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In his The Road to Reality, Roger Penrose espouses three distinct realities - the physical, mental and mathematical.

The physical and mental are basically good old dualism, although he is an atheist and the mental aspect is accordingly shorn of angels dancing on pinheads. The mathematical is in essence Plato's realm of ideals.

Although my own ideas differ in much detail from his, this eternal triptych or whatever it is called appeals to me. However I remain unconvinced that the worlds of Plato and of experience are necessarily distinct. It might be that every quale of experience is attached to some ideal, and that every ideal has a quale attached to it, such that quale and idea are merely aspects of a single entity. It seem to me that information theory, especially in its philosophical aspect of semantics, must have a strong role to play in resolving this question. But I need to better understand the reasons for considering these worlds distinct.

Dualism has been flogged to death in philosophical circles, but has this kind of triple-ism received significant attention?

Guy Inchbald
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    It's similar to Popper's [three worlds](https://en.wikipedia.org/wiki/Popper%27s_three_worlds), though Popper did not restrict world 3 to math as Penrose does. Don't know what kind of analysis this received from others though. If you're interested in the concept of associating qualia with mathematics or information structures and removing the notion of a distinct physical realm, you might check out Chalmers' "double-aspect principle" at https://www.informationphilosopher.com/solutions/philosophers/chalmers/ and I discussed a version of this at https://philosophy.stackexchange.com/a/72799/10780 – Hypnosifl Dec 08 '20 at 20:42
  • Logic is binary and does not allow triplicities. Actually these are 3 pairs in a cycle; information theory is reductionistic and it will not be of much help; best thing to do is to consider the semiotic triangle. Tegmark and pals discussed the topic in 2006 https://arxiv.org/pdf/physics/0510188 . – sand1 Dec 08 '20 at 21:11
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    @sand1 - Logic is about propositions, the "three worlds" is a metaphysical idea which doesn't involve any denial that every well-defined proposition is either true or false. – Hypnosifl Dec 08 '20 at 21:13
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    @sand1 *Classical* logic is binary, three-valued logic with something like undecided for the third value is arguably implicit in human reasoning, and was explicitly pondered at least as far back as Ockham. Fichte's dialectic triad (often misattributed to Hegel) also comes to mind. Not that this has any non-metaphorical import, even under binary logic one is free to make triple or multiple classifications: Agrippa's trilemma/pentalemma in epistemology, trichotomy (less, more, equal) in classical mathematics, etc. Peirce also constructed trialistic metaphysics (different from Popper's). – Conifold Dec 08 '20 at 21:27
  • The point was that we can't consider meaningfully more than two things at once, and that is the way to understand the semantic triangle, Effron's dice or Penrose's "tripleism". (Btw many people still remember the tribar on the cover of Hofstadter's book) – sand1 Dec 08 '20 at 22:13
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    @sand1 - Logic doesn't say anything about not being able to "consider meaningfully more than two things at once", and you can certainly have individual propositions in logic that concern more than two objects or properties or sub-propositions. – Hypnosifl Dec 08 '20 at 23:21
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    @sand1 Can't we? Parmenides thought that we can think only One, and even not-One is unthinkable. And yet we do conceive change easily. Already Plato resolved it into a triad, being/non-being/becoming. Hegel suggested that reason can rise above “*thinking that belongs to the understanding alone*” and “*the mere logic of the understanding*”. I think many people are with Plato and Hegel on this. Peirce was in his semiotic, his Thirdness is the way of the mind. Secondness is the way of action, we do need a yes/no to act, but that is a pragmatic necessity, not an intellectual one. – Conifold Dec 09 '20 at 01:12
  • Thanks, all. Chalmers' mind-body dualism is essentially an information-physicality dualism. A consequence of it is panpsychism, in order that the physical may retain its dual information aspect in the absence of a living brain. I find this unacceptable on two counts: the structures needed to support cognition are absent from the Universe at large, and eternal truths/ideals appear to be independent of any given Universal state. If there is a mind-information equivalence, it needs to accommodate such criticisms. – Guy Inchbald Dec 09 '20 at 11:38
  • @GuyInchbald - Do you allow for a difference between "cognition" and qualia, so that a system might have qualia even if it didn't have cognition? And how would you define cognition, does it require a complex brain or would even simple systems that respond adaptively to changes in their environment (like nematode brains responding to basic sensory information or immune systems responding to invaders or ant colonies laying down scent trails to food sources) potentially be counted as engaging in "cognition" of a sort? – Hypnosifl Dec 10 '20 at 22:56
  • @Hypnosifl As the main question shows, I am vacillating between different positions. certainly, there is a strong scientific view that cognitive behaviour involves a capacity for modelling, prediction and decision-making. On the other hand, much of the brain's cognitive processes go on unconsciously and only a kind of executive dashboard gets to experience the qualia of consciousness. My own views do not contradict science. – Guy Inchbald Dec 11 '20 at 10:32
  • -1: It's a common mistake to think the Platonic forms refers solely to mathematical form. It doesn't. This is a truncation of Plato's theory. – Mozibur Ullah Oct 07 '21 at 11:17

2 Answers2

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Roger Penrose, The Road to Reality (Vintage, p.1029)

each of the three worlds - platonic mathematical, physical, mental - has its own kind of reality and each is founded in the one that precedes (the worlds being taken cyclically)

There are monists, dualists, pluralists, etc.

Dualism has been flogged to death in philosophical circles, but has this kind of triple-ism received significant attention?

Obviously it has not; usually it is reduced to some dualism and next it can be flogged to death. Apparently the main problem comes from a kind of prejudice that every ordering is hierarchical while cyclical arrangements created by non-transitive relations are brutally ignored. Popper's proposal is that for any two elements of his construct there is one that is more fundamental but there is not a most fundamental one among the three. German idealism has proposed mind, Physicalism insisted on matter and Platonism upheld mathematics.

'Rock, paper, scissor' game is a well known example and I have always wondered how the Ancient Greeks have not discovered something similar. The earliest mention seems to be from the 18th c. about three chess players among who no one is the best. Kenneth Arrow made popular the idea in mid-20th. c. Penrose exposed his ideas in the Tanner Lectures of 1994/5 and they were published with comments[1]; Tegmark and al. [2] discussed it in 2006 after The Road to reality appeared and their paper contains enough details; a Fqxi essay from 2017 also commented the idea[3].

Refs. [1] Penrose R., The Big, the Smalland the Brain (1997), includes comments by A. Shimony, N. Cartwright, and S. Hawking: see Fig 3.3; earlier it appears in his Shadows of the Mind (1994) [2] Tegmark M., et al On Math, Matter and Mind arXiv:physics/0510188v2 [3] Losev A., A Fundamental Loop

sand1
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    Comments have so far led me to Plato, Frege and Popper as triple-ists. All were significant philosophers. So I find the "obviously not" opener to this answer somewhat unjustified. – Guy Inchbald Dec 09 '20 at 11:46
  • This is a good answer, but it can be improved. It would be useful to add reference to Popper's Tanner Lecture https://tannerlectures.utah.edu/_documents/a-to-z/p/popper80.pdf and Frege as prior major thinkers. This recent triplest essay also cites Paul Davies positively: http://www.steelpillow.com/blocki/philosophy/threelevels.html – Dcleve Jan 09 '21 at 21:44
  • @Dcleve That "recent triplist essay" is my own work in hand! Towards the end, it poses the question I am asking here. Davies' main exposition of his thesis appears to be his book *The Demon in the Machine* (the titular resemblance to Arthur Koestler's *The Ghost in the Machine* must be no coincidence), which I evidently need to get a copy of. – Guy Inchbald Jan 10 '21 at 08:03
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    @GuyInchbald -- About half of philosophers ascribe to lower p platonism of one type or another (math, and ethics are the two most popular areas to admit to realism for). Platonism plus emergent consciousness gets one to triplism, and that is how Popper got there, despite his initial physicalist inclinations. Popper's book length treatment of this is The Self and Its Brain. – Dcleve Jan 11 '21 at 07:37
  • Information is one subset of the world of ideas. Another is logic. Neither create consciousness nor quales -- they are as different from quales as water is from fear. Popper noted that consciousness has an intrinsic time element, while ideas are timeless. The dramatic failure of the 3/4 century plus long effort of AI to somehow have algorithms create consciousness, has been a pretty definitive demonstration that consciousness and math/logic/algorithms/information are simply two distinct and unrelated areas. – Dcleve Jan 11 '21 at 07:45
  • @Dcleve "they are as different from quales as water is from fear" - or perhaps as the heads of a coin is from its tails; can you produce the one without the other? I am afraid the rest of that comment betrays similarly flawed opinionation. But my original question is not about validity, it is about precedent. Anyway, I have now ordered a copy of Davies' book, and thank you for the Popper reference, which now takes its place on my wants list. – Guy Inchbald Jan 11 '21 at 11:33
  • Heads and tails of coins are two examples of the same logical category, a surface. They are intrinsically coupled. And one can map one to the other. Fear and water are logically disconnected/unrelated categories. They are orthogonal. One cannot map one to the other. You are not understanding disconnectedness/orthogonality/non-mappability. The example was not an argument by analogy, but an example to help you understand the concept. – Dcleve Jan 11 '21 at 15:10
  • @GuyInchbald --The Strong AI Project, for the last 75 years, has operated on the hope that consciousness is an emergent phenomenon from some TBD feature of processing. It started with the assumption that all processing generates consciousness, but discovered pretty quickly that was not so. Then there was hope that faster throughput would hit an emergence threshold. Something like 7 orders of magnitude later, that is a non-starter. Then neural net processing, and self-learning/self-editing, global workspace architecture, and higher order processing have all been proposed, all with failure. – Dcleve Jan 11 '21 at 15:14
  • Yes, it is possible in principle that we can find some relation which closes the apparent logic mismatch, and triggers an emergence event. But pragmatic empiricism does not operate of "is it logically possible that this dead end idea is somehow salvageable despite 3/4 century of failure" but instead draw inference off the failure, to look elsewhere for the source of consciousness. I am a pragmatic empiricist, so this logic mismatch and total failure to overcome it despite running at that wall for 3/4 century -- looks pretty decisive to me. – Dcleve Jan 11 '21 at 15:19
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I think that Karl Popper's idea of three worlds is a quite nice idea as it defines a middle ground between (or synthesis of) the physical and the mental.

  • World 1 - The physical world.
  • World 2 - The mental world, all the knowledge and ideas being processed in one individual mind. There are billions of World 2:s on Earth.
  • World 3 - Culture. This includes all the changes that humans have made to World 1, all human-created information.

World 3 resides within World 1, but it is created by World 2:s. World 3 is the way how World 2:s communicate with each other through World 1.

Mathematics belongs to World 2, as it is knowledge about World 1.

Pertti Ruismäki
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    The world of ideas, abstract objects, and hypotheses, Popper's World 3, pre-existed world 2. And Math is part of world 3. Popper treats world 2, awareness/consciousenss, as emergent from world 1 of matter. That emergence proved to be USEFUL to life, as it happened to give the ability to interact with, and make use of world 3, for the few material objects which had developed the consciousness emergence trick. Life could then do experiments in virtual space, which can be far less fatal than doing them all physically. – Dcleve Sep 28 '22 at 20:16