A Vagueness Imperative, is not making a case. It is a manufactured phrase designed to replace the word God so as not to upset the sensibilities of "scientific materialists." Pure obfuscation embedded in long paragraphs in the hope that the sleight of hand is not noticed. In short (I do prefer getting to the point), nonsensical babble masquerading as intellectualism. — Rich

I think you're tilting at windmills. Your "getting to the point" is just a repetition of dogma, a mantra. You love Bergson. Cool. I like Bergson, too. If that's the last word for you and everything else is a conspiracy to cover up his final revelation of the Truth, then I'm OK with that. Proceed. Believe. Preach on.

Doesn't this boundary have a spatial location? Haven't you said this boundary is neither the line that marks the edge of the green area, nor the line that marks the edge of the white area? It is somehow a third line inbetween that executes "a transition". So we have the mystery of a third located entity that is neither the one thing, nor the other, by being a third thing?

You really are making a muck of this.

It is somehow a third line inbetween that executes "a transition" — apokrisis

No. I denied that there is any in-between. A transition is a process - your eye goes from green line to white line. It's not a thing. There is NOTHING between the white line and the green line. What have I been telling you for the whole time? Are you so heavy headed that you cannot read a simple sentence?

You are thinking mathematically, but I'm telling you how things are in reality. Mathematics is just an approximation, that's why you can infinitely divide in mathematics, but obviously can't do that in reality.

I denied that there is any in-between. — Agustino

Of course you did. You said there was a boundary in-between. You also denied this. The boundary had its own location. But then it also doesn't. It all seems to make some weird kind of sense as an example of the PNC failing to apply.

There is NOTHING between the white line and the green line. — Agustino

You mean there is A nothing in-between the white line and the green line. Otherwise how are you claiming them to be actually separated if there is no thing to separate them? And if you take that position, you have created some third thing that has some bare property of location, and can somehow effect the change which is a transition, and yet says "nothing" when it comes to the important question of where does one hue leave off, the other one begin.

You are thinking mathematically, but I'm telling you how things are in reality. Mathematics is just an approximation, that's why you can infinitely divide in mathematics, but obviously can't do that in reality. — Agustino

Ah. I see. The problem is now that the maths is "approximate". And when the reason for that is pointed out - the logical vagueness where the PNC fails - you missed the point. You come blundering in with the usual half-baked response of the naive realist, muttering about how you can tell me all about the world as it actually is without all the philosophical bullshit.

Great work!

I think you're tilting at windmills. Your "getting to the point" is just a repetition of dogma, a mantra. You love Bergson. Cool. I like Bergson, too. If that's the last word for you and everything else is a conspiracy to cover up his final revelation of the Truth, then I'm OK with that. Proceed. Believe. Preach on. — t0m

The difference is that Bergson was direct. He didn't need to invent stuff out of thin air.

A philosophy that depends upon Vagueness as its center is actually more than that, it is deliberately obtuse and full of nothing. Worthless in all respects.

So in answer to the OP, we have pages upon pages of not only Vague but impenetrable Nonsense. For Materialists this is not only sufficient, it is all that is available. "It just happens", over and over and over again. Thank you for the well constructed (concocted) argument.

1/9 = 0.1111111111 repeating, agreed?

So if I multiply both sides by 9, I get 9/9 = 0.99999999 correct? So how are the two not equal? I think the idea behind this is rather that decimal notation cannot capture the value of a number to the same precision as fractions can. — Agustino

You cannot actually reach a conclusion when you multiply a repeating decimal. You have to round it off in order to perform the procedure. So when you say that .11111 repeating, times 9, equals .99999 repeating, you are just assuming this because you cannot actually complete the task. Demonstrate for yourself, by dividing 9 into .99999 repeating. You'll keep placing another 1 until you decide that you'll keep on doing this forever, so you designate it as repeating. But this decision is based on some inductive principle, rather than a mathematical principle.

But I agree with what you say about fractions. Some ratios, like pi, cannot be properly expressed in numerical notation. So these ratios are designated as irrational, and this is in way contradictory, an irrational ratio. We could look into the nature of these irrational ratios, to speculate why they exist, which I have done before. It appears like when we move from one spatial dimension to two spatial dimensions, there is an inherent incommensurability between the two systems of coordinates. So for instance, a circle's diameter is one dimension, and the circumference is two dimensions, and there is a incommensurability between them. Likewise, two perpendicular sides of a square represent equal distances from a point, in two different dimensions. But the hypotenuse which relates these two equal distances is incommensurable, just like the circumference of a circle which represents equal distance from a point in two dimensions.

There are other interesting features of fractions, such as those found in wave representations like in music. I think that the study of ratios ought to be a science in itself.

If you want to say they are not equal, then what number is there between them? Two numbers that are not equal are after-all separated by another number. The problem of mathematics is that continuity cannot really be broken into discreteness without creating such paradoxes. — Agustino

So I don't think it's a question of if .99999 repeating is not equal to 1, then there must be a number in between them. It is that .99999 repeating is not really a number, because numbers are definite, conclusive, as you say, discrete, like 1 is. But .99999 repeating is inconclusive, indefinite, expressing an unending continuity, So it's not a number. It signifies something which cannot be expressed as a number. This is similar to the categorical separation you explain to apokrisis above. We use "equal" within the category of mathematics, but .99999 repeating is outside of this category so "equal" cannot be applied. Once we round off the repeating decimal, it is expressed in the form of a number, but it's true nature has been compromised in order to do this.

A philosophy that depends upon Vagueness as its center is actually more than that, it is deliberately obtuse and full of nothing. Worthless in all respects. — Rich

1) First there is the Vagueness (the Dao) — Rich

Hmm. The master truly challenges us with his koans.

Some have an emotional investment in the word "God" and others have an emotional investment in the word "No God". — Agustino

I agree. Some atheists might deny that preference or irrationality is involved in their position, but not all of them do. (I would be called an atheist by most theists). "Pure reason" can function as one more idol. That's why I mentioned that collision of rhetoric or sophistry in the Kojeve thread. Just about everyone thinks that they are rational. It's the other guy who's all turned around. Why won't he listen to me reason?

For me what we have here generally is obviously the clash of personalities in terms of creative seduction (sometimes intimidation). We trade stories. "Here's my vision of my world the absolute truth about our world. Here's who I think you should be. Here's who I think I am. Here's who I think you are. " I'm not complaining or accusing. Just describing what I see. Your results may vary.

You said there was a boundary in-between. — apokrisis

No, I never said there was anything in-between. There is no in-between. There is no empty space between the white line and the green line, the two are touching.

Furthermore you keep changing between transition, boundary, etc. and the discourse is becoming confusing. They are not the same. The boundary of the green surface is a green line. The boundary of the white surface is a white line. The two boundaries are touching. The transition is seen simply by the eye jumping from one line to the other.

It all seems to make some weird kind of sense as an example of the PNC failing to apply. — apokrisis

The PNC does not fail to apply. You have not shown this at all. All that you have demonstrated is that you have a wrong conception of the problem. You conceive of a real problem as a mathematical problem, but the two aren't the same.

You mean there is A nothing in-between the white line and the green line — apokrisis

No, I mean there is nothing between them, exactly as it sounds. There is no line between them.

Ah. I see. The problem is now that the maths is "approximate". And when the reason for that is pointed out - the logical vagueness where the PNC fails - you missed the point. — apokrisis

No, that is exactly the problem. That you confuse the math with reality - the map with the territory - and then go backwards from the infinite divisibility of mathematical space and postulate a necessary vagueness in real space. The vagueness only exists in the map, not in the territory. You have been fooled by the map and are unable to see its limitations.

So your version is that we have two lines that are touching but separate? Seems a little self contradictory given the definition of a line is that it has zero width. Does the PNC apply somehow? Something that doesn't extend in a direction, and so is definitely separate, also still extends in that direction, and so is able to touch?

I can see that you might be struggling to follow the logic of Peirce's example if you are unfamiliar with the philosophy of maths. This is a good clear primer on the continuum issue - why Peirce was following Aristotle in treating the numberline and dimensionality generally as the potentially infinite, not actually infinite - http://uberty.org/wp-content/uploads/2015/07/Zalamea-Peirces-Continuum.pdf

But another example of the vagueness/PNC~generality/LEM dichotomy which is basic to his logic is the triangle. A triangle is a general concept that forms a continuum limit - a global constraint - that then can't be exhausted by its particular instances. An infinite variety of particular triangles can be embraced by the general notion of a triangle.

So the LEM does not apply to this generality as a triangle can, in genus~species fashion, be equilateral, isosceles, or scalene. Of course the triangle must be a three-sided polygon, but that is talking of a still higher level generality of which it now partakes as a definite particular.

Peirce's point was that a general represents one notion of the indeterminate. As a description of a global constraint, the LEM fails to apply to it because contrary possibilities are not being excluded. Family resemblances are allowed within it.

Then vagueness is defined dichotomously to the general. Where generality allows you to say any particular triangle can be either scalene or isosceles, vagueness speaks to the indefinite case where there is as yet no triangle specified and so there is no fact of the matter as to whether it is scalene or isosceles. It is not a contradiction to say the potential triangle is both.

So the general is the global continuity that absorbs some category of all difference or particularity. The vague is the local generativity or spontaneity that produces all manner of difference or particularity.

You've leapt into a conversation without understanding its metaphysical intent, trying to turn it into a "commonsense" view of deep matters - commonsense representing the reductionist view of reality where crisp particulars are simply taken for granted, and so all causality is just a matter of composition or construction.

Peirce, like Aristotle, was fundamentally challenging that with a holistic or systems view of causality. So the laws of thought - in talking about the logic of definite particulars - are taken as being emergent. They have to develop their counterfactual definiteness within the two bounding and complementary limits of the vague and the general, or metaphysical Firstness and Thirdness.

So your version is that we have two lines that are touching but separate? Seems a little self-contradictory given the definition of a line is that it has zero width. — apokrisis

Well if you want your vagueness to apply only to mathematics and epistemology that is fine, but I thought we were talking about ontology. I've already told you that in mathematics space is infinitely divisible, hence where the paradoxes arise from. You were asked in the conversation with MU to provide an example of vagueness which showed that vagueness was ontological, not epistemological. In other words, that it belonged to the terrain, not to the map that we have.

I'm an engineer (by degree anyway), and so it's been very well-ingrained into my blood to be sceptical of mathematics and mathematical models and to be aware that they are very limited in describing reality. You seem - coming from a background of theoretical physics/science - not to have this awareness of the limitations of mathematical modelling. In engineering you are trained to think about the result you obtain through maths, and if it doesn't make sense, you are to reject it - that should be the impulse. You should definitely not accept an absurdity just because it emerges from the calculations. And by no means should you ontologise mathematics. Engineering is very concrete in that sense - it always goes back to reality, and discards mathematical models when they're no longer useful. Physics seems - in its version as theoretical physics - to, unfortunately, have the opposite tendency.

For example, some of the equations we use in hydraulics break in certain conditions. That means that they give results which involve infinity. We know that in reality there is no infinity, what happens is that a chaotic pattern of flow emerges that can no longer be handled by the equations. So, in that case, we don't ontologise the mathematical results and claim that there is some vagueness or anything of that sort. Our mathematical models simply cannot predict accurately beyond that point. But that's a fault with the models not with reality.

It seems that you have ontologised mathematical models of the Universe and have developed your entire philosophy out of that. The problem is of course that you've just confused the map with the territory.

I'll look at the resource you provided, it will be interesting, but mathematics is not reality or ontology. You are either looking to discuss a mathematical paradox, or you are looking for the underlying reality involving real - not mathematical - space.

Well if you want your vagueness to apply only to mathematics and epistemology that is fine, but I thought we were talking about ontology. — Agustino

It is about logic - reasoning itself. So it is mathematical in that maths is our most rigorous language of reasoning. It is epistemology as the right way to reason is mission critical. And then it is ontology, because equipped with the right reasoning, the right logical framework, we can hope to make the best sense of what reality actually is.

You were asked in the conversation with MU to provide an example of vagueness which showed that vagueness was ontological, not epistemological. In other words, that it belonged to the terrain, not to the map that we have. — Agustino

This understanding of what is required just confirms you are a naive realist. Peirce established the proper pragmatic basis for a logico-scientific understanding of reality.

Rather than just a map and a territory, there are the three things of a modelling relation. The "map", or mediating level of sign, is a living and adaptive "umwelt".

So the map isn't the territory of course. But more than that, it doesn't aim to re-present the world. It aims to ignore that world as much as possible. So the map comes to be a map of our own interpretive interests as much as a map of the external reality. It is a picture of ourselves as much as it is a picture of the thing in itself.

The famous example is the London Underground map. It is a picture of our interest in getting from A to B in terms of changing trains. It does this by ignoring the actual geography of the world as much as it can.

So the Peircean argument is internalist. All we can know of the world is the beliefs that we are prepared to hold about it, the beliefs we are prepared to act by.

This doesn't deny the thing in itself. But it should also alert us to the fact we don't really care about the world in some disembodied fashion. The maps we make are as much a self-portrait - indeed, the very act of creating that "interpretive self" - as they are a re-presentation of the world as it might be said to be in terms of its own set of interests.

The map faces both ways. It mediates rather than represents. So our realism is psychologically indirect. And that is a feature not a bug as otherwise "we" - as a packaged set of interpretive habits - could not even "exist" unless we could find ourselves in the very maps we create. Our maps make our purposes concrete in a way we can then actually talk about ourselves as a further ontological fact of existence.

I'm an engineer (by degree anyway), and so it's been very well-ingrained into my blood to be sceptical of mathematics and mathematical models and to be aware that they are very limited in describing reality. You seem - coming from a background of theoretical physics/science - not to have this awareness of the limitations of mathematical modelling. — Agustino

Nice try at boxing me in. But that pragmatic intersection between theory and practice is exactly what I have a good meta-theoretic understanding of.

It is about logic - reasoning itself. — apokrisis

Mathematics, logic, and reasoning are not the same thing. Mathematics is a set of tools, based on logic and intuition that allows us to create, in some limited circumstances and for special purposes, models of the world. Logic is a different branch of study than mathematics.

Reasoning itself is much larger than logic and mathematics and includes elements of noetic intuition (as per Aristotle and Plato).

So it is mathematical in that maths is our most rigorous language of reasoning. — apokrisis

No, mathematics is just a tool of reasoning. It's not the only tool in our toolbox, and probably not even the most important one. What Spinoza called intuition, what Plato called noesis, what Einstein referred to as imagination - that is more important than mathematics, since it is what sees into the very first principles themselves.

And then it is ontology, because equipped with the right reasoning, the right logical framework, we can hope to make the best sense of what reality actually is. — apokrisis

No it isn't ontology, that's a non-sequitur. At most, it would provide you with tools that would enable you to do ontology. However, "right reasoning" is much more than the correct logical framework.

This understanding of what is required just confirms you are a naive realist. Peirce established the proper pragmatic basis for a logico-scientific understanding of reality. — apokrisis

Yeah, I wasn't aware that Peirce is a god who cannot be challenged. Please. Put up some argument, don't tell me the historical antecedents of your view.

So the map isn't the territory of course. But more than that, it doesn't aim to re-present the world. It aims to ignore that world as much as possible. So the map comes to be a map of our own interpretive interests as much as a map of the external reality. It is a picture of ourselves as much as it is a picture of the thing in itself. — apokrisis

Exactly. That's why you cannot use the map to do ontology. You must go back to the things themselves.

So the Peircean argument is internalist. All we can know of the world is the beliefs that we are prepared to hold about it, the beliefs we are prepared to act by. — apokrisis

Wait, how do you jump from the nature of maps and models, to how we can know about the world? Do you mean that we can only know about the world through models? And if so, what justifies that?

This doesn't deny the thing in itself. But it should also alert us to the fact we don't really care about the world in some disembodied fashion. The maps we make are as much a self-portrait - indeed, the very act of creating that "interpretive self" - as they are a re-presentation of the world as it might be said to be in terms of its own set of interests. — apokrisis

Okay, but as you can see this cuts your own branch. If this is the case, then you cannot be doing ontology with your philosophy. You can at most be creating narratives that are useful for particular purposes, such as advancing scientific discoveries, while, as per your own statements, leaving you blind to others, which don't interest you. In this case ontology, theology, etc.

Nice try at boxing me in. But that pragmatic intersection between theory and practice is exactly what I have a good meta-theoretic understanding of. — apokrisis

Yeah, you understand it at a meta-THEORETIC level ;)

I'm stifling a yawn. How could your replies become so anodyne so fast?

I'm stifling a yawn. How could your replies become so anodyne so fast?
2 — apokrisis

Oh? So my remarks regarding your philosophy's incapacity to reach the level of ontology isn't something you disagree with? Fine. I never knew you had such small ambitions ;)

To clarify this, as I said before, I hold no issue with you if you want to tell us that vagueness exists at the level of the model or the map. But I do have an issue if you want to claim that vagueness is ontological, and exists at the level of the terrain, not just of the map.

But I do have an issue if you want to claim that vagueness is ontological, and exists at the level of the terrain, not just of the m — Agustino

Well you would have to make that argument then. So far you have only told me about your own map of the territory. And that turned out to have separated togethernesses.

Well you would have to make that argument then. So far you have only told me about your own map of the territory. And that turned out to have separated togethernesses. — apokrisis

Well, I will make an argument once you explain to me how you go from the vagueness in the map to vagueness in the territory. I'm looking to see how you derive your ontological vagueness at this point. We've arrived at there being some vagueness in the map. How do we go from this epistemological vagueness to the ontological one? This may be a more productive route given the way none of the other routes have worked with you so far.

As for the argument you want - I've already made the argument you're looking for, namely that vagueness in the territory is contradictory and impossible. That is because any sort of potentiality always presupposes an actuality which is prior to it. You've gone over this with MU in this thread, and with me in another older thread a few weeks ago. There cannot be any primordial chaos, infinite potential, vagueness and the like - some minimal degree of order and act are always required.

Now, what problems do you have with that argument (and with how it was expressed starting with Aristotle)? By means of what would an infinite potential, in the absence of act, actualise itself? In concrete terms, why would there be any sort of fluctuation in the first place if there is a necessarily inert vagueness in the first place? If there is a fluctuation it seems to me like there is some act already. A fluctuation isn't a potency. And please don't answer me with "Why wouldn't there be a fluctuation, what's there to stop it?" -_- . Because if you answer that way, I will ask why a fluctuation and not something else, what's there to stop it?

I will make an argument once you explain to me how you go from the vagueness in the map to vagueness in the territory. — Agustino

The usual way. Measurement.

For instance, engineers are always telling me that my definite models of reality turn out not to fit the world in vague ways. Quantum wavefunctions still need to be collapsed. Chaos turns out to forget its initial conditions. The way the maps keep failing look to be trying to tell me something deep about the essential spontaneity of the territory.

For instance, engineers are always telling me that my definite models of reality turn out not to fit the world in vague ways. Quantum wavefunctions still need to be collapsed. Chaos turns out to forget its initial conditions. The way the maps keep failing look to be trying to tell me something deep about the essential spontaneity of the territory. — apokrisis

Aha! Exactly. Now we're getting onto something. So the phenomenon is very similar to this.

When we're attempting to apply our models to reality at the smallest scales possible (and wherever behaviour is non-linear and chaotic) we notice that we're unable to predict what will happen, even though the phenomena - according to our laws - are entirely determinate.

So our models do not fit the world, in all sorts of "spontaneous" and unpredictable, vague ways. So from this fact, to your conclusion, there are still some steps required. Namely, you have to show us how we go from this fact of being unable to model certain aspects of reality concretely, to there being a vagueness in reality. Clearly there is a vagueness in the models - they provide vague answers, which differ spontaneously and in unpredictable, vague ways from reality.

But just like in the case of the coastline paradox, you cannot extend the mathematical conception of space - where space, for example, is infinitely divisible, and hence it becomes impossible to determine the length of some fractals whose limit diverges to infinity when you attempt to calculate it using the mathematical methods we have at our disposal today - you cannot extend this mathematical conception to real space. That's an unwarranted assumption, and it would be wise to suspect the mathematical model to be responsible for the vagueness and not reality. Reality is not vague, but it's not vague in a way that we cannot know.

So in a similar manner and by analogy, you wouldn't suspect reality to be responsible for the vagueness that is noticed by the lack of correspondence between your expectations - as given by the model - and the reality.

There cannot be any primordial chaos, infinite potential, vagueness and the like - some minimal degree of order and act are always required. — Agustino

You mean like a fluctuation?

If there is a fluctuation it seems to me like there is some act already. — Agustino

And a direction too. The degree of order is also minimal, remember.

why would there be any sort of fluctuation in the first place if there is a necessarily inert vagueness in the first place? — Agustino

Why would inertness be necessary? The very fact something exists shows that by necessity it couldn't be.

Of course vagueness doesn't even exist according to your own map of reality. You rely on God to kick things off. Or divine circular motion to swirl things about. Or something equally bizarre.

You mean like a fluctuation? — apokrisis

Surely it could be a fluctuation I do not care what it is for the purposes of this discussion, but it must be something actual, not an infinite potential, vagueness and the like.

Why would inertness be necessary? — apokrisis

Because you want it to be an infinite potential, a vagueness where no act is present. If that's the case, then it is necessarily inert since it cannot actualise itself. Its chaos - as it were - prevents it from creating anything spontaneously, even a fluctuation. That's how chaotic it is.

The very fact something exists shows that by necessity it couldn't be. — apokrisis

Yes, and this was Aristotle's argument to show the primacy of act over potency in his metaphysics.

Of course vagueness doesn't even exist according to your own map of reality. You rely on God to kick things off. Or divine circular motion to swirl things about. Or something equally bizarre. — apokrisis

You can rely on the fluctuation, but you cannot rely on the infinite vagueness to account for the fluctuation. If you want, the fluctuation can be a brute fact in yours - that's not a problem within the constraints of this discussion. But you cannot rely on the infinite vagueness. So scratch that out. That's the mythological element. The beginning point is a fluctuation for you, as for science actually. Science cannot get beyond that assuming that there is even a beyond.

Aha! Exactly. Now we're getting onto something. So the phenomenon is very similar to this. — Agustino

Sure. You get infinite outcomes if your model offers no lower bound cut-off to limit material contributions. So your example illustrates my points quite nicely. Our measurements coarse grain over fractal reality. We are happy to approximate in this fashion. And then even reality itself coarse grains. The possibility of contributions must be definitely truncated at some scale - like the Planck scale - to avoid an ultraviolet catastrophe. Vagueness is required at the base of things to prevent the disaster of infinite actualisation.

Also how much do you understand fractals? Note how they arise from a seed dichotomy, a symmetry breaking or primal fluctuation. That is what the recursive equation with its log/log growth structure represents.

Surely it could be a fluctuation I do not care what it is for the purposes of this discussion, but it must be something actual, not an infinite potential, vagueness and the like. — Agustino

As the first fluctuation, it would have as yet no context. History follows the act.

So as I said before, the fluctuation is the birth of both material action and formal direction. But it takes longer for direction to seem firmly established as that requires a history of repetition.

It seems the mistake you keep making is to forget I am arguing for the actualisation of a dichotomy - the birth of matter and form in a first substantial event. You just keep talking about the material half of the equation.

Note the more subtle point about fractals. As a dichotomous growth process, they directly model this issue of convergence towards a limit that I stressed in earlier posts.

Think about the implications of that for a theory of cosmic origination. It argues that a world that can arise from a symmetry breaking - a going in both its dichotomous directions freely - does in fact have its own natural asymptotic cut off point. The Planck scale Big Bang is not a problem but a prediction. Run a constantly diverging process back in time to recover its initial conditions and you must see it converging at a point at the beginning of time.

This has in fact been argued as a theorem in relation to Linde's fractal spawning multiverse hypothesis. So if inflation happens to be true and our universe is only one of a potential infinity, the maths still says the history of the multiverse must converge at some point at the beginning of time. It is a truly general metaphysical result.

Another way to illustrate this is how we derive the constant of growth itself - e. Run growth backwards and it must converge on some unit 1 process that started doing the growing. Thus what begins things has no actual size. It is always just 1 - the bare potential of whatever fluctuation got things started. So a definite growth constant emerges without needing any starting point more definite than a fleeting one-ness.

So from a variety of mathematical arguments we find that any tale of infinitely diverging processes tells us conversely also the tale of a convergence to some necessary cut-off limit. Run history backwards and we must arrive at a common point.

As the first fluctuation, it would have as yet no context. History follows the act. — apokrisis

Okay, no disagreement there.

It seems the mistake you keep making is to forget I am arguing for the actualisation of a dichotomy - the birth of matter and form in a first substantial event. You just keep talking about the material half of the equation. — apokrisis

It's difficult to make sense of what you're trying to say here because you're using words differently from Aristotle it seems to me. Matter is inert, it is form which is act, and actualises. So form is imposed on the inert matter (which is potential), and this form would be the fluctuation. But note that form must be independent to and prior to matter.

You get infinite outcomes if your model offers no lower bound cut-off to limit material contributions. — apokrisis

Right, so then the mathematical concept of space as infinitely divisible isn't how real space actually is. It's important to see this.

Our measurements coarse grain over fractal reality. We are happy to approximate in this fashion. And then even reality itself coarse grains. The possibility of contributions must be definitely truncated at some scale - like the Planck scale - to avoid an ultraviolet catastrophe. — apokrisis

Yeah, so reality eliminates all those infinities that are inherent in our mathematical models. Our initial predictions that blackbodies would emit infinite amounts of UV were based on the mistake in our mathematical model of assuming an infinite continuity going all the way down, while the truth is that things are cut off at one point, they become discrete.

Vagueness is required at the base of things to prevent the disaster of infinite actualisation. — apokrisis

I don't follow this.

Also how much do you understand fractals? Note how they arise from a seed dichotomy, a symmetry breaking or primal fluctuation. That is what the recursive equation with its log/log growth structure represents. — apokrisis

Well that's a metaphorical way to put it regarding the "primal fluctuation". They do arise from a symmetry breaking, or rather that the process of constructing a fractal involves a symmetry breaking. Regarding the recursive eq, are you talking about fractal dimensionality? As in log(number copies)/log(scale factor)?

But another example of the vagueness/PNC~generality/LEM dichotomy which is basic to his logic is the triangle. A triangle is a general concept that forms a continuum limit - a global constraint - that then can't be exhausted by its particular instances. An infinite variety of particular triangles can be embraced by the general notion of a triangle.

So the LEM does not apply to this generality as a triangle can, in genus~species fashion, be equilateral, isosceles, or scalene. Of course the triangle must be a three-sided polygon, but that is talking of a still higher level generality of which it now partakes as a definite particular. — apokrisis

OK, so the concept of a triangle is "a plane figure with three sides and angles". Let me see if I can figure out how the LEM does not apply here. You say that any particular triangle, must be one of a number of different types of triangles. Where does the LEM not apply? It doesn't make sense to say that the concept of triangle in general must be a particular type of triangle, just like it doesn't make sense to say that the concept of animal, in general must be a particular type of animal. So it's just a case of categorical separation. It doesn't make sense to attribute a species to the genus, that's a category error, not a failure of the LEM. If we insist that the concept of colour must be either red or not red, and find that this is impossible, it is not that the LEM does not apply, it is a simple category mistake.

Then vagueness is defined dichotomously to the general. Where generality allows you to say any particular triangle can be either scalene or isosceles, vagueness speaks to the indefinite case where there is as yet no triangle specified and so there is no fact of the matter as to whether it is scalene or isosceles. It is not a contradiction to say the potential triangle is both. — apokrisis

This I can't make any sense of. We have the concept of triangle. Your claim seems to be that if there is no particular triangle, then this particular triangle the potential triangle, may be both scalene and isosceles. I'm sorry to have to disappoint you, but yes, this is contradictory. Don't you see that you are saying that there is no particular triangle, then you say that this particular triangle, the potential triangle, which has already been denied, is both. Don't you see that to affirm something and deny it, both, is contradiction? To say that there is the potential for a triangle which is either isosceles or scalene, is not the same thing as saying that there is a potential triangle which is both. The latter affirms that there is a particular triangle, the potential triangle, which is both isosceles and scalene. And that's contradictory nonsense.

It's difficult to make sense of what you're trying to say here because you're using words differently from Aristotle it seems to me. — Agustino

Well yes. I must have spent quite a few pages in this thread making it plain that my claim is that prime matter would be an active and not inert principle. Then the prime mover would not be an active principle in the normal sense of effective cause, just "active" in the sense of an emergent limiting constraint on free material action.

There are quite a few difference I would have with a scholastic understanding of Aristotelean metaphysics. That was rather the point.

Matter is inert, it is form which is act, and actualises. So form is imposed on the inert matter (which is potential), and this form would be the fluctuation. But note that form must be independent to and prior to matter. — Agustino

Now you are repeating what I have disputed. And I have provided the rationale for my position. So instead of just citing scholastic aristoteleanism to me, as if that could make a difference, just move on and consider my actual arguments.

Right, so then the mathematical concept of space as infinitely divisible isn't how real space actually is. It's important to see this. — Agustino

It is also important to see that Peirce's mathematical conceptions are based on the duality of generality and vagueness. So you can both have a general continuum limit and also find that it has potential infinity in terms of its divisibility. In fact, you've got to have both.

And funnily enough, real space is like that. Just look at how we have to have the duality of general relativity and quantum mechanics to account for it fully. One describes the global continuity of the constraints, the other, the local infinite potential, the inherent uncertainty that just keeps giving.

Yeah, so reality eliminates all those infinities that are inherent in our mathematical models. Our initial predictions that blackbodies would emit infinite amounts of UV were based on the mistake in our mathematical model of assuming an infinite continuity going all the way down, while the truth is that things are cut off at one point, they become discrete. — Agustino

It amusing that you talk about this as some mathematical mistake.

You are trying to paint yourself as the commonsense engineer that is never going to be fooled by these crazy theoretical types with their dreadful unrealistic mathematical models. And yet an engineer has a metaphysics. He believes in a world of clockwork Newtonian forces. That is the right maths. And on the whole it works because the universe - at the scale at which the engineer operates - is pretty much just "classical". There is no ontic vagueness to speak of.

Of course, the beam will buckle unpredictably. An engineer has to know the practical limits of his classically-inspired mathematical tools. The engineer will say in theory, every micro-cause contributing to the failure of the beam could be modelled by sufficiently complex "non-linear" equations. The issue of coarse graining - the fact that eventually the engineer will insert himself into the modelling as the observer to decide when to just average over the events in each region of space - is brushed off as a necessary heuristic and not an epistemic embarrassment.

Even proof that the model can't be computed in polynomial time won't dent the confidence of "a real engineer". Good enough is close enough. Which is why real world engineering projects fail so regularly.

So forget your engineer's classically-inspired commonsense understanding of maths here. Peirce was after something much deeper, much more metaphysically sophisticated.

Regarding the recursive eq, are you talking about fractal dimensionality? As in log(number copies)/log(scale factor)? — Agustino

Yes.

You say that any particular triangle, must be one of a number of different types of triangles. Where does the LEM not apply? — Metaphysician Undercover

Of course the LEM applies to any particular triangle. It doesn't apply to the notion of the general triangle.

It doesn't make sense to say that the concept of triangle in general must be a particular type of triangle, — Metaphysician Undercover

Exactly.

It doesn't make sense to attribute a species to the genus, that's a category error, not a failure of the LEM. — Metaphysician Undercover

Yep. The LEM fails to apply. It doesn't even make sense to think it could. It is definitional of generality that it doesn't.

Your claim seems to be that if there is no particular triangle, then this particular triangle the potential triangle, may be both scalene and isosceles. — Metaphysician Undercover

Before a particular triangle has been drawn, it may be scalene or isosceles. That is the potential. And so while still just a potential, it is not contradictory to say this potential triangle is as much one as the other. That is, what it actually will be is right at this moment vague - as defined by the PNC not being applicable and any proposition that pretends otherwise being a logical failure.

Of course the LEM applies to any particular triangle. It doesn't apply to the notion of the general triangle. — apokrisis

The laws of logic are rules of predication, how we attribute predicates to a subject. If your subject is the general notion of a triangle, the rules apply. The subject is identified as the triangle, by the law of identity, and the other two rules of predication apply.

The LEM fails to apply. It doesn't even make sense to think it could. It is definitional of generality that it doesn't. — apokrisis

It is only when you define "generality" in the odd way which you do, as a potential particular, that the laws of logic might fail to apply. But this definition is a category mistake because there is a well respected categorical separation between the general and the particular, and you seem to define the general as a type of particular.

You justify this denial of the categorical separation by claiming that the distinction between general and particular is relative only. The triangle is general in relation to isosceles but particular in relation to geometrical figure. But all you have here is relations of generalities. You have not identified a particular. The PNC and LEM rely on the law of identity, the identification of a subject. Until you ,move to identify a particular, it is a foregone conclusion that the laws of logic do not apply.

So you can talk about your generalities all you want, and how the laws of logic are inapplicable to your talk about generalities, but this is just an epistemic failure on your part. It is a failure to identify a particular in order to move forward using the laws of logic. These claims you make about generalities have no ontological bearing, because there is no evidence that such unidentifiable generalities exist anywhere but in the indecisive human mind. And when you move to identify "generality" as a particular thing with ontological status, like apeiron, vagueness, or pure potential, we can apply the principles of logic, despite the fact that you do not want us to, and will not listen to our conclusions.

Before a particular triangle has been drawn, it may be scalene or isosceles. — apokrisis

Don't you see this as nonsense? There is no triangle. It hasn't been drawn, it isn't even conceived of in the mind of a person who might draw it. Yet you say that it may be scalene or isosceles. That's nonsense, there is nothing there. If you instruct a person to draw a triangle, we might say that the person has these options, but that is not to say that there is a potential triangle which is both scalene and isosceles.

And so while still just a potential, it is not contradictory to say this potential triangle is as much one as the other. That is, what it actually will be is right at this moment vague - as defined by the PNC not being applicable and any proposition that pretends otherwise being a logical failure. — apokrisis

That's nothing but irrational nonsense. You have identified the potential for a triangle, a person might draw a triangle. From here, you want to identify the triangle which might be drawn, and say that since it's not drawn yet, it's both isosceles and scalene. But that's nonsense, because the person might draw a square or a circle, or nothing at all.

The triangle is identified as potential, and this means that its existence is contingent. If its existence is contingent, then it may or may not be. If there is reason to believe that the existence of the triangle will be necessitated (the person was instructed to draw a triangle), we can consider the possibilities. It may be isosceles, it may be scalene, etc.. But to say that there is an identified triangle, the "potential triangle", and it "is as much one as the other", is pure nonsense, because what is actually the case is that the probability for one triangle is equal to the probability for the other triangle.

Therefore there is not an identified "potential triangle" which consists of all the contrary possibilities. There is the possibility for many different triangles, contrary triangles. Each potential triangle has features which are consistent with the laws of logic. So we can adequately describe the situation without the irrational nonsense which insists that the laws of logic do not apply. The situation of "potential triangle" is treated as the possibility for many different triangles, as well as other things, each consistent with the laws of logic. It is not treated as one triangle which has features which are inconsistent with the laws of logic. The latter is irrational nonsense, and there is no need for the claim that laws of logic do not apply.