Charles Babbage used an example suggested by the computational power of his calculating engine to suggest that ‘miraculous events’ might be as lawful as the regularities presumed by ‘vast inductions’. In this paper I revisit the issue by employing a simple shape grammatical example. Induction and emergence are contrasted.
DiamondC, 1976Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 (Harvester Press, Hassocks, Sussex).
3.
HodgesA, 1983Alan Turing: The Enigma (Hutchinson, London).
4.
JamesW, 1907Pragmatism (Longman, Green, New York).
5.
MarchL, 1976, “The logic of design and the question of value”, in The Architecture of Form Ed. MarchL, (Cambridge University Press, Cambridge) pp 1–40.
6.
RussellB, 1919Introduction to Mathematical Philosophy (George Allen and Unwin, London).
7.
StewartI, 1989Does God Play Dice? The Mathematics of Chaos (Basil Blackwell, Oxford).
8.
StinyG, 1975Pictorial and Formal Aspects of Shape and Shape Grammars (Birkhauser, Basel).
9.
StinyG, 1994a, “Shape rules: Closure, continuity, and emergence”Environment and Planning B: Planning and Design21s49–s78.
10.
StinyG, 1994b, “Sketch 3: Freedom to March in Planning and Design”Environment and Planning B: Planning and Design21s5–s6.
11.
WittgensteinL, 1956Remarks on the Foundations of Mathematics Eds von WrightG HRheesRAnscombeG E M; 3rd edition, revised and reset, 1978 (Basil Blackwell, Oxford).