How can minds like ours exist in a physical universe like ours?
Invited presentation at:
APA Conference Eastern Division, 2021
https://www.apaonline.org/event/2021eastern
Chair:
Peter Boltuc (University of Illinois at Springfield)
https://sites.google.com/site/peterboltuc/home
Extended Abstract (PDF)
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/sloman-apa-2021.pdf
This document is
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/sloman-apa-lecture.html
NB. This talk has been superseded by my presentation at the Sussex
University COGS seminar on 16 Feb 2020. The online notes for the Sussex talk
(updated after the presentation) are here:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/sloman-chemneuro-sussex.html
The talk announcement and video can be found here:
http://www.sussex.ac.uk/cogs/seminars,
including a link to the video of the talk and discussion. (Search for "16 Feb"
or "Sloman").
As a new developing organism grows more complex, for instance a chicken embryo in an egg, the mechanisms required to extend that complexity in later stages also grow more complex, with increasingly sophisticated uses of information about what has been done so far, what needs to be done next, and what resources are still available (e.g. unused matter in the egg) to be used for later stages of development.
In addition to physiological assembly, the construction processes must also provide specifications for behaviours of parts of the developing organism, which will be highly species-specific (e.g. heart pumping blood, mouth producing sucking actions in humans, beak being used to peck for food in newly hatched chicks).
Control processes in the earliest stages of reproduction may be semi-automatic chemical reactions triggered by spatial proximity between portions of DNA, RNA, and other molecules in the embryo's environment.
At later stages, extending a partly built embryo will involve creating and combining more complex new components in more complex relationships, using increasingly complex information processing, including spatial reasoning processes, to select assembly actions, instead of simply allowing neighbouring chemical particles to interact in accordance with laws of physics, which may suffice to explain the earliest processes of development of a new organism.
I conjecture that the more complex chemical control processes include forms of spatial reasoning that are precursors of ancient human mathematical reasoning that led to discoveries in geometry, a subset of which were combined in Euclid's Elements.
A later version of these ideas may provide a new defence of Immanuel Kant's philosophy of mathematics.
I suspect this is closely related to Alan Turing's ideas about the role of chemistry, summarised in a single sentence in his Mind 1950 paper: "In the nervous system chemical phenomena are at least as important as electrical". He did not say in what way, but I suspect his 1952 paper on chemistry-based morphogenesis was a side-effect of his intended longer term exploration of what could be achieved in developing organisms by chemical mechanisms, combining both discrete and continuous processes, unlike Turing machines and digital computers, which are entirely discrete, and also totally unlike neural networks, since they are not available in an embryo until a relatively late stage of development.
Chemical machinery used for pre-natal spatial control in assembly processes, may later form the basis of post-natal spatial reasoning, including ancient discoveries in geometry, supporting Kant's philosophy of mathematics.
These ideas illustrate a form of metaphysics that allows for dynamic production of new kinds of entity, relationship, and process, across both developmental and evolutionary time-scales. Chemistry based forms of representation may permit forms of reasoning that have gone unnoticed by philosophers, psychologists, neuroscientists and philosophers of mathematics!
Moreover, some of the deepest suggestions come from facts we all know about chickens, but fail to think about in the right way: I failed to attend to them until a few weeks ago!
These ideas have implications concerning the nature of consciousness, especially spatial consciousness, in many species with varying kinds of intelligence. Aspects of spatial consciousness in humans led to a large collection of mathematical discoveries in geometry long before Euclid. Pythagoras' theorem had been proved in several different ways at least a thousand years before Pythagoras was born! Several hundred different proofs have been discovered.
All current theories about the nature of mathematical cognition that I have encountered fail to account for some of the phenomena, although Immanuel Kant had some correct intuitions. It is widely believed that Kant's theories about mathematical knowledge were refuted by the scientific discoveries of of Einstein (supported by Eddington's observations in 1919), and displaced by more recent theories of mathematical reasoning developed by Frege, Russell, Hilbert, Turing, Gödel, and others.
However, I think Kant had deep insights that were correct, but hard to state precisely, and they have implications regarding mechanisms in human brains that make possible the forms of reasoning that led to ancient mathematical discoveries in geometry.
But it is not clear how the mechanisms referred to by Kant can be implemented in brains or other physical machines.
In contrast, the mechanisms postulated and studied in current neuroscience, referring to properties of neural networks in brains and widely modelled in artificial neural networks, are incapable of explaining those ancient mathematical capabilities.
That's because those mechanisms are entirely based on collection of statistical evidence from which probabilities are derived. E.g. that's at the core of the impressive performance of AI systems like Deep Mind (see https://deepmind.com/). But it is also responsible for their serious limitations, as regards abilities to replicate ancient mathematical discoveries, or discover mathematical necessities or impossibilities.
Why can't neural net mechanisms (such as Deep Mind) replicate ancient mathematical discoveries? Neurally inspired deep learning systems are now in constant use and being applied to increasingly difficult problems, with stunning successes, typified by Deep Mind winning a GO tournament a few years ago, beating the human world champion, Lee Se-Dol.
But if used without an additional theorem prover they have a deep flaw: they collect statistical evidence and derive probabilities, but since very high and very low probabilities are completely different from necessity and impossibility they cannot replicate mathematical discoveries, for example discoveries such as Pythagoras' theorem or derive the formula for the area of a triangle. No amount of statistical evidence, no matter how high the probability it supports, can establish necessary truth, or impossibility.
Unfortunately I've discovered that our modern educational systems do not ensure
that all students have an opportunity to learn to find proofs in Euclidean
geometry, which used to be a standard part of a good academic education, but was
abandoned in many countries in mid 20th century, for very bad reasons. This
means many highly educated philosophers are incapable of understanding one of
Kant's most important claims (discussed below). People lacking that education
can start to catch up by watching this presentation by Zsuzsanna Dancso at
MSRI:
https://www.youtube.com/watch?v=6Lm9EHhbJAY
(There are many more introductions to Euclidean geometry. Avoid those that
merely present theorems and formulas or constructions without giving proofs.)
Why can't powerful logic-based theorem provers replicate ancient mathematical discoveries?
Modern theorem provers are able to produce chains of formulae that constitute logically valid proofs, and many of them are extremely powerful, for instance in proving that computer programs have certain desired properties. But the forms of reasoning that they employ are based on modern concepts and techniques that were unknown to ancient mathematicians: they are discoveries/inventions of the last few centuries.
So the fact that a computer can prove things using a modern theorem prover does not mean that it can replicate the forms of mathematical discovery used by ancient mathematicians, such as Archimedes, Euclid, Zeno and many others several thousand years ago.
I'll give some examples of ancient forms of reasoning then briefly consider claims made by David Hume with which Immanuel Kant (rightly in my view) disagreed. But the fact that Kant is correct leaves open the question: how do brains achieve the results discussed by Kant?
I claim that known brain mechanisms do not provide the answer, and will suggest that the explanation may one day be found in sub-neural chemical mechanisms. Roger Penrose has famously made similar claims, and uses similar examples to mine. But he doesn't draw the biological conclusions I'll propose later. I don't know whether he would disagree with the claims I make at the end about chemical processes involved in construction of an organism.
Example: Pythagoras' theorem
Ancient mathematicians discovered (and proved) that if squares are
constructed on each side of a right angled planar triangle, then the area of
the square on the hypotenuse must be
the sum of the areas on the other two sides.
(See
https://en.wikipedia.org/wiki/Pythagorean_theorem.)
This theorem applies only to triangles in a plane, e.g. not on the surface of a sphere. So in this image (from Wikipedia) the area of Square C is the sum of the areas of the squares A and B:
Here's a link to
a "dynamic" proof, on Wikipedia:
https://upload.wikimedia.org/wikipedia/commons/9/9e/Pythagoras-proof-anim.svg
Very crudely, David Hume, depicted above, on the left, claimed that there are
only two kinds of knowledge:
"True by definition" applies to all truths that can be proved using only logic and definitions. An example is "No bachelor uncle is an only child", which can easily be proved from the definitions of "bachelor", "uncle" and "only child", using only logical reasoning.
Hume famously claimed that if someone claims to know something that is neither of type 1 (empirical) nor of type 2 (mere relations between ideas, or definitional truths) we should "Commit it then to the flames: for it can contain nothing but sophistry and illusion", which would have included much theological writing. and much philosophical writing by metaphysicians.
[I apologies to Hume and Hume scholars: this presentation over-simplifies Hume's position in order to contrast it with Kant's claims, below.]
Immanuel Kant's response (1781)
In response to Hume, Immanuel Kant, depicted above, on the right, claimed that
there are some important kinds of knowledge that don't fit into either pair of
Hume's two categories ("Hume's fork"), for they are not mere matters of
definition, nor derivable from definitions purely by using logic. He pointed out
that instead of Hume's single distinction between two categories of knowledge we
need to take account of three different distinctions: the analytic/synthetic
distinction, the empirical/non-empirical (empirical/apriori) distinction, and
the necessary/contingent distinction: See Sloman 1965.
So using Kant's distinctions we can locate ancient mathematical discoveries in relation to three different distinctions.
For example, it is true that we are in the midst of a Covid-19 pandemic, but it could have been false, perhaps if certain human behaviours had been different.
Another example: I am now in Birmingham in England. In principle I could now have been somewhere else at this time, e.g. in Berlin, in Germany. So that is a contingent truth.
If something is a necessary truth, then there are no possible circumstances in
which it could be false.
There are also necessary falsehoods. E.g. 3 + 5 = 9 is false and could
not have been true in any circumstances (without changing the meaning of what is
being said. So it is necessarily
false and its negation is necessarily true.
In short: Kant replaced Hume's single division of types of knowledge into two categories, with a much richer analysis making use of three different divisions, producing six categories. Not all combinations are possible, however. E.g. something cannot be both apriori and necessarily false. For more detail see Sloman(1965).
In his argument against Hume, Kant drew attention to kinds of mathematical knowledge that do not fit into either of Hume's two categories: since we can discover by means of special kinds of non-logical, non-empirical reasoning (that he thought was deeply mysterious, since he was unable to explain how the reasoning mechanisms worked), that "5+3=8" is a necessary truth, but not a mere matter of definition, nor derivable from definitions using only logic.
Kant thought such mathematical discoveries in arithmetic, and discoveries in Euclidean geometry were synthetic, not analytic and also could not possibly be false, so they are necessary truths, and because they are not based on or subject to refutation by observations of how things are in the world, such knowledge is non-empirical, i.e. a priori.
For a more careful and detailed, but fairly brief explanation of Kant's three
distinctions. apriori/empirical, analytic/synthetic and necessary/contingent,
see
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/kant-maths.html
Spatial reasoning not in Euclid's Elements
The proof below of the triangle sum theorem discovered by Mary Pardoe, a young
mathematics teacher, around 1971 would not be valid according to Euclid's
Elements, because line segments cannot be rotated in Euclid's version of
geometry. It later turned out that she was not the first person to have
discovered this proof. See the report in
https://www.cs.bham.ac.uk/research/projects/cogaff/misc/triangle-sum.html
Example: slice a vertex off a convex polyhedron
For readers who have not personally had the kind of geometric discovery
experience described by Kant here is an example, that, as far as I know does not
occur in standard geometry text books but is closely related to examples in
Shephard (1968). Try to answer this question
without reading any geometry textbooks: If there is a solid convex polyhedron,
and exactly one vertex is sliced off with a single planar cut, e.g. using
a very thin planar saw, how will the number of vertices, edges and faces (V, E
and F) of the new resulting polyhedron be related to the original three numbers?
Note that this question can be given a definite answer only if the polyhedron is
convex: i.e. any straight line joining two points on the surface of the
polyhedron lies entirely inside the polyhedron, or on its surface.
Readers who are unfamiliar with this aspect of convexity are invited to think about lines joining pairs of points on the surface of a cube. If the two points are on the same face of the cube, the line joining them will lie entirely on the surface. If the points are on different faces, but not on the boundary of either face, then the line joining them will lie entirely inside the cube, except for the two endpoints of the line. (Why?) So, on a convex polyhedron any straight line joining two points on the surface of the polyhedron with either lie entirely on the surface, or will have endpoints on different surfaces while all the remaining points on the line are in the interior of the cube.
What mechanisms in your brain could enable you to make such discoveries? There are many more discoveries that can be made by thinking about solid objects. An example, with illustration, is provided here, with a question printed below in blue:
Solid, opaque, convex, polyhedron with partly visible faces, edges and vertices.
Use a planar cut that removes exactly one vertex, e.g. the top one.
How will the numbers of vertices, edges and faces of
the remaining polyhedron differ from the original numbers?
Readers should attempt to answer the question about how the numbers will change before reading on!
This can be done using spatial reasoning abilities, as opposed to logical or algebraic reasoning abilities. If you find the question hard to understand, the discussion below may help to provide an understanding of the problem.
The fact that such mathematical discoveries are concerned with impossibilities and necessary connections, implies that they cannot be achieved by mechanisms, such as statistics-based neural nets that are capable only of using statistical evidence to discover probabilities, that are liable to be changed by future evidence.
Mechanisms that collect statistics and derive probabilities simply cannot model or explain or replicate ancient human abilities to discover geometrical impossibility or necessity since impossibility and necessity are not extremes on scales of probability: they are totally different concepts.
Current AI also includes powerful theorem-proving and problem-solving machines that use modern logic and arithmetic. However those logical techniques were discovered only relatively recently, and there is no evidence that they played any role in the reasoning of the great ancient mathematicians.
Discovering empirically that our physical space is not Euclidean no more refutes Kant's commendation of discoveries by Euclid and others than discovering that the surface of a sphere is non-Euclidean proves Kant (or Euclid) wrong. (For more details see http://www.cs.bham.ac.uk/research/projects/cogaff/sloman-1962/thesis.html#Hempel).
Einstein vs Kant?
It is widely, but erroneously, believed that Immanuel Kant's philosophy of
mathematics in his Critique of Pure Reason (1781) was disproved by Einstein's
theory of general relativity (confirmed by Eddington's observations of the solar
eclipse in 1919, establishing that physical space is non-Euclidean).
This no more refutes Kant's position (as I understand it) than demonstrating that the surface of a sphere is inconsistent with Euclidean geometry. E.g. the closest thing to a straight line on a sphere is a geodesic, and it is easy to make a triangle on a sphere bounded by three geodesics where all the angles of the triangle are right angles, adding up to 270 degrees not 180 degrees as in Euclidean geometry.
That belief is erroneous if Kant was not making a claim about physical space but about one of the types of space that we can think about, e.g. by imagining some basic features, or abstracting them from perceived objects (e.g. the 2D space on the surface of a spherical object, or an egg shaped object, or a toroidal -- circular tube shaped -- object), and then deriving implications of these basic features, by thinking about the features themselves, i.e. not merely manipulating sentences describing those features.
Without much difficulty you should be able, for example, to think of alternatives to a circular tube forming a 3D ring, or toroid, by imagining various deformations of that shape, e.g. twisting it into a figure 8-like shape, or introducing sharp corners and flat surfaces, turning the tube into a square picture-frame like shape, perhaps with with a very thick frame. Some of the mathematically possible deviations from familiar Euclidean space are much harder to think about than others. Compare thinking about 1000-dimensional shapes embedded in a 1001-dimensional space.
Just as we can use sentences in a spoken, written, or thought language to consider new possibilities and then derive consequences of those possibilities, we can also use non-linguistic forms of representation to visualise possibilities and then derive consequences. That's the sort of thing ancient mathematicians did when they first made their discoveries, and similar exercises of spatial imagination play a role in the thinking of mechanical engineers, architects, designers of new furniture or tools, dress-makers, and many others who work on spatial structures, including inventing new, useful, types. How that is possible needs to be explained by a theory of how brain mechanisms work.
Non-human spatial intelligence (e.g. Betty the crow)
I suspect other intelligent animals can do something similar to a limited
extent, but can't talk about it or reflect or their discoveries using an
internal language, as humans can. A striking example was Betty the New
Caledonian Crow whose problem solving abilities were made famous in 2002 by a
video showing her bending a piece of wire in order to lift a bucket of food out
of a vertical glass tube. Details are available here
http://users.ox.ac.uk/~kgroup/tools/tool_manufacture.shtml
However the researchers did not think it worth mentioning in their reports that
Betty solved the problem in several different ways, as shown by videos available
on their web site.
Pre-verbal Toddler Mathematicians
I suspect spatial reasoning abilities evolved before the development of (human)
language-based reasoning, because they seems to exist in many non-human
intelligent species without human languages, and some examples of intelligent
spatial reasoning are evident in pre-verbal human
children (as illustrated in this video of child with pencil:
http://www.cs.bham.ac.uk/research/projects/cogaff/movies/vid/pencil-video-cropped.ogg
As a mathematics student around 1958 I encountered philosophers claiming that Kant had been proved wrong because Einstein and Eddington had demonstrated that Euclid's results were not true of physical space, I felt that they were mistaken because Kant's claims corresponded to my experience of doing mathematics. My 1962 DPhil thesis (now online) defended a slightly modified version of Kant's claim that many important mathematical discoveries are non-empirical, non-contingent, and non-analytic (i.e. not just logical consequences of axioms and definitions), but did not explain how brains or machines could make such discoveries.
Later, I hoped to use AI to build a computer model of a mathematical reasoner making the same discoveries about space as the ancient geometers had. But this has proved very difficult. I now think that is because brains do things that cannot be done on digital computers, because they use forms of reasoning that include both discrete and continuous changes, whereas digital computers are capable only of discrete changes. One of the consequences of using discrete representations is that thinking about rotations has problems.
If thinking about a rotating ball requires locating the ball in a discrete space, then there will be problems about smooth rotation. That's because during even small rotations points on the ball further from the centre of rotation will move through different numbers of spatial locations and if the motion has to using stepping through a discrete grid, maintaining the shape of the ball during rotation would be impossible. We are able to think about and reason about continuous transformations that would be impossible in a discrete machine. It's clear that brains can reason about and visualise continuous changes, though it is not clear how. Perhaps such thinking makes use of sub-neural chemistry, which combines discrete chemical bonds that can change discretely and continuous motion through space. This thought may have been the motivation for Turing's work on continuously diffusing chemicals that interact Turing 1952. Whatever the mechanisms are, it is clear that humans can think about, and visualise continuous motions of various kinds, and it is not clear that digital computers can make the same discoveries about continuous spaces. (Is that why Turing claimed, in his thesis that computers were capable of mathematical ingenuity, but not mathematical intuition?)
Alternative popular accounts of mathematical knowledge are mistaken
Theories of mathematical knowledge put forward by psychologists,
neuroscientists, logicians, AI theorists, and recent philosophers of mathematics
fail to account for some of the facts noticed by Kant concerning the
complexities of mathematical discovery and their relationships with spatial
consciousness (in humans and other animals).
There are many researchers in psychology and neuroscience who try to investigate development of number competences, and think they have found evidence that number concepts are innate. That's because they don't understand that a full grasp of natural numbers (1, 2, 3, etc.) depends on understanding that the relationship of one-to-one correspondence is necessarily transitive , a type of understanding that Piaget showed many years ago (1952) does not develop until age 5 or 6 in humans.
Spatial and temporal one-to-one correspondence are two special cases of this discovery. Spatial consciousness formed the basis of ancient human mathematical consciousness in topology and geometry centuries before Euclid, and even longer before the development of logic-based formal foundations for (some) mathematics.
Readers who have never had personal experience of discovering geometric
constructions and proofs may find this online tutorial by Zsuzsanna Dancso
useful:
https://www.youtube.com/watch?v=6Lm9EHhbJAY
Without such personal experience it is impossible to understand what Immanuel Kant was talking about in his discussions on the nature of mathematical knowledge in his Critique of Pure Reason Kant(1781)
There are many more online geometry tutorials of varying quality. The worst ones merely present geometric facts to be remembered -- like some bad mathematics teaching in schools?
Sub-organism precursors of mathematical competences
I suggest that long before such spatial consciousness evolved in ancient humans
and other animals, partly analogous capabilities, namely increasingly
sophisticated abilities to detect and make use of spatial structures and
relationships, must have evolved for use in ancient
mechanisms assembling complex molecular structures during processes of
biological reproduction, such as the processes of assembling a chick, or a
crocodile, inside an egg.
How can we understand these processes? Is this a good analogy?
Interactions between millions of relatively unintelligent termites can produce
termite cathedrals with amazingly complex internal structures
https://www.nationalgeographic.com/news/2014/8/140731-termites-mounds-insects-entomology-science/
Even more surprisingly, interactions between millions (billions?) of increasingly "intelligent" molecular assembly mechanisms during development in a plant seed, chicken egg, or mammalian foetus, are crucial to construction of most of the visible organisms on this planet, including plants and animals.
During those construction processes (in an egg, seed lying in soil, or a womb) how much is known about all the different stages of construction, and how much of the process is just local self-organisation -- like poured pebbles forming a heap through local interactions? Are there additional processes analogous to construction of scaffolding, or components to be assembled, or tools for assembly, or control sub-systems for controlling the tools?
As far as I can tell, many, or most, of the details of the intermediate stages in such construction processes are still unknown, although evidence is accumulating in uncoordinated research in a variety of scientific and engineering disciplines, including biochemistry, embryology, and immunology.
The results will need to be combined in the philosophical (metaphysical, meta-biological) project outlined here.
Evolution confronts spatial complexity
As assembled structures become more complex, so must the mechanisms extending
and combining those structures.
So if a developing organism in an egg acquires more interconnected interacting parts, then the mechanisms controlling further development will become more complex. In an egg these developments start before there is a brain. There must be mechanisms in the egg that are capable of building and manipulating continuously changing structures. Could those mechanisms also be responsible for some ancient forms of reasoning about continuous space?
The increasing complexity of such reasoning may include:
(i) increased size of the chemical structures involved in the construction processes,
(ii) increased complexity of the information required for selecting and executing next steps in the construction and
(iii) increased complexity of the mechanisms required to acquire and use the information.
I suspect there is already a lot more known about such mechanisms than I am aware of, though its full significance for reproductive processes may not yet be known! The existence of newly hatched chicks, crocodiles and other self-assembled organisms is evidence for the existence of the mechanisms, but not the details of their operation, nor my claim that as the assembly progresses, new assembly mechanisms must be constructed to deal with greater complexity of the assembly tasks, including use of increasingly complex information-based control mechanisms.
In cases where the assembly continues without any interaction with details of the environment that the organism will later inhabit, the competences produced in the new chic, or other hatchling, cannot be derived from trial and error learning mechanisms, such as neural nets used to gain information about the environment by interacting with it.
These ideas lead to a (still under-developed) biology-based interpretation of Immanuel Kant's theory of mathematical consciousness, referring to evolutionary and developmental precursors of spatial consciousness in vertebrates, and some other spatially intelligent species, such as octopuses Godfrey-Smith (2017).
Meta-configured genomes
The relationship between what is explicitly in the genome, i.e. directly
encoded in DNA, and the "long range" influence of the genome in an adult
organism is complex and indirect. This is perhaps clearest in the case of human
linguistic competences: only the human genome, among known species, has the
ability to produce adult individuals communicating and understanding (giving and
receiving information) in a rich human language.
But the languages used for communication by adult humans vary enormously, in syntactic structures used, semantic contents expressed, communicative functions, and the modes of production (e.g. spoken languages, signed languages, written languages, typed languages (using keys on a computer keyboard), and the skin-contact language developed by Helen Keller's teacher Anne Sullivan for communication with the deaf and blind child. (See https://en.wikipedia.org/wiki/Helen_Keller).
Such diversity in the relationships between what is in the genome and the long
term effects of genome contents raises serious challenges for simple
theories of what genes are, what they can do, and how they are related to their
products. Compare the criticisms in
Godfrey-Smith(2007).
(Note: Unpublished research by Francesca Bellazzi at Reading University is also relevant.)
The Meta-Configured genome (MCG) theory, initially developed with biologist
Jackie Chappell, and more recently with Peter Tino, attempts to show how this
lack of specificity in the genome can illustrate both the great power of
products of biological evolution and the diversity of mechanisms and
sub-processes used in gene-expression. An introduction to the MCG idea
(including a short video) can be found here:
http://www.cs.bham.ac.uk/research/projects/cogaff/movies/meta-config
Gene expression in a Meta-Configured Genome
Cascaded, staggered, developmental trajectories, in complex organisms, in which
later processes of gene expression (down arrows more to the right) use
"parameters" acquired from results of earlier processes (down arrows more to the
left) in increasingly complex ways.
In human versions of these mechanisms, spatial-cognitive abilities concerned with perception and action are later extended by additional self-reflective mechanisms, used in diagnosing flaws in behaviours, repairing them, or teaching them to others. The development of linguistic competences (whether spoken, signed, written or (nowadays) typed language) illustrates complexities of meta-configured genomes.
Some non-human primates share aspects of these competences -- partly illustrated by their ability to engage in various kinds of play with humans and among themselves (e.g. between parents and offspring) found in orangutans and gorillas, for example. Compare the complex relations between humans and some varieties of dogs (e.g. sheep-dogs).
What goes on in eggs, or in a womb?
Recent (unpublished) extensions of the Meta-configured Genome theory suggest
that in addition to the externally observable multi-stage changes in competences
there are also unobservable multi-stage changes in competences used
within developing individuals before they emerge from eggs or wombs, including
multi-stage processes in chicken eggs, crocodile eggs, and other eggs, producing
increasingly complex internal structures and internal behavioural competences
that repeatedly extend/enrich the processes of development used to produce the
new chicks or baby crocodiles that eventually emerge from their eggs ready to
perform quite complex actions (e.g. chicks pecking for food and following the
hen) very soon after emerging from the egg.
Similar comments can be made about processes in a mammalian womb, though there are more complex pre-natal interactions with the mother than in the case of egg-laying species.
This completely undermines currently fashionable theories that assume all complex intelligent behaviours must be products of extended processes of learning by interacting with the environment in order to train neural nets.
Such theories also fail to take account of the fact that some (proto-mathematical) spatial reasoning competences include abilities to recognize examples of impossibility and necessity, which, as Kant pointed out, cannot be based on empirical learning. Impossibility and necessity cannot even be expressed in standard neural net models that deal only with probabilities.
I am trying to provide a window into a large, mostly unexplored, jungle of ideas, in which some old philosophical problems are related to previously unnoticed aspects of biological evolution and development in a variety of species, including humans. The still incomplete theory being developed includes:
-- complexity and diversity of evolved abilities to develop competences
relating to external spatial structures and processes and many internal
structures and processes: at one extreme, competences of single-celled organisms,
through species using increasingly complex chemically controlled biochemical
construction processes during reproduction and early development, especially in
more recently-evolved organisms such as vertebrates born or hatched with
extremely complex physical bodies combined with very powerful,
extendable control mechanisms with many layers of complexity, including
mechanisms for
internal behaviours such as production and growth of new body parts, development
of mechanisms for digestion of food, tissue repair, waste disposal, immune
responses, and many more.
-- e.g. processes in hatching eggs of chickens, alligators, etc., during which increasingly complex and varied body-parts are assembled in increasingly complex and varied relationships, before new individuals emerge from the shells,
-- based partly on multi-layered construction of new construction mechanisms within unhatched eggs,
-- including mechanisms for constructing information-based control mechanisms
complex developmental processes within eggs, at later stages,
-- especially in organisms born or hatched with significant pre-assembled cognitive competences, e.g. newly hatched chicks, ducklings, baby crocodiles, with spatial competences, and even some mammals (deer) that find their way to the mother's nipple and run with the herd soon after birth,
--
and increasingly complex and diverse developmental processes across evolutionary
time scales (compare insects and vertebrates),
--
evolving increasingly complex metaphysical creativity of developmental
processes,
--
using increasingly complex and varied biochemical mechanisms in those
developmental and evolutionary processes,
--
far beyond the scope of "neural net"-based explanations of spatial
intelligence (e.g. since neural nets cannot discover, or even represent,
necessity or impossibility),
--
with deep implications for neuroscience, philosophy of mathematics and
philosophy of mind, including varieties of consciousness,
--
and philosophical relevance of aspects of a wide variety of scientific
research fields, including physics, biochemistry, developmental biology,
immunology, sub-cellular neural mechanisms, neural abnormalities and their
effects,
despite many remaining deep gaps in our current knowledge about such processes.
Notes:
--
Some of these ideas were triggered by reading
Erwin Schrödinger's ideas in What is life? (1944) regarding the
importance of quantum mechanisms for reliable reproduction.
--
Compositionality is normally thought of as a feature of human languages.
However there is a more general concept that is applicable to many of the
processes of evolution and development referred to above, as discussed in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/compositionality.html
There is fragmentary evidence that Alan Turing was thinking about a project of this sort when he wrote his 1952 paper on chemistry-based morphogenesis, explaining formation of surface patterns on organisms, while his unstated long-term intention was much deeper and more important than explaining how visible patterns form. The label "Meta-Morphogenesis" was introduced to refer to that more ambitious project in Sloman(2013).
\cite{Sloman-Turing--4}.
Continued development of
the project since then is reported in a growing collection of online documents referenced in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/meta-morphogenesis.html
,
which include a theory of evolved construction-kits, including construction-kits
created during processes of development of individual organisms in fertilized
eggs, or seeds.
There seems to be little or no recognition of these processes and their implications in current philosophy of mind, psychology, neuroscience and AI. So theories developed in those fields are incapable of producing adequate explanations of a variety of phenomena, including spatial learning and reasoning in many species, ancient processes of mathematical discovery in geometry and topology, long before Euclid, and important aspects of human consciousness, including forms of proto-consciousness involved in multiple layers of increasingly complex information-based control mechanisms during development from fertilised eggs. Insofar as the key processes crucially involve both discrete and continuous change they cannot be fully replicated on digital computers, though they can be implemented in chemical processes for reasons pointed out in Schrödinger's 1944 Book, though he apparently did not notice their importance beyond explaining the possibility of reliable biological reproduction.
Development of this "tangled network" of ideas began in 1958/9 when I switched from mathematics to philosophical research on the nature of mathematical discovery, defending Kant's view of mathematical knowledge as non-empirical, synthetic (not derived from definitions using logic), and concerned with necessary truths and necessary falsehoods (impossibilities). This led to a DPhil thesis (Oxford) in 1962. I later felt the claims and arguments could be improved, after encountering Artificial Intelligence, and learning to program, starting around 1970. A book, The Computer Revolution in Philosophy, resulted in 1978. It was later digitised and placed online at http://www.cs.bham.ac.uk/research/projects/cogaff/crp/ then repeatedly updated/extended with references to related AI topics and projects.
A full account of what minds and brains can do would have to explain how ancient mathematical brains made discoveries in geometry and topology centuries before Euclid, using forms of spatial reasoning processes that make it possible to detect examples of impossibility and necessity. I don't think anyone currently understands how brains represent and detect, spatial/geometric impossibility and necessity.
This is not a general requirement for models of mind, e.g. models of affective
states and processes, e.g. desires, emotions, attitudes, etc. using
information-processing architectures containing multiple interacting
sub-systems, discussed in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/vm-functionalism.html
In contrast, pre-verbal human toddlers, illustrated in http://www.cs.bham.ac.uk/research/projects/cogaff/misc/toddler-theorems.html nest-building in weaver-birds and crows, and spatial intelligence in squirrels, elephants, orangutans, dolphins, octopuses and many other species, require abilities to represent and reason about necessity and impossibility, closely related to ancient mathematical abilities. Probabilistic neural nets cannot represent or reason about these modalities.
There is still a great deal to explain about varieties of spatial monitoring and control not only in whole organisms but also in enormously complex and little understood chemical control and assembly processes in eggs that produce chickens, alligators and other animals, and in related construction processes and mechanisms in mammalian reproduction.
I am sure that if Alan Turing had not died in 1954 he would by now have taken these ideas much further than I have -- and in the process explaining his obscure distinction between mathematical intuition and mathematical ingenuity. https://www.cs.bham.ac.uk/research/projects/cogaff/misc/turing-intuition.html
I suspect Turing would have agreed that Mary Pardoe's (re-) discovery of the non-standard proof of the triangle sum theorem, presented above, was an example of use of mathematical intuition. She found that her students understood and remembered it more easily than the standard Euclidean proof that depends on properties of parallel lines.
Note for philosophy teachers
I suggest that, in view of what we now know about life, and the rate at which
such knowledge is being extended, teaching philosophy of mind and philosophy of
mathematics without teaching any evolutionary and developmental biology is
educationally misguided.
https://www.youtube.com/watch?v=PhOqP_GasVs
Baby Crocs Hone Hunting Skills -- National Geographic
https://www.youtube.com/watch?v=nOkq69T6j7E
Ducklings first feed after hatching. First Swimming baby ducks.
Hatched without mother. (Incubated??)
https://www.youtube.com/watch?v=9jRSgZVhWvw
Baby chicks with hen.
https://www.youtube.com/watch?v=OsoNKlyFtpI
Chimpanzees React to Their Reflections in a Mirror
CenterForGreatApes
https://video.nationalgeographic.com/video/00000144-0a34-d3cb-a96c-7b3dd2970000
Mother crocodile takes babies swimming, to hunt for food.
William Bechtel, Adele Abrahamsen and Benjamin Sheredos, (2018), Using diagrams to reason about biological mechanisms, in Diagrammatic representation and inference, Eds. P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz and F. Bellucci, Springer, https://doi.org/10.1007/978-3-319-91376-6_26
Godfrey-Smith, P. (2007). Innateness and Genetic Information. In P. Carruthers,
S. Laurence, & S. Stich (Eds.),
The Innate Mind Volume 3: Foundations and the Future
(pp. 55-105). OUP.
https://petergodfreysmith.com/PGS-InfoAndInnate.pdf
Godfrey-Smith, P. (2017). Other Minds: The Octopus and the Evolution of Intelligent Life, William Collins.
Carl G. Hempel (1945), Geometry and Empirical Science, in American Mathematical Monthly, 52, 1945, also in Readings in Philosophical Analysis eds. H. Feigl and W. Sellars, New York: Appleton-Century-Crofts, 1949, http://www.ditext.com/hempel/geo.html
Kant, Immanuel (1781). Critique of pure reason, (Translated (1929) by Norman Kemp Smith), London: Macmillan. Retrieved from https://archive.org/details/immanuelkantscri032379mbp/page/n10/mode/2up
Piaget, J. (1952). The Child's Conception of Number. London: Routledge & Kegan Paul.
Schrödinger, E. (1944). What is life? Cambridge: CUP.
A. Sloman, (1965) `Necessary', `A Priori' and `Analytic', in Analysis 26, pp. 12--16, http://www.cs.bham.ac.uk/research/projects/cogaff/62-80.html#1965-02
Sloman, A. (2013). Virtual machinery and evolution of mind (part 3) Meta-morphogenesis: Evolution of information-processing machinery. In S. B. Cooper & J. van Leeuwen (Eds.), Alan Turing - His Work and Impact (p. 849-856), Amsterdam: Elsevier. http://www.cs.bham.ac.uk/research/projects/cogaff/11.html#1106d
Aaron Sloman, 2013,
Virtual Machinery and Evolution of Mind (Part 3)
Meta-Morphogenesis: Evolution of Information-Processing Machinery,
in
Alan Turing - His Work and Impact,
Ed. S. B. Cooper and J. van Leeuwen,
pp. 849-856,
Elsevier,
Amsterdam,
9780123869807,
http://www.cs.bham.ac.uk/research/projects/cogaff/11.html#1106d
A. M. Turing, 1952, The Chemical Basis Of Morphogenesis,
Phil. Trans. R. Soc. London B 237, 237, pp. 37--72,
https://www.cs.bham.ac.uk/research/projects/cogaff/movies/apa/videos.txt
https://www.youtube.com/watch?v=9jRSgZVhWvw
Hens and chicks
MURGI Hen Harvesting Eggs to Chicks new "BORN" Roosters and Hens Small Birds
https://www.youtube.com/watch?v=QPqcSKhtxKk
Ducklings around the lake. (4.24 starting to paddle)
https://www.youtube.com/watch?v=KBm698UoROs
Newly Hatched Ducklings [2008] --
All waiting for last eggs to hatch.
'Peak hype': why the driverless car revolution has stalled
https://www.youtube.com/watch?v=QPqcSKhtxKk
PYTHAGORAS wikipedia
https://en.wikipedia.org/wiki/Pythagorean_theorem
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham