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SUMMARY:Picturability and the mathematical ideals of knowledge: Leibniz ve
 rsus Newton - Stephen Gaukroger (University of Sydney and University of Ab
 erdeen)
DTSTART:20091126T163000Z
DTEND:20091126T180000Z
UID:TALK20371@talks.cam.ac.uk
CONTACT:Alex Broadbent
DESCRIPTION:There had been a widely-held view in the seventeenth century t
 hat the Fall had dulled Adam's senses\, and that the use of artificial aid
 s might effect the restoration of their pre-lapsarian acuity. But while th
 ere had also been a widespread view that reason too had been impaired in t
 he Fall\, this was generally diagnosed in terms of the passions triumphing
  over reason\, the remedy being to control the passions. I offer an interp
 retation of Leibniz's account of the calculus as holding that artificial a
 ids can correct reason itself.\n\nNewton developed a version of infinitesi
 mal calculus in the early 1670s but abandoned it on the grounds that it us
 ed procedures that could not be justified. They were black boxes: one put 
 in the premisses and generated the right results\, but had no grasp on wha
 t was going on in the middle. In fact\, both Newton and Leibniz agreed tha
 t infinitesimal calculus required justification in terms of limit procedur
 es\, which were geometrical and open to inspection at every stage. The dif
 ference was that Newton believed that this meant that any procedure using 
 infinitesimal calculus had to be translated into geometrical limit procedu
 res\, whereas Leibniz believed that it was only the general technique that
  had to be justified in terms of limit procedures\, and that\, once this w
 as done\, it was not required that one justify each and every operation em
 ploying infinitesimals in this way. Leibniz's approach is not driven by pr
 agmatic concerns\, however\, but rather by a view that the calculus extend
 s human capacities in new ways into new areas: it goes beyond our natural 
 faculties and hence we cannot expect our natural faculties to be able to l
 egitimate it. This raises the general question of whether we can employ pr
 ocedures of enquiry whose workings transcend our faculties.
LOCATION:Seminar Room 2\, History and Philosophy of Science\, Department o
 f
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