You return to the point that 'each is the measure of the other' so I think that's key to your argument, I'm just not comprehending it yet... — keystone

It’s the logic of a reciprocal or inverse operation. How do we recognise the discrete except to the degree in lacks continuity. How do we recognise continuity except to the degree it lacks the discrete. One is present to us to the degree the other is absent.

Grey is the vague. It can then become white to the degree it sheds its blackness, and black to the degree it leaves behind its white. We have two ultimate limits where black = 1/white and white = 1/black.

AS rejects any number that is not useful to humans, such as Pi beyond a few decimal digits. Ultra-ultrafinitism? — Real Gone Cat

That does have some sense if you wanted to play with it as a conjecture. What would be the best rebuttal? Would we start by saying we couldn’t limit the scope of future human ambitions and the numbers that would involve?

There is a line of thought if you wanted to be serious about dismissing it.

Likewise he made the point that animals and even tribal human cultures don’t require a number sense beyond one, two, a few and many. So where does that leave our love affair with an unbounded capacity for assigning distinct names to an infinity of values?

Again a perfectly fair start to a discussion that can draw on plenty of scholarship.

How often do random or confused starting points lead to entertaining discussions on PF? Far more often than the dogmatic exposition of something anyone could read up as the received view in an undergrad textbook I would say.

So yes, give AS a break. :smile:

Why am I nuts? — Real Gone Cat

If you believe @Agent Smith was being that cunning and conspiratorial in framing his OP.

What would be the point?

No, I don't believe the continuum is everything. I think that the computer/mind lies outside the continuum. For example, when you imagine a sphere your mind exists outside that sphere. — keystone

Huh? Weren’t we about talking about how we “picture” the continuum just as much any other mathematical object like a sphere? Non sequitur here.

In our mind, we are neither thinking of everything nor nothing. We can only think of something. I don't believe in the existence of either extreme. — keystone

Can you picture a hypersphere as easily as a sphere? Does that make you doubt that it is a constructable object? Is your whole argument going to be based on what you personally find concretely visible in your minds eye? That’s a weak epistemology that won’t get you far.

When a line is cut, none of the line is lost. It is just divided. — keystone

And when the line is joined, is nothing gained? If there is no gap due to the cut then is there no connection if there is a join?

You just seem to be saying stuff. I can’t picture a cut which doesn’t result in a gap. Are you now claiming you can see that just as vividly as a sphere? Is this an argument where we just accept your word on everything? The rules for constructing mathematical objects is becoming unclear.

You're the first to ever entertain my idea on cutting a continuum. (or perhaps you have the same idea) — keystone

It’s a standard kind of idea. For instance - https://en.wikipedia.org/wiki/Dedekind_cut

The part I have trouble with is your use of 'everything'. I think your 'everything' is every 'potential' thing. My 'everything' is every 'actual' thing (which doesn't include objects/events that don't exist/happen). — keystone

Yep. I mean an everythingness that is a universal potential and not some set of actual things.

Actualisation indeed eliminates possibilities. Which is how one would argue for infinity as an unbounded process rather than an actualised value.

What exactly do you mean by this? I don't think 'a state of everything' needs to exist for 'something' to exist. — keystone

Can you picture getting something from nothing? Can you picture being left with something having carved away most of everything?

One of these two is more picturable, no?

It is also the central principle of physics in being the principle of least action. The sum over possibilities or path integral.

I couldn’t find an argument to reply to here. Sorry.

Anyway, it's not clear to me what his view is: Does he grant that there is no greatest number, while suggesting that there is a greatest practical number? Or does he hold that there is a greatest number period? — TonesInDeepFreeze

All of the above. :grin:

His position is vague. But one can develop it in a fruitful direction - like ultrafinitism.

I did reply half-seriously to what was the actual OP. Cosmology does recognise that the visible universe is a bounded region with a maximum entropy condition. It contains some finite number of degrees of freedom.

The OP is too clearly an example of ultrafinitism to be an accident. — Real Gone Cat

That is nuts. You think @Agent Smith is pretending to be a finitist when he is really an ultrafinitist at heart?

This little drama sounds more and more like that scene in Life of Brian…

That is to say, there is no necessity in what we value.. There are strong tendencies perhaps, but not necessities. — schopenhauer1

My metaphysics is constraints-based. And a constraint is inherently permissive. What is not prevented is free to happen. Or indeed, must happen eventually, in the long run, at some point. :grin:

So you are arguing against a different worldview here.

I am only pointing out the holes of your manufactuered naturalistic fallacy (LIFE and its necessary BALANCE as applied to humans who have reasons.. — schopenhauer1

You are showing you don’t understand my position - which is that of natural philosophy or systems science.

Reality is a system of relations. Reality becomes stabilised at the point where it’s contraries - as in its global constraints and local freedoms - come into a steady dynamical balance,

This is a value free view of reality. It just is what it is. That is the only way that anything can be in terms of persisting existence.

I simply state how we have our individual reasons, whatever the factors are that allows that (and recognizing it is indeed an iteration of individual with society). — schopenhauer1

Existence is irreducibly complex in its hierarchical organisation. You can’t just wish the fact away if you want to make metaphysical level claims about the human condition in the real world.

. Balance here might be used as a weasily word to imply both descriptive and normative, but it cannot be both. You are either giving your opinion or describing some cycle. One does not become the other though. — schopenhauer1

A dynamical balance is only normative in the sense that it underlines the fact that a system must dissipate to persist. That is step 1. Then step 2, it has to be evovable to survive perturbation to that dissipative structure.

So adaptablity, creativity, spontaneity and even foresight are part to the same picture as the normative habits that are the history which has so far shaped a system with the power to persist.

My metaphysics doesn’t shackle the natural world in the mechanical way you want to presume.

But WHY we should want this.. WHAT we are trying to aim for are totally out of the realm of the descriptive. — schopenhauer1

Then we become the only animals with unreasons. And not particularly equipped to persist as part of reality.

If memory serves, [Widlerberger is] a finitist.
— Agent Smith

That is quite missing the point. Wilderberger, as I glean, is an ultrafinitist. — TonesInDeepFreeze

Then I mentioned that, more particularly, he's an ultrafinitist. — TonesInDeepFreeze

Your notion of “mentioning” is as disingenuous as your definition of “being constructive”. We can leave it there.

I merely pointed out that we can address the reference to Wilderberger more specifically than generally. — TonesInDeepFreeze

So you made a pointless point as if you were adding some significant and necessary correction to the discussion.

Of course I do get why you felt it worth saying. This is how you troll @Agent Smith. If he says something true, you have to make it seem untrue by pretending some even more sophisticated textbook distinction - one beyond his ken - was at stake.

He trolls you his way, and you troll him your way. And so it will continue. :ok:

That is quite missing the point. Wilderberger, as I glean, is an ultrafinitist.

Finitism has a broad range. …

So what is salient about Wilderberger is not just that he's a finitist but that he's an ultrafinitist. — TonesInDeepFreeze

A point of logic. How is the statement that Wildberger may be a finitist rendered untrue by him being also some subset of that set?

I’m sure that is a basic error that needs pointing out to stop the internet descending into crackpottery and ignorance.

What was the salient point in the discussion that demanded a need for the further distinction?

However, a rude attitude seldom yields anything productive: — Kuro

I think you can even be rude if you are funny with it. And hammering a crackpot could be constructive if you explain yourself well enough that others are engaged and learning something.

I think being too nice can be unproductive as well. Discussions have to have energy.

But this particular interaction seemed just an attempt to whack the stubborn pupil over the head with the textbook.

I mean it is not as though "actual mathematics" doesn't have textbooks by Norman J Wildberger as well. :rofl:

[No slight on Wildberger who I really enjoy.]

If the burden of reasons falls on the individual as an "allegiance to Enlightenment" then it cannot be external customs any more that provides reasons, but our own. — schopenhauer1

No, it is about the interaction between a self and its society that is meant to be the rational relation. It is the rationality of this two-way street – the relation that strives for a win-win solution.

Both sides are saying "let's be reasonable about this". Life is about striking the pragmatic balance.

That is in the existentialist wheelhouse. That is to say, meaning, motivation, authenticity of one's own goals and roles, and the like. — schopenhauer1

Now you have gone off into one-sided Romanticism. The self as the sole arbiter.

This monism is at the root of all your problems. Your model of mind is solipsistic. All that exists is your experience – the "inevitable" pain, boredom and suffering of having been born. You frame your world as one where all burdens have been imposed on your passive experiencing and you seem to lack any authentic agency. But in reality, your mind if formed by social construction as well as inherited genetics and neurobiological habit. Then on top of that, there is this new level of semiosis that has opened up with the Enlightenment's theory of the civilised human condition.

Some of us seem to find it a positive step forward. Living in a civilisation is rather comfortable and entertaining. We get to have a lot of personal freedom to the degree that makes collective sense.

The problem is that the utopian promises haven't truly planned out because the Enlightenment didn't dig deep enough to understand "rationality" at the level of nature itself. Nature is a thermodynamic enterprise. Those are the rules that all organisms must play by. Civilisation requires a more sophisticated theory of itself for its progress not to turn into a self-delusion.

So sure. There is much to criticise. Rationally.

But that starts with accepting that the human condition is semiotic and thus a hierarchical structure of relations, not an atomised collection of solipsistically isolated and passive consciousnesses, weighed down by un-asked for burdens, and being self-deluding to the degree they deny the existential horror of it all.

But I find it worthwhile to post the corrections to the record. I don't have an inflated sense that this makes any "hill of beans" difference in the outcome of humankind or the world. It's just, for me, satisfying, even if only in principle, to articulate and enter my comments. And I believe it is constructive to do that. — TonesInDeepFreeze

I'm questioning your definition of "constructive".

I don't know what kind of person he is away from posting, but I find him to be flippantly dismissive in my interactions with him as a poster. — TonesInDeepFreeze

Now reading further back in the thread, your excuses seem even thinner. Don't you realise that the more dogmatic you become, the more flippant will be the reply in this situation. That is how the dialectics of real life social interaction works. So you are producing the very thing you are complaining of in the end.

Rather than stamping out crackpottery, you are fanning its flames. :clap:

Crankery corrodes knowledge, understanding, clarity and communication. — TonesInDeepFreeze

Sure. But again, this is you now setting your self-appointed standards for the site. And there are moderators who actually are responsible for deciding the limits of tolerance.

So I understand your point of view. But pragmatically, have you achieved a measure of success? By your own admission, hammering on @Agent Smith doesn't seem to have the desired effect. You can set him as much reading homework as you like, but that becomes performative if you have no real expectation anything will change.

And while I don't begrudge them the prerogative to do that, I don't begrudge myself the prerogative to refute it and denounce it. — TonesInDeepFreeze

This speaks of a joyless rigidity to life. And you are mistaken if you think "actual maths" trumps "actual philosophy" on a philosophy website. It's a simple category error.

The site could crack down harder on folk's critical thinking skills, of course. :grin:

I have explained over and over that in rigorous mathematics: — TonesInDeepFreeze

I really do not understand why someone would keep spouting the same mistakes over and over, even when explained to him, — TonesInDeepFreeze

But you are on a philosophy site. And one that is far from rigorous in its willlingness to allow all types of speculative thought. So no need to continually clutch your pearls in shock at the rude habits of the nasty natives.

More productive would be to engage in the deeper issue being expressed - the fact that physics may indeed be in ontological conflict with maths on the issue of whether infinity is usefully thought of as potential or actual. The result of a generating process or the existence of an actual value.

The idea of a largest number makes no sense to either of these positions. But the idea of largeness being arbitrary does.

On the physicalist side of the debate, the ontological argument is that reality is relational. It is born of a structure of constraints. Stability can’t be taken for granted as existence is a process - the process of instability being stabilised.

In that light, we can well wonder what the numerical value of pi is in a real world where we are not even sure if the metric is flat - just flat to some currently measured degree of precision.

Likewise, if the values of numbers are being understood as the limits of terminating processes, it becomes legitimate to ask if all the irrationals have generating algorithms, or just some of them, like pi? So what is going on there.

If you come on to a philosophy site, you ought to expect a traditional rivalry - such as that between potential and actual infinity - to be treated as an open and interesting question, even if the level of discussion is lay.

and calculations would keep ending in ERROR like on early calculators. — unenlightened

Sounds like you can remember Texas calculators and Polish notation too. :up:

Eloquently said! — jgill

Stop it. Nothing makes me doubt what I just wrote more than someone's apparent agreement. :grin:

But I was thinking of you and rock climbing mathematicians the other day when I caught up with this sad story – https://profmattstrassler.com/2019/08/06/a-catastrophic-weekend-for-theoretical-high-energy-physics/

And also read this NYT story on how physicists (or at least mathematical physicists) are keen on mountaineering and bouldering - https://www.nytimes.com/2001/02/20/science/a-passion-for-physical-realms-minute-and-massive.html

I always thought from my experience that maths types were invariably into classical music. It was the physicists who scaled peaks.

For what its worth, I don't like a landscape that presents a technical challenge – one that has to be solved like a riddle. I like running fast and dangerously on twisty goat trails in the hills in a way that becomes quite unconscious. While listening to punk rock. A flow experience.

But the problem with setting a largest number is that it rules out irrational numbers such as pi, sq-root 2 etc because they cannot continue to infinity as decimals and therefore become expressible as ratios. — unenlightened

Out of curiosity, do you have citations on this point? I would argue something somewhat different. But I'm interested if there are discussions that support your view here.

I am happy you have finally found a number to use in place of infinity. You could show us how that works with the Lorentz factor. — jgill

But what is there left to move when the Cosmos arrives at its de Sitter heat death condition where all its degrees of freedom are embedded in its event horizon.

Time and change – as scaled by the Lorentz factor - have effectively ground to a halt. The only action is the quantum sizzle of the radiation attributed to the event horizon. We have reached the edge of the conformal disk in a finite fashion. The universe beyond may be supraluminally infinite. But it too is most likely to be in the same generalised condition.

So this may be the surprising thing. The reciprocality of the Planckscale start to the Comos means that a Big Bang with a minimum spatiotemporal scale and maximum energy density just simply turns itself inside out to become an equally finite Heat Death of maximum spatiotemporal scale and minimum energy density.

Lorentzian invariance would thus be emergent as particles formed with local momentum and inertial mass. And then it would dissolve from relevance as those particles get swept up and their energy radiated over the cosmic event horizon.

Of course, there is the little issue of the dark energy sustaining the whole show after the Heat Death. From that perspective, the Comos does expand forever and so "something" is always being added in terms of an infinite metric.

But once everything we physically could care about has reached its max ent state, do all those extra degrees of freedom actually count for anything? Even if there is potentially an infinite amount of them as dark energy repulsion just keeps stacking up in its supraluminal "biggest picture" way?

And it is still a remarkable thing if the cosmos had to find a way to close itself in this fashion so as to achieve concrete existence. It had to have a cut off at the beginning of the reciprocal kind that could once again be its cut off at the end.

Let's imagine a line where cuts have been made to mark all rational points (I don't believe this is possible, but let's go with it for now). I believe you cannot mark any more points on this line. If you throw a dart in between the rational points then you will hit an indivisible line segment. That is as discrete as it gets, and even then the line is securely continuous. — keystone

The cuts are 0-dimensional so they are illusions of convenience. If you throw a dart at the line you will always hit the line, never the cut. The cuts have measure 0 after all. — keystone

The problem here is that the real number line is the mathematical object that was in question, surely? So as a construction, it hosts both the rational and the irrational numbers as the points of its line.

Now, like Peirce and Brouwer, you might want to make more ontic sense of this by employing the notion of intervals.

And so the claim becomes that reality has a fundamental length – the unit one interval. There is a primal atom of 1D-ness or continuity. There is an object or entity that begins everything by already being both extended and truncated. And in being both these things as a primal symmetry state – possessing a canonical oneness both as a contradiction and an equality – it can then become the fundamental length that then gets either endlessly truncated, or endlessly extended.

The equality of 1 can be broken by a move in either direction. And each move creates a ratio - a rational number - that speaks to the number of steps taken away from home base. If you can count upwards to a googol/1, then you can divide downwards to 1/googol. The reciprocal relation between extension and truncation is right there explicitly in the symmetry breaking of the unit 1 interval.

Now as reciprocal directions of arithmetic operations, each would seem to extend infinitely. Or at least, they are unbounded operations. The higher you can count with this system, the smaller you can divide its parts. But could you reach actual zero, or actual infinity? Well the obvious problem is that this would mean squeezing your origin point - the unit 1 - out of actual existence. The whole way of thinking would lose its anchoring conception of the truncated interval that set the whole game of approaching its dichotomous limits going.

So yes. If you just think of numbers as rationals – ratios that embody reciprocal actions on a fundamental length – then actual completed infinities and actual 0D points or cuts become anathema to the metaphysical intuition.

What then happens when you add the irrationals? Does that change anything?

The usual way of picturing it is that the number line becomes so infinitely crowded by markable points that it is effectively a continuum. Infinite extension and infinite truncation become the same thing. A new state of symmetry. A new unit 1 state. The continuum is that which is neither truncated nor extended. The concept of a finite length anchoring things is dissolved and becomes vague.

In hierarchy theory terms – Stan Salthe's "basic triadic process" – this is a familiar state of affairs. The small has become so small that it just fuses into a steady blur. The large has by the same token become so large that it has completely filled the field of view.

You wind up in a world where there is a global bound that arises because continuity has been extended so much that its truncated ends have crossed the event horizon (as cosmology would call it). And likewise, the local bound has become so shrunk in scale that it is a fused blur of parts (a wavefunction as quantum physics would call it). And then that leaves us, as the observing subject, surrounded by a bunch of medium sized dry goods – objects that embody both truncation and extension in terms of looking like composite wholes made of divided parts.

So we can make sense of the rationals as intervals on a continuum – the symmetry of the unit 1 being equally broken in both its complementary directions. And then when this asymmetry is maximised, you wind up in this hierarchical situation where you live in a world of truncated lengths, but then are semiotically closed in by a global bound of holographic continuity (synechism or constraint, in Peirce speak) and a local bound of quantum discreteness or fluctuation (tychism or spontaneity, in Peirce speak).

But that is connecting with the physics. A richer notion of mathematics that includes time and energy along with space. I'll get back to the issue of the irrationals.

Now for me, it seems clear enough that the familiar irrational constants – pi, phi, e, delta – are again unit 1 ratios, but ratios generated by growth processes. So e for example scales the compounding growth of a unit 1 square, not a unit 1 interval. That is why it is incommensurate. It is a unit 1 dropping in on the numberline from a higher dimensionality.

Surds have the same story. That then leaves the unbounded cloud of numbers with random decimal expansions. Some like pi, phi, e, delta have their generators in a higher dimension as I argue. But that isn't even a drop in the ocean of all the infinitesimals that seem to exist and so make the numberline infinitely dense with dimensionless points or cuts.

One view that appeals is that all these meaningless numbers with random decimal expansions mark nothing in particular. They are in fact the tychic spontaneity of Peircean semiotics – the inability of nature to suppress or constrain all its surprises. Down at the ground level of truncation, it is just fluctuation – the seething instability of the quantum vacuum, filled with its virtual particles and zero point energy (to use some much abused terms).

But maybe also, all these random fluctuations are actually ratios of some kind – visitors from another dimension like the growth constants. Maybe they all have a generator that makes each of them a unit 1 story in a bigger picture, one with infinite dimensionality. Or unbounded dimension.

So the infinitesimals becomes a blur of unit 1-ness that results from a numberline living in infinite relational dimensionality, just as Cantorian infinity establishes its own unit 1-ness by becoming the point where counting goes "supra-luminal" – crosses the event horizon in physical terms.

Something is certainly going on here with the irrationals. Some definitely have their higher dimensional generators like the unit square, the unit rectangle, the unit circle, the unit Pythagorean triangle. Crisp and necessary mathematical structure arises out of the swamp of algebraic symmetry breaking.

Do the rest of the irrationals have a similar story of geometric necessity behind them? Or are they just a blur of surprises and accidents. A blur of differences that don't make a differences and hence that which serves as the blank and continuous backdrop to the constants of nature which in turn have the most supreme importance.

I think Peirce and Brouwer argue towards a world where the number line starts off from the conception of truncated intervals – the infinity of truncation~extension operations that can act on the unit 1 length. That gives us the rationals that are completely at home in the world so defined.

Then you get the intrusions from higher mathematical dimensions – ratios or symmetry breakings from a larger universe of rational shapes. These pop on the line in ways that don't fit so exactly.

This then leads to a view of the number line that is a continuum of fluctuations. But now we are counting all digits with random decimal expansions as a something rather than a nothing.

It is information theory all over again where both meaning and nonsense are assigned the same bit-hood status. Signal and noise are in the eye of the beholder. What matters in the new counting system is there is the truncated interval – the ensemble of microstates. Information theory becomes about counting all actualised differences, not the differences that make a difference (even if that dichotomy can then be recovered with other relational measures like the notion of mutual information).

Anyway, the picture I have in mind is a continuum which is composed of rational intervals – truncated lengths that appear over all possible length scales. Eventually these lengths become either too large or too small and so exceed our pragmatic grasp. We live in a world where energy and time matter, along with (3D) space. And so it is simply a fact of living in that world which imposes a cosmic event horizon and a Planck scale cut-off. As an intuitionist would say, we haven't got the time or energy to pursue either the promise of unbounded interval expansion or unbounded interval truncation.

But into this rational continuum creeps some irrational numbers that really matter – the rare visitors from higher-D ratios.

And also then, we have the noisy background crackle that is the randomness of all the other unbounded decimal expansions we can imagine as truncation operations. If they have generators, then in the spirit of Kolmogorov complexity, there is no actually simpler algorithm available but to print out every entropic digit. They represent the limit of the generatable. Another way of saying they are merely the meaningless noise that can't be squeezed out of any system. The quantum uncertainty that one knows one finds at the Planck cut-off of any system made of actual material stuff.

I don't want to dive into what happens at the Planck scale, — keystone

If you want to argue for potential infinities over actual infinities, then the real world is surely the better place to test your case.

Arguing against maths using physicalist intuition becomes Quixotic if maths simply doesn’t care about such things. Physics at least cares.

What I have said is that - as the history of metaphysics shows - there are two camps of thought about the physical world. Broadly it divides into the reductionism of atomism and the holism of a relational or systems approach.

The systems approach is triadic and says reality is a self organising hierarchical structure. So it deals with the potential and the actual by saying, yes, well both exist. It ain’t either/or. You have being and becoming. This makes sense as you also have necessity to complete the triad.

This triadic metaphysics reveals itself in many guises. Aristotle’s hylomorphism, Hegel’s dialectics, Peirce’s semiotics. So it gets confusing. But it offers a structure that can be used to see that modern physics is recapitulating the same holistic moves. The Planck triad of constants is a key sign of that.

So I am arguing from a particular metaphysical point of view. And I am saying reductionism is a monistic, concrete and object-oriented metaphysics in which the concept of potential doesn’t even make sense. Reductionism is comfortable with a world in which things either exist or fail to exist. Atoms and void. The nearest reductionism gets to a state of potential is allowing for some concrete ensemble of statistical possibilities.

This entified approach to existence carries over to talk about dimensionality. Dimensionality doesn’t develop. It simply exists, or fails to exist, in a concrete countable way. A point is a 0D object. A line is a 1D object. End of discussion. There is no “why” as to how it might be the case, given the limited ontological options that reductionism employs.

It you are fed up with hitting that brick wall, then that is where a systems metaphysics is worth a spin. It takes the bigger story seriously. It offers models that speak to the notion of pure potentiality - as that which can then birth self-organising reciprocal limits - in things like Anaximander’s Apeiron, Aristotle’s prime matter, Peirce’s logic of vagueness, the quantum foam of quantum gravity physics.

So I have urged stepping back and considering how one could even talk about continua except within the limits of a dichotomy - the dichotomy of the discrete~continuous.

You are talking about the fundamentality of the interval - a concrete or actual object that is a finite length that is thus both discrete and continuous at the same time. Well how does the finite interval get to be a combination of apparently contradictory properties. How could that state of affairs develop from something more fundamental? What is the deeper story on how finitude itself can arise?

So the choice is not between the zero-D point that makes no ontological sense and the truncated 1D interval that suddenly makes sense. You can claim to have no problem with an infinity of cuts and yet have a problem with an infinity of points.

I would say the 0D point and truncated interval are in the same class of question-begging objects. Both are atomised entities lacking a properly motivated existence.

If you want to move the argument forward, well at least talking about truncated intervals highlights the contradiction that a reductionist metaphysics embodies, but a systems metaphysics seeks to explain.

How do the discrete and the continuous combine in the one actualised object? How does such a state of affairs develop? And out of what?

The inverse relation between points and continua is that the point is nothing and the continuum is something. — keystone

You mean the continuum is everything. That is the opposite of nothing. Then what you call continua are the line segments that are fall inbetween these two complementary extremes.

In terms of length, the point is exactly 0 and the line is some positive number. If you're talking about something of infinitesimal length, you are talking about some tiny line segment. If that's the case then you are only talking about continua. — keystone

These are your words. But if the line is cut, then you are also talking about a lack of line with some infinitesimal length, not a 0D point.

This just helps show that the idea of a 0D point is ontically problematic and in need of much better motivation than you are providing. You assume too much without providing the workings-out.

Nothing cannot be used to measure something (0+0+0+0... always equals 0). Whereas something can be use to measure nothing (e.g. 5-5=0). There is an imbalance here in this relationship suggesting that continua are more fundamental. — keystone

Nothing and everything are really the same. A void and a plenum are either too empty to admit change, or too full to admit change. White noise is both every song ever written, or that even could be written, played all a once, and no song being played at all.

Continua are certainly then something. And since something cannot come from nothing, continua must exist as a constraint on a state of everything. This is the better route to getting towards the intuitionist view of the continuum as having numbers with as many decimal places as you care to produce them.

The constraint on mining the number line for some particular value at a point is time and energy. If you develop a tight enough context, you can produce a matching degree of certainty.

Again, it is all about the reciprocal relation. The one physics cashes out in terms of entropy and information these days.

The structure of a continuum is not defined by points, it is defined by an equation(s). Aside from being impossible, you would never try to provide an infinite list of points to completely describe a line (Cantor). You would just provide an equation - a finite string of characters to perfectly describe how points would emerge if cuts are made. — keystone

Sure. Behind it all is symmetry and symmetry breaking. Numbers are based on the maximum symmetry that is their identity operation - 0 for addition, 1 for multiplication. This first step suffices to produce the integers. Then more complex algebra gives you further levels of symmetry to populate the number line more densely with other symmetry breakings.

There are generators of the patterns. You start with the differences that don’t make a difference. Then this yields a definition of the differences that do.

Again the logic of the dialectic and the basis of semiotics. Stasis and flux are a dichotomy. Mutually dependent and jointly exhaustive. Each is the measure or the other.

I don't understand how continua + equations are vague. If I say I'm thinking of a plot containing the curves x=0, y=0, and y=x^2 you know exactly what I'm thinking of. — keystone

The operation is crisp or determinate to the degree it is robustly dichotomised. It is vague to the degree there could be some doubt.

To use the usual example, when you say x=0, are you talking about 0.00…. to some countable number of decimal places. Have you excluded x=0.0000….a gazillion places later …0001?

There could be a vagueness about this nought of which you speak so freely. There could be some uncertainty you have failed to eliminate.

The fundamental forces run their couplings. They are all fractured and very different in the cold/large universe of today. But all their strengths and properties (probably) converge at the Planck scale in one simple Grand Unified Theory – a vanilla form of quantum action that is the contents of a general relativity spacetime container of smallest scale.

Are you thinking of a specific study? Does anyone in a tribal society act simply because they wanted to, or is it always tribal custom? — schopenhauer1

Yep. I am thinking particularly of Catherine Lutz studies of self-regulation in Ifaluk islanders and how they frame right and wrong not as personal but public values. There are good collections of such anthropology in Harre and Parrott's The Emotions, and Harre's The Social Construction of Emotions.

So the argument is not that tribal custom always prevails over personal impulse. It is that the tribal view sees the reasons for their behaviour being constrained as concretely external – the customary way. And civilisation was all about teaching folk to internalise things.

The constraints on the self became abstractions to be contemplated internally. We had to "see" right and wrong as impersonal truths that we might know directly through reason, and so see through what were merely the contingent truths of some ragtag band of unphilosophical, not even rational, savages.

You can be a tribal society or you can be a part of civilization, but none of that is something you can choose. — schopenhauer1

But the difference with civilisation is that it promises you a material world which can be organised with abstract freedom. The possibility of constructing a heaven on earth. :razz:

Not my fault that the Enlightenment led to the Industrial Revolution before the tribal mindset could complete its evolution towards an angelic state of accord.

So choices become possible with reason. But fossil fuel wanted to be burnt. We became its vehicle. That wasn't how the Enlightenment was meant to play out.

This is the world that has actually been given us. You can either accept its challenge or ... spend your short life pointlessly complaining.

So individuals with reasons is a human event that is magnified by cultural practices of Enlightenment values. We call this modernity. It has been diagnosed by the Existentialists and existentialists. — schopenhauer1

Don't forget the Romantic reaction which is a deeper source of the problems now. Existentialism sits on that side of the divide.

Enlightenment civilisation can turn us into good and pragmatic citizens. But romanticism makes us dream of becoming our own gods. Or at least supermen. Or failing all else, at least social media influencers. :up:

Some think that math somehow produces reality. That if math doesn't track common sense, everyday reality exactly, there needs to be an explanation. That something is wrong. — T Clark

Sure. But reality scales. It “runs its couplings” in physics-speak. The maths that best describes reality has to do the same.

So the everyday folk conception or reality - and the maths that might describe that - is based on the current experienced state of the Cosmos, when it is vast, cold, and a couple of degrees from the limit of its heat death.

That is a world in which an object#oriented ontology of “medium sized dry goods” seems to make “fundamental sense”.

But physics tells us that this is not fundamental, just a passing stage. The Big Bang had quite a different kind of ontology. And physics has worked up a decent account of the maths required to track how each stage evolved into its next.

And again, it is the kind of triadic/holistic/dialectic systems view I’m talking about. Peircean semiosis.

Somewhat related, my understanding is that the planck length applies to measurement, not space itself. — keystone

The Planck length emerges out of the triad of dimensional constants, c,G and h. Which happen to be reciprocally yoked.

So zoom in on the Planck scale and you find the same metaphysics I have described. The smallest length is also the hottest temperature. Spacetime becomes so buckled that it dissolves into the vagueness of a quantum foam. It has neither length nor points, flatness nor curvature, in any proper contextual fashion.

Event and context become the same size. And so neither can be distinguished from its other. The Planck scale speaks to a fundamental cut-off for all such metrical relations.

You say that the idea of an absolute continuity as the alternative is offensive to the ontic intuition. — keystone

Think of how the speed of light is an absolute limit on the velocity of a mass. The mass can be accelerated to some arbitrary speed approaching light speed, but it can’t actually arrive at light speed. The limit bounds the velocity of mass as an absolute. But the velocity of the mass is always some shade within that limit.

The reciprocal argument makes that explicit. The approach to a limit is asymptotic as it is always yoked to its divergence from its other pole. For a mass, it likewise can never be absolutely at rest, although it can approach that minimum velocity with arbitrary closeness.

So as I argued, continuity is measurable as the absence of discreteness. The fact you can choose to truncate your decimal expansion in search of some specific numberline value only shows you didn’t exhaust its capacity for discreteness and thus also failed to demonstrate it is as securely continuous as you might want to assume.

What is the dimension of purely empty abstract space? One might say that it is infinite dimensional, another might say that it is 0-dimensional. — keystone

I think the maths of manifolds and topology would want to give a more sophisticated answer than that.

And physics likewise would give you something more complex as all actual spaces come with time and energy too. Vacuums are quantum.

As I mentioned, if we are talking spaces with algebraic dimension, then there is a whole structuralist story about that as well.

So arguing against the infinite numberline in terms of a Euclidean geometry conception might already be heading off in the wrong direction - even if it is a hardy perennial of philosophical debate.

No, no matter how many times you cut a continua it never becomes more point-like. In a similar way, no matter how many times you cut a string it never becomes 'nothing-like'...since it always remains 'something-like'. — keystone

But a string has a width. And so you can eventually chop it so much that the width exceeds the length. At which point, your analogy is in trouble.

The width of your string would have to shrink every time the length of your continua is cut. That would preserve your claimed geometric relation.

But now we are into the log/log realm of the fractal. We are into the reciprocal relation of two processes yoke together that my triadic metaphysics describes, and not the monistic notion of a single process - a continuity of cutting - that you want to claim.

I would draw it like this: ----o o---- (note that the o is like an open interval)
Of this diagram, the cut is this: o o (note there's nothing actually there, the point is not an actual object) — keystone

There is a huge literature on how to handle terminal points of continua. I’m not arguing against the maths that maths finds useful.

But I am pointing to the deeper metaphysical issue that this kind of discussion reveals. We wind up with a threeness because you are demanding that two continua separated by a cut is still also the one continuum.

So rather than finding a point on a line, we create two lines with a cut that leaves them with a point sealing their bleeding ends, and some kind of gap inbetween … that is not a point, just the absence of even points now? An anti-point perhaps? Or what?

It all falls apart to the degree we try to apply everyday folk metaphysics - a Euclidean form of realism.

A more sophisticated metaphysics would let you analyse the situation in terms of a unit of opposites. A dialectical process. The numberline doesn’t need to get cut, but neither is it ever whole. The numberline instead always exhibits its twin reciprocal properties of being both limitlessly integrated and limitlessly differentiable.

To have this kind of character - to have as emergent properties the opposite conceptions of being cleanly cut and being smoothly unbroken - then requires the third thing of a logic of vagueness.

The line that can be both cut and connected is describing a state that is maximally binary in its ontology. That claim of absolute bivalent crispness in turn must find its grounding contrast in its own opposite of being the “minimally vague”. The numberline could be other. It could be just a swamp of vagueness. It could be a fractal Cantor dust for instance, where you could never know whether you land on a cut or a line.

So again, maths can take a simple view and dispose of its metaphysical issues as cheaply as it wants. The whole numberline debate is then of metaphysical interest perhaps largely as it reveals how quickly we indeed do stop short in our metaphysics generally.

We find some kind of monistic formula that identifies “a fundamental thing”. And that’s it. Job done.

I’m just arguing that the numberline debate is another example revealing that any holist ontology has to be triadic.

I can keep going down this route whereby each term gets smaller and smaller, but the overall sum of each line remains 5. Something evolves to something, no matter how many times you cut it up. Points are not the limiting case of continua. — keystone

But with a Dedekind cut approach, aren’t you just stabbing your finger down on the point marking one or other side of the cut continua … and never knowing which of the two terminating points you have touched. There is always the third ground thing of a vagueness?

Each cut leaves a left and right point. But you don’t know which side of the divide you are pointing to. And so “left vs right” is a radically indeterminate claim. The PNC fails to apply.

What is the usual problem of an object-oriented ontology that I'm facing? — keystone

It binds you to a monistic and reductionist conception of nature.

As I say, thinking that way is fine if all you want to do in life is construct machines. That can be your reality model.

But for natural philosophy and metaphysics, not so much.

For me, pi is clearly a number. — T Clark

Pi is a ratio. Diameter~circumference. So it is actually an algorithm. And it can vary between 1 and infinity as it is measured in a background space that ranges from a sphere to a hyperbolic metric.

How all that actual physics translates to claims one might want to make about numberlines and irrational values is another issue.

There are so many ways to undermine the metaphysics implicit in the continuum that perhaps this ought to be taken as confirmation that it is a useful concept that doesn’t demand further justification in terms of realist explanations?

Maths just defines it and gets on with it. And that is fine. It is what maths does.

I like to highlight the many unreal aspects of the conception from a realist metaphysics point of view. Another big one is the assumption the ground of counting ain’t divergent as you zero in on some arbitrary point.

Chaos theory and fractals illustrate how this might be the case. Scale matters. As you zoom in, you can no longer be sure that any point belongs to the line or a gap in the line if you are dealing with something fractal but space filling like a Cantor dust or Peano curve. If everything diverges on the finest scale, how do you plonk down your finger on some defined spot with any true certainty?

But the fact that the real world undermines the simplicities of the metaphysics that maths finds useful is part of the epistemic game here. The more holes there are in the story, the more we can take it as all just a story about reality - that works with “unreasonable effectiveness.”

We can take comfort in the transparency of it being a model. We can get on with using it within the limits in which it looks to be useful.

I am proposing that instead of constructing the whole from the parts, that we construct the parts from the whole. — keystone

Yep. So construction gets replaced by constraint. And then my point is you go the next step of seeing construction and constraint as the two halves of the one system. Which is where you arrive at a triadic metaphysics – the one where a vague potential gets organised by the reciprocal deal of construction~constraint.

We start with the highest dimensional continuum of interest. — keystone

Which would be the "infinite dimensional" continuum ... unless you can find some larger argument that tells you what actually regulates the emergence of algebraic structure.

So when algebra is placed under the constraint of having to preserve normed division, you get the reals, complex, complex, quartonions, octonions and even the 16D sedonions. But you also get a petering out of the mathematical properties you are trying to preserve.

To me, that is a good structuralist argument. You might think any number of dimensions might still contain algebra. Or you might think that only one dimension contains "real algebra". Well actual algebra acts as a constraint that gives you something intrinsically more complex when it is run over the whole space of what seems possible.

And quantum theory even suggests complex numbers as the true centre for algebraic structure – as it makes commutativity count out in the real world of particles and symmetry breaking.

So I am saying I wouldn't deal with the metaphysics of the number line in isolation. It is illustrative of the far bigger conversation we need to have about how holism in mathematical conception plays out. The same principles have to cover mathematical structure in general – as category theory argues, having absorbed the metaphysics of Hegel and Peirce.

Might the same apply to objects in the abstract world? Might continua be fundamental instead of points? — keystone

This is a rather basic level of discussion. Again, how could it even be a continua unless it could be cut? How could it even be a 0D point except as the positive absence of any dimensioned extension?

I draw attention to the fact that you want to make one thing "the fundamental". This is monism. This is reductionism. This is not holism.

Holism says everything is a system of relations. And so the first number you need to get to is two. Some pair of "fundamental things" in relation. This in turn only makes sense when you get to three "fundamental things" in relation.

You have to get to the point where the relating of things is itself dualised in some limit case fashion. You have to arrive at a metaphysical dichotomy or reciprocal relation where one of the things is your local scale of being – your world-constructing collection of individual parts – and the other is then your global scale of being, or the constraints, habits, laws, emergent macro-properties, downward causality, etc, that is the generalised holism of the system in question.

So if you want to apply the strength metaphysics to questions about mathematical structure, you have to count to three in terms of "fundamental things". But fortunately three is then enough. Its a theorem in network theory that all networks of relations reduce to "threeness". :grin:

Or in other words, no matter how many times I cut up a piece of paper, never will it vanish to nothingness. — keystone

But each piece also gets more pointlike. So eventually the matter becomes obscured by arriving at that even more fundamental thing of being a vagueness.

The cut has to be sandwiched between the two ends of two lines. Each end of the line is a point. At what point does the point marking the cut – that is, the absence of a point at that point – get marked off from the other two points marking the starts of a pair of now separated continua?

You will be familiar with these kinds of arguments. And they make no real sense because they talk about dimensionless points and dimensioned lines without any clear definition of the relation between the two. There is no operation connecting them.

But if you have an argument based on a reciprocal relation, then each only exists to the extent it is a limitation its other. And that is how you recover the intuitionist ontology of Brouwer.

An infinite amount of cutting will result in an infinite number of number line pieces. And an infinite amount of gluing will put the number line back together.

But that then means you have to be able to both cut and glue. The two actions go hand in hand. If either action runs out of steam, so does its "other".

So it is easy to picture just forever cutting a line. Or instead, just forever gluing points. Yet both are equally one-eyed perspectives in a mathematical reality where this has to be in fact a reversible operation. The two sides of the equation need to be resepcted by our ontic interpretation.

And what do we get when we roll back the reciprocal operation of cutting~gluing back to its primal origin where it is first detectable as a structure-forming relation?

Points and lines are what we see by the end in a rather black and white fashion. But what were they as some kind of distinction of this type first started to swim into view?

The thing is that we can't go the limit. — keystone

But the fact that we can approach the limit – both limits – with arbitrary closeness is how we know they are there. The limit is precisely that which isn't reachable in the end. But it certainly defines the direction we need to keep going from the start.

And this only makes sense if we are starting from the symmetry breaking of a dichotomy. The initial split is simply a reaction against the logical "other".

So each limit is defined as heading in the opposite direction of what is being left behind. Continuity is the impulse to put as much distance from discreteness as possible. Discreteness is likewise the intent of becoming as discontinuous as can be imagined.

So at the start of things – the foundational conditions which is a logical vagueness – the need is for a direction that leaves something behind. So there is the need for two things in fact. And both of them are trying to leave each other behind. If there are more than two things trying to leave each other thing behind then nothing really gets left behind in a maximal or extremitising way. Again, that is the definition of a dichotomy – mutually exclusive and jointly exhaustive.

Thus logic can define the start of a distinction in terms of a reciprocal desire to simply separate. From there, both sides will go as far as they can go towards matching limits. But because this dividing is only real for as long as distance is being created between the two, then neither can actually become separated "in the limit" as they remain yoked together by their need for this opposition.

The point and the line, or the infinitesimal and the infinite, are actualised to the degree they are actively divided.

With this parts-from-whole construction, objects are finite and processes are potentially infinite...and there are no paradoxes. — keystone

Again, this suffers all the usual problems of an object-oriented ontology. Reality is better understood in terms of relations – processes and structures.

Ooof.. is that a slight against any tribal society that doesn't have "civilization"? You save it by adding "socialized" though. — schopenhauer1

Or instead, cultural anthropology shows us that tribal order doesn’t expect the giving of individual reasons, just knowledge of collective custom.

Civilisation shifts the social conversation to a different space where you are suppose to construct your own systems of constraint. You get to have your personal freedoms if you swear allegiance to the abstractions of Enlightenment values.

So same thing in some lights. Very different in others. I wouldn’t want to mindlessly lump them together … as you are at risk of doing. :razz:

That seems like a false dichotomy of "social formulas" and "acting on reason". Both seem off to me. — schopenhauer1

Or instead, just how cultural anthropology would frame the shift in semiotic scale from hunter-gatherer to cities and social democracy as a way of life.

Rather, reasons are formed by way of a being that can self-identify as an individual that can produce outcomes in the world and knows there are choices that lead to those outcomes. — schopenhauer1

How does one come to self-identify as an individual except via social construction?

A failure to understand this fact is at the base of much modern angst. So no surprise you must fail to understand it and thus preserve your right to complain about “imposed burdens” rather than accepting that your persona is a co-creation of the company you choose to keep.

Reading gloomy old philosophy texts could have been where it all went wrong.

Having reasons is a burden. It means we choose to do something and we think it leads to various consequences for doing so. It isn’t just an impulse that drives us with absolutely no awareness. — schopenhauer1

You are missing the obvious. Society requires us to have reasons for our actions. It is the "burden" of being civilised, or even just socialised.

Most folk thus grow up learning to just fabricate excuses for their actions. They become expert sophists. They explain away why they did what they did in some socially-acceptable formula of words.

Actually learning how to act on reason is rarer. Rather than an imposed burden, it becomes an effective skill. It means life can be lived with rational goals in mind. Life can be shaped by measurable purpose.

Of course, you still have to work with the world that is given to you. Self-actualisation can't transcend the given world, only operate to best advantage within it.

So you still get to complain about the "burden of existence" if you have made that your larger goal in life. :up:

Perhaps I should have written that I believe it is impossible to imagine assembling points to form a continuum. — keystone

Like many who are philosophically inclined, I am happy to accept actual infinities as a useful mathematical simplification – an epistemic trick – but not something that makes proper ontological sense.

But note also that simply switching your ontological support from parts to wholes – from 0D points to 1D lines – doesn't fix the deeper issues. You just set yourself up for the same puzzle at the next geometric level – where we have to glue together the infinity of 1D lines that construct the 2D plane, the infinity of 2D planes that make up the 3D volume, the 4D hyperspace, and so on, presumably all the way up until we hit ∞D space.

So the idea of 0D points – some kind of absolute notion of discreteness – is offensive to the ontic intuition. But the same should apply to its dichotomous "other", the idea of an absolute continuity as the alternative.

We need a more subtle metaphysics. We need an intuition that itself sees parts and wholes, the discrete and the continuous, as the two emergent parts of the one common rational operation.

This is simple enough. It is just the unity of opposites of ancient times, the dialectics of Hegel, the semiotics of Peirce (in particular).

This would see the discrete and the continuous as being each others limiting case. Each stands as the measure of its other. The two form an inverse or reciprocal relation. A dichotomy is that which is both mutually exclusive and jointly exhaustive. You boil everything down to two precisely opposed limitations. And they are the measure of each other in the form that the discrete = 1/continuity, and continuity is similarly = 1/discreteness.

What does this mean for number lines? It says that while we must think of the 1D whole being constructed of 0D points, that claim must be logically yoked to its "other" of each 0D point existing to the degree the 1D continuity of the line has in fact been constrained.

Constraint is the "other" of construction. Global constraint is the downward causality of holism that matches the notion of construction, which is the upwards causality of reductionism.

So the number line is composed of its 0D parts to the degree that it is also able to limit the continuity that would deny the presence of such 0D parts. And we see this in the emergence of the matching limits of the infinite and the infinitesimal.

Infinite = 1/infinitesimal, and infinitesimal = 1/infinite. Each value relies on its "other" as the source of its own crisp identity. The number line – as our little dichotomised universe of possibility – has to be able to express both polar extremes to express either polar extreme. The points of the line are only as unboundedly tiny as the unbounded extent of the line can ensure this to be the case.

Step back and this fits the kind of metaphysics where what is real emerges as a limitation on an Apeiron or Vagueness – an unbounded potential or limitless everythingness.

The number line would start off as any and every kind of possibility. The principle of noncontradiction would fail to apply to any statement about it, and so it would be formally "vague".

But then a reciprocal operation gets going. You have a separation in which a kind of locality starts to appear within a kind of globality. You get a move towards a collection of parts that simultaneously - in equal reciprocal measure – reveals the larger context that is the continuous whole.

I mean it doesn't even make sense to talk about 0D points except in the context, or in contrast, with the presence of the 1D line, right?

And the more you dig down and keep finding ever more definite points – the infinitesimals – the stronger and better defined becomes the global continuum that has the kind of structure in which such a set of points could clearly exist. You get the co-arising of the continuum. And indeed, the whole Cantorian kit and kaboodle if you keep adding richer structure to your story.

Why not? The more you develop the definition of "the discrete", the more that is based on the refinement of the definition of "the continuous". The two directions of determination are reciprocally yoked. And once you see that, the whole deal becomes less ontologically contentious.

Although it also becomes more ontologically contentious in that you have to shift folk from thinking that the discrete vs continuous issue is an either/or question, to realising that it is a dialectical one. Both co-arise from the common ground of a logical vagueness. Hence without both, you ain't got either.

Freud would be a prime example of the romantic turn in his claim that the human animal is essentially irrational. A stew of feeling with a thin veneer of socialised rationality pasted over the top.

From the science point of view, Freud was a crackpot. The interesting part of the story is why his “theories” resonated with the cultural mood of his times. Or more accurately, the generation that followed.

"Humanities and social sciences are no longer useful in academia." — Christopher

Every academic field requires the humanities and social sciences, which is why philosophy is considered the "mother of academia." — Christopher

Consider this. The humanities were a product of Enlightenment philosophy – the belief that humanity could be understood in a rational and naturalistic light.

But the Enlightenment engendered its own Romantic reaction. Rationality and naturalism were rejected as fundamental.

So what happens as academia and philosophy come to incorporate that same romantic metaphysics within their own social universes?

One might well wonder the value of studying courses taught in that anti-Enlightenment spirit.

Thus it is not about rejecting the humanities and social sciences in toto. It is about picking wisely what you choose to study.

think apokrisis is decently close to this as well — fdrake

Thanks. :up:

My point is all about bringing logic back into the real world by showing how it is in fact grounded in the brute reality of a pragmatic modelling relation.

The mystery of logic, truth, intentionality, etc, are that they are clearly in one sense free inventions of the human mind. They transcend the physical reality they then control. This is a puzzle that leads to idealism - including the idealising of logic as "just a free mathematical construction, which also seems to have a Platonic necessity about its axiomatic basis".

But semiotics makes it clear that this idealistic freedom is the result of the "epistemic cut" in which a code – some vocabulary of symbols that can be ordered by syntatic rules – is then able to "speak about reality" from outside that reality.

The word "possum" could mean anything. As physics – a sound wave, a reverberation, emitted by a vocal tract – it is just a meaningless noise. And a noise that is costless to produce. Or at least the metabolic cost is the same as what any other noise of a few syllables might cost us.

The physics of the world thus does not constrain the noises we make in any way. And that is why these noises can come to have their own idealistic world of meaning attached to them. We are free to do what the heck we like with these noises. We can create systems of rules – grammars and syntax – that formalise them into structures that bear meaning only for "us".

So idealism is made to be something that actually exists in the physical world because this world can't prevent costless noise patterns being assigned reality-independent meaning. Noise can be turned into information and there ain't a damn thing the world can do about that transcendent act of rebellion against its relentless entropy.

But then humans have to still live in the world and do enough to cover the actual small cost of speaking about the world in the free way that they do.

So the freedom of truth-making is in fact yoked to the profit that can be turned on being a speaking creature. It all has to reconnect to the physics. And of course, as human history shows, being speaking creatures living in shared communities of thought, in fact can repay an enormous negentropic dividend.

To the extent our model of the world is "true" – pragmatically useful – we gain power over the entropy flows of our environments and can bend them to our collective will.

The problem in the discussions here are that logic gets treated as something actually transcendent of this rooted, enactive, organismic reality of ours. But even logic – and information in general – is finding itself becoming properly reconnected in physics.

Turing invents universal computation? Computer science eventually matches that by showing reality has its fundamental computational limits. The holographic principle tells us any computation does have some Planck scale cost – a cost which is small, but not actually zero. And so try to build a computer with enough complexity to tackle really intensive problems and it would shrivel up into a black hole under its own gravity.

Information theory puts computing back firmly in the world it thought it had transcended.

And the same ought to be happening for logic.

Which is where semiotics comes in. It defines the line between rate independent information and rate dependent dynamics in a way that is biological rather than merely computational.

Logic as maths led to computers as logic engines. Blind hardware enslaved by blind software, with the human element – the intentionality and truth-making – once more floating off above the heads of all the physical action in some idealist heaven.

Semiotic approaches to truth-making discovers logic to lie in the way that the connection between models and their realities is reliant on the device of the mechanical switch. This is the fundamental grain of action because it is where the effort of executing an intent becomes symmetric with halting that intent. And so that intent becomes a free choice.

You can flick the light on or off. You can push the nuclear doomsday button or leave it alone. The greatest asymmetry between a choice and its result can be imposed on nature by making the metabolic cost of choosing option A over option B as entropically symmetric as possible.

To me, putting this modelling relation front and centre of the philosophy of logic would clear up the old truth-maker chestnuts forever. We could move on to more interesting things.

Mechanistic logic has confused people's metaphysics for quite a long time now. Roll on organismic logic. Let's reconnect to the systems view of reality that has been chuntering along in the background ever since Anaximander. Let's finally understand what Peirce was on about as he laid its general foundation.

Another kind of philosophical mind asks whether such a demand is justified. — Cuthbert

Sure. For every action, it’s reaction. The Enlightenment, hence Romanticism. AP, hence PoMo.

But that just tells you dialectics is the true totalising discourse. :razz:

Greek philosophy quickly got there with its unity of opposites and Aristotelean systems thinking. Peircean semiotics cashed it out in the modern era (after Hegel and others had kicked it about).

So the fundamental unity is to be found in a model of causality that places the accidents and necessities of reality in their appropriate systematic relation.

It is how you would glue unity and plurality together as the one system that is the key insight. And Anaximander certainly started that ball rolling at the dawn of Greek thought.

2. Myth allows for a multiplicity of explanations, where the explanations are not logically exclusive (can contradict each other) and are often humorous. — javi2541997

I like CJ Rowe's papers on this point.....

Archaic thought in Hesiod
https://fdocuments.net/document/archaic-thought-in-hesiod.html

Anaximander and the Relation Between Myth and Philosophy in the 6thC
https://ir.icscanada.edu/bitstream/handle/10756/291049/Rowe_William_V_1979_MPhilF_Thesis.pdf?sequence=1&isAllowed=y

He points out how the transition from myth to philosophy is marked by a broader psychological shift to demanding a consistency in all causal explanation.

The mythic mind is tolerant of holding many apparently conflicting explanations true at the same time. Gods can be both the personification of natural forces and human characters in social tales without that seeming an odd way of rationalising. Whereas the philosophical mind demands a reduction to some common cause that stands behind all things.

(1) says "The kettle is boiling" and (2) says "La bouilloire est en ébullition". — Michael

:up:

If it points to anything, it points to itself. — Banno

So we go down and down, diligently following all the little arrows pointing to our supposed destination, to arrive at the final arrow ... that points at itself.

No wonder folk feel short-changed by this kind of shenanigans.

Semiotics fixes that for you. It formalises the necessary connection between model and world by saying one eventually arrives at a mechanical switch. You have a bit that can be physically flipped. You have some informational state that also does some useful real world work.

Logic can be treated as some kind of Platonic abstraction. But that is why it encounters its Godelian limits. Pointers that don't point at anything but themselves.

Logic makes better sense when it is seen as an exercise in semiotics – an organism's efforts to gain regulatory control over its entropic environment.

Truth is pragmatic. It is all about a bunch of switches being flipped in a manner that itself sustains the whole enterprise that is about intelligent habits or routines of switch flipping.

So logic is the construction of a selfhood that can live in its world. It is not about mathematical abstraction, except in the service of entropy regulation. And so it is pointers all the way down to the pointer that must be physically flipped in a way that then recursively sustains the entire edifice of pointing.

See kettle. Want boil. Flip switch. Make tea. Realise this is useful. Repeat ad infinitum until the pragmatic connection between the model and the world – between the rate independent information and rate dependent dynamics, as Pattee puts its – breaks in some way.

But there really are the two different worlds on either side of the same "ultimate pointer" – the mechanical switch that mediates semiotically between the information and the dynamics.

So the kettle is either on or off. Boiling or not boiling. Human intelligence has contrived a world where life has the purest semiotic logic. We can regulate the flow of entropy at the press of a button. The pointer at the end of the line is the pointer that points the material world in the way that best fits our desires.

And in enforcing that system of mechanism on the world, we in fact create a world that is now inanimate – over-ruled in terms of having is own desires – along with the inner self that is now defined in terms of all the power it has accumulated in its button-pressing fingertips.

No wonder the situation seems a little Cartesian, setting up the eternal duel between baffled idealist and naive realist.

But semiotics is the theory of truth that properly connects the self and its world by understanding there has to be the "epistemic cut" in the form of the canonical switch – the "sign" or "pointer" that is the bridge because it is equally much part of the ideal realm as the material realm. It stands with its feet in both camps in being the intentional opening and shutting of the unintentioned entropic flows which pass through it.

This is all a lot easier to understand when dealing with biosemiosis – the action down at the level of enzymes and other molecular machinery.

But even at the level of linguistic and logical semiosis, it is easy to see that utterances are meant to regulate habits of action. Words and numbers are used by the human social organism as a system of switches to keep folk collective pointed in an entropically self-sustaining state of organisation.

The laws of thought only ever arose in the search to view nature as "switchable". And we by consequence became creatures who were all about the act of hitting those damn switches.

A system of logical switches became all that we could see. But does it actually make sense that following the hierarchy of pointing down to its roots and you should expect the final pointer to point to itself?

Nope. The job of the pointer is to point at its intended real effect. And at the level of some actual switch, it gets to produce that effect as a direction physically imposed on an entropic flow.

That the kettle is boiling is a statement about the world being neutered of its intentionality and it having been pointed physically in the direction we desired.

This would be why Kant talked about the thing-in-itself as if nature might have its own intentions in play. Idealism then says these desires must be properly organismic. Realists reply instead that facts are facts – entirely inanimate.

Pragmatism and semiotics then slips in between these two eternally raging camps to point out that nature's "desires" are fairly minimal and not organismic. But start sticking in the right regulatory machinery – the semiosis of codes or informational switches – and you do get the new thing of the organism. You get dissipative structure that has innate intelligence and self-organisation.

The "price" is that its truths are pragmatic. They are neither subjective, nor objective. Instead this distinction between a self and its world is what emerges from the useful action of seeking to make the world as one would wish it to be. Truth is an effective setting of the switches. The construction of an Umwelt, or a view of the world as it is with ourselves fully embedded in its reality.

I agree with Smil that people should be told the truth, which is that we all have to use much less energy if we want to ameliorate (probably the best we can hope for) global warming while we try to make the inevitably slow transition to more sustainable energy sources. — Janus

Smil is right but the problem is that then folk start accepting that there won’t be any orderly transition so the game becomes about survivalist scenarios, both at personal and state levels.

The calculus quickly gets ugly.