I of course accept this, but so far fail to see its significance. — javra

The significance, as I see it, is that thinking in terms of number is, along with identity, an artificially exact mode of thought. Also, I think it is good practice to draw conceptual distinctions wherever we find that we can; it helps to understand how we think.

I'd instead focus on the discreetness of physical givens as discerned by awareness. Something which, as an indefinite amount of something, we commonly term quantity in the English language. Which we then use numbers to more precisely quantify in definite manners. — javra

That something stands out perceptually is not that it is actually separate from its environment; it is just that we can distinguish it. That said observations of animals show that they often distinguish the same things as we do; notably items of food.

Our distinguishing things depends on our nature, and on the nature of what is distinguished. When we distinguish a single tomato, there is not an "indefinite quantity of something" in the sense that you were using the term 'quantity', that is as number: on the contrary there is an exact number of tomatoes; in this case one. We might even say that there is an exact mass and volume of tomato there, although we cannot say precisely what that is.

I don't know the background of the guy you've quoted. Is the guy trying to conceive of what reality is like, or would be like, in the complete absence of all awareness in the cosmos? — javra

No, Bateson was one of the seminal "information" thinkers; well worth a read.

The exactitude of numbers has everything to do with awareness's aptitudes - especially here addressing that of humans - — javra

Apropos of this, another quote from the same book:

"Some birds can somehow distinguish number up to seven. But whether this is done by counting or by
pattern recognition is not known. The experiment that came closest to testing this difference between the
two methods was performed by Otto Koehler with a jackdaw. The bird was trained to the following
routine: A number of small cups with lids are set out. In these cups, small pieces of meat are placed.
Some cups have one piece of meat, some have two or three, and some cups have none. Separate from the cups, there is a plate on which there is a number of pieces of meat greater that the total number of pieces in the cups. The jackdaw learns to open each cup. Taking off the lid, and then eats any pieces of meat that are in the cup. Finally, when he has eaten all the meat in the cups, he may go to the plate and there eat the same number of pieces of meat that he got form the cups. The bird is punished if he eats more meat from the plate than was in the cups. This routine he is able to learn.

Now, the question is: is the jackdaw counting the pieces of meat, or is he using some alternative method
of identifying the number of pieces? The experiment has been carefully designed to push the bird toward
counting. His actions are interrupted by his having to lift the lids, and the sequence has been further
confused by having some cups contain more than one piece of meat and some contain none. By these
devices, the experimenter has tried to make it impossible for the jackdaw to create some sort of pattern or rhythm by which to recognize the number of pieces of meat. The bird is thus forced, so far as the
experimenter could force the matter, to count the pieces of meat.

It is still conceivable, of course, that the taking of the meat from the cups becomes some sort of rhythmic
dance and that this rhythm is in some way repeated when the bird takes the meat from the plate. The
matter is still conceivably in doubt, but on the whole, the experiment is rather convincing in favor of the
hypothesis that the jackdaw is counting the pieces of meat rather than recognizing a pattern either of
pieces or of his own actions.

It is interesting to look at the biological world in terms of this question: Should the various instances in
which number is exhibited by regarded as instances of gestalt, of counted number, or of mere quantity?
There is a rather conspicuous difference between, for example, the statement "This single rose has five
petals, and it has five sepals, and indeed its symmetry is of a pentad pattern" and the statement "This rose has one hundred and twelve stamens, and that other has ninety-seven, and this has only sixty-four." The process which controls the number of stamens is surely different from the process that controls the number of petals or sepals. And, interestingly, in the double rose, what seems to have happened is that some of the stamens have been converted into petals, so that the process for determining how many petals to make has now become, not the normal process delimiting petals to a pattern of five, but more like the process determining the quantity of stamens. We may say that petals are normally "five" in the single rose but that stamens are "many" where "many" is a quantity that will vary from one rose to another.

With this difference in mind, we can look at the biological world and ask what is the largest number that
the processes of growth can handle as a fixed pattern, beyond which the matter is handled as quantity. So far as I know, the "numbers" two, three, four, and five are the common ones in symmetry of plants and animals, particularly in radial symmetry."

That something stands out perceptually is not that it is actually separate from its environment; it is just that we can distinguish it. — Janus

I'm not getting this. Edit: A predator's perceived prey that stands out perceptually isn't separate from the prey's environment?

When we distinguish a single tomato, there is not an "indefinite quantity of something" in the sense that you were using the term 'quantity', that is as number: on the contrary there is an exact number of tomatoes; in this case one. — Janus

"A quantity" is an unspecified amount. "A number" is a specified quantity. Q: "What is the quantity of tomatoes you've purchased from the store?" A: "One." Conceptually, quantities consist of numbers - whether or not the latter are specified. To go back to Bateson's initial quote, what would a numberless measurement of length, for example, be?

As to Bateson's latest quote, interesting as it is to read, it only speculates without evidencing what is speculated.

Just found this on line:

https://www.quantamagazine.org/animals-can-count-and-use-zero-how-far-does-their-number-sense-go-20210809/

it starts:

An understanding of numbers is often viewed as a distinctly human faculty — a hallmark of our intelligence that, along with language, sets us apart from all other animals.

But that couldn’t be further from the truth. Honeybees count landmarks when navigating toward sources of nectar. Lionesses tally the number of roars they hear from an intruding pride before deciding whether to attack or retreat. Some ants keep track of their steps; some spiders keep track of how many prey are caught in their web. One species of frog bases its entire mating ritual on number: If a male calls out — a whining pew followed by a brief pulsing note called a chuck — his rival responds by placing two chucks at the end of his own call. The first frog then responds with three, the other with four, and so on up to around six, when they run out of breath.

Practically every animal that scientists have studied — insects and cephalopods, amphibians and reptiles, birds and mammals — can distinguish between different numbers of objects in a set or sounds in a sequence. They don’t just have a sense of “greater than” or “less than,” but an approximate sense of quantity: that two is distinct from three, that 15 is distinct from 20. This mental representation of set size, called numerosity, seems to be “a general ability,” and an ancient one, said Giorgio Vallortigara, a neuroscientist at the University of Trento in Italy.

And it gets better as you read the article.

But wait, what if all this is not counting but "pattern or rhythm recognition"? I'll skip on this debate.

Instead, you could reply to what I initially asked.

Either via the idealism of Platonic Realism or the materialism of today's mainstream views, how can one have numbers in the complete absence of discrete amounts of givens - i.e., of quantities? (if nothing else, there would yet be a quantity of numbers by the shear presence of the number(s) addressed) — javra

I'm not getting this. Edit: A predator's perceived prey that stands out perceptually isn't separate from the prey's environment? — javra

I meant not separate in any ontological sense. The prey and the predator are parts of the environment that only stand out in the sense of being noticed.

As to Bateson's latest quote, interesting as it is to read, it only speculates without evidencing what is speculated. — javra

Speculation or conjecture, more or less informed, is all we have; what more do you expect?

But wait, what if all this is not counting but "pattern or rhythm recognition"? I'll skip on this debate. — javra

As Bateson says pattern recognition is possible with small numbers of things; beyond that we would need to count them to know how many there are.

Conceptually, quantities consist of numbers - whether or not the latter are specified. To go back to Bateson's initial quote, what would a numberless measurement of length, for example, be? — javra

Apart from counting, quamtities do not strictly consist in numbers, or at least not in number alone. A certain quanity of tomatoes will weigh a certain number of milligrams, a different number of grams, kilograms, ounces pounds, stones and so on. Same with volumes. So it is numbers plus units of measurement.

There can be no numberless measurement, but a length is a length, regardless of whether it is measured.

Instead, you could reply to what I initially asked.

Either via the idealism of Platonic Realism or the materialism of today's mainstream views, how can one have numbers in the complete absence of discrete amounts of givens - i.e., of quantities? (if nothing else, there would yet be a quantity of numbers by the shear presence of the number(s) addressed) — javra

I'm not sure what you are saying or asking there. I'll attempt an answer if you care to clarify.

I'm not sure what you are saying or asking there. I'll attempt an answer if you care to clarify. — Janus

That's OK. Thanks

OK, suit yourself.

I meant to respond to this when the thread first came out because I am working on a different sort of argument from reason. I do not think this argument works with common, highly nominalist versions of reductive physicalism.

In most versions of physicalism, which tend to embrace the computational theory of mind (still seemingly the most popular theory in cognitive science), a belief is just an encoding of the state of the external environment. This encoding exists within a system that can be defined as an agent. Agents need not be conscious, they simply need goals and a set of possible behaviors to decide from when attempting to actualize those goals. Decisions on how to act given some goal x and some set of beliefs y can be described in computational terms. This "set of beliefs," is represented as a database of atomic propositions, a "knowledge base," and the behavior selection process can be described well enough through backwards chaining searches on the knowledge base.

Under this view, a belief is true just in case the representation of the enviornment of which the agent is a part (the world) corresponds to the actual enviornment. It's that simple. The claim that "no belief is rationally inferred if it can be fully explained in terms of nonrational causes," is simply the result of a misinterpretation of what "rational," should be taken to mean. The world is rational because it obeys a set of rules that govern how it progresses from state to state which can be fully described mathematically, perhaps even fully described computationally. Future states are deducible from current ones. All beliefs are thus the product of a rationally describable set of steps, essentially a "program running on a quantum computer," as it is often put. States in a program are all logical consequences of prior states, so "rational." Assuming "rational," to mean "the result of an agents beliefs," as Lewis does is arguably begging the question.


The encodings inside the physical system making up the agent don't have to fully describe the world as it is to be true. Indeed, organisms cannot encode all the data they are exposed to without succumbing to entropy (Terrance Deacon's "Towards a Science of Biosemiotics," has a good explanation of this). This means that a true belief is just a representation of the world that is in some ways isomorphic to actual states of affairs in the world. A belief can be consistent with many states of affairs and is true just in case it corresponds to the actual state of affairs.

Thinking through computable toy universe examples, there doesn't seem to be any reason why a toy universe can't contain a subsystem that instantiates the logical computations that (allegedly) result in the creation of agents (and conscious agents at that). Parts of the universe simply interact such that the agent subsystem comes to represent a compressed, partial description of the universe within itself. These descriptions are the knowledge base, which is what it uses to compute ways of achieving its goals (goals which generally include maintaining homeostasis and reproduction, with these goals being explained by reference to natural selection).

Beliefs then are just other names for physical subsystems within a physical agent, e.g. patterns of neuronal activity. Such beliefs are created due to physical causal mechanisms. Belief, the verb, is just the description of what the enumeration of these physical belief subsystems "feels like" to a conscious agent.

Knowledge then is justified true beliefs. Beliefs are justified if the methods employed by the agent to vet their beliefs have proven themselves to be successful in the past (inductive support) and if any deduction used in vetting/creating these beliefs is sound. Since AI can already build proofs, I don't think there should be too much argument that causal processes can be used to cross check soundness.

This view works regardless of how consciousness arises, or even if it is eliminated, because agents are not defined in terms of possessing first person perspective, but rather through having goals. First person experience is thought to be totally described, somehow, by physical casual processes anyhow, so adding it won't change anything.

Given this view, I don't see how this argument works at all. Lewis seems to conflate the proposition that "the universe and causal forces are meaningless," as in, "devoid of moral or ethical value and describing nothing outside themselves," with agent's beliefs necessarily also being "meaningless," as in "the beliefs must not actually be in reference to anything else." The first sense of the term "meaningless" is not the same as the second. A toy universe with just a bunch of floating balls and a Pac Man that tries to eat them can be meaningless in the first sense while the Pac Man could have meaningful representations of the locations of the balls encoded within itself provided there is some medium for interaction (e.g. light waves bouncing around to hit the Pac Man's eyes).

Basically, a lack of external reference does not imply a lack of internal reference.

FYI: One of the pioneers of digital philosophy (re: pancomputationalism/digital physics) died a couple of weeks ago, Edward Fredkin. If you are not familiar with him, here's a wiki article with a summary of view on the fundamental nature of information ...

https://en.m.wikipedia.org/wiki/Digital_physics#Pancomputationalism

I became aware of Fredkin through references to him in the writings / interviews of
David Deutsch,
Seth Lloyd,
Max Tegmark,
Stephen Wolfram,
Richard Feynman,
John Wheeler,
Frank Tipler,
Eric Drexler,
Douglas Hofstadter,
Nick Bostrom et al.
In the history of Western philosophy, speculations as divergent as Peirce's semiosis-tychism (pragmaticist), Leibniz's monadology (rationalist) and Democritus-Epicurus' atomism (materialist) are the closest analogues to digital philosophy I've yet found.

I'm not convinced (it does not seem to me to follow), however, 'that if physical events-regularities are computable (which they are), then physical reality must be a "computer" executing a nonphysical program (and, in your case, Gnomon, that's written by a "nonphysical programmer")' – at best, this hasty generalization is too unparsimonious and the pseudo-speculative equivalent of (neo-Aristotlean / neo-Thomistic / neo-Hegelian) "intelligent design". :eyes:

@Wayfarer @universeness @apokrisis @Janus

I feel like Platonism is so heavily ingrained in mathematics that even those trying to run from it can find themselves simply lapsing into it from another direction. Part of this has to do with specialization in academia IMO. If, being a scholar focused on mathematical foundations, you're not generally going to be able to do a lot of work or teaching on other fields, the fields where a Platonist would say numbers are instantiated, then your field, by definition, places you in a silo where your experience of mathematics is necessarily "floating free of the world."

Rather than a set of immutable numbers, which seems less defensible today, we can have a set of possible, contextually immutable axioms, which define a vast, perhaps infinite space of systems. The truths in the systems are mutable, because there are different systems, but then there is a sort of fall back, second-order Platonism where the existence of the systems themselves, and relations between them, are immutable.

To go back to Bateson's initial quote, what would a numberless measurement of length, for example, be?

Couldn't this be accomplished by simply referencing objects' extension in relation to one another? Indeed, this is how our measurement systems tend to work. We take an arbitrary phenomenon and use it as a base and describe other phenomena in terms of their relation to the base. I wouldn't agree that a ratio is essentially a number either, as a ratio is necessarily a comparison between things, be they discrete entities or parts of a whole.

But more to the point on animals having some ability to conceive of numbers, I'm not sure if that demonstrates too much in either direction. Human nature seems to produce a strong tendency to want to think of things in terms of discrete objects. We have some good reason to think this tendency is the result of evolution, since it causes a great deal of difficulty in trying to conceptualize how the world appears to actually work at very large or very small scales. That is, the discrete object view appears to work only at the scales relevant to evolution. It also makes it hard for us to conceive of continua, hence the endless appeal of the Eleatic Paradoxes. However, mathematics also shows us that this conception of numbers is much shakier than was originally thought. I feel like there is support for the supposition that the illusion of discreteness is just a useful survival trick as much as for the idea that innate numeracy denotes the existence of numbers "out there, sans mind."

how can one have numbers in the complete absence of discrete amounts of givens - i.e., of quantities?

Imagine a continuum, for example a line, of finite length. Our line has an uncountably infinite number of points but also a finite length. Take some section of the line, arbitrarily, and compare how many lengths of the section fit within the whole. There are sections of the line that exist such that the line can be broken into n segments of equal length, where n is a natural number. No initial discreteness required, right? All that is required is that the points of the line differ from each other in some way; then we can define this difference in reference to a given segment's length relative to the whole to produce numbers for a coordinate system.

I've always found the reverse argument more interesting, the claim that numbers are essential for reality, or at least our understanding of it.

We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.
Mathematical entities are indispensable to our best scientific theories.
Therefore, we ought to have ontological commitment to mathematical entities.

That's a brief summary of the Quinte-Putnam Indispensability Argument. In response to this, I know some folks actually have made some headway in describing areas of physics without reference to numbers, although it isn't exactly pragmatic to do so. Anyhow, if some hitherto unformulated version of logicalism is true, and numbers are reducible to logos, it seems to me like this argument is moot (and that the concept of logos spermatikos ends up beating out divine nous as a better explanation of "how things are," IMHO.)

Quite a few pancomputationalists also seem to embrace ontic structural realism, that the universe is the mathematical structure describing it, so I'm not even sure if it makes sense to talk about a physical computer and a non-physical program, as the distinction seems to collapse.

I think the whole concept of pancomputation suffers from the fact that computation itself is poorly defined. The most common explanations make reference to "what Turing Machines do," because that's the easiest way to describe computation, but then Turing Machines are themselves an attempt to define what human beings do when carrying out instructions to compute things. But then human consciousness is also explained in terms of computation, making the whole explanation somewhat circular.

Read Seth Lloyd, David Deutsch and Stephen Wolfram – 'computation' has been operationally defined quite rigorously for decades.

The most common explanations make reference to "what Turing Machines do," because that's the easiest way to describe computation, but then Turing Machines are themselves an attempt to define what human beings do when carrying out instructions to compute things. But then human consciousness is also explained in terms of computation, making the whole explanation somewhat circular. — Count Timothy von Icarus

Do you have a citation supporting "Turing Machines are themselves an attempt to define what human beings do"?

I've been under the impression that Turing conceived of the TM as a sort of minimalist CPU, and I wonder whether Turing himself would have thought of TMs as more than a conceptual tool for use in thinking about what human beings do, rather than an attempt at defining what human being's do.

Anyway, I think computationalism has a large element of looking for the keys under the street lamp because that's where the light is. Computation is a human invention that is as it is, because it is relatively easy for us to think in such terms.

Connectionism is much closer to where it's at when considering the way human thought really works. Perhaps it is harder for most people to think in connectionist terms though.

Thanks for engaging with what I've previously asked!

To go back to Bateson's initial quote, what would a numberless measurement of length, for example, be? - javra

Couldn't this be accomplished by simply referencing objects' extension in relation to one another? — Count Timothy von Icarus

Yes, you are quite right. (Realized this after posting, but deemed that editing it would be a bit much ... in any case, my bad here.) I would however better reword the concern I have in this way:

-- Can one have any measurement that is devoid of any discrete givens which we - either thinkingly or unthinkingly - enumerate (i.e., determine the amount of) via numbers?

If not, then it currently seems to me that measurement necessitates number in some way or another.

Notice that in the very quoted sentence number (a definite amount; i.e., a definite quantity) is necessarily specified in order for cogent semantics to obtain (what I've boldfaced). Likewise, while a ratio might not be itself interpreted as a number (debatable) it will yet, I so far find, necessarily consist of a relation between numbers - at the very least between quantities (the plurality of which is itself a quantity) which we hold the potential to enumerate. Else, in measurements that strictly concern relations, such as greater than or lesser than, there will always be an at the very least implicitly addressed number of givens to which the relations applies. I'm for example weak on pure theoretical mathematics, but I so far can't find any exception to this.

I feel like there is support for the supposition that the illusion of discreteness is just a useful survival trick as much as for the idea that innate numeracy denotes the existence of numbers "out there, sans mind." — Count Timothy von Icarus

As to whether lesser animals can count, as philosophy it's right up there with whether lesser animals are in fact conscious - to which might as well be appended the issue of other minds. In short, I'm convinced that they do, but, as with those who'd disagree, can't provide conclusive philosophical evidence of it - at least not in a forum format. So, I won't debate the issue.

Still, the pivotal issue I was addressing is that, as I currently find it, discreteness is contingent on the occurrence of awareness - such that if awareness then discreteness (and as an important meta-example: the occurrence of one awareness or more will each be a discrete given). And, furthermore, that numbers are only then contingent on the occurrence of discreteness. This irrespective of one's metaphysical interpretation(s) regarding the consequent significance in respect to the cosmos we inhabit. (e.g., a materialists' view that an awareness-devoid cosmos is possible or, else, an idealist's view that such is impossible - as two among other metaphysical perspectives)

So I'm here in full agreement that "numbers 'out there, sans minds' [by which I here understand, tersely stated, "a plurality of discrete awareness"]'" can only be a fallacy.

how can one have numbers in the complete absence of discrete amounts of givens - i.e., of quantities? - javra

Imagine a continuum, for example a line, of finite length. Our line has an uncountably infinite number of points but also a finite length. — Count Timothy von Icarus

Right here, in the very semantics of what a line is, is the occurrence of quantity in the form of "points" - such that this quantity minimally consists of more than one point. In addressing "a" continuum one is likewise specifying a quantity - not two or three continuums but one. So the occurrence of quantity is a requite aspect of any continuum - be it real or strictly conceptual.

ake some section of the line, arbitrarily, and compare how many lengths of the section fit within the whole. There are sections of the line that exist such that the line can be broken into n segments of equal length, where n is a natural number. No initial discreteness required, right? All that is required is that the points of the line differ from each other in some way; — Count Timothy von Icarus

Maybe the "discreteness" here addressed by you has a specialized mathematical meaning? But in the ordinary sense I've addressed it it specifies something being separate, distinct, individual. Hence, in the sense I intend the very sections of the line that are compared are thereby discrete (to our awareness of them as such - otherwise no comparison could be made).

BTW, one could then address point-free topology as another example to be provided - but, here too, tmk there will be discerned some form of separateness somewhere (e.g., sets), such that discreteness (and hence quantity) yet obtains.

So, I again find that the (maybe I should specify, cosmic) occurrence of quantity is requisite for the occurrence of numbers (be the latter's occurrence also cosmic or, else, strictly located in individual minds as some would have it).

I've always found the reverse argument more interesting, the claim that numbers are essential for reality, or at least our understanding of it. — Count Timothy von Icarus

This in fact isn't too different from my own personal metaphysical views. Only that I maintain quantity - as in "discrete givens" - to be essential to existence rather than to reality (with "existence" here roughly understood as all which "stands out" in any way) and, thereby, to physical reality (which exists); this, thereby, concurrently necessitating the ontic occurence of numbers in the cosmos (however sentience might represent them symbolically; e.g. as "IV", as "4", or as "four"). But I don't want to digress into my own metaphysical views concerning this.

All the same, of main interest here is the issue of how numbers could be had in the complete absence of quantity.

Anyhow, if some hitherto unformulated version of logicalism is true, and numbers are reducible to logos, it seems to me like this argument is moot (and that the concept of logos spermatikos ends up beating out divine nous as a better explanation of "how things are," IMHO.) — Count Timothy von Icarus

:grin: I could go with that. (but then these touchy terms hold different connotations to different people, for instance, that of "spermatikos" say by compassion to the terms "in-fluence" or even that of "inspiration (aka, to breath in or, more archaically, roughly, to be breathed into psychically)") But yes, a Heraclitean-like, cosmic logos of the type addressed stands in direct logical contradiction to an omnipotent and omniscient creator deity whose "words" make up the world.

I'm not convinced — 180 Proof

Yeah, digital physics fails at the gate for me even as an epistemology, let alone an ontolotgy.

As Wiki notes:

Extant models of digital physics are incompatible with the existence of several continuous characters of physical symmetries,[7] e.g., rotational symmetry, translational symmetry, Lorentz symmetry, and the Lie group gauge invariance of Yang–Mills theories, all central to current physical theory.

Informational atomism has to be able to handle the dichotomy of the discrete-continuous. It must make a world that exists as a dynamical balance between these metaphysical limits. Every bit must be both locally separated and yet globally connected. The openness of local degrees of freedom must be closed by global constraints. Etc.

So even constructing a map of the territory is an issue according to this no go argument - https://arxiv.org/pdf/1109.1963.pdf

And when it comes to taking literally the claim that “reality is a computer program”, you have to scratch your head at how it can in any sense run without material hardware or a handy power socket.

Digital physics was a weird one. The Planck triad of constants does surely tells us something deep about the fundamental grain of the Universe. But that would be that nature is triadically structured (is irreducibly complex) in systems fashion and arises out of the dichotomisation or symmetry breaking that can oppose spacetime extent to spacetime content.

https://thephilosophyforum.com/discussion/comment/586530

It is relations rather than computations that are going to be metaphysically fundamental.

And when it comes to taking literally the claim that “reality is a computer program”, you have to scratch your head at how it can in any sense run without material hardware or a handy power socket. — apokrisis

:up:

— Wayfarer

sarcastically & superciliously ridiculed your & my spooky immaterial opinions in this thread about general Reason instead of particular Things. Specifically, he poo-poos my information-based posts postulating something like a data-processing-universe theory.

From his reply : "I'm not convinced (it does not seem to me to follow), however, 'that if physical events-regularities are computable (which they are), then physical reality must be a "computer" executing a nonphysical program (and, in your case, Gnomon, that's written by a "nonphysical programmer")' – at best, this hasty generalization is too unparsimonious and the pseudo-speculative equivalent of (neo-Aristotlean / neo-Thomistic / neo-Hegelian) "intelligent design". Apparently he connects my personal theory with those of several famous mathematicians & physicists. So, it looks like I'm in good company. FWIW, since I avoid engaging in put-down polemics, here's my response indirectly addressed to 180 :

My only knowledge of Ed Fredkin came in Robert Wright's 1988 book : Three Scientists And Their Gods, Looking For Meaning in an Age of Information. Wright said, "He posits not only laws but a law enforcement agency : a computer. Somewhere out there, he believes, is a machinelike thing that actually keeps our our individual bits of space abiding by the rule of the universal cellular automaton, With this belief Fredkin crosses the line between physics and metaphysics".

Wright later asks, "where is this computer that Fredkin keeps talking about". Fellow physicist and Information theorist, Rolf Landauer noted the flaw in Fredkin's theory, infinite regress : "It's turtles all the way down". Wright goes on to ask, "if matter is made of information, what is the information made of?" Apparently Fredkin's god-like cosmic computer is just an ontological metaphor, and not subject to ultimate empirical evidence. Likewise, my own hypothetical god-like Enformer is just an immaterial metaphor, and not amenable to materialistic challenges. It simply provides a way to think about the kind of Ultimate Origin questions that Plato & Aristotle answered with the metaphor of a First Cause. Sure the container of the metaphor is a material brain, but what is the substance of an abstract metaphor?

Would you (180) also accuse Fredkin, a certified genius, of "hasty generalization" and "unparsimonious and the pseudo-speculative equivalent of (neo-Aristotlean / neo-Thomistic / neo-Hegelian) intelligent design"? Is his "law enforcement agent" a god-of-the-gaps posit to cover our ignorance of ultimate answers? Is his "computer" a self-programmed natural intelligence, or an artificial intelligence created by an even more intelligent Programmer? Is human intelligence merely an accidental pattern of a hypothetical "universal cellular automaton"? Perhaps, it just doesn't matter, literally. :smile:

PS__180's Materialistic worldview seems to force him to assume that the information & ideas encoded into a computer program are made of some kind of exotic matter. He doesn't understand that the matter is a container for information, not the ideas per se.

In most versions of physicalism, which tend to embrace the computational theory of mind (still seemingly the most popular theory in cognitive science), a belief is just an encoding of the state of the external environment. — Count Timothy von Icarus

All very well, but this seems to me to be overlooking or taking for granted a great deal of what is required by such an encoding. I can see how it is perfectly applicable when it come to animals responding to stimuli, but reason is able to do a great deal more than that. It generalises and abstracts, from the particular to the universal. Sure, if you treat life as a kind of model or a game, this approach makes sense - 'Sim Life'. But is it philosophy?

This view works regardless of how consciousness arises, or even if it is eliminated, because agents are not defined in terms of possessing first person perspective, but rather through having goals. — Count Timothy von Icarus

That's what makes it reductionist. You can set aside the first person perspective, and with it, the reality of existence, by treating it as a model, or a board game, as if you were surveying the whole panorama from outside it - when you're actually not.

Lewis seems to conflate the proposition that "the universe and causal forces are meaningless," as in, "devoid of moral or ethical value and describing nothing outside themselves," with agent's beliefs necessarily also being "meaningless," as in "the beliefs must not actually be in reference to anything else." — Count Timothy von Icarus

I think his argument is situated with reference to the classical atheistic materialism of the culture of his day. Have you ever encountered Bertrand Russell's A Free Man's Worship? Published around the turn of the 20th century, it was an anthemic essay dedicated to the purportedly brave and clear-eyed scientific vision of a Universe driven wholly by the forces of physics and man as 'accidental collocation of atoms'. Jacques Monod's Chance and Necessity was another landmark work in similar vein. That vision is also the subject of enormous commentary in 20th century literature, art, drama and philosophy. But I think that hard-edged mentality is already on the wane, 21st century science is more engaged with questions of meaning, acknowledgements of the human aspect of all the sciences and a renewed sense of mystery. The hard edged kind of atheistic materialism that his argument was aimed at will always have its advocates, but there's an abundance of alternatives today (I am enjoying Adam Frank's articles, he's a physics scholar and popular science commentator, see his Science Claims a God's Eye View and his current 'mission statement'.)

'In Aristotle, nous is the specific faculty that enables human beings to reason. For Aristotle, this was distinct from the processing of sensory perception, including the use of imagination and memory, which other animals can do. For Aristotle, nous is what enables the human mind to set definitions in a consistent and communicable way, and provides the innate potential for different persons to understand those universal categories in the same logical ways (and note that Kant adopted Aristotle's categories almost unchanged)..... In this type of philosophy, later considerably elaborated by neoplatonism, it came to be argued that the human understanding (nous) somehow stems from this cosmic nous, which is however not just a recipient of order, but also a creator of it.'

Two things fill the mind with ever new and increasing admiration and awe, the more often and steadily we reflect upon them: the starry heavens above me and the moral law within me. I do not seek or conjecture either of them as if they were veiled obscurities or extravagances beyond the horizon of my vision; I see them before me and connect them immediately with the consciousness of my existence. — Immanuel Kant

Would you (180) also accuse Fredkin ... of "hasty generalization" and "unparsimonious and the pseudo-speculative equivalent of (neo-Aristotlean / neo-Thomistic / neo-Hegelian) intelligent design"? — Gnomon

Yes and no.

Yes, Fredkin's "computer universe" proposal/conjecture is, in fact, an unparsimonious hasty generalization. Read Seth Lloyd, David Deutsch & Stephen Wolfram.

No, I only "accuse" you, Gnomon, of pseudo-speculations, etc: "enformationism" = "intelligent design" = "pan-en-deism" = "first cause/unmoved mover" (i.e. WOO-of-the-gaps). :smirk:

Is his "law enforcement agent" a god-of-the-gaps posit to cover our ignorance of ultimate answers?

I'll drink to that. :up:

Is his "computer" a self-programmed natural intelligence, or an artificial intelligence created by an even more intelligent Programmer?

This "computer" metaphor amounts to an infinite regress – it's "enformers" all the way down. :lol:

Is human intelligence merely an accidental pattern of a hypothetical "universal cellular automaton"?

Define "human intelligence". :sparkle:

Sure, computation has been operationally defined since Turing's "On Computable Numbers With an Application to the Entscheidungsproblem," and Church's introduction of Lambda Calculus, and their findings re: the Church-Turing Thesis was later extended conceptually to physical systems more generally with the discovery that relatively simple cellular automata could simulate a Universal Turing Machine. The computable numbers, as Turing says, "may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means."

However, an operational definition is not what is wanted when discussing the ontological underpinnings of the universe in the same way that explaining matter as "the amount the spring on a spring balance stretches when something is placed upon it," fails to adequately explain matter in all its aspects.

In any event, even the operational definition is widely acknowledged not to be fully rigorous, as the term "algorithm," on which the Church-Turing thesis hangs itself lacks a rigorous definition.

The problem gets even more dicey when one starts talking about the physical instantiation of computation. There is considerable debate and myriad different camps vis-á-vis the question of how to define computation in this respect. Central to this debate is the problem that, if pancomputationalism is true, and every physical system is a computer, then the core thesis of computational theory of mind, that the brain is a computer, becomes trivial (this is why pancomputationalists have jumped on IIT, although to my mind I don't get how IIT doesn't imply panpsychism, which Tegmark at least seems prepared to bite the bullet on).

On the other hand, permissive mapping accounts of physical computation allow virtually every system to be "computing," every possible computable function (Putnam and Searle make this argument) making the concept of computation itself trivial. I for one can certainly see how these issues can motivate people to cast in with semantic explanations of computation, even if I'm not ready to join them.

There is certainly no widely accepted definition of what makes a physical system a computer, and in this aspect the current operational definition itself is sorely lacking. I am not aware of many attempts at a theoretical definition, maybe because Liebnitz seems to have done as good of a job as possible off the bat? Although I also think the shadow of Platonism in mathematics makes it difficult to work on defining an abstract process that necessarily take "steps" (time) and which is itself defined by recursion (e.g. Godel's early work on computation).



Sure, check out his original paper "On Computable Numbers With an Application to the Entscheidungsproblem." The term "computer" in Turing's day referred to a person who computed figures for their job. He makes specific references to people in crafting the idea of a TM. For example, the requirement that the machine's memory be finite is justified by "the fact that the human memory is necessarily limited." Turing is specifically idealizing what a human being does when "computing" figures with a pen and paper. For more detail you can also check out: https://plato.stanford.edu/entries/church-turing/#MeanCompCompTuriThes

I agree with the keys and streetlight metaphor but I also think pancomputationalism does get at an essential element of how the world works. I am just not convinced that Turing's definition is appropriate for what we wish to describe, in part because continua do appear to exist in physics, although a fully discrete universe certainly hasn't been ruled out.

It's worth noting that Turing's claim is not that "anything that follows law-like behaviors or instructions must be computable." His claim is merely that a Universal Turing Machine can compute all functions that any Turing Machine can compute and this statement is paired with an argument for why the UTM is a good definition for effective computation, while this definition is bolstered by providing an example of an uncomputable number. This does not imply that there cannot be machines that can do things UTMs cannot do.

The reason I mention the above is that, even if it were satisfactorily confirmed that some elements of physics are surely uncomputable via a UTM, I don't not think this would be a death blow to pancomputationalism. Rather, we might be able to adopt some sort of new formalism to describe such uncomputable law-like behavior, and we'd likely give it some sort of new name like "super computation," although hopefully it'd be something more clever than that.

:up:

That's what makes it reductionist. You can set aside the first person perspective, and with it, the reality of existence, by treating it as a model, or a board game, as if you were surveying the whole panorama from outside it - when you're actually not.

Exactly. However, the problem of whether or not consciousness can actually be fit into such a physicalist model, which is something such models need to be able to explain if they are to be satisfactory to most people, seems like a separate problem from the one Lewis is pointing out. If we assume that physical systems, as described per physicalism, can indeed produce first person experience, then Lewis' argument doesn't seem to work.

I don't think abstraction is a particularly hard problem for the physicalist either. Tropes and universals can be described in mathematical, computable terms.

So my point would be that argument just doesn't seem to add much. Obviously it is true that physicalism is deeply broken if it is unable to ever explain the most obvious fact of existence, first person experience. No extra argument is really needed if you can prove that an ontology has a giant "the world we experience," hole in it. However, since no system can currently "explain everything," and since plenty of previously mysterious phenomena have successfully been explained in physical terms, I don't think this is a KO of physicalism either. It certainly doesn't work the way arguments that superveniance, as presented in popular forms of physicalism, is incoherent work. If accepted, these do seem to "KO" at least popular varieties of physicalism. That seems to be the type of argument Lewis is going for, but I don't think it works.

Have you ever encountered Bertrand Russell's A Free Man's Worship?

No, I generally tend to steer clear of primary sources for Russell, at least on that sort of thing, because I find him to be one of the most uncharitable, self-assured philosophers out there and it rubs me the wrong way. I'm familiar with the vision from Stace's "Man Against the Darkness," though. I find it sort of funny in a way, because for the Stoics and many early Christians the fact that the world did move in such a law-like way was itself evidence of the divine Logos, not an argument against the divine.

If we assume that physical systems, as described per physicalism, can indeed produce first person experience... — Count Timothy von Icarus

But we cannot so assume.

Tropes and universals can be described in mathematical, computable terms. — Count Timothy von Icarus

By rational agents - human beings - augmented with intentionally-designed artefacts - computers and calculators. Were those rational abilities absent, there would be no apprehension of tropes or universals. I know it's already been suggested that crows can count, but try explaining the concept of prime to them.

I find it sort of funny in a way, because for the Stoics and many early Christians the fact that the world did move in such a law-like way was itself evidence of the divine Logos, not an argument against the divine. — Count Timothy von Icarus

That is a subject in history of ideas (associated with Arthur Lovejoy's book The Great Chain of Being: A Study of the History of an Idea, published 1936.) One of the major historical themes explored is 'man's changing vision of the cosmos' - from the demiurgos of Plato, to the biblical creation myths, to the mechanical universe of the early modern period, where God became a ghost in his own machine. The concept of natural laws was originally identified with ideas emanating from the One, then as divine commandments, and then as physical laws absent any intentionality or design - which is the view expressed by Russell in that essay. It is that kind of materialism which is challenged by the argument from reason.

I know it's already been suggested that crows can count, but try explaining the concept of prime to them. — Wayfarer

To try clarify what was suggested, by me at least: If crows can count, then crows (as with apes and other lesser animals) obviously cannot count the way humans do: via use of language and its conceptual constructs. But then crows can't understand a rock as object the same way we do either - e.g., that it consists of minerals, subatomic particles, etc. Still, crows can hold awareness of some rudimentary properties of rocks well enough to intentionally make use of some rocks as tools - not like us, they can't build a skyrocketing pyramid from them, but they can drop them on things in attempts to crack these things open.

In parallel to their, by comparison, minuscule understanding of physical objects in the world, crows might well be able to apprehend rudimentary aspects of definite quantities existing in the world which we humans linguistically refer to by the term "numbers".

This teeny-weeny aptitude of apprehension will quite obviously differ by great magnitudes in comparison to an average human's. But this does not mandate that there is an absolute on/off switch in-between.

That our human psyches are leaps and bounds more awareness-endowed than those of all lesser animals does not of itself then indicate that there was no evolutionary cline in awareness and the intelligence that accompanies it.

As another parallel, that one can't explain calculus to a five-year-old doesn't then imply that the five-year-old has no awareness of specific quantity whatsoever.

Not claiming to know that lesser animals do or don't count. But if they do, this does not then make their aptitudes of understanding on par to our own. Its why we term them "lesser" animals - due to us being the most evolved (here strictly meaning, developed) animal we know of by far.

I'm not convinced (it does not seem to me to follow), however, 'that if physical events-regularities are computable (which they are), then physical reality must be a "computer" executing a nonphysical program (and, in your case, Gnomon, that's written by a "nonphysical programmer")' – at best, this hasty generalization is too unparsimonious and the pseudo-speculative equivalent of (neo-Aristotlean / neo-Thomistic / neo-Hegelian) "intelligent design". :eyes: — 180 Proof

:100: I totally agree with you here.

Rather than a set of immutable numbers, which seems less defensible today, we can have a set of possible, contextually immutable axioms, which define a vast, perhaps infinite space of systems. The truths in the systems are mutable, because there are different systems, but then there is a sort of fall back, second-order Platonism where the existence of the systems themselves, and relations between them, are immutable. — Count Timothy von Icarus

I don't think that this works. The reason why different systems are needed is because incompatibilities arise between one and another. Incompatibility makes it impossible to have immutable axioms which would be applicable to all systems.

The problem is right at the foundation, the nature of a unit, one. We can assume an ideal unit, "one", but then the things which we allow ourselves to do with "one" through stated axioms, must be consistent with what we can actually do with one object, in practise. In practise though, we find that different types of things, or objects, allow us to do different types of activities with them. This is very evident with division. Each type of thing has specific ways which it can be divided. In mathematics, the common principle is to allow that the unit "one" can be divided in any possible way. This does not properly represent the restrictions on division which exist in reality.

I don't think that this works. The reason why different systems are needed is because incompatibilities arise between one and another. Incompatibility makes it impossible to have immutable axioms which would be applicable to all systems. — Metaphysician Undercover

:up:

Incompatibility makes it impossible to have immutable axioms which would be applicable to all systems.

Absolutely. That's why the pivot is to just think in terms of all the possible coherent systems. There isn't one set of immutable axioms but rather a landscape of systems as your new fixed objects. At least that's how I've seen the conception developed in some cases.

But, as I understand it, while numbers tend to get grounded in quite abstruse work within set theory that there is less general confidence in, they can also be grounded using category theory. Barry Mazur has some relatively approachable stuff on this, although I certainly don't get all of it.

Timelessness remains either way, mathematics is eternal, not involved in becoming— in most takes at least. This, I think, may be a problem. Mazur had an article on time in mathematics but it didn't go that deep. But I recently discovered Gisin's work on intuitionist mathematics in physics, and that is quite interesting and sort of bound up with the philosophy of time. The Nature article seems stuck behind a paywall, but there is this Quanta article and one on arXiv.

https://arxiv.org/abs/2011.02348

https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/

From his reply : "I'm not convinced (it does not seem to me to follow), however, 'that if physical events-regularities are computable (which they are), then physical reality must be a "computer" executing a nonphysical program (and, in your case, Gnomon, that's written by a "nonphysical programmer")' – at best, this hasty generalization is too unparsimonious and the pseudo-speculative equivalent of (neo-Aristotlean / neo-Thomistic / neo-Hegelian) "intelligent design". — Gnomon

Again, I'll reply to you, because dialoging with 180 is like talking to a snarky wall. He says that, in his superior wisdom, he is convinced that physical events are indeed computable --- as Wolfram, Tegmark, etc claim --- but he is "not convinced . . . that physical reality must be a computer executing a nonphysical program". His incredulity toward anything "nonphysical" is built-in to the dogma of Materialism, and non-physical Intelligence is taboo. But many mathematicians, such as Wolfram & Tegmark are platonist in their view of the ontological status of mathematics/logic*1. That's mainly because math & logic are about systematic interrelationships (meanings), not isolated things (atoms in void). Likewise, a computer program is not a material object, but an imagined sequence/system of events, mathematically encoded into a complex Algorithm (a conceptual procedure, not a physical thing).

So, a real computer --- perhaps including the universe --- is a physical/material machine designed by a Designer to process some mathematical software encoded by a Programmer, with some eventual end in mind. The input-to-output procedure is typically aimed at future knowledge of something not otherwise knowable --- otherwise, why bother to do the math? If that statement is true of the PC running non-physical software on your desktop, why is it a "hasty generalization" to conclude that the evolving universe also requires some kind to mind to explain the origin of both the hardware computer and the software code? Apparently, for 180, there is no such thing as software : it's all hardware, all the way down*3.

180's Materialistic worldview seems to be based on pragmatic scientific Reduction, instead of theoretical philosophical Generalization*2. But reduction to what? The ancient Atom of Materialism has proved elusive & uncertain to the quantum scientists, who now mostly think of Reality as a Mathematical Field of some kind. Which is why Tegmark wrote his book : Our Mathematical Universe, My Quest for the Ultimate Nature of Reality. Yet, for him, the universe itself seems to be the ultimate Atom of reality. So he doesn't bother to make the next logical step, from computer (logical) universe to a universal (rational)] Programmer. Ironically, due to the inherent randomness of cosmic evolution, the fate of the universe is unpredictable. Unlike the instant creation of Genesis, even the Programmer of gradual evolution could not know the final outcome, except by running the Program to its conclusion*4. :smile:


*1. Is math non physical? :
Math is not physical (composed of matter/energy), though all physical things seem to conform to it.
https://www.askphilosophers.org/question/24527

*2. Philosophical Generalization :
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model).
https://en.wikipedia.org/wiki/Generalization

*3. Software :
Software of a computer is actually a collection of data or some type of instructions that dictates the computer how to perform some work. From this definition it is quite evident that software is a completely massless collection of instructions. So, it can't be the physical part of a computer.
https://www.quora.com/Are-all-the-physical-parts-of-a-computer-called-software
Note --- The computer is a material hardstuff (hyle), but the software is immaterial mindstuff (morph, form)

*4. " Ultimately, it would be fair to say the Universe itself is chaotic and therefore unpredictable."
https://www.sciencefocus.com/science/chaos-theory-why-the-universe-is-a-massive-unpredictable-mess/

I am not sure I am getting the argument. In particular, I am not sure I understand Premise 1. Why would the explanation of a belief in terms of non-rational causes prohibit the belief from being rationally inferred? Is the concern overdetermination of the belief?

Is the concern overdetermination of the belief? — NotAristotle

Something like that. Put it this way: if a belief is a consequence of a brain condition, then it is not held on the basis of logical necessity. It is arguing that if our ability to reason logically is merely a result of physical processes, such as the firing of neurons, then there are no grounds to trust that our logical conclusions are valid. Our logical reasoning would be explained in terms of physical processes, undermining the sovereignty of reason.

Again, I'll reply to you, because dialoging with 180 is like talking to a snarky wall. — Gnomon

Totally hear you on that. But your use of the metaphors of information and information processing introduce many difficulties from a philosophical point of view. My own approach is more oriented around 'history of ideas' and understanding how ideas influence cultural dynamics and entrenched attitudes, leavened somewhat with my engagement with Buddhist praxis. I try and situate what I write against that context. I am not much in favour of 20th century Anglo-American philosophy which overall is oriented around scientific naturalism and armed to the teeth against anything suggesting idealism (although there is a healthy idealist strain in current culture also.)

(The) Materialistic worldview seems to be based on pragmatic scientific Reduction — Gnomon

I'll take a step back. How modern physicalism, naturalism or materialism evolved is, I think, not very difficult to discern. The watershed was René Descartes, and the confluence of his work with Newtonian physics and Galileo's cosmology. This sets up the modern worldview (bearing in mind we're now situated in a post-modern world, but I'll leave that aside for now.) The 'universal science' at the heart of this method, based on precise analysis of measurable attributes using Cartesian algebraic geometery and calculus, is the basis of the success of the modern scientific method. The famous Cartesian description of the mind as 'res cogitans', literally, 'a thinking thing', however, has had calamitous consequences, as it seemed very difficult to establish what, exactly, it means. Meanwhile, the concentration on the purely measurable and quantitative aspects of the universe in the discovery of modern scientific method provided many astounding breakthroughs. Within that context, scientific materialism is the consequence of attempting to apply the very successful methods deployed by science to the problems of philosophy (in the absence of any real insight into what those problems are.) That's it in a nutshell, as far as I'm concerned. (I think in all likeliood, phenomenology and existentialism is far nearer the mark than anglo-american philosophy, but I'm not well-schooled in that either.)

As regards mathematical platonism - I had a minor epiphany about that. It was simply this: that whilst every material object is composed of parts and has a beginning and an end in time, this does not apply to numbers and other mathematical objects (although later I realised that only prime numbers are strictly indivisible.) At the time of this realisation, I thought 'aha! This is why the ancients held mathematics in such high esteem: they're nearer the "unconditioned origin of being"'. And the fact that the intellect is able to grasp these ideas is evidence for a kind of dualism, although not of the Cartesian kind. (I've attempted to follow that thread through the labyrinth, but the subject matter is arcane and difficult, and demands a much greater knowledge of all the classical texts than I will ever have.)

One of my all-time favourite Buddhist texts was subtitled 'Seeking truth in a time of chaos'. Don't loose sight of the fact that modernity - actually, post-modernity - is chaotic. There's a lot of turmoil, vastly incompatible opinions and worldviews all jostling one another for prominence. Learn to live with it, but I recommend not trying to tame the waters. It's beyond any of us to to that.