John P. Burgess; Mary Leng. Mathematics and Reality. Oxford: Oxford University Press, 2010. ISBN 978-0-19-928079-7. Pp. x + 278. Philosophia Mathematica 2010; 18 (3): 337-344. doi: 10.1093/philmat/nkq013
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The position of scientific instrumentalism, found with variations in works from Vaihinger's Philosophie des Als Ob to van Fraassen's Scientific Image, has four components as follows.
There is no good justification for believing that atoms and other unobservables exist; so it should be presumed that they do not.
There is no serious hope of being able to explain away the commitment of current science to atoms as merely apparent.
There is no serious hope of being able to develop an alternative science uncommitted to atoms.
It is appropriate to suspend disbelief in atoms when doing science, so long as one recognizes when doing philosophy that atoms are merely useful fictions.
The analogous mathematical instrumentalism consists of parallel components concerning numbers and other abstracta. In the mathematical case,...
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