"utility, beauty, and sustainability", I would say are not components of the building, but aspects (properties) of the whole. So I agree with your sentiment, but am inclined to think that "causal relations" - which implies that they are distinct parts (components) of the whole - is not quite the right way to articulate the point. — Ludwig V

The components have properties, and when they interact with each other, other properties emerge. I think the utility, beauty, and sustainability of a building are Emergent Properties, and the parts, features, and configurations from which they emerge are not so distinct. They can depend on each other, or emerge from one and the same part.

For example, the durability of reinforced concrete slabs means that they can be carried by a sparse grid of columns (instead of a forest of columns or thick walls) which, in turn, enables freedom for efficient, flexible, and aesthetically varied organization of the spaces (e.g. with thin walls or open plans). Such a building is easy to change and adjust to passing trends and uses, hence sustainable. If we change the durability of the slabs then we also change the building's practical, beautiful, and sustainable properties, since they emerge from the same part and its configuration.

I think the utility, beauty, and sustainability of a building are Emergent Properties, and the parts, features, and configurations from which they emerge are not so distinct. They can depend on each other, or emerge from one and the same part. — jkop

I agree with what you say. Indeed, it seems obvious. At present "emergent properties" seems to be pretty much a label for the undefined. I think the most useful approach is not to affix a label and try to answer the question "what is an emergent property", but to consider and understand cases and then work out how they are related. Then we'll know whether to pin one label on all the cases or maybe different labels for different, but similar cases. So your comments on reinforced concrete slabs seem entirely appropriate. The label doesn't help and can get in the way
d

This question directs some light onto what makes Tarskian's definition of philosophy interesting: — ucarr

I have many problems with this - and with self-reference. Not the least of which is that I'm inclined to think that if a language cannot talk about itself, then there is something it cannot talk about, so it is incomplete. Nor is there anything wrong with self-reference. Some specific uses of it are problematic, but since I'm not committed to avoiding all logically problematic uses of language by ruling them out of court in advance, I'm not much bothered by them. I don't think they give rise to any major problems of philosophy. Logicians and mathematicians have adopted the project of constructing a language with a grammar that rules such statements out. That's their choice. But it seems clear that a language that include those possibilities is perfectly workable.

I am wondering, however, whether self-reference may not be part of the distinction between science and the humanities. There is history of history, literature about literature, philosophy about philosophy. Metamathematics is presumably about mathematics, but I'm not sure whether it is mathematics or not. But there isn't physics about physics or chemistry about chemistry. More than that, can there be science of science. I doubt if it could follow some version of scientific method, including the experimental method, so would such a discipline be scientific?

A statement is philosophical, if it is a statement about another statement. For example: It is irrelevant that it is raining today. — Tarskian

I'm afraid I'm completely stuck in my opinion that the example is not a philosophical statement, unless you mean that it being used as a philosophical example makes it a philosophical statement. Which I think would be unduly stretching the scope of philosophy.
For another example "This work is copyright". I think that's legal and not philosophical at all. Yet it occurs in (or at least around) philosophical texts and is about them.

I have many problems with this - and with self-reference. Not the least of which is that I'm inclined to think that if a language cannot talk about itself, then there is something it cannot talk about, so it is incomplete. Nor is there anything wrong with self-reference. Some specific uses of it are problematic, but since I'm not committed to avoiding all logically problematic uses of language by ruling them out of court in advance, I'm not much bothered by them. — Ludwig V

This calls attention to something essential in human nature: acts of communication work with logic in application. You can't communicate if you're not being logical in a public sense, which is to say logical in a way that the common people can understand.

Every academic discipline has to keep checking (and updating) its logic as it goes forward, making additions to its database. At the end of the nineteenth century, science_physics underwent a revolution with the transition from Newton to Einstein_QM. Deep ramifications about how to view the material reality are still being distilled.

Revolutionary turns in the picture of reality are best times for philosophy and philosophers.

I don't think they give rise to any major problems of philosophy. — Ludwig V

If self-reference(s) is the antecedent to "they," then I might start thinking of you as being a radical QM materialist, as I am. For what I've seen so far (not exhaustive), scientists and logicians still maintain a white knuckle grip on the Principle of Non-Contradiction. Here at TPF, many debaters think they've scored a slam dunk whenever they discover a contradiction from the opposition.

Logicians and mathematicians have adopted the project of constructing a language with a grammar that rules such statements out. That's their choice. But it seems clear that a language that include those possibilities is perfectly workable. — Ludwig V

More evidence of your radical inclination.

Yes, Tarskian's claim is particularly interesting in terms of its generality:

A statement is philosophical, if it is a statement about another statement. For example:

It is irrelevant that it is raining today. — Tarskian

It dovetails with Gödel and, with a marvelous concision, translates his premise into verbal language. Now it's easy to see that all axiomatic systems, first order, generate statements not strictly proven within the scope of the axiomatic system from which they arise. This is a powerful generalization of the premise of incompletion, both axiomatic and existential.

When we apply essential incompletion to philosophy itself, so that now we're evaluating philosophy's evaluation of something else, we find ourselves at the second higher-order: evaluation of evaluation of a proposition.

What we're seeing now is the process of how ground rules keep giving rise to more ground rules. Ha, ha, ha! We must now laugh at ourselves in our quest to compile everything into one system elegant in its simplicity.

Another nemesis of the would-be wise, standing alongside of contradiction, is the infinite series.

I'm afraid I'm completely stuck in my opinion that the example is not a philosophical statement, unless you mean that it being used as a philosophical example makes it a philosophical statement. Which I think would be unduly stretching the scope of philosophy. — Ludwig V

You can apply critical thinking to any predication. In some instances that might render you as a pedant, but you can do it.

I am wondering, however, whether self-reference may not be part of the distinction between science and the humanities. — Ludwig V

Indeed, it is. It's the heart of the difference. It's the heart of the challenge to the Newtonian physicist to change the vision to QM. The observer cannot be abstracted from the experiment. From this we understand there is no abstraction. Instead, there are relationships. Loop quantum gravity tells us there are atoms of discontinuous space. Seemingly continuous space is an effect of the limits of human eyes.

Now we see that incompletion generalized dovetails with the fall of abstraction, landing us in a world that demands a future created from... what?

...can there be science of science. I doubt if it could follow some version of scientific method, including the experimental method, so would such a discipline be scientific? — Ludwig V

Philosophers, as we've been seeing in my post, are cognitive grammarians. Thinking about thinking amounts to examination of the ground rules for any predication.

Ground rules are the foundation supporting methodology. Therefore, any discipline that generates methodology also generates ground rules. In this way, philosophy is more inclusive than science. The methodology for the scientific method might not be scientific, but it is philosophical.

At present "emergent properties" seems to be pretty much a label for the undefined. — Ludwig V

I can understand why it would seem that way, but I'll try show emergence in a different light.

Suppose I design an electronic circuit that has the property of producing accurate measurements of something. I, in principle, could explain in an enormous amount of detail, why these specific components, interconnected with each other in this specific way, results in the emergent property of the design. For such an explanation to succeed, the person I am explaining this to, would need more than a four year degree in electrical engineering provides as background knowledge.

Neither of us probably wants to go through such an explanatory process. :wink:

So it seems reasonable to me, to see understanding of emergence as something particular experts have, and that non-experts for practical purposes, have to be left with the seemingly hand-wavey explanation, "The property emerges from the physical structure of the device."

If self-reference(s) is the antecedent to "they," then I might start thinking of you as being a radical QM materialist, as I am. For what I've seen so far (not exhaustive), scientists and logicians still maintain a white knuckle grip on the Principle of Non-Contradiction. Here at TPF, many debaters think they've scored a slam dunk whenever they discover a contradiction from the opposition. — ucarr

The Principle exists, but only rarely applies. You have to define your language very carefully to produce one. A fundamental rule of language appears to be to design itself to avoid the possibility f being faced by one, allowing third possibilities and shades of grey. A binary choice is almost always artificial.
A contradiction can only do harm when it has not been spotted. The self-reference paradoxes are completely transparent and consequently do no harm (so far as I can see) - except to the poor souls who think they have to "solve" it.
Compare the awkwardness about If P then Q when P is false. This is well understood. People have reacted in various ways. When it is not spotted it could do harm, but I don't see any need to get excited about it. (My solution is that truth values do not apply in this kind of case - and that is not a third truth value.
I'm not sure how serious I am here, so I reserve the right to contradict myself if you reply!

It dovetails with Gödel and, with a marvelous concision, translates his premise into verbal language. — ucarr

I didn't appreciate that. I got too annoyed at the revelation that he didn't want a definition. He wanted an algorithm that would enable an AI to distinguish philosophical texts from the rest. What would be the criterion of success? THAT would be the definition.
Not that definitions are all that important. Geach, long ago, wrote a wonderful article excoriating the Euthyphro because Socrates equated not knowing what piety is with being unable to define it. He was quite right.

The methodology for the scientific method might not be scientific, but it is philosophical. — ucarr

I hoped you would say that. So science, in the end, is grounded in human beings. Worse than that, not in a scientific, but history and philosophy. Oh dear!

The observer cannot be abstracted from the experiment. — ucarr

Yes. But the observer, in my book, is not an abstraction - a point of view. (At most, a point of view is a location for a possible observer.) An observer is a person.

I, in principle, could explain in an enormous amount of detail, why these specific components, interconnected with each other in this specific way, results in the emergent property of the design. — wonderer1

I'm sure you could. Thank you for letting me off the detail. I agree that the "emergent" physical property of the gate "emerges" from the design. But the design emerges from the designer. Physics cannot even recognize a design, much less apply its laws to it.

So it seems reasonable to me, to see understanding of emergence as something particular experts have, — wonderer1

Yes. I like the idea that it is about particular cases, rather than some very general abstraction. Generality is there the hand-waving comes in.

So it seems reasonable to me, to see understanding of emergence as something particular experts have,
— @wonderer1
Yes. I like the idea that it is about particular cases, rather than some very general abstraction. Generality is there the hand-waving comes in. — Ludwig V

one can have a rather good understanding of how tornadoes work while being entirely ignorant of particle physics. The point generalizes to more complex and longer-lived entities, including plants and animals, economies and ecologies, and myriad other individuals and systems studied in the special sciences: such entities appear to depend in various important respects on their components, while nonetheless belonging to distinctive taxonomies and exhibiting autonomous properties and behaviors...
...
The general notion of emergence is meant to conjoin these twin characteristics of dependence and autonomy. It mediates between extreme forms of dualism, which reject the micro-dependence of some entities, and reductionism, which rejects macro-autonomy — SEP

So in the case of architecture, there are parts, features, and configurations from which three general properties emerge: utility, beauty, and sustainability.

Those properties are functionally separate, and they typically counteract eachother in ways that call for compromises, because the success of the composition is dependent on them.

In this sense, they are both emergent properties and components of the architecture.

The special sciences won't answer how they causally emerge, nor how a balanced or distributed composition satisfies the success of a building. Yet every effect has a cause, and for millennia we have known that buildings should be practical, beautiful, and sustainable.

The observer cannot be abstracted from the experiment. — ucarr

Yes. But the observer, in my book, is not an abstraction - a point of view. (At most, a point of view is a location for a possible observer.) An observer is a person. — Ludwig V

Okay. Proceeding from the observer as an always local person, if we bind the thinking of an always local person to that always local person, then it too, is always local, and the abstraction of abstract thinking starts dissolving.

If there's no omnipresent, eternal, neutral spacetime within which dynamical material things and material systems animate themselves, then we have a wide-ranging field of local events attached to the evolving relationships linking animate things.

There is no vastness of creation because material relationships pose resistance to generalization.

The simple binary of concrete/abstract hasn’t dissolved away to nothing, but it has become faint.

What would be the criterion of success? THAT would be the definition. — Ludwig V

Might it be an ability to see how cognitive objects such as language, and cognition itself, per Gödel, will generate valid statements unprovable within the boundaries of supposedly axiomatic systems?

There may not be any elegant simplicity axiomatic to everything.

There may not be any elegant simplicity axiomatic to everything. — ucarr

If we define true arithmetic as the set of all facts in arithmetic, i.e. arithmetic reality, then we can see that the set of Peano's axioms is not just a lossless "compression" of arithmetic reality.

Peano's "compression" loses a lot of information.

Godel's incompleteness theorem expresses that the set of Peano's axioms is a lossy compression of arithmetic reality.

So, Peano's axioms are equivalent to some jpeg image of the scene of which you have taken a picture.

True physics would be the set of all facts in the physical universe, i .e. physical reality.

Any proposed set of physical axioms does not need to be a lossless compression of physical reality either.

The compression is actually allowed to lose a lot -- or even most -- of the information contained in physical reality.

The compression merely needs to be sound.

If the compression deems a fact to be true, then it must indeed be verifiably true in the uncompressed reality.

The compression is allowed to be even very lossy.

If a fact appears in uncompressed reality, it is fine that it gets forgotten in the compression.

Nothing guarantees that there would be just one way to create a lossy compression of physical reality. But then again, nothing guarantees that a lossy compression even exists.

There are lots of image compression algorithms, both lossless and lossy ones:

https://en.m.wikipedia.org/wiki/Image_compression

There is absolutely no guarantee that such thing does not exist for physical reality.

Godel's theorem is in fact relatively simple. It says that the compression that we have for natural numbers is lossy (and not lossless).

The compression is actually allowed to lose a lot -- or even most -- of the information contained in physical reality. — Tarskian

Not if you want to reconstruct reality rather than a pale comparison. In any case, it sounds like you're apply concepts in data processing to "reality" which seems... off, to say the least. Is there a basis for it? I'm always interested in metaphysical speculation of that kind.

Not if you want to reconstruct reality rather than a pale comparison. — AmadeusD

That would require the axiomatic system to be a lossless compression of the reality that it compresses.

If there is no particular given limit to the complexity of the truths that this reality can contain, then Chaitin's incompleteness theorem prevents the existence of a lossless compression of this reality.

https://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin's_incompleteness_theorem

There exists a constant L (which only depends on S and on the choice of description language) such that there does not exist a string s for which the statement

K(s) ≥ L (as formalized in S)

can be proven within S.

K(s) is the complexity of a particular theorem s while L is the maximum complexity that theory S can prove. Technically, K(s) is the size in bytes of the smallest possible program that can output s, i.e. its Kolmogorov complexity.

https://en.wikipedia.org/wiki/Kolmogorov_complexity#Compression

It is straightforward to compute upper bounds for K(s) – simply compress the string s with some method, implement the corresponding decompressor in the chosen language, concatenate the decompressor to the compressed string, and measure the length of the resulting string – concretely, the size of a self-extracting archive in the given language.

it sounds like you're apply concepts in data processing to "reality" which seems... off, to say the least. Is there a basis for it? — AmadeusD

Gödel's incompleteness and Chaitin's incompleteness are indeed related. In "true but unprovable", Noson Yanofsky writes:

http://www.sci.brooklyn.cuny.edu/~noson/True%20but%20Unprovable.pdf

Gregory Chaitin described an innovative way of finding true but unprovable statements. He started by examining the complexity of the axioms of a logical system. He showed that there are certain statements that are much more complex than the axioms of the system. Such statements are true but cannot be proven by the axioms of the logical system. The following motto is sometimes used to explain this:

“A fifty-pound logical system cannot prove a seventy-five-pound theorem.”

In particular, basic arithmetic is a logical system that has a level of complexity and so there are certain types of statements that are true but too complex to be proven using basic arithmetic. The main point for our story is that within basic arithmetic we can always find more complicated statements of a certain type. Hence, there are infinitely many true but unprovable statements.

In simple terms, if the optimally compressed self-extracting archive of the axiomatic system is smaller than the one for the theorem, then the axiomatic system cannot prove this theorem.

In fact, last year (2023) David Zisselman even made the effort to formally prove Gödel's incompleteness theorems from Chaitin's incompleteness theorem:

https://arxiv.org/pdf/2302.08619

A proof of Gödel’s incompleteness theorems
using Chaitin’s incompleteness theorem

Abstract

Gödel’s first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin’s incompleteness theorem and a very basic numbers extension.

As opposed to the usual proofs, these proofs don’t use any fixed point theorem and rely solely on sets structure. Unlike in the original proof, the statements which can be shown to be unprovable by our technique exceed by far one specific statement constructed from the axiom set.

Our goal is to draw attention to the technique of number extensions, which we believe can be used to prove more theorems regrading the provability and unprovability of different assertions regarding natural numbers.

The intriguing part is that Zisselman does not need Cantor's diagonalization in any shape or fashion (which above he equivalently calls "a fixed point theorem") to prove Gödel's theorems. As far as I know, nobody else has pulled that off.

I'm always interested in metaphysical speculation of that kind. — AmadeusD

The foundational crisis in mathematics does indeed have a distinct metaphysical sonority to it. It describes issues in arithmetic reality but it may actually also apply to physical reality, if both realities happen to be structurally sufficiently similar.

Okay. Proceeding from the observer as an always local person, if we bind the thinking of an always local person to that always local person, then it too, is always local, and the abstraction of abstract thinking starts dissolving. — ucarr

I don't know what you mean by "bind". If a local person indulges in abstract thinking, and shares that thinking with other local and non-local thinkers, how does the abstraction of abstract thinking dissolve?
(Don't forget that is the abstract dissolves, so does the concrete.)
I have no problem with the idea that mathematical objects are real or that we can generalize from the particular to the general.

The simple binary of concrete/abstract hasn’t dissolved away to nothing, but it has become faint. — ucarr

I didn't understand a lot of the intervening ideas. But this inclines me to retort that perhaps it needs to become faint. Binary oppositions are almost always less clear and definitie than some people would like to think.

Might it be an ability to see how cognitive objects such as language, and cognition itself, per Gödel, will generate valid statements unprovable with the boundaries of supposedly axiomatic systems? — ucarr

I have a lot of difficulty with the idea of something true but unprovable. How could we know that such things exist, and if we do, how do know what they are? But this is a bit more specific and so it helps. I still haven't seen an example of such a truth and would love to do so.

There may not be any elegant simplicity axiomatic to everything. — ucarr

Perhaps there isn't. But isn't that just a methodological principle that applies when there are competing theories in play? In any case, it only requires us to choose the simplest of available theories, so it would be hard to refute. By the way, what is the criterion for simplicity? Kolgorov complexity?

Which is all very interesting and important. I mean that.

However, it occurred to me that, as a definition, "Statements about statements" captures far too much, but we've been over that. More important is this - Berkeley's Dialogues for example can be read as a philosophical text, but also as a historical or religious text. The difference is not in the text, but in the approach to the text. Philosophy is not simply matter of texts, but of an activity, a skill, a language game, or several language games. The disciplines are different ways of reading (in the large sense) and responding to them.

PS One can also read Berkeley as an exercise in rhetoric. The text is riddled with it.

True physics would be the set of all facts in the physical universe, i .e. physical reality.

Any proposed set of physical axioms does not need to be a lossless compression of physical reality either.

The compression is actually allowed to lose a lot -- or even most -- of the information contained in physical reality.

The compression merely needs to be sound. — Tarskian

If the compression deems a fact to be true, then it must indeed be verifiably true in the uncompressed reality. — Tarskian

Since "deem" is a synonym for "judge," we see that compression herein is a process of translation. Humans frequently talk about something being lost in translation.

The foundational crisis in mathematics does indeed have a distinct metaphysical sonority to it. It describes issues in arithmetic reality but it may actually also apply to physical reality, if both realities happen to be structurally sufficiently similar. — Tarskian

Representation, though essential to cognition, imposes limitations. I think Gödel, Chaitin and Zisselman are examining these limitations logically. The translation from an axiomatic system to its power set necessarily entails loss, so there is no perfect alignment all the way to identity linking a term with its translation.

If these logical limitations translate to physics, then perhaps we're looking at thermo-dynamical systems that upwardly evolve to morpho-dynamics and, from there, to teleo-dynamics with translation losses occurring throughout the process.

Now we come to the need to look at the issue of the resolution of a rendering from one form to its correspondent via translation. I'm guessing that as the level of resolution rises, it approaches intersection with an infinite value, and thus there is no axiomatic system that completely represents reality.

Now we have a concept of reality as an infinite value. This leads me to see that knowing reality is always necessarily incomplete. This reasoning is my argument for seeing how the scope of incompleteness encompasses logic, math, science, philosophy and empirical cognition. The arts, in a symmetrical configuration, are limited by the items of the previous list.

We have examination of the "what," limited by the lossy representationality of cognition on the one side; on the other side we have empirical examination of "what it's like" to be a self-conscious sentient, the "how" (they are experienced) of the predications of the other side, limited by the lossy existentiality_noumenonality of being on the other side.

Wittegenstein has already confronted much of this. However, because reverential silence in the face of the creation is no fun for philosophy, here we are, confronting it again with our own words.

And now, talking out of the other side of my mouth, let me make the following speculation: if the gap between knowing and being is strategic, then we might rejoice at the unsolvable mystery of the future.

There's always another narrative awaiting expression and, it's not a case of endless cycling through repeating patterns across a fixed totality, better known as that charming misconception: universe.

No. Instead, because of strategic incompletion, a thermo-dynamic wisdom, future is empowered to be distinct in its uniqueness, existing beyond mere permutation of the fixed axioms and conserved laws of a unified system. There is distinct locality. There is no unity.

Yes, as e.g. Spinoza points out, human knowledge of unbounded (infinite) reality is necessarily perspectival and therefore bounded (finite). Basic epistemic mereology (re: maps < terrain), no? Also consider the ancient method of exhaustion. I think your "strategic incompleteness" overstates the case and incoherently conflates teleology with formalism with empiricism.

Okay. Proceeding from the observer as an always local person, if we bind the thinking of an always local person to that always local person, then it too, is always local, and the abstraction of abstract thinking starts dissolving. — ucarr

I don't know what you mean by "bind". If a local person indulges in abstract thinking, and shares that thinking with other local and non-local thinkers, how does the abstraction of abstract thinking dissolve? — Ludwig V

QM tells us the observer perturbs what s/he observes. So, the cognition of a sentient keeps everything local to itself in the act of observing. Thus, seemingly far-ranging observations via mental gymnastics, what we call "knowing by reasoning alone," are mostly forestalled in their abstraction from the local_empirical to the cognitive_general.

So science, no less than politics, is local. By extension from this, then, my experience of relativistic effects cannot be identical to yours as each perturbs by observation in its own way. For this reason, we imbibe artistic works in search of a particularly unique voice, although it's understood each voice is singular.

I didn't understand a lot of the intervening ideas. — Ludwig V

All of my ideas are simple, even if oftentimes communicated opaquely. This is a signal shortcoming of the high-speed, low-resolution feedback looping native to the intuitive learning_reasoning process that drives the content of my writing here (and elsewhere).

I have a lot of difficulty with the idea of something true but unprovable. How could we know that such things exist, and if we do, how do know what they are? But this is a bit more specific and so it helps. I still haven't seen an example of such a truth and would love to do so. — Ludwig V

It might help to look at some examples of a false premise leading to a true conclusion. @Tarskian can probably help you with this. (With such examples, you have a true conclusion not proven by the false premise that leads to it.)

There may not be any elegant simplicity axiomatic to everything. — ucarr

But isn't that just a methodological principle that applies when there are competing theories in play? — Ludwig V

If the competing theories are incommensurable, each with strengths and weaknesses, standard practice entails looking for the elegant simplicity.

By the way, what is the criterion for simplicity? — Ludwig V

I suppose it means that in a given time period for a foundational theory, no one can discover a form more basic.

However, it occurred to me that, as a definition, "Statements about statements" captures far too much... — Ludwig V

Berkeley's Dialogues for example can be read as a philosophical text, but also as a historical or religious text. The difference is not in the text, but in the approach to the text. — Ludwig V

Here you give us a good example of statements about statements. In other words, through what lens of interpretation do you approach a given text? Well, as I've been saying, no one reads a given text exactly as another reads it. This because each individual perturbs what s/he observes individually. Thus, we have evidence cognition spins out narratives of narratives. Now we see that when we insert cognition into the "what," it becomes the "how."

QM tells us the observer perturbs what s/he observes. — ucarr

If by "observer" you mean measurement and by "observes" you mean measures, then I think you're correct here about QM. Afaik, "sentience" itself cannot "perturb" quanta since classical-scale systems (e.g. brains-sensoriums) cannot directly interact with planck-scale systems. That way leads to the dark side (imo, p0m0 / Berkeleyan nonsense :sparkle:).

QM tells us the observer perturbs what s/he observes. — ucarr

Isn't that old news in a new bottle? Only physicists needed QM to tell them about the specificity of observation and its distortion in the process of communication.

Well, as I've been saying, no one reads a given text exactly as another reads it. This because each individual perturbs what s/he observes individually. — ucarr

You are looking at only one side of the coin. We learn to read from each other (and we learn the language that we read and communicate in) and we learn all the skills of knowledge. Sharing and correcting
.

I suppose it means that in a given time period for a foundational theory, no one can discover a form more basic. — ucarr

So "simple" means "more basic"?

Yes, as e.g. Spinoza points out, human knowledge of unbounded (infinite) reality is necessarily perspectival and therefore bounded (finite). Basic epistemic mereology (re: maps < terrain), no? — 180 Proof

Yes. :up:

I think your "strategic incompleteness" overstates the case and incoherently conflates teleology with formalism with empiricism. — 180 Proof

Okay. Your helpful analysis empowers me to see that: teleology | formalism | empiricism are a triad of modes of cognition incorrectly (logically) articulated in my premise in its present state. Also, the scope of the territory claimed by my premise is too large_inclusive.

In this sense, they are both emergent properties and components of the architecture. — jkop

I don't understand why you include components when I thought you were saying (correctly) that utility, beauty and sustainability are the result of other components, but not one of them. I think this may be a category issue.

The special sciences won't answer how they causally emerge, nor how a balanced or distributed composition satisfies the success of a building. Yet every effect has a cause, and for millennia we have known that buildings should be practical, beautiful, and sustainable. — jkop

"Every effect has a cause" may be true, in a way. But it does not follow that every effect must have a cause which is a specific component of the building. The cause of utility might be an effect of the totality of the building as built, rather than as a collection of components.

...since classical-scale systems (e.g. brains-sensoriums) cannot directly interact with planck-scale systems. — 180 Proof

How do you characterize ontically and empirically the physicist and its experimental_inferential connection to planck-scale phenomena?

QM tells us the observer perturbs what s/he observes. — ucarr

Isn't that old news in a new bottle. — Ludwig V

I like to think that when I zoom out to include my premise from another one of my conversations: strategic incompleteness, the new bottle perturbs the old news into something interesting: the semi- universe, by design - I'm not making a supernatural claim here but, instead, a thermo-dynamical claim - won't let us arrive at closure for either the "what" or the "how."

Oftentimes we don't know (or appreciate) it, but we're fortunate not to arrive at a final closure for things. As a matter of fact, our happiness depends upon the continual forestalling of final closure.

Well, as I've been saying, no one reads a given text exactly as another reads it. This because each individual perturbs what s/he observes individually. — ucarr

You are looking at only one side of the coin. We learn to read from each other (and we learn the language that we read and communicate in) and we learn all the skills of knowledge. Sharing and correcting — Ludwig V

Yes, our experience is rooted within interrelationships. There seems not to be any existing thing utterly isolated and alone. There's always the hope of being understood.

I suppose it means that in a given time period for a foundational theory, no one can discover a form more basic. — ucarr

So "simple" means "more basic"? — Ludwig V

"Basic" as the criterion for "simple" expresses an ideal of efficiency and clarity and certainty.

...since classical-scale systems (e.g. brains-sensoriums) cannot directly interact with planck-scale systems (re: decoherence).
— 180 Proof

How do you characterize ontically and empirically the physicist and its experimental_inferential connection to planck-scale phenomena? — ucarr

My layman's best guess: only the interaction of the measuring-apparatus and "planck-scale phenomena" is manifestly ontic – quanta (e.g. photons) "perturbing" quanta – and the physicist's readings of her measurements (thereby making inferences) are empirical.

utility, beauty and sustainability are the result of other components, but not one of them. — Ludwig V

True, but I'm not saying they're components of themselves. They're components of the architecture.

Their own components result in practical, beautiful, and sustainable parts of a building, but the building won't be successful as a building by merely having such parts.
These, in turn, must be composed (e.g. balanced or distributed) in ways that make the building successful as a building.

That's composition on a more general level than the compositions of utility, beauty, and sustainability (which in turn are composed of more specific parts, features, configurations, materials, chemical compounds, atoms, or particles in fields of force).

the new bottle perturbs the old news into something interesting: — ucarr

I'm suggesting that it has been over-hyped and is rather less interesting than one would have thought, given all the fuss.

There's always the hope of being understood. — ucarr

Be fair. Sometimes we are understood, and sometimes we manage to sort out misunderstandings.

"Basic" as the criterion for "simple" expresses an ideal of efficiency and clarity and certainty. — ucarr

Well, those are all good things.

True, but I'm not saying they're components of themselves. They're components of the architecture. — jkop

Perhaps my problem is a verbal one. "Components" suggests that they are parts of the building in the sense that the roof and the windows are parts of the building. But they aren't. I would much prefer "aspects" of the building, or of the architecture, whichever you prefer.

Their own components result in practical, beautiful, and sustainable parts of a building, but the building won't be successful as a building by merely having such parts.
These, in turn, must be composed (e.g. balanced or distributed) in ways that make the building successful as a building. — jkop

Yes, you could have parts of the building that meet those critieria. But the basic point, I think, is that they are holistic. If we say that the frontage of the building is beautiful, that's a description of the whole frontage not of any part or segment of it. If we say that the building is very practical, we mean that the building as a whole is practical.

Short version - holistic aspects of the building.

"Every effect has a cause" may be true, in a way. But it does not follow that every effect must have a cause which is a specific component of the building. The cause of utility might be an effect of the totality of the building as built, rather than as a collection of components. — Ludwig V

No, its utility may become available when it's built, but just being available does not cause anything, unless it already has the property, which can attract and initiate use.

Short version - holistic aspects of the building. — Ludwig V

Here's a sketch of different levels of composition that I'm thinking of:

Architecture is a composition of practical, beautiful, sustainable parts.

The practical, beautiful, sustainable parts of architecture are composed of materials, structures, processes.

The materials, structures, processes are composed of minerals, organic or other chemical compounds, geometries, structural design, causal chains, relations to contexts etc.

How do you characterize ontically and empirically the physicist and its experimental_inferential connection to planck-scale phenomena? — ucarr

My layman's best guess: only the interaction of the measuring-apparatus and "planck-scale phenomena" is manifestly ontic – quanta (e.g. photons) "perturbing" quanta – and the physicist's readings of her measurements (thereby making inferences) are empirical. — 180 Proof

Sounds right to me too. So we have a translation from ontic to empirical. Must we always suppose there's something lost in the translation?

QM tells us the observer perturbs what s/he observes. — ucarr

Isn't that old news in a new bottle? — Ludwig V

the new bottle perturbs the old news into something interesting: — ucarr

I'm suggesting that it has been over-hyped and is rather less interesting than one would have thought, given all the fuss. — Ludwig V

There's always the hope of being understood. — ucarr

Here I'm proceeding from the notion of QM entanglement connecting observer with observed. Effect: nothing is truly unseen. In the grapevine mesh of existing things, for each thing, there's always one observer who sees that thing as it is in truth. Is this not a charming article of faith warding off depression?

Be fair. Sometimes we are understood, and sometimes we manage to sort out misunderstandings. — Ludwig V

I need your help in understanding how I'm being unfair.

Abstraction is the nature of "translation", so yes: necessarily something is lost (e.g. map =/= terrain).

I have a lot of difficulty with the idea of something true but unprovable. How could we know that such things exist, and if we do, how do know what they are? But this is a bit more specific and so it helps. I still haven't seen an example of such a truth and would love to do so. — Ludwig V

There are good reasons why it took until 1931 for Godel to discover that these things even exist. Until then, most people were pretty much convinced that they didn't exist.

In fact, Godel insisted that his theorem was intuitionistically unobjectionable because he had given a witness (example) for his existence proof.

As to be expected, the example is rather contorted.

The theorem itself says that there are logic sentences that are (true and unprovable) or (false and provable) -- assuming that they are decidable, in the context of particular theories such as Peano arithmetic.

Godel's example is:

"This is not provable."

Assuming that this sentence is decidable, it is true or false.

If it is true, then it is (true and unprovable).
If it is false, then it is (false and provable).

Hence, the sentence is (true and unprovable) or (false and provable). Therefore, it is a legitimate existence witness for his theorem.

A better example, Goodstein's theorem, was later discovered for which the theorem itself can be expressed in Peano arithmetic but the proof cannot, making it (true and unprovable) in that context.

Godelian sentences are fiendishly difficult to detect in arithmetical reality because in that context we systematically use soundness to discover truth: the sentence at hand is true because it is provable. Arithmetical vision requires calculation. It is virtually impossible to detect an arithmetical fact without calculation.

On the other hand, if we had a copy of the theory of the physical universe, observing physical Godelian facts would be trivially easy.

Unlike in arithmetical reality, in physical reality we do not need to know why exactly a physical fact occurs in order to be able to observe it.

Our eyes do not have to calculate a fact in order to see it. Our eyes just see it. We are perfectly able to see things with our eyes that we do not understand or cannot possibly predict (up to a point, of course).

Godelian facts massively outnumber provable facts. If we actually had a copy of the theory of the physical universe, we would immediately notice that most of what our eyes can see, is not provable from it.

(By the way, this is a simplification because our eyes may also use "calculations" in order to "see".)

Thank you very much for this. I hope you won't mind if someone who is neither mathematician or logician makes some ignorant comments - purely in a spirit of enquiry. Perhaps it's worth saying that I don't really have an opinion about whether Godel is right or not. It doesn't offend my sensibilities. It's way above my pay grade, so that's a legitimate possibility for me.

"This is not provable."
Assuming that this sentence is decidable, it is true or false.
If it is true, then it is (true and unprovable).
If it is false, then it is (false and provable).
Hence, the sentence is (true and unprovable) or (false and provable). Therefore, it is a legitimate existence witness for his theorem. — Tarskian

This is not contorted. It's perfectly straightforward. Self-reference. I've long held the heretical view that the "witness" is not decidable. Is there any reason to suppose it must be? Of course, you could assign a third truth value to undecidable sentences, but I suppose that would be cheating.

A better example, Goodstein's theorem, was later discovered for which the theorem itself can be expressed in Peano arithmetic but the proof cannot, making it (true and unprovable) in that context. — Tarskian

Yes. I thought that something along these lines would probably work. However, you seem to be assuming that if a theorem can be expressed, it must be true. In which case, if that assumption is correct, it is provable. Or is that idea just an assumption or an axiom or something?

Godelian sentences are fiendishly difficult to detect in arithmetical reality because in that context we systematically use soundness to discover truth: the sentence at hand is true because it is provable. Arithmetical vision requires calculation. It is virtually impossible to detect an arithmetical fact without calculation. — Tarskian

Yes. That's what puzzled me.

On the other hand, if we had a copy of the theory of the physical universe, observing physical Godelian facts would be trivially easy.
Unlike in arithmetical reality, in physical reality we do not need to know why exactly a physical fact occurs in order to be able to observe it. — Tarskian

But not knowing why my observation is true is not the same as its being unprovable. Surely that will only work if what I observe is incapable of being proved, as opposed to my not knowing how to prove it. If I knew that it was unprovable, I think I would either not believe my eyes or at least suspend judgement.

Our eyes do not have to calculate a fact in order to see it. Our eyes just see it. We are perfectly able to see things with our eyes that we do not understand or cannot possibly predict (up to a point, of course). — Tarskian

Well, maybe. I think most people believe that my brain does the calculations. I can see where the ball is going to land and catch it, without consciously doing any calculations or being aware of any calculation going on in my head. It's a tricky philosophical issue.
In any case, wouldn't calculations after the event prove that I did see what I saw?

(By the way, this is a simplification because our eyes may also use "calculations" in order to "see".) — Tarskian

I'm sorry I don't understand that. Do you mean that my eyes may follow heuristic principles, rather than calculations? Quite likely. But then my seeing would be an educated guess, which could be proved right (or wrong) after the event.