So Hume's premises should be accepted over others because he is "doing psychology?" And it's not problematic that they are self-undermining because its "psychology?"

But surely past thinkers were just as much engaged in a psychology of knowing, so why are they all to be dismissed and Hume to be accepted on sheer assertion?

So Hume's premises should be accepted over others because he is "doing psychology?" — Count Timothy von Icarus

Not at all. We know induction is invalid. Hume presents an empirical answer, not a logical one. If you have a better, present it for consideration. We might apply a bayesian calculus to choose between the options...

replied:
the unexpected — Banno

You seemed to want to safely distance yourself from that. OK. So what do you deduce from the unexpected? How is the sudden need for an explanation also the idea of an explanation? When are you going to start saying something sensible here rather than posturing?

Yes! Again, we are not disagreeing with what's been said; I'm just pointing out that this is not logic. — Banno

But then…

One has reason to suspect a general principle lurks. It is worth shaping up in systematic fashion through deducing the consequences of such an explanation and then seeking the evidence that would offer inductive support. Or abduction as inference to the best explanation. — apokrisis

Note the move involved. From the particular to the general and from the general back to the particular. The surprise, the principle, the prediction. If you can get back out what you first put in, you’re in good shape.

So you simply reply in bad faith. It’s all you’ve got. Lame and performative efforts to pretend you are waving and not drowning.

You already have your causal relation, before you start on the logic of checking it. You bring it in to confirm your bias. That's the criticism. — Banno

Tediously you again skip over the deduction that fleshes out the move from the particular to the general.

If first comes the particular surprise as you argue, then has to come its general explanation. After that you have something to test.

And how is it confirming a bias? It is seeking to confirm the general explanation of the particular surprise. The confirmation comes then in the form of narrowing the scope for doubt, not for actually asserting complete faith in some prior hazy belief.

It is like you haven’t even been introduced to science as a method. You come up with the whackiest claims.

Abduction is not a formalisable process that can provide an algorithmic answer to Hume's scepticism. — Banno

To go from the particular to the general isn’t that hard to understand surely? Why else is fundamental physics all about seeking the symmetries that explain Nature? If symmetry is getting broken, then what is the symmetry is the sensible question. What is the general ground to the particular event? What is the wider principle that would make some unexpected event a matter of course? It’s all pretty bleeding simple.

You are making such a fool of yourself with your strained efforts to deny the obvious. But why stop now that you are on a roll? :up:

So what do you deduce from the unexpected? — apokrisis

Deduce? Nothing - that's the point!

When are you going to start saying something sensible here rather than posturing? — apokrisis

Soon after you start listening.

Good night.

We know induction is invalid. — Banno

Who gives a fuck about validity. Pragmatism is about being happy that reasoning can be useful. What matters is defining reason in a reasonable fashion. Mathematics might want proof. But then where does its axioms come from? What is the psychological process that grounds them? When does all the specious bullshit stop?

You have to sound reasonable when you make your grant application. — apokrisis

Is that a law of nature? I think it's the advice of a propagandist. Scream softly or the children might hear.

Who gives a fuck about validity — apokrisis

That explains quite a bit.

Soon after you start listening. — Banno

Look at the big sook. Not one reply to any point I have made. Just the usual posturing and deflection.

Is that a law of nature? I think it's the advice of a propagandist. Scream softly or the children might hear. — unenlightened

I appreciate your effort. But as a zinger, it’s a complete fail. Take some pride in your work if you want to wound.

That explains quite a bit. — Banno

Zing!!!!

Take some pride in your work if you want to wound. — apokrisis

I don't want to wound at all, and I'm not applying for a grant. I'm not even remotely saying anything original to take pride in. I'm interested in the attempt to defeat Hume, who I see as one of the great defenders of the nascent science, in the name of a false and contrived rationalism. I think it is a great pity and a disservice to science and to humanity. Science is not a religion; it makes no eternal pronouncements but remains humble, provisional, seeking understanding not overseeing. So maybe cut out the bullying posture a bit; it's unscientific.

By “we”, you mean you. — apokrisis

While @Banno can be as annoying as you to try to have a conversation with, in this he speaks for me as well. You are obscure Apo. It took me ages to decode from your posts your view of consciousness, which turns out to be a fairly straightforward reductive functionalism. Presumably obscurity is your intent, or you wouldn't speak the way you do. You decline interrogation (unless sympathetic), which is your prerogative of course. You say interesting stuff sometimes, but it's hard going to ask questions to get it clarified. Which is what philosophers like to do. @Banno is hard going as well, and slides away. @180 Proof, like you, relatively quickly moves to insult and condescension, although perhaps less so now. Everyone else submits pretty much, except for some of the crazy ones who get banned.

You claimed to be responding to my jest…

You have to sound reasonable when you make your grant application. — apokrisis

…with…

Is that a law of nature? I think it's the advice of a propagandist. Scream softly or the children might hear. — unenlightened

So forgive me if that came across as unhelpful twaddle. What did you really mean to say and do you think it was a helpful contribution?

You are obscure Apo. — bert1

Or is it that the pool has its shallow end yet also its deep end. Then even its paddling pool.

If I am obscure then you are…?

...and slides away — bert1

Cheers. If there is something in particular that I ought follow up on, let me know.

So of corse there are no 'well-documented occurrences of exceptions to nature's "laws"", as you say... because when they happen, it's good scientific practice to change the laws so as to make the exception disappear. — Banno

I'm thinking of laws as being descriptions of observed regularities. Then there are theories which purport to explain the ways in which those regularities function and their relation to other regularities. So we don't have well-documented cases of the most general natural invariances failing to obtain.

You seem to be talking about the theory side. So, for example, we had the Newtonian understanding of gravity and then the Einsteinian understanding, but the observed effects of gravity didn't change or ever fail to obtain as far as we know.

So are we to say that "the laws of nature are not merely codifications of natural invariances and their attributes, but are the invariances themselves", while also saying that we can change them to fit the evidence? Hows' that going to work? We change the very invariances of the universe to match the evidence? — Banno

So, in line with what I wrote above, you seem to be talking about what I'm not talking about. We can have two meanings of "the laws of nature"—one sees them as being conceptual codifications of the observed invariances and the other sees them as the invariances themselves. One doesn't have to be right and the other wrong—they are merely two different ways of thinking about it.

Or is it just that what we say about stuff that happens is different to the stuff that happens, and it's better if we try to match what we say to what happens? — Banno

Right, what we say about things is not the things themselves, and we should try to match what we say with what happens.

Indeed. And if laws are constraints, then the regularities can be statistical. Exceptions get to prove the general rule. — apokrisis

The regularities seem rigid on the macro-scale—and that is the macro-manifestation of the statistical averages operating on the micro-scale? That seems to make sense.

We want to avoid arriving at some transcendent power that lays down arbitrary rules. Instead we want laws to emerge in terms of being the constraints that cannot help but become the case even when facing the most lawless situations. — apokrisis

Right, I'm more sympathetic to the idea that nature's regularities have evolved like habits than that they are given as eternal verities by some imagined lawgiver.

So your reminder for this morning. As you do tend to slither away.

We are going with your suggestion that the unexpected starts the game. And so the question is how does a line of thought logically unfold from there if you are a rational inquirer into Nature of the kind that we would regard as conforming to the pragmatic epistemology of a scientist?

I replied, that being struck by some particular fact, we would look to its general explanation. And that is how Peirce sets up IBE. The logical move is to think that the exceptional exists within the greater context of the universal. And so we isolate the particular and look for how it might fit into some larger generality.

If something is merely "unexpected", then this could be the kind of accident that generally happens. The avalanche slides, the beam buckles. It could be something that should have happened but didn't. The lift arrives but its door doesn't open, the house was burgled and yet the dog didn't bark. It could be that shit was shoved through your letterbox and you want to find out who did it.

So there are events we immediately and habitually interpret as being in the class of mere accidents or failures of normal prediction. Generalities of those kinds. Or there are events which suddenly seem untoward – paradigm breaking – because they don't immediately assimilate to your regular structure of belief.

"Shit through my letterbox? But I'm such a nice guy! Widely admired. Was it some unlikely accident? Does this kind of thing just have to be expected as a general fact of the neighbourhood? Am I in fact not so popular as I thought?" [Hurriedly rejects the last paradigm shifting notion as just too ugly to even investigate further.]

So you can see how the abductive step goes. Casting around in a general fashion. Accidents can explain things as one extreme of how particulars are caused, then intention or lawful necessity can get the credit at the other end of this causal dichotomy. The idea of generality itself developed with the logical structure of the symmetry-breaking dichotomy.

The exciting thing would be dimissing mere accident, rejecting also a known general cause, and so having to figure out something new. The stage of thought we are labelling abduction is already passing from its the level of a habitual classification of the unexpected event to now the attentional level of feeling the need to inquire more closely. We have to actually wheel out the epistemic method that secured those previous classification skills as ingrained IBE and get prepared to work this one out at the level of fully attentive and rationally structured inquiry.

Friston's Bayesian brain, in other words. Embodied cognition. Peircean semiosis. All the models of cognition as having the structure where IBE becomes the sedimentary layers formed by a lifetime of learning how best to understand the world as it exists for "us" at its centre. You build up the wisdom of habits, and then keep on adding to that store of what works for you in the same manner.

The logic of the reasoning arc is the same. But a habit is just your many particular experiences of the world suitably generalised to the point they feel automatic. Attention is what you wheel in when you need to take a little more time to figure out a proper fit to a known generalisation, or even to begin adding some new habit of interpretance as a useful addition to the sedimented layers.

If you are truly flexible of mind and rigorous of thought, you might even be able to unravel old established thought patterns. Dissolve some sedimentary layers that may seem so deeply embedded that they have become undoubtable, but now you see they are habits that were wrong. Or just not general enough to continue to take up so much space in your head.

So there we have the complex but quite logical structure of abduction. The structure that evolution itself has already discovered and which organises every brain or cognitive enterprise. The unexpected arises. And it immediately is recognised as significant in some fashion as it doesn't seem to answer to the logical dichotomy of chance~necessity. It fits neither with your notions of mere chance, nor known regularity. IBE at the first habit level of response glitches. You must pause and reason it out in a more positively inquisitive fashion.

The IBE logic of habitual response becomes now the IBE logic of the attentional response. You cast around. If not mere accident, nor known regularity, then what? We have discarded whole categories of experience and narrowed the scope of our thoughts to see this unexpected particular as in fact the clue to some deeper mystery. And what do we do when we are Sherlock Holmes? Deduce consequences and seek inductive confirmation.

Take the particular, identify its generality, generate the prediction that would best test this new rule. The ability to now predict the particular from its general rule is all the proof you will ever need, or could ever get, that you are right in your thinking. Congrats. You have a new thought habit thanks to the logic of IBE. You can dichotomise or symmetry-break any event you come across as an example of a know regularity. Or the other thing of a difference that doesn't make a difference – to you. Just an accident to be dismissed as such.

That is a summary of a thesis that should after so many years be quite familiar to your ears. But your ears don't listen. Your brain doesn't engage. Your spidey senses just flash red alert. Danger, danger, Will Smith! Our impression management shield is failing! Slide away fast pretending you made an argument that was a celebrated success and lunch now calls you to your real world duties. :up:

Right, I'm more sympathetic to the idea that nature's regularities have evolved like habits than that they are given as eternal verities by some imagined lawgiver. — Janus

When you face a lumpen realist, there is no harm in shaking up their presuppositions with a dose of what seems like idealism.

The lumpen realist has to be the closet idealist anyway. They are the ones who believe in "the laws of nature" as sacrosanct verities. Truths spoken by ... well someone in the position to know.

Showing that it is alright to psychologise nature by talk of sedimentary habit and the evolutionary cosmos might help them one day to come out of the closet of their own accord. Let a little happy diversity into their shuttered lives. :grin:

Why think that, other than that it's possible? — Relativist

Sorry, missed this. Because laws are descriptive and don't really explain anything. Intention is explanatory. Although this might still be vulnerable to @unenlightened's defence of Hume, I'm not sure.

Because laws are descriptive and don't really explain anything. — bert1

That is not the view of law realists. They suggests there to be an ontological basis for the observed regularities.

Example: two objects with opposite electric charge (e.g. electron & proton) have a force of attraction between them. This force is a necessary consequence of their properties. The properties and force are ontological.

I'm thinking of laws as being descriptions of observed regularities... You seem to be talking about the theory side. — Janus

Yes, I suppose so. So how to proceed. I suspect that, as with most of these sorts of problems, it's as much about the choice of wording as the way things are. We agree that there are regularities, and that "what we say about things is not the things themselves, and we should try to match what we say with what happens".

I'm interested in the move from what Apo calls "the specific to the general". And I take this to be the focus of Hume's scepticism. Incidentally, that word, "scepticism", seems to frighten some folk (@Count Timothy von Icarus), as if Hume were showing that science can't work - quite the opposite, as @unenlightened points out. Better, Hume takes science as granted, and looks to see how it might work; finds that it can't be based on a logical deduction, and looks for an alternative.

Since it was questioned, let's go over the logic of induction again. Apo said

To go from the particular to the general isn’t that hard to understand surely? — apokrisis

But yes, that is exactly the problem. The move from any finite sequence of specific statements to a general statement is invalid. More formally, from f(a), f(b), f(c)... we cannot deduce U(x)f(x). This is the "scandal of induction". It is a philosophical problem - scientists and engineers just move on without paying it much attention. But it is part of the plumbing of our understanding of the world, and will niggle at those who worry about such things.

And Hume's response is much the same as that of the scientists and engineers mentioned above - just move on. He talked of moving on as a "habit". Since his time others came up with other suggestions. Most famously, perhaps, is falsification, a very clever response. Instead of proving that U(x)f(x), why not assume it and look for a counter-instance - and x that is not f? We can't prove an universal, but we can disprove it... or so Popper supposed. There are problems there, too, of course.

Now all of this is the standard history of the philosophy of science - regardless of what some here think. The scandal of induction has been the central problem for philosophy of science. Check me on this, if you like. There is a distinct eccentricity in suggesting otherwise, presumably a consequence of a desire to highlight the role or Pierce. Quite specifically, neither Pierce's version of abduction, nor the more recent variations, have satisfactorily answered Hume. And by "satisfactorily" here I mean that it has not gained any general acceptance as a way around the scandal. See the SEP articles for more on this. Point is, I'm right about it. Where the answer sits at present is more in Bayesian Calculus, which accepts Hume's point, and instead of looking to justify our scientific theories as true, looks to choose which ones are most believable.

That is the topic of this discussion, so far as I can see.

Now I don't think you and I, and even Apo and I, are really very far from agreement on this. It is, after all, what happened. But the narcissism of small differences keeps the posts... interesting.

The acrimony is a shame, but Apo and I have butted heads since before this forum came about. He's convinced by a form of pragmatism that I find wanting, and as is my want, I like to point out the problems with such things.

By the way, since it is a concern of yours, I did prepare this post using AI. I fed paragraphs in, read the response and then edited the text so as to account for issue identified by the AI. Some of the wording was changed as a result, I think for the better, or I wouldn't have made the change. It perhaps also helped in setting a less aggressive tone than i might otherwise have chosen. I believe this is well within the guidelines of the forum. If you don't like that, you do not have to read my posts.

The move from any finite sequence of specific statements to a general statement is invalid. More formally, from f(a), f(b), f(c)... we cannot deduce U(x)f(x). This is the "scandal of induction". It is a philosophical problem - scientists and engineers just move on without paying it much attention. But it is part of the plumbing of our understanding of the world, and will niggle at those who worry about such things. — Banno

And what prevents deduction moving from the general to the particular? Or induction moving from the particular to the general? And so the pincer movement on truth as the pragmatism that I describe?

I think when you talk about plumbing, you mean digging another long drop. And mistaking philosophy for applied predicate logic and set theory is like trying to do the Highland fling on one leg.

And oddly, set theory claimed to reach the infinite whereas Peirce preached finitude. That’s what hopping around on one leg gets you. Abstract nonsense.

Most famously, perhaps, is falsification, a very clever response. Instead of proving that U(x)f(x), why not assume it and look for a counter-instance - and x that is not f? We can't prove an universal, but we can disprove it... or so Popper supposed. There are problems there, too, of course. — Banno

Hence the useful dichotomisation of nature into chance and necessity. The set of all the accidents and the set of all the lawful regularities. And the statistical rules for inferring which of these sets is most likely the one you have just pulled that unexpected particular from.

Do we falsify the belief or challenge the doubt? It all winds up back at the same place. Reason bounded by its dichotomous logic. The truth balanced between particularity and generality. Deduction and induction able to do their complementary thing as they have been set up dialectically as each other’s inverse operation.

Now all of this is the standard history of the philosophy of science - regardless of what some here think. — Banno

Yeah. I’m sure Hume was an exam question back in Epistemology 101. Its own important moment in Enlightenment history. One really ought to give the 15 minutes of fame it deserves.

But to elevate it to the Gospel of St Hume? A bit much.

Point is, I'm right about it. Where the answer sits at present is more in Bayesian Calculus, which accepts Hume's point, and instead of looking to justify our scientific theories as true, looks to choose which ones are most believable. — Banno

So you mean I’m right. You just nicked my punchline. And left off the dichotomy. The bit that continues on to say the theories that are the most believable because they are also the least doubtable. :lol:

We have the pragmatist pincer movement that places us somewhere actually measurable on a spectrum. Some place that a sigma confidence can be assigned, the null hypothesis ranked against. Between doubt and belief, we can land in some justified Bayesian spot.

I think we agree, unless I've misunderstood. Epistemology is about justification, truth of beliefs, i.e., when a belief counts as knowledge or as rationally warranted.

Abduction, on the other hand, concerns how hypotheses arise. It’s more about possibilities, not their justification. So, it belongs to the context of discovery, not the context of justification. Abduction is pre-epistemic, it produces candidates for knowledge but doesn’t by itself confer warrant. It’s how we start to think, not how we come to know.

Cheers.

In Hume, the regularity of events is a given, and has a strong psychological foundation. Hence, it is said that Hume is doing psychology. However, thanks to differential geometry, we know that a continuous space gives rise to discrete spaces where regularities can appear. Regularity occurs in a discrete space.

I wonder if it is possible to change approaches, to move from psychology to geometry (and physics). Considering that in Kant, for example, the extensiveness of space (a discrete space) as pure intuition is a condition of possibility for objects of experience, this may create a bridge in this change of approaches.

Why take regularity as something given and without genesis? If regularity is an EFFECT, this would completely change the issue of the laws of nature and their origin. Since, and this is not casuality, these laws are also presented as something given and without origin.

AI response:

regularities appear naturally in discrete spaces. In fact, discrete spaces are often studied specifically to analyze and understand these regular patterns. The field of discrete mathematics, which includes areas like combinatorics and graph theory, is built on the foundation of studying such structures and the rules that govern them.

This is so interesting.

Nice. We have to take care here with what we do, though. Hume was looking for a justification for the move from specific instances to general rules. If that is our task, there's the danger of circularity.

If we follow Hume, our best theories of physics function because our habits are such as to recognise patterns in the stuff around us, but that we are not justified (or warranted) deductively in recognising those patterns. Induction is a habit, not a justification. No further explanation is given for the fact of that regularity.

If I follow your suggestion, which is somewhat like Apo's, the geometry of space is such that gives rise to the patterns we see. So what is recognised through habit is a result of the structure of space. (Is that right?).

Now here's the potential circularity: we understand the geometry of space because we recognise the patterns. Our understanding of geometry is derived from our recognition of those patterns. We would have geometry explaining the patterns only because those patterns justify geometry.

A response might be - will be - that geometry is not justified by those patterns we find around us, but the condition that makes such patterns recognisable - regularities as the necessary consequence of how experience is structured.

But I'd suggest that this might amounts to saying little more than Hume already said - that there are patterns. I don't see how "constraints on what patterns are possible" is a great change from Hume. He acknowledge that not just any pattern would do, after all. That there is some constraint is one thing; that there is this particular constraint, quite another. Explaining that there must be some constraint is not explaining why there must be this particular constraint.

Putting it another way, perhaps more in line with Wittgenstein, any explanation must have a grounding, something that is taken as granted and against which the explanation takes place.

In any case, Apo will be able to fill you in on more along these lines lines, if you can make sense of it. I remain unconvinced; not that there is not something interesting to be said here, but that it works as a reply to Hume's scepticism and the stuff thereafter.

Now here's the potential circularity: we understand the geometry of space because we recognise the patterns. Our understanding of geometry is derived from our recognition of those patterns. We would have geometry explaining the patterns only because those patterns justify geometry. — Banno

But wouldn't that be an anthropocentric position? Hume tells us that there are habits and regularities, but he does not tell us the nature of those. This is where we stop doing psychology, and perhaps the issue can be approached from another point of view.

For me, there is a realism in Hume that is the realism of habits and human nature, which serves as the basis for him to say something about induction and deduction. In other words, his knowledge of human nature is the ground on which he bases his criticism. This realism would play against him: he is talking about the nature of something, in this case the nature of man as a creature of habits. And in that sense, his position cannot take precedence over a geometric-physical description. In fact, here the geometric-physical description takes precedence, as it is capable of asking why the regularities are presented to us as they are.

In short, anthropology weighs too heavily on Hume. Which is a realistic description of human nature. But being realistic, he can no longer deny the validity of other realistic descriptions that go even further and can explain the nature of regularities. Hume cannot be absolutely sceptical. And what consequences does this have for the problem of induction? That is not yet clear to me. I need to think about it more. But perhaps the problem of induction is simply an anthropological problem.

And here Kant comes in with his discrete space and time. They are the condition of possibility of experience and therefore of the recognition of regularities. I find a relationship between this and differential geometry that allows us to understand extensive and discrete space as originating from continuous spaces. And from here, everything that follows in physics revolves around the origin of the regularity of the laws of nature, and ultimately the origin of the laws themselves. Discretisation is a process that goes from the continuous to the discrete (quantisation, quantum mechanics) and much more...

That is not the view of law realists. They suggests there to be an ontological basis for the observed regularities.

Example: two objects with opposite electric charge (e.g. electron & proton) have a force of attraction between them. This force is a necessary consequence of their properties. The properties and force are ontological. — Relativist

Sure, that is a possibility. But it raises a lot of questions about the details of this objective, but invisible and all-powerful, existence that laws partake of. Are the laws all omnipresent? If so, how does that fit with them being numerically distinct? Or is there really one big law that explains everything? Do laws change? Eternal god(s) without the personality?

Cheers. If there is something in particular that I ought follow up on, let me know. — Banno

I feel a bit bad now. I was remembering conversations on the philosophy of mind. Your awareness of academic philosophy is valuable and noticed.

If we follow Hume, our best theories of physics function because our habits are such as to recognise patterns in the stuff around us, — Banno

Hume is deeply uninteresting. He says something obvious about cognition. It is modelling. And now we can move along swiftly.

Peirce gets us back to ontology. His exciting idea is that epistemology and ontology both have the same essential causal self organising structure. Mind is of course modelling and the Cosmos is the physical reality. But still. The metaphysical level logic is the same in important ways. And it has to be so as that is the only way self organisation can take place.

So bang on about Hume all you like. Peirce already fixed up science as a rational method. Epistemology is sorted. Move on.

But what about this crazy idea that the Cosmos is an evolutionary process of taking habits? A growth of rational structure. Something that begins as a vague everythingness and then develops with a systems logic of downward acting constraints and upward constructing degrees of freedom. A whole complex metaphysics of Firstness, Secondness and Thirdness. Or potentiality, actuality and necessity. The irreducibility of the triadic relation.

You have this whole story laid out. One that was there at the start of philosophy with Anaximander and continues to bob about in the background through Pythagoras, Heraclitus, Aristotle and Plato. Then reappears with German Naturphilosphie - though mixed up with Christian theology and the wishful thinking of the Romantics. And finally we get science and maths really along for the ride as systems science and complexity theory fire up.

So Peirce was there at the right moment in history to set out a basic template of self-organisation as a general logic. A logic of both epistemic systems and ontological systems. He gave the reason for why we would have brains that echo the logic of the world. A system is a system is a system. And that is what we need to get to the bottom of.

Of course, this is all rather complicated and demanding. Unfamiliar and scary. Who even needs it if our only pragmatic interests are in building better machines. Reductionism gives you mechanics. You get engineering and computing. Systems are about holism and self organisation. We can pretend that more complex engineering and computing will get us to that too.

But anyways. That is my puzzle. There is this big exciting stuff to sink your teeth into. And science is already eating philosophy’s lunch. Even a modest metaphysical hit like Ontic Structural Realism is only really catching up to 1960s quantum field theory.

Yet maybe that is how it should be. Philosophy doesn’t even seem very good at teaching critical thinking anymore. Maybe it just is now a curatorial exercise. The museum of old ideas. In this room we have Hume. In another we have a dusty old crew that includes the Austins, Collingwoods and Davidsons. No one hardly visits that anymore. The exotic Continentals are more the crowd pleasers.

So rehash Hume for an umpteenth time. The interesting thing about abduction is that it does have its logical structure even if you want to draw a line between hypothesis discovery and theory development. There is the sudden aha! The leap from the particular to the general. The reframing that reveals a fact in a new light. The thing Peirce was getting at in how he set up IBE.

The surprising fact, C, is observed. But if A were true, C would be a matter of course. Hence, there is reason to suspect that A is true.

If the world is generally this way as a system of constraints, then the kind of regularities it would generate - the kind of fluctuations or degrees of freedom it would result in - would have this particular character as a matter of course. Guess the correct rule and you will get the kind of variables it must have to be able to operate.

Why take regularity as something given and without genesis? If regularity is an EFFECT, this would completely change the issue of the laws of nature and their origin. Since, and this is not casuality, these laws are also presented as something given and without origin. — JuanZu

This is just what I’m talking about. Why are electrons and photons the way they are? Well the answer just jumps out once you can understand gauge symmetry. This is the marvel of gauge applied to Maxwell’s equations of electromagnetism. The fact that U(1) is the simplest complex number Lie group simply demands that reality has electric charge and the massless vector boson we call the photon.

So the holism of quantum field theory says the excitations of Nature must be shaped by fundamental symmetries. And the abductive hoops that science went through to sort out the Standard Model of particle physics are entertaining to read. All the maths of gauge groups was known. So the small library of possible symmetries was known in the same way Plato could know that regular solids could even exist. But fitting the particles popping out of the colliders into the right slots took all sorts wrong turns. Protons and neutrons turned out to be SU(3) - and so were triplets of quarks. The weak force had to have previously been the SU(2) electroweak force and then broken by a matching SU(2) scalar field - the Higgs - to be turned into a force now with massive particles and also reorganised to release the U(1) photon which had been effectively caged inside it.

It is like the world could only be composed of atoms that were spheres, cubes, tetrahedrons, and the other Platonic solids. But here we are now stripping geometry down to algebra and so allowing the maths to range over all the normed division algebras. No longer just the reals, but the complex numbers that embed quantum spin in every fundamental particle, and the quaternions that are especially useful to understanding the half-spin fermions.

So abduction in particle physics became about a small library of Platonic structures that existed because they had irreducible symmetry. And then firing up the collider to look for the tell tale particles that these symmetries would have to produce in their various combinations.

There were the surprises, like the nine kinds of mesons produced in hot collisions. That made sense when it clicked that mesons were actually short lived quark-antiquark pairs. The SU(3) symmetry that gave three colours of the quarks also gave the nine possible pairings of quarks - eight charged and the ninth neutral. The physical reality just drops out of the symmetries that constrain the possible structures of nature, The big deal that Ontic Structural Realism was all about.

So reality had this systems logic. Reality had to be classical because you have real number matrices describing the Poincare symmetry group of special relativity. And it had to be quantum because you have the complex numbers matrices of the gauge theory underpinning quantum field theory. If these number systems could exist as themselves algebraic symmetries, then nature had to express them as the forms its excitations took. Even the classical vs quantum divide boils down to the restrictions that mathematical logic creates for itself.

So Peirce proposed a deep connection between the self-organising mind and a self-organising universe. This led to his triadic logic, his tale of irreducibly hierarchical systems order. Forget the reductionist logic used for deduction and other mechanistic tales of causal entailment. Peirce was on to something way more fun. A logic large enough to forge a world.

And now science really has a sense of what it is looking for. Mathematical strength models of symmetry coupled to colliders or any other instrument which could manifest the particle that must exist as some combination of broken symmetries at a given temperature of the Universe.

Yes again, it is not the deductive logic with its valid arguments that seem so important to some frittering their time away in the margins of philosophy. It is the grand vision Peirce had of a notion or the logical or the rational that could be a theory of everything. A theory of the self organising system, whether that system was epistemic or ontic. Whether it was psychology or physics, mind or matter.

So stuff Hume. Stuff weedy complaints about abduction being an invalid logic, and possibly not even a logic. It is all so trivial. Useful in small ways. But also builds in habits of thought that actively prevent understanding logic as a metaphysical-strength enterprise.

A journey which philosophy started and science is having to complete. Getting at the Cosmos as the growth of rational habits, the manifestation of inevitable order, a process of dialectical evolution. A natural logic truly worth understanding even jf you just want to get at the cognitive mechanics of forming inferences to the best explanation.