"For mathematics is after all an anthropological phenomenon."
(Wittgenstein, Remarks on the Foundations of Mathematics)
No, though it is partly a biological phenomenon.
29 Aug 2013
13 Jul 2018; 24 Mar 2019; 4 Apr 2019
22 Sep 2013; 21 Nov 2013; 9 Sep 2014; 7 Dec 2014; 29 Mar 2015; 4 Sep 2016;
N.B. The order of items listed here is not significant.
The order may be revised later.
Many of the documents are available in both html and pdf formats.
If you prefer pdf, try changing the url to end in 'pdf'. If that
fails restore the 'html' suffix.
Key Aspects of Immanuel Kant's Philosophy of Mathematics
Ignored by most psychologists and neuroscientists
studying mathematical competences
The Triangle Sum Theorem
(Old and new proofs, including Mary Pardoe's Proof, using a
rotating arrow, or pencil.)
Triangle Qualia/Triangle Theorems
Hidden Depths of Triangle Qualia (Especially their areas.)
Theorems About Triangles, and Implications for Biological Evolution and AI
The Median Stretch, Side Stretch, and Triangle Area Theorems:
old and new proofs.
Toddler theorems (proto-mathematical discoveries) --
what they are and some examples
toddler exploring 3-D topology with
On seeing that X is impossible, and seeing why X is impossible, with a large
collection of examples.
Pardoe Geometry (P-Geometry: adding constrained motion to Euclid)
Compare the "neusis" construction in the next document:
How to trisect an angle in P-geometry. Including a criticism of
Poincaré's philosophy of mathematics.
Alan Turing's 1938 thoughts on intuition vs ingenuity
in mathematical reasoning.
Did he unwittingly re-discover key ideas first presented
in Immanuel Kant's philosophy of mathematics?
Abstract of talk on this to Zurich philosophy students, March 2019.
Non-monotonic angle change as a vertex moves on a line:
Discovery of a necessary connection between two different
continua: variation in location of a point and variation in
size of an angle, easily discovered by non-mathematicians.
(And some surprisingly complex variants of a simple problem.)
Surprisingly Rational Circle Segments
CHAPTER 8 On Learning About Numbers: Problems and Speculations (1978)
Chapter 8 of
The Computer Revolution in Philosophy: Philosophy science and models of mind
Biology, geometry, philosophy of mathematics and Kantian robotics?:
The case of p-geometry and angle trisection
Edinburgh Informatics Forum,
Mathematical Reasoning Group Seminar 25th Aug 2015,
Talk 108: Why is it so hard to make human-like AI (robot) mathematicians?
Especially Euclidean geometers.
Talk at PT-AI 2013 Oxford, 22 Sep 2013
Closely related draft paper:
Extending Turing's Pattern: From Morphogenesis to Meta-morphogenesis
Invited contribution to Cybertalk Magazine, September 2013
Biology, Mathematics, Philosophy, and Evolution of Information Processing
I try to show that biological evolution (blindly) made use of mathematical
domains long before humans existed on this planet -- e.g. the domain of designs
for homeostatic control systems, including negative feedback loops of various
sorts, and sub-domains of the domain of chemically controlled morphogenesis
discussed in Turing (1952), among many others.
Reasoning About Rings and Chains
(Impossible linking and unlinking)
Reasoning about continuous deformations of curves, e.g. on a Torus.
Illustrating topological and semi-metrical reasoning in everyday life.
Knots: discovering theorems about them
From Molecules to Mathematicians:
How could evolution produce mathematicians from a cloud of cosmic dust?
What might Turing have done if he had lived longer?
How might it have helped us understand biological evolution,
and how evolution produced mathematicians?
Notes for a presentation to the Midlands Logic Seminar: 1st November 2013
How can a physical universe produce mathematicians?
Metaphysical, Biological, Evolutionary Foundations for Mathematics
(As opposed to logical or set-theoretic foundations.)
Midlands Logic Seminars, Tuesday 24th Feb 2015
What is Life?
Erwin Schrödinger on the Chemical Basis of Life
This is a collection of extracts from Schrödinger's 1944 book
What is life?
with some comments added by me, mainly trying to clarify what I think he is
saying and why I think it is so important for anyone trying to understand how
life as we know it is possible in this physical universe. This includes
understanding how evolution could have produced mathematicians like Euclid.
The Meta-Configured Genome
Based on collaboration with Jackie Chappell
Different relationships between genome and competences
(Preconfigured vs meta-configured competences: Chappell and Sloman)
Incomplete note on problems of rotation in a discrete space
What could have led to euclidean geometry?
Why is it so hard to get machines to reason like our ancestors
who produced Euclidean Geometry?
Ideas about "Representational
in Annette Karmiloff-Smith's Beyond Modularity (1992)
Abstract for talk to mathematics school leavers
(17 April 2013)
Evolutionary transitions in information-processing
Far more and more varied than most people seem to have noticed?
Did life on earth start on dust particles?
The theory of Nasif Nahle, Monterrey, Mexico. If true this alters some of the domains
of competence required by earliest organisms.
Papers related to mathematics, philosophy, and life in the CogAff web site.
To be pruned, sorted, annotated.
ADDITIONAL ITEMS TO BE MERGED
School of Computer Science
The University of Birmingham