TPF : Proposed new law of Evolution

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Fri Nov 10, 2023 3:34 pm

Information here is a synonym for entropy. — Nils Loc

That is a common misinterpretation of Shannon's definition of Information, in terms of abstract mathematics, not of human vocabulary. As I attempted to describe in a post above, Shannon bracketed the meaningful realm of Information mathematically, within a broad range of possibilities from [100% to 0% (White or Black pixels) ] (typically expressed as "1/0" {all or nothing})*1. But the meaningful information is limited to the [something] range between {99% and 1%} : shades of gray.

Those extreme (all or nothing) cases are completely meaningless {entropic} except to denote statistical probabilities. Hence, digital computer "bits" are inherently open & undefined, allowing them to communicate almost infinite expressions of meaning, for interpretation by our imperfect analog minds. Hence, Information is a synonym for "Knowledge" & "Intelligence" & "Negentropy" (the opposite of Entropy).

Secret "codes" are unintelligible, until interpreted by the receiver. So, Shannon developed an automatic method for "breaking" the code, via standardized rules*3.


*1. What is the Shannon theory of information entropy?
Shannon considered various ways to encode, compress, and transmit messages from a data source, and proved in his famous source coding theorem that the entropy represents an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel.
___ Wikipedia

*2. Negentropy :
In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy.
https://en.wikipedia.org/wiki/Negentropy
Note --- Normal distribution (average) lacks the "Difference that makes a Difference" that we know as "Meaning" for the human Receiver of data. For a computer, the meaning does not matter.

*3. Encoded Information :
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium.
https://en.wikipedia.org/wiki/Code

Binary Code :
Does this series if 1s & 0s (computer language) mean anything to you?
If not, then it's Entropic (zero information) compared to natural language text.
500_F_224901003_4KNpLNpMXCSLeVcUHScBaEu4MLEJ9wt3.jpg

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Fri Nov 10, 2023 3:38 pm

A missing law to be added to Darwin's theory? Darwin's theory was made in 1859 and is outdated... Darwin didn't even know about genes, we've unraveled so many other mechanisms for evolution since then, such as genetic drift, gene flow, mutations,... — Skalidris

Yes. Darwin's theory was limited to Biological systems, and he could only guess about some unknown means for communicating information from one generation to another, and one species to another : what we now know as "Genes". So, his theory of how animals & plants evolve was long overdue for a scientific update.

Ironically, this new "law" is an addition to Physical systems ("classical laws of motion, gravity, electromagnetism, and energy") and also to Meta-physical systems ("We identify universal concepts of selection—static persistence, dynamic persistence, and novelty generation—that underpin function and drive systems to evolve through the exchange of information between the environment and the system.") The latter are not physical/material things, but merely "Patterns" & "Configurations" and Memes that are not Perceived, but Conceived.

Note --- Quotes above are from the PNAS paper, proposing a "New Law" or Principle of progressive change in natural systems.

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Fri Nov 10, 2023 3:45 pm

Those extreme (all or nothing) cases are completely meaningless {entropic} except to denote statistical probabilities. Hence, digital computer "bits" are inherently open & undefined, allowing them to communicate almost infinite expressions of meaning... — Gnomon
Gnonsense. — wonderer1

Sorry for the confusion. I was groping for a polite way to make "sense" of an erroneous assertion by ↪unenlightened : that "Information is Entropy". I noted that it's a common misunderstanding, but one that might reveal a novel way to look at the antithetical relationship between Information and Entropy*1. Those terms are not equal, but opposite in meaning. Instead, Information is equal to Negentropy*2.

So, I re-interpreted Shannon's definition of Information in terms of 1s & 0s, as a reference to Bookends, not the Books ; Carrier of meaning, not the Content. Unfortunately, my groping attempt to describe that unfamiliar & unconventional perspective may sound like "Gnonsense", because it is literally Unorthodox, Atypical, and Eccentric. Maybe, over time, I will be able to find a more Gnomeaningful way to express that contradiction. :-P


*1. In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. ___Wikipedia
Note --- 100% and 0% quantities of Information are not "averages", but Extremes. Which I referred to metaphorically as "Brackets" or "Bookends".

*2. Negentropy is reverse entropy. It means things becoming more in order. By 'order' is meant organisation, structure and function: the opposite of randomness or chaos.
https://simple.wikipedia.org/wiki/Negentropy

*3. Quote from a previous post to ↪Wayfarer
trying to untangle the babble :

Thermodynamics doesn't deal with Uncertainty, but merely the normal range of temperatures between Planck Heat & Absolute Zero. Yet, Information was defined in terms of a relative position between absolute Certainty and absolute Ignorance. Both mathematically idealized thermal states are devoid of "Difference", being All or Nothing. Anything outside that natural range would be super-naturally Certain. — Gnomon


INFORMATION IS IN THE MIDRANGE, NOT THE EXTREMES
the-a-to-z-of-books.jpg?s=612x612&w=0&k=20&c=mDo1cP0K0Y-p1A5_ChU32wHJf42pFdp77mMCfanwu3Q=

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Mon Nov 13, 2023 11:15 am

Philosophy and physics come at the issue from separate perspectives. A key point of philosophy, I would assert, is that it is grounded in rational contemplation of the human condition. It ought not to overly rely on science, except perhaps insofar as scientific discoveries impact the human condition. But Wittgenstein himself said that “even if all possible scientific questions be answered, the problems of life have still not been touched at all.” — Wayfarer

I think you have touched on the antithetical Frames of Reference that divide many of the posters on this forum : Empirical vs Theoretical (metaphysical) Philosophy and Theoretical vs Empirical (physical) Science. Adherents of those disparate worldviews find it difficult to communicate with their opposite number. They speak mutually unintelligible dialects of the same language*1, because they approach "Reality" from different directions (presumptions) as noted by Joshs in the quotes below*2*3.

I am totally ignorant of Wittgenstein's linguistic philosophy, but your quote seems to hit the same presumptive nail on its convictional creedal head. Ironically, those advocating Empirical Philosophy, typically define Metaphysics as religious nonsense. On the other head, I have asked several posters who seek empirical evidence to support philosophical conjectures, "why are you posting on a Philosophical Forum?" They are typically scornful of my references to Metaphysics and Essences, which apparently don't exist in their worldview, except as examples of Antiscience babble. So, where can we obtain a Babble-fish*4 to translate for us? Are you available for that multilingual job?


*1. There's a saying from the days of England's great war-time leader Sir Winston Churchill in which he describes the United States and his own country as being two nations "divided by the same language."

*2. "they show the empirical sciences what is hidden to them in their own naive assumptions." — ↪Joshs

*3. " Its self-evi­dence lacks scientific grounding in the universal life-world a priori, which it always presupposes in the form of things taken for granted, which are never scientifically, universally formu­lated, never put in the general form proper to a science of essence"
↪Joshs


*4. What is the Babelfish ?
Adams' novel The Hitchhiker's Guide to the Galaxy features the Babel Fish, “probably the oddest thing in the universe” (Adams 60), which gives its host the ability to “instantly understand anything said…in any form of language”
https://www.scienceandfiction.fiu.edu/l ... babel-fish

BABELFISH with optional BS detector (gas bladder)
Blog_Babelfish-750x422-c-default.png
3 days ago

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Mon Nov 13, 2023 11:25 am

those advocating Empirical Philosophy, typically define Metaphysics as religious nonsense. — Gnomon

[i] That’s more characteristic of positivism, really. There is a school of thought called ‘constructive empiricism’. Constructive empiricism is a philosophical perspective on the nature of scientific theories proposed by Bas van Fraassen in his 1980 book "The Scientific Image." It contrasts with scientific realism in important ways. Scientific realism holds that science aims to give us true descriptions of the world, including unobservable phenomena. Constructive empiricists, on the other hand, argue that the goal of science is not to find true theories, but rather to develop theories that are empirically adequate. . . .
it simply refrains from making metaphysical commitments about the reality of unobservable entities. —
[/i]Wayfarer

Thanks. I had never heard of "Constructive Empiricism". CE sounds like a good policy for Practical Scientists : "to refrain from making metaphysical commitments about the reality of unobservable entities". The old "refrain" of "shut-up and calculate" seems like a similar pragmatic attitude toward impractical scientists who dabble in the Meta-Physical aspects of Quantum Physics --- sometimes mis-labeled as "Quantum Mysticism"*1 --- but are actually "abstract" & "unobservable" entities & forces, and open questions about Being & Reality.

I made-up the descriptive term "Empirical Philosophy" to refer to posters on this forum, who do not "refrain from making metaphysical commitments". When they accuse me of avoiding the traditional referent of "metaphysics", from Catholic Metaphysics*2 (4th - 5th centuries AD) ; I typically point back to an even older antecedent of the term, in Aristotle's (5th century BC) encyclopedia of Nature. The section of his documents, that later came to be labeled "metaphysics"*3, was literally placed "after" the documentation about the physical world. And it discussed non-physical & abstract topics that distinguished Greek Philosophy from both Material Nature, and from Greek Religions. Philosophy is not a science of Things, but of Ideas. "Meta-Physics" is not about mysticism, but about the "unobservable", but inferrable, underpinnings of Nature.

I haven't been successful in convincing the "Empirical Philosophy" posters, such as ↪180 Proof , to look past Augustine & Aquinas to the man who literally wrote the book. Being a non-religious naturalist, Aristotle is harder to pin the "mystical" label on. So they mis-direct the thread toward a well-known taboo of science, in order to avoid dealing with the philosophical ideas I'm actually talking about. When I post about Quantum Physics, I'm referring to its philosophical implications, not to its physical facts. But it's easier to apply prejudicial Straw-Man labels, such as "New Age", than to argue non-empirical abstract concepts and "unobservable entities", such as those raised by the quantum pioneers of invisible subatomic physics. Such distracting labels don't prove anything, except blind prejudice.


*1. Quantum mysticism :
Before the 1970s the term was usually used in reference to the von Neumann–Wigner interpretation, but was later more closely associated with the purportedly pseudoscientific views espoused by New Age thinkers such as Fritjof Capra and other members of the Fundamental Fysiks Group, who were influential in popularizing the modern form of quantum mysticism. . . . .
Physicists Werner Heisenberg and Erwin Schrödinger, two of the main pioneers of quantum mechanics, were interested in Eastern mysticism, but are not known to have directly associated one with the other. In fact, both endorsed the Copenhagen interpretation of quantum mechanics.

https://en.wikipedia.org/wiki/Quantum_mysticism

*2. Catholic Metaphysics :
The Marginalization of Metaphysical Thinking . . . .
The most powerful intellectual movement during the last two centuries has been the Enlightenment Project. The Enlightenment Project comprises both the view known as scientism, namely, that science is the whole truth about everything and that it is the ground of its own legitimation, as well as the program to transcend the human predicament by gaining complete technological mastery of the physical and social environment. It is a project that was originally formulated by French philosophes in the last half of the eighteenth century, was preserved by positivist movements in the nineteenth century, and has dominated universities in the twentieth century. . . . .
What room is there for metaphysics in such a view? The only version of metaphysics permissible is secular Aristotelian naturalism.

https://metanexus.net/catholic-metaphys ... ghtenment/

*3. Metaphysics (Aristotle) :
The work is a compilation of various texts treating abstract subjects, notably substance theory, different kinds of causation, form and matter, the existence of mathematical objects and the cosmos, which together constitute much of the branch of philosophy later known as metaphysics.
https://en.wikipedia.org/wiki/Metaphysics_(Aristotle)

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Mon Nov 13, 2023 11:40 am

By strange co-incidence, there's another journal article about a very similar idea to the one that this OP was about, which was also published in October. . . .
Somehow, I feel the publication of these two articles, from different teams, using different theories, about the same general issue, is more than coincidence (queue X Files theme).
— Wayfarer

I have saved a PDF of the Assembly Theory article*1, but haven't read it in detail yet. Coincidentally, I noticed that one of the authors is Sara Walker*2, of the Santa Fe Institute (SFI) for the Study of Complexity*3. She is a physicist and an astrobiologist, and that combination of abstract Math & ambitious Life may require looking at the world from a different perspective. Ironically, this "theory was developed as a means to detect evidence of extraterrestrial life from data gathered by astronomical observations or probes" ___Wiki.

The alternative perspective of the SFI is Holism, the key to emergence of complex physical & meta-physical systems. Yet, as you well know, the notion of Integrated Whole Systems is often met with knee-jerk negativity by those who are prejudiced against, what they label as, a "New Age" worldview. FWIW, I am, in no meaningful sense, a disciple of New Age gurus. And my philosophical thesis is intended to be a post-quantum-science update of the worldwide Spiritualism of pre-scientific ancient cultures. But, I am sympathetic to it's generalizing, inclusive, and comprehensive philosophical perspective*3, which is literally non-scientific (non-reductive), but not anti-science (opposed to scientific methods)*4.

A related article is entitled : How Purposeless Physics underlies Purposeful Life*5. How did inert Matter (momentum) manage to become self-motivated (purposeful)? Such "how" or "why" questions shine a spotlight into the gap to be filled by a Missing Law of Complexification in Evolutionary Theory. Darwin proposed two requirements for the emergence of biological novelty : Variation & Selection. But, the latter is a negative, weeding-out, action*6. And, the positive production of novel forms is unexplained by the laws of physics. So, the source of variation & complexification may await a 21st century law of evolution. Hence, the need for something like Assembly Theory.

Is this confluence of science & philosophy a coincidence, or a conspiracy?


*1. Assembly Theory :
Scientists have grappled with reconciling biological evolution with the immutable laws of the Universe defined by physics. These laws underpin life’s origin, evolution and the development of human culture and technology, yet they do not predict the emergence of these phenomena. Evolutionary theory explains why some things exist and others do not through the lens of selection. To comprehend how diverse, open-ended forms can emerge from physics without an inherent design blueprint, a new approach to understanding and quantifying selection is necessary
https://www.nature.com/articles/s41586-023-06600-9
Note --- The term "design blueprint" in connection with Evolution, is a trigger-word to those for whom "design"*5 is a taboo notion, associated with monotheistic religions. Unfortunately, my information-based term EnFormAction is also booed & tabooed by those who believe in the creativity of random accident.

*2. Sara Imari Walker is an American theoretical physicist and astrobiologist with research interests in the origins of life, astrobiology, physics of life, emergence, complex and dynamical systems, and artificial life. ___Wikipedia

*3. What is complexity science theory? :
Complexity science suggests that the whole is not the sum of the parts. Emergent properties of the whole are inexplicable by the parts. In complexity, studies of natural and human systems are explained by both kinds of analysis - micro (or analysis of the parts) and macro (or holistic analysis).
https://www.napcrg.org/media/1278/begin ... module.pdf

*4. Complexity Science :
Our traditional views of cause-and-effect assume a linear worldview in which the output of a system is proportional to its input. This predictable perspective derives from an additive model in which the system is the sum of its parts.
https://www.napcrg.org/media/1278/begin ... module.pdf

*5. Darwin’s Greatest Discovery: Design Without Designer :
" Darwin accepted that organisms are “designed” for certain purposes, that is, they are functionally organized." ___Francisco Ayala, evolutionary biologist
https://www.ncbi.nlm.nih.gov/books/NBK254313/

*6. Natural selection works by weeding less fit variants out of a population.
https://evolution.berkeley.edu/misconce ... -bad-gene/


↪180 Proof

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Tue Nov 14, 2023 4:42 pm

I’ve often made the point that there is a well-known meme from Norbert Weiner, founder of cybernetics, often quoted on the internet, to wit ‘information is information, not matter or energy.’ This has been seized on in such a way that information is regarded as a kind of updated or more sophisticated form of matter-energy, or that by substituting the concept of information for that of matter, a more adequate metaphysics can be developed. The problem is that information is not a metaphysical primitive in the sense that matter or energy were thought to be. There is no such thing as information per se, it something that is always output or derived. Hence treating information as a metaphysical ground of being, akin to how materialism regards matter, is complex and controversial. — Wayfarer

That is an important distinction for understanding the multipurpose roles of Information (EnFormAction) in the world. Some TPF posters like to think of Information as-if it's an objective (physical) thing, such as a bit of Matter, or a unit of Energy. Instead, it's a (functional) relationship and a dynamic (meta-physical) process, that unites disparate parts into meaningful patterns of wholeness. I often refer to Information as a "shape-shifter" that can't be pinned-down to a single Particle or Shape. Instead, it's the Platonic Principle of Form. :smile:


Quote from OP :
"In essence, the new ‘law of increasing functional information’ states that complex natural systems evolve to states of greater patterning, diversity, and complexity "

Enformy :
In the Enformationism theory, Enformy is a hypothetical, holistic, metaphysical, and natural trend, force, or principle, that counteracts Entropy & Randomness to produce complexity & progress.
https://blog-glossary.enformationism.info/page8.html
Note --- You won't find this term in science books, because it's a custom-made coinage to describe a novel concept, that has not yet been recognized in the context of reductive & materialistic Science. Yet, it may serve as a shorter name for the "Law of Functional Information" referred-to in the OP. I doubt that it qualifies as a (reductive) Scientific "Law", but more like a (holistic) Philosophical Principle.

Forms :
Platonic Forms are Archetypes : the original pattern or model of which all things of the same type are representations or copies. Eternal metaphysical Forms are distinguished from temporal physical Things. These perfect models are like imaginary designs from which Things can be built.
https://blog-glossary.enformationism.info/page13.html
Note --- Archetypes are not real implemented objects, but ideal design concepts --- universal potential, not actual instances.

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Mon Nov 20, 2023 10:49 am

Certainly one can find synonyms such as "supernatural", "spiritual", or "supernal", this while on a philosophy forum, rather than claiming that metaphysics is founded upon, or else is about, magic. Or at least qualify what type of metaphysics one is referring to. Or not. At the end of the day, just sharing perspectives here. — javra

Off-topic :
I like to use "Meta-Physics" as a synonym for Philosophical issues. And the referent - antecedent - denotation is to Aristotle's ancient writings, not to medieval Catholic scholarship, or modern academic arguments. So, I use the term primarily to distinguish mental-rational-holistic topics from material-scientific-reductive studies. Unfortunately, some on this forum seems to insist that it's a synonym for "anti-science".

On TPF, it seems impossible to work around the hard prejudice attached to that taboo term ; even when I specify "what type of metaphysics" I'm referring to. I could just say "philosophy", but for Materialists & Physicalists, even that well-known category seems to be limited to objective sense-based themes, and excludes any subjective concepts known only via Reason, such as the possibility of Kantian transcendence. That anti-philosophy bias strictly limits the range of topics we can discuss calmly & rationally to those certified by pragmatic Science. Are you aware of any common synonyms of Metaphysics that are not associated with "supernatural" or "spiritual" or "religion" or "magic"?

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Mon Nov 20, 2023 10:58 am

This is a bit like preaching to the choir, here. I’ll only add that any new metaphysical postulations (e.g. as to the nature of causality) will need to remain conformant to established data obtained via the scientific method. But maybe this goes without saying. — javra

Unfortunately, although most of the authors of the original paper --- On the roles of function and selection in evolving systems --- are professional scientists, their collective conclusion (postulation) seems to be based on speculative philosophical reasoning instead of firmly "established" scientific data.

So, your cautionary note made me question the scientific criteria for Causality*1. And it seems that scientists typically depend on philosophical reasoning for such immaterial & non-sensory connections between a physical input (cause) and a material output (effect). Moreover, Kant & Hume*2 cast doubt on our ability to firmly "establish" scientific criteria to prove physical causation. And any attempt to define Causation metaphysically gets befogged in the murk of philosophical jargon and denial of its provability*3.

Even Darwin's presumption --- of a causal connection between one generation of a species and a later different form --- seems to be little more than a personal opinion. Was Selection the Cause of evolutionary novelty? If so, determined by whom? The lack of a defined beginning of the series, and the missing links between stages, seem to imply that the phenomenon of "Causation" itself is a subjective logical inference (belief), instead of an objective sensory observation (fact). Such open questions suggest that, without a specified First Cause, any postulation of Causation, and Evolution, becomes circular*4. Hence, the necessity for a conjectured "Law" to fill the causal gap.


*1. What is scientific definition of causation?
Causality (also called causation, or cause and effect) is influence by which one event, process, state, or object (a cause) contributes to the production of another event, process, state, or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause.
https://en.wikipedia.org/wiki/Causality
Note --- No mention of a causal Agency to initiate a sequence of events. Hence, either infinite or circular.

*2. Kant and Hume on Causality :
Kant agrees with Hume that neither the relation of cause and effect nor the idea of necessary connection is given in our sensory perceptions; ...
https://plato.stanford.edu/entries/kant-hume-causality/
Note --- The relation between Cause & Effect is an Induction, not a Deduction ; a theory not a fact.

*3. The Metaphysics of Causation :
For each of these putative causal relations, we can raise metaphysical questions: What are their relata? What is their arity? In virtue of what do those relata stand in the relevant causal relation? And how does this kind of causal relation relate to the others? Of course, there is disagreement about whether each—or any—of these relations exists. Russell (1912: 1) famously denied that there are any causal relations at all, quipping that causation is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm” (see also Norton 2003). Others may deny that there is a relation of general causation or influence at all, contending that claims like 2 and 3 are simply generalizations about token causal relations (see §2.1 below). There will also be disagreement about whether these relations are reducible, and, if so, what they can be reduced to—probabilities, regularities, counterfactuals, processes, dispositions, mechanisms, agency, or what-have-you.
https://plato.stanford.edu/entries/caus ... taphysics/

*4. Evolutionary Causation :
Most scientific explanations are causal. This is certainly the case in evolutionary biology, which seeks to explain the diversity of life and the adaptive fit between organisms and their surroundings. The nature of causation in evolutionary biology, however, is contentious. How causation is understood shapes the structure of evolutionary theory, and historical and contemporary debates in evolutionary biology have revolved around the nature of causation. Despite its centrality, and differing views on the subject, the major conceptual issues regarding the nature of causation in evolutionary biology are rarely addressed. This volume fills the gap, bringing together biologists and philosophers to offer a comprehensive, interdisciplinary treatment of evolutionary causation.
https://mitpress.mit.edu/9780262039925/ ... causation/

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Re: TPF : Proposed new law of Evolution

Post by Gnomon » Mon Nov 20, 2023 11:03 am

It seems I might have been too terse in my reply. Certainly: science is thoroughly founded upon philosophy and in no way the other way around. . . . . I hope this better presents my position regarding science and causation (as just one example of science and metaphysics in general). — javra

No worries mate.

Sorry, if I gave the wrong impression. I was not criticizing your post. But, I was prompted to do some Googling on the Science vs Philosophy, and Causation vs Randomness, questions. I happen to agree with your position on the primacy of Philosophy, not only in history, but also in generality. However, some posters on TPF seem to feel that Philosophy is little brother to its dominant younger sibling in terms of economic importance. Yet that top 10 rating depends on where you place your values : material vs mental, or instrumental (means) vs terminal (ends).

Regarding Causation, the origin & direction of causation (First Cause ; Teleology) is not important for materialists. What matters to them is tangible results. Modern science is unsurpassed in producing predictable products and marketable merchandise*1. The quantum genie is now out of the bottle, and granting all kinds of pragmatic wishes. But few are asking philosophical questions about Wisdom, Ethics, & Proportion.

I suppose the postulated New Law of Evolution will be judged, not by its abstract universal Truth, but by its concrete lab Results. :)



*1. The Manhattan Project grew rapidly and employed nearly 130,000 people at its peak and cost nearly US$2 billion (equivalent to about $24 billion in 2021). Over 90 percent of the cost was for building factories and to produce fissile material, with less than 10 percent for development and production of the weapons.
https://en.wikipedia.org/wiki/Manhattan_Project
Apparently the cost to produce two bombs was "worth it" in terms of the existential threat of German & Japanese political, economic & military dominance. For more philosophical considerations, some would disagree. Especially, since one psychologically expensive product of that technology is the mushroom cloud hanging over mankind. Perhaps, some of that psychic cost is offset by the income from almost a century of high-grossing apocalyptic movies. ;)

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