TPF : Shannon Information

A place for discussion of ideas presented in the BothAndBlog, or relevant to the Enformationism thesis.
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Re: TPF : Shannon Information

Post by Gnomon » Mon Dec 28, 2020 12:43 pm

Harry Hindu is speaking of this as a matter of following rules, but I don't see any evidence of any such rules. — Metaphysician Undercover

Perhaps he is referring to the rules of Syntax, which are conventional, and the rules of Semantics, which are mostly intuitive. :smile:

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Re: TPF : Shannon Information

Post by Gnomon » Mon Dec 28, 2020 6:55 pm

The point remains the same, even if you express it in this way. All that meaning between 1 and 0 cannot be expressed in the digital system. — Metaphysician Undercover

Yes, but the digital system is just one facet of the whole system -- the Universe. Our world is a two-sided coin. You can't see both sides at the same time. But you can choose which side to look at. In the communication of Information, Shannon chose not to look at the intentional Meaning of its contents, but to focus on the Container, which is neutral toward Meaning. The point being, that the invisible side of the cosmic coin is still there, like the dark side of the moon. See image below. :smile:

Right, that's why all that meaning (information) ends up being contradictory and "un-knowable". — Metaphysician Undercover

Quantum information that is in superposition is indeed "un-knowable" until a measurement is taken. The measurement is a Choice of what to look at. Quantum theorists have argued about the significance of a Delayed Choice experiment. But don't ask me to make sense of it in this context --- it's just an analogy. Superposition may be confusing, but not necessarily contradictory. :grin:

Delayed Choice : https://en.wikipedia.org/wiki/Quantum_eraser_experiment

That's why the Shannon use of "information" is distinct from most common usage. — Metaphysician Undercover

Yes. But it's the Distinction-that-made-a-Difference in causing a Phase Change in history from the Industrial Age to the Information Age. By changing how we think of Information, he was able to gain power over it. For example, the Bit is a distinction -- a difference (1) that makes a difference (2). The first difference is physical (an empirical observation), and the latter difference is personal -- meaning (a theory or feeling). That's why some people feel that Shannon's indirect creation (Robots) are like Frankenstein's soulless monsters.

Information Age : This surprising result is a cornerstone of the modern digital information age, where the bit reigns supreme as the universal currency of information.
https://www.quantamagazine.org/how-clau ... -20201222/

The point being that I don't see any evidence of rules of semantics, and the rules of syntax need to be interpreted. — Metaphysician Undercover

The rules of Syntax (structure) are partly objective, and can be applied to any language or culture. But the "rules" of Semantics (meaning) are partly subjective & personal, yet may also be embedded in Jung's Collective Consciousness, or in Freud's Unconscious, or Chomsky's Deep Structure. Don't take those metaphors literally. They merely indicate that part of what-we-know-intuitively, and the rules-of-behavior we follow, are inherited with the human body. Hence, such standards, while important, are not inherently formal or rational. :nerd:

Rules of Semantics : Semantic rules make communication possible. They are rules that people have agreed on to give meaning to certain symbols and words. Semantic misunderstandings arise when people give different meanings to the same words or phrases
http://www.ai.mit.edu/projects/dm/these ... doff69.pdf

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http://gnomon.enformationism.info/Image ... f-size.jpg

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Re: TPF : Shannon Information

Post by Gnomon » Mon Dec 28, 2020 7:01 pm

The appeal to authority is insufficient until you bring out the evidence presented by those authorities. — Metaphysician Undercover

Since I am not an authority on the subject of Semantics and Syntax, I was referring you to some authorities that do see evidence of commonalities, if not formal "rules", in human communication. If you are really interested in the evidence, you can click on the links. But, it seems that you have something against the idea of natural logical structure in communication. And I'm not quite sure what that objection is. :)

I don't see that people agree on rules before communicating with each other. — Metaphysician Undercover

Well, except for some picky-picky philosophers, most people don't have to establish formal rules before they communicate. Instead, most of us learn the rules informally at our mother's knee, and just by growing up in a particular culture, or may even inherit some mental structure biologically. That's what I referred to as "Intuition".

Are you arguing against Chomsky's theory of innate language structure? I generally agree with the notion, but I've never studied the theory in detail. So he may have over-stated his case. But what does that have to do with Shannon's theory of Parsimonious Transmission of Information? :D

Born Ready for Language
: Chomsky based his theory on the idea that all languages contain similar structures and rules (a universal grammar), and the fact that children everywhere acquire language the same way, and without much effort, seems to indicate that we're born wired with the basics already present in our brains.
https://www.healthline.com/health/child ... sky-theory

For and against Chomsky : https://www.prospectmagazine.co.uk/maga ... nstchomsky

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:18 pm

I have nothing against "natural logical structure in communication". But we cannot conclude that natural logical structure implies rules, just because artificial, or formal logic consists of rules. In fact, that's what I see as the difference between formal logic, and natural logic, the former consists of rules, the latter does not. — Metaphysician Undercover

I think I'm beginning to see your objection to the notion of "rules" in communication. Apparently you are thinking of imposed "explicit" formal rules, while I'm talking about innate "implicit" informal commonalities. As a rule (i.e. normally) humans are born with something like a mental template for language.

My position on inherent human behaviors (instincts) is basically that of cognitive psychologist Stephen Pinker in The Blank Slate. He calls it "the language instinct", which gives humans an advantage, over most animals, in social communication. Anyway, I doubt that our concepts of communication are very far apart. It's just another failure to "first define your terms". :joke:

Rules :
1.one of a set of explicit or understood regulations or principles governing conduct within a particular activity or sphere.
1a : a prescribed guide for conduct or action. b : the laws or regulations prescribed by the founder of a religious order for observance by its members. c : an accepted procedure, custom, or habit.


As a Rule : usually, but not always.

The Blank Slate : arguing that human behavior is substantially shaped by evolutionary psychological adaptations
https://en.wikipedia.org/wiki/The_Blank_Slate

The Language Instinct
: Pinker argues that humans are born with an innate capacity for language. . . . . but dissents from Chomsky's skepticism that evolutionary theory can explain the human language instinct.
https://en.wikipedia.org/wiki/The_Language_Instinct

Then, very clearly, your proposal that people must agree on rules in order for communication to be possible, is false. — Metaphysician Undercover

That is not what I was proposing. Sorry for the mis-communication. :smile:

I really do not see how you can portray learning how to talk as a matter of learning rules. — Metaphysician Undercover

OK. I'll try to avoid using the term "rules", since it seems to trigger your indignation. Instead, I'll use something like "norm". The human language instinct is not a "law of nature" or a "man-made rule", but it is common enough to view it as "the rule rather than the exception". :cool:

Rule
: If something is the rule, it is the normal state of affairs.

Language structure
: You're born with it
https://www.sciencedaily.com/releases/2 ... 122316.htm

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:26 pm

Isn't a "rule" necessarily formal though? That's the point, to talk about Innate, informal commonalities, as if they are rules, appears like a mistake to me. — Metaphysician Undercover

Apparently, in your strict vocabulary of technical terms, that might be the case. Since I'm not a professional scientist, I tend to use such jargon more loosely. Besides, in psychology, formal "rules" or "laws" are hard to come by. Most behaviors that psychologists take-for-granted are more like rules-of-thumb than empirically-confirmed-natural-laws. That's why The Diagnostic and Statistical Manual of Mental Disorders has to be regularly updated to weed-out definitions of disorders that turn-out to be too broad or too narrow or just plain wrong. :smile:

7 Psychological Rules That Can Make Your Life Shine Brighter :
https://brightside.me/inspiration-psych ... er-533910/

That might be the case, if we both see this "instinct" as an unknown concerning its true nature, then we have commonality here. — Metaphysician Undercover

The "language instinct" is a well-known effect, but its cause is a matter of debate. Stephen Pinker says that "A three-year-old toddler is "a grammatical genius"--master of most constructions, obeying adult rules of language." And he attributes those "rules" to a combination of Nature and Nurture. But he provides lots of observational evidence, so the mechanism behind the human talent for language is not exactly unknown. Some may claim it's a miracle, but Pinker thinks it's a Darwinian adaptation. :smile:

The Language Instinct
: To Pinker, a Massachusetts Institute of Technology psycholinguist, the explanation for this miracle is that language is an instinct, an evolutionary adaptation that is partly "hard-wired" into the brain and partly learned.
https://www.amazon.com/Language-Instinc ... B0049B1VOU

but we have no approach to the cause of that commonality. If we say that the person is following a rule, we create the illusion that we know why the person is acting in that particular way. — Metaphysician Undercover

All I can say to that is, Pinker is the reigning expert on psycholinguistics, and he thinks he knows why humans act like they have a special talent for language, that other animals don't. But his theory is based on evolutionary assumptions, that some other linguists, and theologians, disagree with. Yet again, the science of Psychology is inherently Philosophical & Meta-Physical, hence not empirical, and will always be subject to debate. But Pinker's explanation is close-enough for me . . . for now. :cool:

Is psychology a “real” science?
: Does it really matter?
https://blogs.scientificamerican.com/th ... ly-matter/

PS___Shannon's definition of passive carrier "Information" is on the reductive & empirical end of the Science spectrum. But my definition of active causal "EnFormAction" is more towards the holistic & philosophical end, along with Psychology and History. Does that lack of hard evidence invalidate the hypothesis that Enformation might be the driver of evolution --- including the Language Instinct? Maybe. What do you think?

Information/Enformation :
* Knowledge and the ability to know. Technically, it's the ratio of order to disorder, of positive to negative, of knowledge to ignorance. It's measured in degrees of uncertainty. Those ratios are also called "differences". So Gregory Bateson* defined Information as "the difference that makes a difference". The latter distinction refers to "value" or "meaning". Babbage called his prototype computer a "difference engine". Difference is the cause or agent of Change. In Physics it’s called "Thermodynamics" or "Energy". In Sociology it’s called "Conflict".

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:31 pm

Don't you see a problem here? If psychologists are referring to "rules' which account for, or cause certain types of behaviour, and there is really no rules there, then what are they actually talking about? — Metaphysician Undercover

I don't have a problem with that as-if usage of "rules". It's no worse than atheist scientists referring to observed regularities in nature (Laws) as-if they were imposed by a divine authority. When patterns in nature appear to be rule-governed or lawful, I attribute that predictable behavior of natural systems, not to top-down Design, but to bottom-up Programming. Human programs are intentionally teleological, but the final output is unknown until the computation is complete --- or the fat lady sings, whichever comes first. :wink:

Evolutionary Programming
:
Special computer algorithms inspired by biological Natural Selection. It is similar to Genetic Programming in that it relies on internal competition between random alternative solutions to weed-out inferior results, and to pass-on superior answers to the next generation of algorithms. By means of such optimizing feedback loops, evolution is able to make progress toward the best possible solution – limited only by local restraints – to the original programmer’s goal or purpose. In Enformationism theory the Prime Programmer is portrayed as a creative deity, who uses bottom-up mechanisms, rather than top-down miracles, to produce a world with both freedom & determinism, order & meaning. https://en.wikipedia.org/wiki/Evolutionary_programming
http://blog-glossary.enformationism.info/page13.html

Natural Laws : Laws of Nature are to be distinguished both from Scientific Laws and from Natural Laws. Neither Natural Laws, as invoked in legal or ethical theories, nor Scientific Laws, which some researchers consider to be scientists’ attempts to state or approximate the Laws of Nature, . . . Some of these implications involve accidental truths, false existentials, the correspondence theory of truth, and the concept of free will. Perhaps the most important implication of each theory is whether the universe is a cosmic coincidence or driven by specific, eternal laws of nature.
https://iep.utm.edu/lawofnat/

If we dismiss this term "rule", and look at the fact that a human being is a free willing and free thinking human being, then we have a different perspective form which we can ask why is a person inclined to act in such a way as to create the appearance that one is following rules, when really there are no rules being followed. — Metaphysician Undercover

My interpretation of evolution as bottom-up design is compatible with human Free Will. :yum:

Freewill Within Determinism : “Determinism is a long chain of cause & effect, with no missing links. Freewill is when one of those links is smart enough to absorb a cause and modify it before passing it along. In other words, a self-conscious link is a causal agent --- a transformer, not just a dumb transmitter. And each intentional causation changes the course of deterministic history to some small degree.” ___Yehya
http://bothandblog2.enformationism.info/page68.html

I have difficulty with the "holistic" approach because in my mind it cannot adequately account for the appearance of intention and free choice. — Metaphysician Undercover

Perhaps you are thinking of the New Age interpretation of "Holism". But my usage is that of the guy who literally wrote the book. It's only "mystical" in the sense that Einstein called "spooky action at a distance". :nerd:

Holism : Regarding the concept of Holism, he says it "has a somewhat mystical association, in its commitment to a single unified whole being the ultimate reality. But there are strong scientific arguments in its favour. . . . The American philosopher Jonathan Schaffer argues that the phenomenon of quantum entanglement is good evidence for holism. Entangled particles behave as a whole, even if they are separated by such large distances that it is impossible for any kind of signal to travel between them."
https://www.philosophybasics.com/branch_holism.html

Neural holism and free will : This approach locates free will in fully integrated behavior in which all of a person's beliefs and desires, implicitly represented in the brain, automatically contribute to an act.
https://www.tandfonline.com/doi/abs/10. ... 5080307765

Holism and Evolution
: although Smuts' meaning differs from the modern concept of holism. Smuts defined holism as the "fundamental factor operative towards the creation of wholes in the universe."
https://en.wikipedia.org/wiki/Holism_and_Evolution
https://reflexus.org/wp-content/uploads ... lution.pdf

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:35 pm

I don't understand this part. Are you making three classifications, scientific laws, laws of nature, and also natural laws. — Metaphysician Undercover

That wasn't my classification, but a definition of "Law" as used in different contexts : Scientific Laws (observed regularities, with no inference of divine regulation), Laws of Nature (religious assertion of divine Lawgiver), and Natural Laws (a legal term, which doesn't take a stand either way on the provenance of the observed order in Nature).:cool:

But you can see, as I've argued, that I don't believe we're justified in even calling what is represented by these laws as "rules' or "laws" or anything like that. — Metaphysician Undercover

OK, "what is represented by these [so-called] laws"? Would you prefer to call them "accidental random patterns in Nature"? Einstein referred to them as "Reason", "order", "harmony", "structure", and "lawful", among other terms. :smile:
Einstein :
. . . "the Reason that manifests itself in nature"
. . . "Scientific research is based on the idea that everything that takes place is determined by laws of nature, and therefore this holds for the actions of people."
. . . "Veneration for this force beyond anything that we can comprehend is my religion. To that extent I am, in point of fact, religious."
. . . "the marvelous structure of existence"
. . ."I believe in Spinoza's God, Who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind."

https://todayinsci.com/E/Einstein_Alber ... ations.htm

I do not see how you can make bottom-up mechanisms consistent with holism. — Metaphysician Undercover

Again, you may be thinking of "Holism" in the New Age sense. Scientists prefer to use the term "Systems" in order to avoid any theological implications. If you think of Evolution as an ongoing Program of world-creation, then the final output is unknown (undetermined), even though the Programmer specified the parameters by which the Solution will be judged. Initial Conditions & Natural Laws are parameters, but the system uses statistical Randomness to instill novelty into the otherwise deterministic system. My essay on Intelligent Evolution is an attempt to introduce the notion of bottom-up creation of an unfathomably huge Uni-verse (one whole) from a minuscule mathematical Singularity. :nerd:

Freewill Within Determinism
: http://bothandblog2.enformationism.info/page67.html

Intelligent Evolution
: http://gnomon.enformationism.info/Essay ... 120106.pdf

Systems Theory
:
A system can be more than the sum of its parts if it expresses synergy or emergent behavior. Changing one part of the system usually affects other parts and the whole system, with predictable patterns of behavior. More parts, means more interrelationships, and more complex properties & activities, including mental functions.
https://en.wikipedia.org/wiki/Systems_theory
http://blog-glossary.enformationism.info/page18.html

Holism ; Holon :
Philosophically, a whole system is a collection of parts (holons) that possesses properties not found in the parts. That something extra is an Emergent quality that was latent (unmanifest) in the parts. For example, when atoms of hydrogen & oxygen gases combine in a specific ratio, the molecule has properties of water, such as wetness, that are not found in the gases. A Holon is something that is simultaneously a whole and a part — A system of entangled things that has a function in a hierarchy of systems. In the Enformationism worldview, our space-time physical reality is a holon that is a component of the enfernal G*D-Mind.
http://blog-glossary.enformationism.inf ... tml#Holism

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:39 pm

So it's clearly fallacious logic to proceed from the premise that natural things are describable by laws, to the conclusion that they are governed by laws. — Metaphysician Undercover

Again, we butt heads over specific vs general terminology. In human societies, governors (kings, congressmen, parliamentarians) make the laws, and the governed people obey the laws. So, if you observe a pattern of obedience to a law, wouldn't you infer that the obeyers were somehow compelled to conform? The observed pattern of behavior can be described in terms of specific actions, or in terms of a governing principle : a Law.

The relevant distinction is between a specific pattern, and the general cause of that pattern. For example, if most cars wait patiently at a red light, is that a random coincidence, or would you infer that there is some governing Law that they are obeying? If you watch long enough, you may see a car that does not stop at a red light, and then is pulled-over by a law-enforcement officer.

Some scientists refer to Natural Laws as merely "habits". The implication is that the predictable regularities of natural behaviors is characteristic of individual actors, not of any general imperative imposed from above. Is this your position? That makes sense from a Reductive (part) viewpoint, but not from a Holistic (system) perspective. So again, our different understanding reflects a preference for looking at Isolated Parts or Whole Systems --- or for Bottom-up Inductive Reasoning or Top-down Deductive Logic. Both approaches are reasonable, but applicable to different contexts. No need to butt heads . . . just define terms and contexts. :smile:

Law is a system of rules created and enforced through social or governmental institutions to regulate behavior, with its precise definition a matter of longstanding debate. It has been variously described as a science and the art of justice.

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

Principle : a general scientific theorem or law that has numerous special applications across a wide field.

Most of The So-Called Laws of Nature Are More Like Habits : There is no need to suppose that all the laws of nature sprang into being fully formed at the moment of the Big Bang, like a kind of cosmic Napoleonic code, or that they exist in a metaphysical realm beyond time and space.
https://www.sheldrake.org/research/most ... ike-habits

Inductive reasoning, or inductive logic, is a type of reasoning that involves drawing a general conclusion from a set of specific observations. Some people think of inductive reasoning as “bottom-up” logic, because it involves widening specific premises out into broader generalizations.
https://www.masterclass.com/articles/wh ... -reasoning

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:42 pm

As far as I can tell, you haven't defined "holism" yet so as to make it consistent with bottom-up creation. — Metaphysician Undercover

Apparently, you haven't looked at the links. The connection between Holism and bottom-up creation is much too complex for a forum post. Instead, I have dozens of essays that look at different aspects of the question --- from the perspective of a top-down Whole, and a bottom-up Holon. You seem to think Top-Down and Bottom-Up are mutually exclusive. But I think it's a question of perspective, point-of-view, frame-of-reference.

The computer program example illustrates that the Programmer writes a top-down strategy for calculating the answer to a problem. But if the answer was already known or knowable, there would be no need to bother with laborious calculation. In my worldview, the Programmer had a question about FreeWill that could only be answered by actually allowing some degree of freedom. Even an omnipotent creator could not mandate moral behavior without permitting agents to choose.

So, I view Natural Evolution as a program of Freedom Within Determinism. Natural Laws place limits upon freedom, but Randomness is free to experiment with various solutions to the question of Survival. Likewise, Natural Selection is a top-down choice of fitness characteristics, but Random mutations provide many potential bottom-up solutions to the Ethics of Freedom. Hence, I view Evolution as an on-going experiment in the creation of Moral Agents. The World System is a whole, and the individual Agents are holons. The System itself is only retro-predictable after the output has been computed. And the Agents are unpredictable in that they are able to choose different paths in life. :cool:

Holistic Systems
: Holistic approaches are those that consider systems in their entirety rather than just focusing on specific properties or specific components. In each case, enormous culture shifts are required in education, training, business, government, and economic models.
http://www.csl.sri.com/users/neumann/holistic.pdf

Holon : something that is simultaneously a whole and a part.
https://en.wikipedia.org/wiki/Holon_(philosophy)

Free Will : The puzzle of reconciling 'free will' with a deterministic universe is known as the problem of free will or sometimes referred to as the dilemma of determinism. This dilemma leads to a moral dilemma as well: the question of how to assign responsibility for actions if they are caused entirely by past events.
https://en.wikipedia.org/wiki/Free_will

Moral Agent : A moral agent is a person who has the ability to discern right from wrong and to be held accountable for his or her own actions. . . . Traditionally, moral agency is assigned only to those who can be held responsible for their actions.
https://ethicsunwrapped.utexas.edu/glossary/moral-agent
Note -- Responsibility is a bottom-up reaction to a top-down forced choice. Cause - Choice - Effect.

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Re: TPF : Shannon Information

Post by Gnomon » Sun Jan 03, 2021 6:47 pm

The human beings have free will to disobey the laws when they desire to, and often do, at risk of punishment. The inanimate objects continue to act as the law describes, without exception. If there is any exception, we do not punish the things, we look for inaccuracies in the law. See the difference? — Metaphysician Undercover

I see the distinction you are making. But the observation that some people voluntarily run red lights, does not diminish the punitive power of the law. That's exactly why we have Law-Enforcers, who can't rewrite "inaccurate" laws. The Exception proves the Rule. :joke:

So, the point I made, is that we cannot proceed logically from the observation that the behaviour of inanimate things can be described by laws, to the conclusion that these things are governed by laws, because of the difference I described above. Being governed by laws implies that the things governed can freely act otherwise. Being describable by laws of science implies that things cannot freely act otherwise. This is a fundamental difference and the incompatibility needs to be resolved. — Metaphysician Undercover

That's exactly why I have made an argument for FreeWill Within Determinism. Which is an update on old theological arguments against Determinism and Predestination of human Souls. Fortunately for us non-theologians, immortal souls are no longer necessary to escape Fate. :grin:

Freewill Within Determinism :
“Determinism is a long chain of cause & effect, with no missing links.
Freewill is when one of those links is smart enough to absorb a cause and modify it before passing it along. In other words, a self-conscious link is a causal agent---a transformer, not just a dumb transmitter. And each intentional causation changes the course of deterministic history to some small degree.”
__Yehya
http://bothandblog2.enformationism.info/page67.html

I don't see that the concept of a holon solves the issue of bottom-up causation. — Metaphysician Undercover

True. Most "holons" don't have any freedom from Top-Down causation. But the exceptional "holon" in my assertion is a "a self-conscious link" in the chain of Causation. Theologians attribute that significant distinction to a divine Soul. But, from a scientific perspective, Free Choice could emerge from evolution along with the exceptional Self Concept of primates. :cool:

Can You See Your Self?
: The mirror test is a measure of self-awareness developed by Gordon Gallup Jr in 1970. The test gauges self-awareness . . . .
https://www.sciencedaily.com/terms/mirror_test.htm

This really doesn't makes sense. Randomness cannot experiment, all it can do is continue in a random fashion. You could assume an agent which experiments with randomness, but then you'd need to account for the existence of that agent. What is this agent, the soul? — Metaphysician Undercover

Again, with the literal picky-picky definitions. My comment was not a statement of natural fact, but an analogy with our common concept of Agency. Of course Randomness is not "really" a free agent, or a scientist. And the agent of Randomness is not a Soul, but the hypothetical Programmer, who metaphorically used a random number generator (algorithm) to produce a patternless distribution of forms, from which Natural Selection (another algorithm) can select those best fitting the Programmer's criteria for fitness. Again, these are not scientific statements, but poetic analogies, referring to questions that are beyond the reach of the Scientific Method, but not beyond philosophical imagination. :chin:

Agency Attribution : to non-humans and non-persons
https://epistemocritique.org/the-right- ... entations/
PS___ I call my hypothetical random agent "Randy". He's my imaginary friend. :yum:

Sorry, officer. I didn't mean to run that red light. I thought I could make it through on the yellow light. Do I need to show you my Poetic License? :yikes:

Poetic License
: the freedom to depart from the facts of a matter or from the conventional rules of language when speaking or writing in order to create an effect.

Philosophical Metaphors
:
https://plato.stanford.edu/entries/metaphor/

Sign seen along the Philosophical highway : "Caution Metaphorical Bumps Ahead".

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