances'

To put it another way, it is rational in a practical sense to assume that the future will resemble the past, because to our knowledge it always has.
— Janus
That says that the future resembles the past, because the future resembles the past...?

Valid, I suppose, but I find it unsatisfactory. — Banno

To repeat, I wouldn't put it that way but instead "the future will most likely resemble the past, because the future has, as far as we know, always resembled the past".

.

Cool. I took that as read. I think the point still stands. "the future will most likely resemble the past, because the future has, as far as we know, always resembled the past" amounts to "The future will most likely resemble the past because the future most likely resembles the past".

I'd still change that to "The future will most likely resemble the past because as far as we can tell, the future has always resembled the past". It's not a tautology.

Note: By "resemble the past" of course I mean broadly speaking. We don't have any reliable records that indicate that there have been periods where such things as gravity failing to obtain, time running backwards, the Sun failing to rise and set, fire freezing things instead of heating and burning them, rivers running backwards, people being suddenly able to breathe underwater, animals changing their forms, people and animals rising from the dead, etc., etc.

"The future will most likely resemble the past because as far as we can tell, the future has always resembled the past". — Janus

Ok. I still don't see that isn't a tautology - or so close as to make no nevermind.

It's not true by definition that the future will, or even likely will, resemble the past because it always has. It's just an expectation based on habit. The only reason I say it is a rational expectation is because past experience is literally all we have to go on —which I think means it would be irrational to ignore it. For examples, it would be irrational to believe that you could jump off a tall building and fail to fall to the ground, but instead be able to fly, or to ignore the science that indicates that humans have contributed to global warming.

Such mock humility. :up:

To repeat, I wouldn't put it that way but instead "the future will most likely resemble the past, because the future has, as far as we know, always resembled the past". — Janus

I prefer the past constrains the future. It has already eliminated a huge range of possibilities. That is what makes the future so predictable. But also leaves it full of contingency.

If I ate the cake this morning, I can be sure I won’t be eating this evening. Not will anyone else. But if I didn’t do so, I could eat it at any future moment. Unless someone else beats me to it. That sort of thing.

I agree with what you say, and for me the idea that the past constrains the future relies on the idea that the '"laws of nature" may evolve over long time periods, but will not suddenly alter.

Model theory omits a link to ontology. It defines what truth is semantically, but does not relate it to anything in the world.

Truthmaker theory does this: a truthmaker is that aspect of reality to which a true statement corresponds. Tarski agreed that the statement, "snow is white" is true, because snow is white. This is standard deflation, but he omits identifying the italicized phrase with a truthmaker.

In my earlier post, I was referring to a model of reality. You were referring to a language model. But you can't get truth out of language without a connection to reality- an ontological grounding. So what I said about a model of reality stands, and I'll apply it here:

It's not true by definition that the future will, or even likely will, resemble the past because it always has — Janus

I agree. However, we could draw inferences about the nature of reality by examining the past, and apply that analysis (that model of reality) to making predictions. This is, of course, the nature of physics.

Isn't "warranted" just another way of saying "best"?
— @Banno
No. Being warranted means to be rationally justified.
A subjective "best" inference may, or may not, be warranted. — Relativist

We seem to be circling. Being warranted means to be rationally justified, and something is rationally justified if it is warranted. The best explanations are the ones which are rationally justified, and those are the ones that are warranted, and they are the ones we accept. A subjective best inference may not be warranted, but then it would not be the best inference, and so not justified, and not the best. — Banno

I hope you don't mind looping back to this. No doubt you will ignore me if you do.

It is clearly true that "warranted" and "justified" are closely related. But they can be distinguished, at least for philosophical purposes, by locating each in a different approach to argumentation. I'm referring to Stephen Toulmin's Uses of Argument. He treats an argument as a process of justification, and a warrant as a specific part of that process. A warrant, for him, is

A statement authorizing movement from the ground to the claim. In order to move from the ground established in 2, "I was born in Bermuda", to the claim in 1, "I am a British citizen", the person must supply a warrant to bridge the gap between 1 and 2 with the statement "A man born in Bermuda will legally be a British citizen" (3). — Wikipedia - Stephen Toulmin

But perhaps there is another distinction that can be marked by "warranted" as opposed to "justified".

A prediction is justified by the fact that there's a depression and westerly airstream out in the Atlantic.
The forecaster is warranted in making the prediction because they are qualified to do so.

I am justified in claiming victory because I saw the winning goal being scored.
You are warranted in accepting that because I told you about it.

Some epistemologists use "warrant" to refer to a justification sufficient for knowledge. The conditions that make it so are open to debate. Nevertheless, I was just treating warrant as synonymous with justification.

Some epistemologists use "warrant" to refer to a justification sufficient for knowledge. The conditions that make it so are open to debate. Nevertheless, I was just treating warrant as synonymous with justification. — Relativist

Well, that just reinforces my opinion that there is no set way to distinguish between them. So your synonymy is not wrong. I'm usually very sceptical about claims of synonymy. There's usually a difference to be found. In this case, perhaps, too many differences for comfort.

Semantics is important, to ensure points are understood as intended.

I notice that the Wikipedia article on justification mentions warrant as "proper" justification for a belief.

Model theory omits a link to ontology. It defines what truth is semantically, but does not relate it to anything in the world. — Relativist

Well, that's just not right. But rather than pursue the issue here, I'm thinking a new thread is needed. I'm thinking of starting a more general chat about one of Gillian Russell's articles on barriers to entailment, so I might leave this for now.

Thanks for the chat here. Let me know what you make of Against Method.

There's two approaches to this, and I'd like to look in to how they relate. The one is the already mentioned Bayesian calculus, which gives us a method for improving on our beliefs. Note that your examples concern our beliefs. There's a difference between the past constraining the future, and the past constraining our beliefs about the future. Bayesian calculus only allows the latter.

The other is Gillian Russell's recent work on logic, just mentioned. That is about the world rather than about our beliefs.

But they can be distinguished, at least for philosophical purposes — Ludwig V

A valid point - I do tend to use "warrant" and "Justification:" synonymously, which is a problem acknowledged in the literature. We've Plantiga's use of "warrant" for whatever it is that turns a true belief into knowledge, and again that's a whole new kettle of fish.

I'm not sure we have an opposition between warrant and justification so much as the one being a sub-class of the other. We are also justified in believing the forecast of a qualified meteorologist.

Are inductions warranted but not justified?