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Extra info for Comprehensive Process Improvement Methodology: Experiences at Caterpiller's Mossville Engine Center (MEC)

Example text

This is simultaneously a reflection and consequence of the role of figures in his argument. On the one hand, a figure is a specific instance of boundary and being bounded so that by constructing figures through problems or QEF propositions Euclid is constructing ‘solutions’ to the general problem located by Definitions 6 and 7. On the other hand, a figure is also defined by its boundary so that by analysing their boundaries and the parts thereof Euclid can prove theorems or QED propositions about figures.

Whatever doubts and controversies have surrounded the larger Hilbert programme, GdG has remained a model of the axiomatic method and its publication has been hailed as the dawn of modern ‘abstract’ mathematics. Once again, in common with Descartes, Hilbert begins his text with a‘problem’, but his ‘problem’ does not in the slightest resemble a Cartesian construction and from this point forward the reader notices 32 FIGURES OF THOUGHT a curious set of points of contact and divergence between the two texts.

3. A closer look at the text once again provides the clue. e. to demonstrate that no one of the axioms can be deduced as a logical consequence of any of the others. His proof of independence involves the construction of geometries— systems whose elements satisfy some but not all of the original axioms. As the total original collection was consistent, any subcollection will also be consistent so its ‘geometry’ will ‘exist’. By then constructing models of these geometries, Hilbert demonstrates that the axiom sets can be assumed to apply or not to apply independently of one another.

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