Christopher Peter ORMELL

Christopher Peter ORMELL, Senior Fellow, EDU, University of East Anglia, Norwich, England NR4 7TZ. Education: Maths and Philosophy degrees at Oxford. Interest in Popper: epistemology, theory of self-reference, philosophy of science. Publications: About 90 articles in Journals and books. My most recent paper is in the Cambridge Journal of Education, 18, 2, 1988, "Is there a future for Liberal Education?". Activities: Editor-in-Chief Mathematics Applicable Group (Mag), Educationalist. During the period 1982-85 I wrote four monographs on understanding during the period 1982-85. The four monographs form a sustained argument which begins with a re-examination of the applicability of mathematics. By pinning down the 'use' of mathematics it is possible to formulate a new and more powerful version of the empiricist view of meaning (Vol.2). This is then applied in Vol.3 to derive a wholly 'naturalistic' view of meaning in pure mathematics. It is argued that Cantor's 'Diagonal Argument' has been seriously misunderstood by successive commentators. It cannot tell us that there are more real numbers than rationals because any realnumber with accredited existence has a generating rule and this can be embedded in the 'greater lexicographic ordering' - a lexicographic ordering of all the symbols ever used by the human race. The reals are, indeed, 'uncountable' but not for reasons of numerousness. Vol. 4 is an ambitious attempt to drive a Popperian-Lakatosian view of science to the limit. It studies the fitness of mathematics to give us the best possible models of physical reality and finds it wanting. This leads to the specifications of a new quasi-mathematical science beyond mathematics which does meet the requirement for models in science. The result is therefore to open up a new kind of scientific (i.e. falsifiable) theorising. These monographs were published by the MAG, EUD, UEA Norwich NR4 7TJ, U.K..