Picture-proofs and Greek construction
Degree GrantorUniversity of Canterbury
Justification in mathematics is a very particular thing; no other field has such high standards placed on the notion of ‘proof’. There is justification and there is evidence. That non-deductive methods have long been seen as belonging to the latter category is uncontroversial. One contrarian to this view is Brown and his belief in a kind of non-deductive justification he calls ‘picture-proofs’. Brown's most recent and thorough treatment of picture-proofs is found in Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures published in 2008; the discussions contained therein will form the basis for this paper. This belief in picture-proofs will be placed in the context of the highly visual culture of Greek mathematics and through this, conclusions will be drawn about the validity and usefulness of these picture-proofs. Sections 1-3 will be devoted to the discussion of picture-proofs and Brown's argument for their existence. In this discussion, further arguments will be provided to supplement Brown's own with the view to establishing the strongest possible account of picture-proofs. Section 4 will consider the role of pictures in Greek mathematics and will introduce the question of whether Brown's interpretation of pictures has a place within Greek mathematics. Section 5 will clearly state what it means to assess Brown's view in the context of Greek mathematics. Following this, an attempt will be made to argue that Brown's views are consistent with Greek mathematics. Section 6 will attempt to bring these ideas together in an example from Euclid. Finally, Section 7 will discuss the state of picture-proofs given the conclusions so far drawn from the paper.
SubjectsField of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010107 - Mathematical Logic, Set Theory, Lattices and Universal Algebra
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