Discussion of some themes in Piaget's two books on
Possibility and Necessity

These notes are available here:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/piaget-possibility-necessity.html
(A PDF version, generated automatically, may be added later.)

Notes For a Joint Meeting of AINC in Computer Science with Developmental Psychology Seminar
Aaron Sloman
School of Computer Science, University of Birmingham.

Installed: 14 Feb 2011
Last updated:
20 Feb 2011; 23 Feb 2011; 11 May 2011; 4 Mar 2013; 16 Jul 2014

Slides (PDF) for the presentation on this topic are available at
http://www.cs.bham.ac.uk/research/projects/cogaff/talks/#talk90

It is not widely known that shortly before he died Jean Piaget and his collaborators
produced a pair of books on Possibility and Necessity, exploring questions about how two
linked sets of abilities develop:

1. The ability to think about how things might be, or might have been, different from the
   way they are.
2. The ability to notice limitations on possibilities, i.e. what is necessary or
   impossible.

• Piaget, Jean, et al.,
  Possibility and Necessity
  Vol 1. The role of possibility in cognitive development,
  University of Minnesota Press,
  Tr. by Helga Feider from French in 1987, (Original 1981)

• Piaget, Jean, et al.,
  Possibility and Necessity
  Vol 2. The role of necessity in cognitive development,
  U. of Minnesota Press,
  Tr. by Helga Feider from French in 1987, (Original 1983)

I believe Piaget had deep insights into important problems for cognitive science that have
largely gone unnoticed, and are also important for research on intelligent robotics, or
more generally Artificial Intelligence (AI), as well as for studies of animal cognition
and how various animal competences evolved and develop.

These topics are relevant to understanding biological precursors to human mathematical
competences and to resolving debates in philosophy of mathematics, e.g. between those who
regard mathematical knowledge as purely analytic, or logical, and those who, like Immanuel
Kant, regard it as being synthetic, i.e. saying something about reality, despite
expressing necessary truths that cannot be established purely empirically, even though
they may be initially discovered empirically (as happens in children).

It is not possible in one seminar to summarise either book, but I shall try to present an
overview of some of the key themes and will discuss some of the experiments intended to
probe concepts and competences relevant to understanding necessary connections.

Presentation overview:I hope to explain

1. The relevance of Piaget's work to the problems of designing intelligent machines that
   learn the things humans learn.
   (Most researchers in both Developmental Psychology and AI/Robotics have failed to notice
   or have ignored most of the problems Piaget identified.)

2. How a deep understanding of AI, and especially the variety of problems and techniques
   involved in producing machines that can learn and think about the problems Piaget
   explored, could have helped Piaget describe and study those problems with more clarity and
   depth, especially regarding the forms of representation required, the ontologies required,
   the information processing mechanisms required and the information processing
   architectures that can combine those mechanisms in a working system -- especially
   architectures that grow themselves.

Implications

That kind of computational or "design-based" understanding of the problems can lead to
deeper clearer specifications of what it is that children are failing to grasp at various
stages in the first decade of life, and what sorts of transitions can occur during the
learning. I believe the problems, and the explanations, are far more complex than even
Piaget thought.

The potential connection between his work and AI was appreciated by
Piaget himself only very shortly before he died, acknowledged at a workshop
on AI and Genetic Epistemology in Geneva 1981

Importance of Piaget's ideas

I now think that Piaget's experiments were important and based on some insights that are
not widely shared, but that his theoretical framework for analysing and presenting the
results is flawed because of his "Stage Theory" of development.

In contrast, Annette Karmiloff-Smith's book Beyond Modularity misses out some of
the important topics discussed by Piaget, but has a better theory of development (though
still in need of refinement -- as she is aware).

I discuss Beyond Modularity informally in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/beyond-modularity.html

Related papers and presentations

Oxford DPhil Thesis 1962,
Knowing and Understanding: Relations between meaning and truth,
meaning and necessary truth, meaning and synthetic necessary truth,
http://www.cs.bham.ac.uk/research/projects/cogaff/07.html#706

Necessary', 'A Priori' and 'Analytic', in Analysis vol 26, No 1, pp 12-16 1965.
http://www.cs.bham.ac.uk/research/projects/cogaff/07.html#701

Interactions between philosophy and AI:
The role of intuition and non-logical reasoning in intelligence,
in Proc 2nd IJCAI, 1971, London, pp. 209--226, (Also published in AI Journal, 1971)
http://www.cs.bham.ac.uk/research/cogaff/04.html#200407

Actual Possibilities, in Principles of Knowledge Representation and Reasoning:
Proc. 5th Int. Conf. (KR `96),
Eds. L.C. Aiello and S.C. Shapiro, Boston, MA, 1996, pp. 627--638,
http://www.cs.bham.ac.uk/research/cogaff/96-99.html#15

And more recent papers and presentations on varieties of affordance, perception of motion,
reasoning with diagrams, toddler theorems, philosophy of mathematics, evolution of
mathematics, etc., including:

(Added: 4 Mar 2013)
http://tinyurl.com/CogMisc/triangle-theorem.html
"Hidden Depths of Triangle Qualia"
(Theorems about triangles, and Implications for Biological Evolution and AI)

Notes for a related talk at AGI 2011 At Google, 3rd--6th August 2011
Toddler Theorems
Reasoning about shapes: curves on a torus.
Biology, Mathematics, Philosophy, and Evolution of Information Processing

Slides from previous related talks are available here.

For more information see presentations on "toddler theorems" and
"Philosophy of mathematics" here:
http://www.cs.bham.ac.uk/research/projects/cogaff/talks/

Maintained by Aaron Sloman
School of Computer Science
The University of Birmingham