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• W205125582 abstract "This presentation will consider different modes of proof that may be appropriate in mathematics and the kinds of belief that underpin them. In particular, it will distinguish between three distinct worlds of mathematical thought: the embodied, the proceptual (using symbols as process and concept in arithmetic and algebra) and the formal. Embodied proof builds from our interaction with the outside world through our senses. It is capable of sophisticated development through language and human interaction to encompass subtle arguments about models of the world, such as Euclidean Geometry. Proceptual proof refers to the use of symbols in arithmetic and algebra (and the wider theory of procepts in which symbols operate dually as process and concept) where a statement can be proved through calculation and manipulation. Formal proof is built by formal deduction from axioms and concept definitions to construct coherent mathematical systems. The presentation will make the case that each of these forms of proof inhabits its own mathematical world of thought with distinct criteria for belief and truth. This will be used to shed light on the mental constructions required for different modes of proof and on the range of cognitive tasks experienced by individuals in their quest for understanding." @default.
• W205125582 created "2016-06-24" @default.
• W205125582 creator A5057983489 @default.
• W205125582 date "2002-01-01" @default.
• W205125582 modified "2023-09-27" @default.
• W205125582 title "Differing Modes of Proof and Belief in Mathematics" @default.
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