For a really fun book on a lot of the "big picture," ways information theory could really become a paradigm shifter across the sciences the book "The Ascent of Information," is quite good. It had a good audio version too.

And then the Great Courses "Science of Information," course is really great too. Probably the best condensed intro I've seen is the intro chapters to "Asymmetry: The Foundation of Information," but it's a hideously expensive small print academic book, so outside of working at a university or LibGen it's not really a good option.

But yeah, it sort of shocks me how this stuff hasn't become more essential to basic science education. It's not a new shift, although it is picking up steam. But it's still crammed into this weird interdisciplinary space the way chaos theory and complexity studies is. The two have a ton in common too. I wish I could have stumbled across a book like "Complexity: A Guided Tour," when I was in school, it would have probably change my life lol.

Thank you very much. I don’t have a clue about what I don’t know about the topic. For example, I don’t have any idea what symmetry has to do with it.

Never heard of The Great Courses. I think I’ll pass on that $239.95 option. :D

Asymmetry: The Foundation of Information Is $42.77 on kindle. That’s no problem.

But maybe I’ll start with The Ascent of Information. Only $9.99, and it sounds very interesting.

It does. Shannon’s theory is often mentioned in this context.

How do you reckon a world would work out, if 2 did not, in fact, equal 2, of if 9 was less than 7? — Wayfarer

If you are speaking of "worlds" in our universe, or in some parallel universe, worlds we can reckon with, then probably yes.

If you are speaking of worlds that are "possible", but not possible for us to envision, then, how could you possibly know? You wouldn't know they were possible to begin with. Are there "things" beyond our comprehension, things we don't know we don't know? How could you know? Why can you assume in some universe beyond our imagination our brand of logic must hold?

Why can you assume in some universe beyond our imagination our brand of logic must hold? — jgill

Logic is in the mind, but not of it. It’s not our invention but what we are able to discover through reason. I really don’t think that the idea of a world where there are no necessary facts is even an hypothesis.

Logic is in the mind, but not [o]f it. It’s not our invention but what we are able to discover through reason. I really don’t think that the idea of a world where there are no necessary facts is even an hypothesis. — Wayfarer

You are saying you can't imagine any sort of alternate world in which the logic we enjoy would not exist. How do you know this is a universal limitation rather than a human shortcoming? A lot hinges on the definition of "possible" and our limitations thereof.

You are saying you can't imagine any sort of alternate world in which the logic we enjoy would not exist — jgill

I’m saying it’s an idle thought. It has no meaning.

I’m saying it’s an idle thought — Wayfarer

With which I agree. Welcome back from your vacation. :cool:

Why thanks, must say, glad to be back. :up:

I think the Great Courses are pretty much all on Audible for like $15 or Amazon for like $10 a month. Or free on Wonderium with a trial and then if you cancel that it's like $9 a month. I don't know who they get to pay their original prices lol, the resellers are way cheaper. Probably an economies of scale thing.

Thanks

Logic is in the mind, but not of it. It’s not our invention but what we are able to discover through reason. I really don’t think that the idea of a world where there are no necessary facts is even an hypothesis — Wayfarer

You are allowing yourself to be fooled by your invented grammar. Mathematics, and the logic it is based on, rests on a peculiar way humans decided at a certain point in their history ( actually, as a gradual process of development) to formulate the idea of the persistingly present, self-identical object. Doing so led to subsequent assumptions such as the law of identity, the law of non-contradiction, geometrical forms such as lines and magnitudes, and propositional statements binding or separating a subject and predicate. Mathematical structures are only ‘embedded’ in the world to the extent that we force the world into such odd forms. But such processes of objectivation are derived modes of thinking which hide within themselves what gives them their sense and intelligibly. Put differently, a persisting object only persists for us in its meaning by continuing to be the same differently.

2+2 is true because of the shared presupposition built into the grammar of 2+2. A=A is true because it is presupposed as a basis for our formulation of objectness. Presuppositions are ‘true’’ in all possible worlds only to the extent that all possible worlds share the same or similar presuppositions. Given that presuppositions are contestable, partially shared constructs emerging from and maintained in actual interpersonal contexts of use, the truth of a proposition is dependent on this preserving of a particular meaningful sense of a proposition. When underlying presuppositions change , the propositions whose intelligibility depends on them dont become false, they either change their meaning and criteria of truth, or become non-sensical. When the sense of a proposition changes slowly enough, we tend not to notice the change in meaning and instead reify the proposition as self-identically repeatable. This is how we end up fooling ourselves into believing that mathematical structures are embedded in the world. What is embedded in the world is human discursive interactions, not the abstract forms that we fabricate out of these relationships.

Really good post. I especially like

And it doesn't make much sense to say "what does the world look like without eyes," or "how would we think about the world without minds." — Count Timothy von Icarus

I hadn't thought of it in those words before. I save that to use when I'm talking about Taoism.

In this view, only the higher, noumenal realm can be causally efficacious, or at least there is only downwards causality from the noumenal onto the phenomenal, not the other way around. To my mind, this creates an arbitrary division in nature that many don't really want to defend, but which it is nonetheless easy to accidentally fall into. — Count Timothy von Icarus

In Taoism, as I see it, the relationship you describe between noumenal and phenomenal is made explicit as the fundamental basis of reality, although rather than "arbitrary" I'd say "human."

Objectivity then is about descriptions that smooth out the differences that arise from variances in subjects' phenomenal experience. You view the same phenomena in many different ways, using tools, experiments, etc., and identify the morphisms between all perspectives. — Count Timothy von Icarus

Do we view the same phenomena or view similar phenomena that we call the same for the convenience of fabricating the kinds of objects that are amenable to mathematical calculation?

there is a strong tendency for the mathematical patterns "at work in," or "describing" natural phenomena to be similar at very different levels of scale — Count Timothy von Icarus

Karen Barad is among those who suggest that the geometric notion of scale must be supplemented with a topological notion of it. What this means is that scales interact each other to produce not just quantitative but qualitative changes in material forms.

the observation of mathematical patterns that describe and predict the world are among the very best established empirical facts. — Count Timothy von Icarus

That’s because the presuppositions concerning the irreducible basis of objectness which underlie mathematical logic guarantee that it will generate a world of excellently established facts. It fits the world that we already pre-fitted to make amenable to the grammar of mathematics. The very prioritization of established facts over the creative shift in the criteria of factuality demonstrates how the way mathematical reasoning formulates its questions already delineates the field of possible answers.

it seems obvious that living things must incorporate within themselves descriptions of nature that are isomorphic to nature. Such descriptions might be highly compressed, based on heuristics that make them prone to error, etc., but this doesn't preclude the fact that they are to some extent accurate descriptions of nature — Count Timothy von Icarus

It depends on how we describe living things. From an enactivist perspective, an organism is an inseparable system of reciprocal relations among brain, body and environment. There is a certain operational closure giving organisms a normative goal-oriented orientation toward their world but, strictly speaking, no inside and no outside, no separable parts or forms. The cognitively knowing organism doesn’t represent its surroundings, it interacts with it guided by expectations and purposes that can be validated or invalidated. If there is anything isomorphic between such self-organizing organisms-environment systems and nature in general it would not be particular contents but a general principle of organization that applies to all living things. Piaget identified such a formal principle as the equilbrating functions of assimilation-accommodation, which he suggested could be extended to non-living complex systems.

I think the sciences are slowly moving away from the idea, exemplified by the periodic table, of pre-existing forms that reappear throughout nature. They are coming to realize that such abstractions cover over the fact that no entity pre-exists its interaction with other entities within a configuration of relations. The ‘entities’ are nothing but the changing interactions themselves, which tend to form relatively stable configurations. According to this approach, the world is not representation but enaction.

This is how we end up fooling ourselves into believing that mathematical structures are embedded in the world. What is embedded in the world is human discursive interactions, not the abstract forms that we fabricate out of these relationships. — Joshs

What a happy coincidence how well the products of mathematical science work! We should all thank our lucky stars.

What a happy coincidence how well the products of mathematical science work! We should all thank our lucky stars. — Wayfarer

That’s the point. To understand the origin of mathematical
logic in certain presuppositions about the way the world is constructed is see why it is not coincidence at all. As you say, the products of mathematical science work well. I would add that they work precisely, accurately in the sense dictated by the demands of formal logic.

As you say, the products of mathematical science work well. I would add that they work precisely, accurately in the sense dictated by the demands of formal logic. — Joshs

I thought that's what I was arguing for :chin:

Incidentally, I haven't attempted Husserl Philosophy of Arithmetic as it seems a very challenging read. But is this thumbnail sketch of Husserl's philosophy of math any good?

"Husserl was interested in the psychological origin of number concepts. He explored how individuals move from concrete individual experiences to abstract generalizations that constitute numerical understanding. For Husserl, numbers aren't just abstract entities; they have their roots in our lived experiences and acts of grouping and collecting.

Husserl examined the act of counting as foundational to the concept of number. Counting isn't just an external action but involves internal acts of consciousness, where one recognizes and groups objects together as units. This grouping then forms the basis for the abstract notion of number.

Collective Combination (Kollektiv-Vereinigung): This is a key term in Husserl's analysis. It refers to the act of consciousness by which we perceive a group of objects as a singular totality. For instance, seeing a group of five apples not just as individual apples but as a collective "five." This act of collective combination is essential for the emergence of numerical concepts in consciousness.

Criticism of Psychologism: While Husserl was interested in the psychological origin of mathematical concepts, he argued against the idea that the validity and truth of mathematical principles were dependent on psychological processes. This distinction paved the way for his development of a rigorous phenomenological method that sought to distinguish between subjective acts of consciousness and the objective structures they intend.

Husserl was deeply interested in how consciousness constitutes mathematical objects and how these acts of constitution relate to the objective validity of mathematical truths."

"Husserl was interested in the psychological origin of number concepts. He explored how individuals move from concrete individual experiences to abstract generalizations that constitute numerical understanding. For Husserl, numbers aren't just abstract entities; they have their roots in our lived experiences and acts of grouping and collecting. — Wayfarer

This is exactly what I've many times said to you, arguing against your Platonic notion of numbers.

I think the sciences are slowly moving away from the idea, exemplified by the periodic table, of pre-existing forms that reappear throughout nature. They are coming to realize that such abstractions cover over the fact that no entity pre-exists its interaction with other entities within a configuration of relations. — Joshs

Perhaps. Quantum theory is still searching for a way to understand what's happening down there. Other sciences, I'm not so sure. Intra-actions . . . who knows?

arguing against your Platonic notion of numbers. — Janus

My only argument is that numbers are real but not material. It's quite compatible with Husserl's attitude as far as I can tell.

Numbers are abstract entities, concepts...they are abstracted from number which is concretely instantiated in the material world. It is no different than saying that "tree" is a generic concept, abstracted from actual trees.

s this thumbnail sketch of Husserl's philosophy of math any good? — Wayfarer

The only issue I have with it is that one could get the impression that the reason Husserl “argued against the idea that the validity and truth of mathematical principles were dependent on psychological processes” was because he thought their validity and truth was dependent on the world. What he was trying to do was avoid psychologism (which he was accused of in Philosophy of Arithmetic) by grounding mathematical principles in transcendental
phenomenology.

Yeah, I get that. I understand this was Frege's criticism of Husserl. But I'm developing the argument that what scholastic realists designated universals were actually structures in consciousness.

It is no different than saying that "tree" is a generic concept, abstracted from actual trees. — Janus

As an abstract concept, it's a universal. More to the point, per my earlier posts in this thread, is that mathematics can be used to make discoveries hitherto unknown about nature herself, thereby demonstrating that they are something more than simply 'mental constructs'.

As an abstract concept, it's a universal. More to the point, per my earlier posts in this thread, is that mathematics can be used to make discoveries hitherto unknown about nature herself, thereby demonstrating that they are something more than simply 'mental constructs'. — Wayfarer

What is the difference between a universal concept and a generic concept? You are talking about math as an aid to science, right...can you give me an example of pure math being used to discover anything about nature? Do you think any discoveries about nature are about nature as it is in itself or merely as it appears to us?

What is the difference between a universal concept and a generic concept? — Janus

Good question. In the context of Aristotle's philosophy, as well as in biological classification and other systems of categorization, a "genus" is a class or group that includes different species. Note however its ultimate source in Aristotle. That's where the concept of 'genera' and 'generic' originated.

Can you give me an example of pure math being used to discover anything about nature? — Janus

See this post about Dirac's predictions of positrons.

Do you think any discoveries about nature are about nature as it is in itself or merely as it appears to us? — Janus

I'm incllined to agree with Bohr's aphorism 'It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.' Also Heisenberg's 'What we observe is not nature in itself but nature exposed to our method of questioning.'

What he was trying to do was avoid psychologism (which he was accused of in Philosophy of Arithmetic) by grounding mathematical principles in transcendental
phenomenology. — Joshs

It seems to me that maths, based on number, is grounded in immanent phenomenology. We encounter diversity, difference and similarity, everywhere.

Good question. In the context of Aristotle's philosophy, as well as in biological classification and other systems of categorization, a "genus" is a class or group that includes different species. Note however its ultimate source in Aristotle. — Wayfarer

Right, so a generic concept is the concept of a class of things which share some salient similarities, a class of species. You haven't said what you think a universal concept is, and whether it is the same or different than a generic concept.

This equation incorporated both the principles of quantum mechanics and the theory of special relativity, describing electron behavior at relativistic speeds. — Wayfarer

This is an equation belonging to quantum physics and relativity theory, not pure math.

I'm incllined to agree with Bohr's aphorism 'It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.' Also Heisenberg's 'What we observe is not nature in itself but nature exposed to our method of questioning.' — Wayfarer

We agree on that.

This is an equation belonging to quantum physics and relativity theory, not pure math. — Janus

Nevertheless it could never have been discovered without mathematics.

For Aristotle, universals are real in the sense that they genuinely exist as aspects or features of particular things (hence, 'moderate realism'.) They are not mere names or linguistic conventions as some nominalists would later argue. In Aristotelian realism, when we recognize a universal like "redness" or "humanity," we are recognizing something real but this universal only exists as it is instantiated in particular objects (like a red apple or a specific human being). So, while universals don't have independent existence outside of particulars as they do in Platonic realism, they are nevertheless genuinely real aspects of the empirical world in Aristotelian realism. There's a nice essay about Aristotelian philosophy of maths on Aeon.

The view I'm developing is that numbers and universals and the like are real, but not manifest or existent. They are implicit in reality and are manifest or instantiated by particulars. It's reasonably close to Scholastic realism. As I understand it, C S Peirce held a similar view, and was opposed to nominalism. 'Peirce understood nominalism in the broad anti-realist sense usually attributed to William of Ockham, as the view that reality consists exclusively of concrete particulars and that universality and generality have to do only with names and their significations. This view relegates properties, abstract entities, kinds, relations, laws of nature, and so on, to a conceptual existence at most. Peirce believed nominalism (including what he referred to as "the daughters of nominalism": sensationalism, phenomenalism, individualism, and materialism) to be seriously flawed and a great threat to the advancement of science and civilization. His alternative was a nuanced realism that distinguished reality from existence and that could admit general and abstract entities as reals without attributing to them direct (efficient) causal powers. Peirce held that these non-existent reals could influence the course of events by means of final causation (conceived somewhat after Aristotle's conception), and that to banish them from ontology, as nominalists require, is virtually to eliminate the ground for scientific prediction as well as to underwrite a skeptical ethos unsupportive of moral agency.'

You are allowing yourself to be fooled by your invented grammar. Mathematics, and the logic it is based on, rests on a peculiar way humans decided at a certain point in their history ( actually, as a gradual process of development) to formulate the idea of the persistingly present, self-identical object. Doing so led to subsequent assumptions such as the law of identity, the law of non-contradiction, geometrical forms such as lines and magnitudes, and propositional statements binding or separating a subject and predicate. Mathematical structures are only ‘embedded’ in the world to the extent that we force the world into such odd forms. But such processes of objectivation are derived modes of thinking which hide within themselves what gives them their sense and intelligibly. Put differently, a persisting object only persists for us in its meaning by continuing to be the same differently. — Joshs

The problem though is that mathematicians do not adhere to the law of identity, they actual violate it. By affirming that whatever is referred to by the symbols on the right side of the "=" symbol is "the same" as whatever is referred to by the symbols on the left side, they use "same" in a way which violates the law of identity.

Nevertheless it could never have been discovered without mathematics. — Wayfarer

Physics itself would not be possible without mathematics. If, as you agree, it is not the task of physics to find out what nature is, but rather to produce models that present the best human understanding of what is observed and measured, then it doesn't seem to follow that mathematics is embedded in nature at all, but rather that it is embedded in the human understanding of nature. But that mathematics is embedded in the human understanding of nature is hardly controversial.

I know it's a bit of a tangent, but you haven't provided a reference for that passage about Peirce you quoted.