"Truth-preservation" is really just consistency, which means not having premises which contradict one another or the conclusion. The validity of deductive arguments is independent of the truth of premises, maybe that's where you're becoming confused; I don't know. — Janus

Maybe I'm not the one who's getting confused ;) I understand very well what truth-preservation is. My point is that it's a concept that is 1) narrow, 2) complicated and 3) deceptive. Don't tell me it's not complicated. It is. There is a much simpler and a much better way to define logical validity. Validity in general, outside of logic, means "the state of being legally acceptable". We can define logical validity in the same exact way, as the state of being legally acceptable. This means that a logical argument is one that abides by the rules of reasoning (whatever they are.) This is broad enough to cover all the different types of validity (not only truth-preservation), it is not unnecessarily complicated and it is not deceptive. It fits every single need perfectly. If we need specific concepts, we can use those too, but we don't have to rely on them all the time. They are, in many situations, inappropriate. Again, that's how I define the concept of validity and that's how I think validity should be defined. It's not how most people think. You don't have to accept it if you don't want to though you can argue against it.

I would have to first understand what you mean (and you haven't explained it in any way that makes it all clear to me) before I could agree or argue against it. So, best leave it, I guess. :s

↪Magnus Anderson

I would have to first understand what you mean (and you haven't explained it in any way that makes it all clear to me) before I could agree or argue against it. So, best leave it, I guess. :s — Janus

You don't understand what it means for a logical argument to abide by the rules of reasoning?

You believe in it not for any reason, but because you can't help it. — SophistiCat

I would not put it that way; I would say that we follow inductive reasoning for the practical reason that there is no alternative, and I would also say that it is reasonable to have faith in it, because, leaving aside (what I would consider unreasonable) radical skepticism, all our experience and understanding confirms that nature is indeed replete with invariance. There seems, on the contrary to be no good reason, beyond a certain kind of carping logic, to question that.

No I can't comprehend your eccentric account of the rules of reason.

↪Magnus Anderson

No I can't comprehend your eccentric account of the rules of reason. — Janus

I don't think that's eccentric. I think that what they teach you in school is eccentric. The rules of reasoning, or inference, is a very intuitive idea.

You know what a mathematical function is, right? It's a relation between two sets where every element from the first set is associated with exactly one element from the second set. Now, I think that this is too strict. Instead of thinking in terms of mathematical functions, I tend to think in terms of partial functions, since these are more relaxed; or better yet, in terms of relations. But even these are kind of strict . . . The basic idea is that you have two sets which may or may not be related to each other. It's sort of like a system except we're not talking about variables, parameters, etc. Well, we can, if you want; we can say we have two variables or two parameters but no more and no less than that. That's what every logical argument fundamentally is. Can we agree on that? We have a set of premises on one side and a set of conclusions on the other side. And we also have connections, or associations, between the two sets (which may also be absent; again, we love general concepts because they give us more freedom.) We need some basic rules to limit what kind of premises and what kind of conclusions are permitted. Once these are set, we need to determine what kind of associations are permitted and/or expected. This is where "the rules of reasoning" kick in. This is what determines whether any given argument is valid or not. No notion of consistency whatsoever. Just associations and rules that determine what kind of associations are legal and what kinds are not. You can't just associate any kind of premise with any kind of conclusion, right? Reasoning is a process that works according to a set of rules. So if you note that "All men are mortal" and that "John is mortal" you cannot conclude that "John is a man". You can't associate these two premises with that conclusion. It's against the rules.

I'm somewhat nonplussed by the conversation here.

Magnus clearly has a simplistic and ill informed understanding of logic, and you have pointed out how his examples of induction are invalid. A valid argument is one in which if the presumptions are true, then the conclusion must also be true.

And it is also I hope clear that on this definition of validity, induction is famously not valid. (x)f(x) does not follow from any number of instances f(a), f(b), f(c)...

Do you agree with this so far?

Yes, I do agree that inductive arguments cannot satisfy the criterion of validity. I have also said that any inductive argument can be re-framed as a deductive argument to which that criterion can then be applied, but I acknowledge that this requires the addition of an extra premise or premises. And I would say that these additional premises would generally consist in the assumption that nature is invariant.

Sweet.

Could we also proceed not by introducing invariance, but instead by introducing a measure of probability?

Yes, I think modern physics makes it seem plausible that invariance is not deterministic, but instead probabilistic; yet it seems that invariance on macro scales does look, for all intents and purposes, deterministic.

Ok. So if there were issues with invarence, we could proceed along another path, and science would not be shot.

So invariance is a conclusion reached after observing the evidence?

It seems that cyclical repetitions of patterns in nature are observed everywhere. The inference that there is either rigidly or probabilistically determined invariance of the microphysical constituents of physical nature seems natural once the idea of supernatural determinants have been rejected.

You can probably see where I am going. The move from evidence to invariance requires an induction, if it is going to be a conclusion.

So i’m Going to suggest that invariance is something of what Sam called a hinge proposition.

I agree, but I don't think of explanatory inferences as conclusions, but rather as conjectures.

Yes, I think modern physics makes it seem plausible that invariance is not deterministic, but instead probabilistic; yet it seems that invariance on macro scales does look, for all intents and purposes, deterministic. — Janus

You don't need invariance. You just need a limit on variance. And probability theory models limits on variance.

So i’m Going to suggest that invariance is something of what Sam called a hinge proposition. — Banno

A better "hinge proposition" - as it is gives its own founding reasons - is the view that invariance is the emergent limit to variation.

And from that metaphysics, the reasonableness of inductive inference follows quite naturally.

Induction only needs extra metaphysical bolstering if invariance is taken as the metaphysically fundamental condition. But if your complaint against the invariance of induction is that nothing prevents nature varying, then a view of induction based on the fact that variation itself can suppress variance means induction has no case to answer on that score.

Deduction, on the other hand, has a metaphysical problem once you grant that nature is fundamentally variable.

I would not put it that way; I would say that we follow inductive reasoning for the practical reason that there is no alternative — Janus

If by "no alternative" you mean a sort of psychological compulsion then that is just what I was saying.

and I would also say that it is reasonable to have faith in it, because, leaving aside (what I would consider unreasonable) radical skepticism, all our experience and understanding confirms that nature is indeed replete with invariance. There seems, on the contrary to be no good reason, beyond a certain kind of carping logic, to question that. — Janus

Aaand... we are back to circular reasoning. There is no good reason, other than an epistemology that is already shot through with induction, to conclude that "nature is replete with invariance." You could take that not as a conclusion but as an assumption and try to ground your epistemology in that assumption*, but that seems like a strange move. An epistemology is something you already have and would find very difficult to let go. Why chuck it out in favor of a less intuitive, less psychologically secure assumption? Pragmatically, this would seem like the less favorable option.

*Or you could do something even more convoluted and put your faith into some religious or metaphysical narrative (a la @apokrisis) from which the regularity of nature would then fall out.

SO are we talking conjectures and refutations - falsification?

That is, we see f(a), f(b), f(c)..., propose the conjecture that (x)f(x), and actively seek to find an example of E(x)~f(x)?

*Or you could do something even more convoluted and put your faith into some religious or metaphysical narrative (a la apokrisis) from which the regularity of nature would then fall out. — SophistiCat

So you are saying that the problem of induction doesn’t hinge on the metaphysical assumption that causality may not be invariant? Curious. What other motivation does it have?

And so I simply say go with that same assumption. Permit nature to vary. And then understand it’s apparent invariance in terms of the self organisation of limits.

After all, that is the world as science has found it to be, if you’ve been keeping up.

Constraint is, as I understand it, simply a limit to what is possible. The opposite of it is freedom.
— Magnus Anderson

Yep. Simple really.

The world we live in, in other words, is stable enough to make induction good at making predictions. This makes perfect sense.
— Magnus Anderson

Yep. You got it again. — apokrisis

Alright. That might be the case. But I think that you're saying a bit more than that. I am not sure. Your insistence that you're not interested in narrow subjects such as logic, epistemology, conceptual analysis, etc suggests to me that your interest lies in devising a theory of everything i.e. a theory that explains how everything in the universe works. And I belive that's what you mean when you talk about metaphysics. Metaphysics = a theory of how everything works. You also talk about how your metaphysics is not reductionistic but instead holistic. How do we interpret this? I interpret it to mean that you are in fact a monist. A dialectical monist. Yin-yang philosophy. You want to unite the opposites. Uncontrolled interaction is not enough. There must be a central force, some kind of God, controlling the antagonism. Hence your focus on trichotomies, triadic conceptual structures. Very reminiscent of Aristotle's theory of golden mean. You have a center and two extremes. Left, middle and right. So in the case of order~chaos dichotomy, you want to subsume the two to a third category which is basically that of order (which explains why you make a distinction between constraints and patterns or regularities which you say are merely observable.) So you're acknowledging the dualism and then reducing it to monism under the guise of trialism. There is chaos but this chaos is subsumed to order. I think that Perice said something along the lines that there is no absolute certainty but that there is absolute truth. That would make him a very clever absolutist in my book. But is he? I am not sure. Further investigation required.

There is chaos but this chaos is subsumed to order. I think that Perice said something along the lines — Magnus Anderson

Peirce said: 1) there was Chance Tychism and from this came 2) Mind and from this came 3) Matter, matter being effete Mind.

Now compare this to Daoism:

First came 1) The Dao (Mind) then came 2) Opposites as waves (Yin/Yang) as a manifestation of the Dao then came 3) Creative energy (Qi) as a inner manifestation of the waves.

What so both have common? The Mind. And was does the Mind do? It explores and learns. Induction, as some may call it is fundamental to experienced life. It is not a question of logical validity.It is what life does.

So you are saying that the problem of induction doesn’t hinge on the metaphysical assumption that causality may not be invariant? — apokrisis

No, I am pretty sure that's not what I was saying. I am not even sure what that means.

And so I simply say go with that same assumption. Permit nature to vary. And then understand it’s apparent invariance in terms of the self organisation of limits.

After all, that is the world as science has found it to be, if you’ve been keeping up. — apokrisis

Right, circular reasoning again. Induction -> Science -> Fanciful metaphysics -> Induction.

Right, circular reasoning again. Induction -> Science -> Fanciful metaphysics -> Induction. — SophistiCat

What's wrong with a circular argument if it takes the form of the scientific method?

The circle is that of abduction, deduction and inductive confirmation. So "induction" gets split into the assuming of some hypothesis and then the assessing of the evidence in favour of that hypothesis (or the lack of good reason to doubt it).

The metaphysics is then informed by that. In Peirce's case, it led him to challenge the prevailing ontic determinism of his day. He argued that the logic of how we reason is in fact the logic of how nature itself must develop its regular habits. So that revised metaphysics - one that sees probability and chance as fundamental in nature - becomes then the new hypothesis.

And what do you know? Shortly after, quantum mechanics was born.

If by "no alternative" you mean a sort of psychological compulsion then that is just what I was saying. — SophistiCat

No, I just mean that there is no viable alternative method.

Aaand... we are back to circular reasoning. — SophistiCat

Not really. We have to make assumptions to get started. As I have shown if you make the assumptions explicit inductive reasoning can be framed in deductive forms. Science bases itself on the assumption that there are "laws of nature" that determine the invariances that are observed everywhere. At the most fundamental level we have the Strong Nuclear Force, the Weak Nuclear Force, the Electromagnetic Force and the Gravitational Force. Then there are the laws of thermodynamics.

Science theory at every level is based on the presumption that these laws hold. Of course there is no merely logical reason why they should hold. But these are the premises of the whole 'argument' of science, and just like the premises of any argument; their soundness cannot be demonstrated by the argument itself, but must be taken on faith. We take these premises on faith simply because there are no viable alternatives; we cannot even begin to imagine what an alternative could look like.

What's wrong with a circular argument if it takes the form of the scientific method? — apokrisis

Its utter pointlessness? I mean, if you've already helped yourself to induction, what's the point of circling back to "justify" it via one of its purported consequences?

I interpret it to mean that you are in fact a monist. A dialectical monist. Yin-yang philosophy. You want to unite the opposites. Uncontrolled interaction is not enough. There must be a central force, some kind of God, controlling the antagonism. — Magnus Anderson

No controlling hand is needed. The dichotomy or symmetry breaking just goes freely to to its equilibrium balance. It finds its own eventual rest state where it is evenly broken across all scales of being. Hence the final state of a natural system that is just forever freely growing in evenly-paced fashion is going to be fractal. It will have the structure of a scalefree hierarchy.

Hence your focus on trichotomies, triadic conceptual structures. — Magnus Anderson

Yep. The triadic structure is the balanced hierarchical relation that emerges from the symmetry breaking.

A hierarchy represents a state of maximum local~global asymmetry. You have opposing limits of scale appearing as a system develops its own history. It becomes a world organised into the general and the particular, the global constraints or laws and the local degrees of freedom.

You have a center and two extremes. Left, middle and right. — Magnus Anderson

No. The dichotomous extremes are the local and the global. The middle is then the spectrum of scales that span the space (and time) inbetween.

So for instance, the Universe is bounded at one end by the Planck scale, at the other by the cosmic event horizon. Then we humans sit about exactly middle.

So in the case of order~chaos dichotomy, you want to subsume the two to a third category which is basically that of order (which explains why you make a distinction between constraints and patterns or regularities which you say are merely observable.) — Magnus Anderson

Well now this is talking about how the whole thing develops.

So in the beginning - as Peirce describes - it starts with the symmetry of a Firstness or Vagueness. There is just the purest kind of chaos. Unbounded fluctuation.

Then you get secondness as fluctuations start to collide or react with each other in deterministic fashion. You get local events happening.

Then, after some time, you get enough local events happening to start to sort things out and create some kind of common history. You get regular patterns or habits emerging. The system develops a memory. A bunch of random local events start to add up in ways that build a general regulating pattern.

This situation is modelled by scalefree hierarchies. Take a case like the network of world airports. An airport could be freely built anywhere. But as the network starts to grow, it becomes convenient to begin to hub them. You will get certain airports becoming very large as the critical node in larger network. The airport system will develop a clear stratification - a hierarchy of airport sizes that is optimal in terms of achieving a total flow of air-traffic through the system.

So in the beginning, there are just a random scatter of airports all around the same size. By the end, there is a stratified and organised system that emerges in a random fashion to satisfy the general constraint of needing to maximise the flow.

No controlling hand is needed. Just a general constraint of having to optimise the dynamics.

So you're acknowledging the dualism and then reducing it to monism under the guise of trialism. There is chaos but this chaos is subsumed to order. — Magnus Anderson

Nothing is being hidden. But one of the difficult mental changes in gear needed to understand Peirce is that Thirdness is the third stage that incorporates the other two stages. So Thirdness is not monistic but irreducibly triadic. As it says on the box. It is only "monistic" in the sense of being holistic - speaking about the oneness of an irreducibly complex whole.

Monism is usually a substantialist's ontology. It is all about a metaphysics of a single stuff - whether that be materialist stuff or spiritual stuff. So quite different from a Peircean metaphysics where all stuff is the emergent product of an irreducibly triadic process.

Likewise, vagueness of Firstness may sound like a monistic stuff, but it ain't. It sounds like some kind of material being, and yet it can't be that. It is just an unformed potential. Substantial being is what it starts to become - once we get to the dyadicity of Secondness, or brute reaction.

Its utter pointlessness? I mean, if you've already helped yourself to induction, what's the point of circling back to "justify" it via one of its purported consequences? — SophistiCat

You are not making sense. How does inquiry even get started unless you are willing to hazard the concrete guess that you are then committed to checking via measurement against the reality you are modelling?

What is it that you are attacking here? I can hear your angry noises, but the target of your unhappiness is very unclear.

Even Hume said we reason inductively because that is what is natural to our psychology. So we only "help ourselves to induction" in the sense that we find ourselves already the products of an evolutionary process. We were born to be pragmatically successful at predicting our worlds.

In Hume's day, there wasn't a lot of science to back up that evolutionary view. But now our best models of neurocognition are explicitly Bayesian. We took the hypothesis and ran with it. The results confirmed the guess.

We take these premises on faith simply because there are no viable alternatives; we cannot even begin to imagine what an alternative could look like. — Janus

I would say not quite. The Newtonian breakthrough involved a metaphysical presumption about invariant laws. And now the modern presumption is that all such invariances must be emergent regularities. All the forces of nature are patterns that emerge in self-organising fashion from collective action.

So Newton talked of transcendent laws. Modern physics is aiming at a story of immanently self-organising constraints.

And the two different ontologies map fairly obviously to a generally deductive or computational and deterministic metaphysics, and generally inductive or probabilistic and developmental metaphysics.

So we do have two alternative metaphysics in play. And each would generate its own particular kinds of hypotheses when it comes down to scientific theory.

Not really. We have to make assumptions to get started. As I have shown if you make the assumptions explicit inductive reasoning can be framed in deductive forms. — Janus

You cannot replace induction with deduction salva veritate, since induction is plausible reasoning and deduction is certain reasoning. If you assume "invariances of nature" of a certain sort, then you can make a case for the viability of inductive inference in general, but you cannot thereby turn any specific inductive inference into a deduction.

As for starting assumptions, I think that induction itself makes for the most natural starting assumption (since we are already strongly predisposed to it) - more so than the rather complicated cocktail of assumptions that you are proposing.

Science bases itself on the assumption that there are "laws of nature" that determine the invariances that are observed everywhere. — Janus

The basic inductive intuition is more local, more restricted than that. Yes, induction implies that we can perceive persistent patterns in nature, but that's it. And that's all the "assumption" that science requires to get going. It does not require us to assume from the start that all of nature is completely subject to laws, much less that these laws form a reductive hierarchy with a fundamental theory of everything at the bottom. Such ideas are viable, but they are not basic, nor are they necessary. Science happily proceeds with local laws and "special" theories.

Yes, I acknowledge the differences between a deterministic and a probabilistic explanation for the laws of nature; my point was only that we have no alternative to the laws themselves to focus our investigations; whether we think of them as ultimately transcendent or as immanently emergent.