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Machines, Logic and Quantum Physics

Published online by Cambridge University Press:  15 January 2014

David Deutsch ,
Artur Ekert  and
Rossella Lupacchini
David Deutsch
Affiliation:
Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, Ox1 3Pu, U.K. E-mail: david.deutch@qubit.org
Artur Ekert
Affiliation:
Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, Ox1 3Pu, U.K. E-mail: E-mail: artur.ekert@qubit.org
Rossella Lupacchini
Affiliation:
Dipartimento Di Filosofia, Università Di Bologna, Via Zamboni 38, 40126 Bologna, Italy.
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Extract

§1. Mathematics and the physical world. Genuine scientific knowledge cannot be certain, nor can it be justified a priori. Instead, it must be conjectured, and then tested by experiment, and this requires it to be expressed in a language appropriate for making precise, empirically testable predictions. That language is mathematics.

This in turn constitutes a statement about what the physical world must be like if science, thus conceived, is to be possible. As Galileo put it, “the universe is written in the language of mathematics”. Galileo's introduction of mathematically formulated, testable theories into physics marked the transition from the Aristotelian conception of physics, resting on supposedly necessary a priori principles, to its modern status as a theoretical, conjectural and empirical science. Instead of seeking an infallible universal mathematical design, Galilean science usesmathematics to express quantitative descriptions of an objective physical reality. Thus mathematics became the language in which we express our knowledge of the physical world — a language that is not only extraordinarily powerful and precise, but also effective in practice. Eugene Wigner referred to “the unreasonable effectiveness of mathematics in the physical sciences”. But is this effectiveness really unreasonable or miraculous?

Numbers, sets, groups and algebras have an autonomous reality quite independent of what the laws of physics decree, and the properties of these mathematical structures can be just as objective as Plato believed they were (and as Roger Penrose now advocates).

Information

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 6 , Issue 3 , September 2000 , pp. 265 - 283
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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