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Arthur asks about the traditional philosophical distinction between invention and discovery in mathematics, and whether mathematical things exist. James replies that anything that exists and is capable of change is physical. He says that discovery relates to pre-existing physical things, whereas invention relates to the original construction of physical things. He says that mathematical things are not physical and do not exist in themselves, but the idea of mathematical things exists and is physical. Arthur disputes this account of physicality. He asks how a mathematical equation can have feelings. James replies that feelings are physical, that mathematical equations do not exist in themselves, and cannot have feelings, but that mathematical equations that exist and change by virtue of being executed on a computer are physical and can have a physical content of feeling. Thus there is no conceptual gap between the mathematical definition of feeling and its physical content. He gives some examples of the feelings that a robot might have.


Dean asks how a robot can have free will. James says that when a robot constructs geometrical perspexes to describe the geometry of the objects it sees, it can re-interpret the geometrical perspexes as programs, thereby extending its original programs. And it can do this as an automatic consequence of its perceptions, thoughts, and actions. Dean debates this and asks how robots can be creative. James gives an algorithm for creativity by constructing a particular dual of an algebraic perspex program. Dean challenges James over some theological issues. Dean then asks if humans are superior to robots because they can think of incomputable things. James agrees that this might be so, but says that it is logically impossible to give a scientific explanation of such an ability, because all scientific explanations are mechanistic and everything that is mechanistic is computable.

© James A.D.W. Anderson, 2001. All rights reserved. Home: http://www.bookofparagon.btinternet.co.uk