A01=Mark Greaves
analytic
Author_Mark Greaves
axiomatic structures
boole
Category=PBB
Category=PBM
Category=QDTL
contemporary formal theories
descartes
diagrams
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
euclidean
extensional graphs
geometers
geometry
graphical properties
kantianism
linguistic formulation
logic
logical systems
math
mathematicians
mathematics
negative perceptions
non-euclidean
philosophers
philosophical research
philosophy
proofs
representational styles
sentential representations
syllogism
venn diagram
Product details
- ISBN 9781575862934
- Weight: 425g
- Dimensions: 16 x 24mm
- Publication Date: 01 Mar 2001
- Publisher: Centre for the Study of Language & Information
- Publication City/Country: US
- Product Form: Hardback
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The use of diagrams in logic and geometry has encountered resistence throughout the years. For a proof to be valid in geometry it must not rely on the graphical properties of a diagram. In logic the teaching of proofs depends on the sentenial representations, ideas formed as natural language sentences such as "if A is true and B is true...". No serious formal proof system is based on diagrams. This text explores the reasons why structured graphics have been ignored in modern formal theories of axiomatic systems. The effects of historical forces on the evolution of diagrammatically-based systems of inference in logic and geometry are explored, from antiquity to the early 20th-century work of David Hilbert. From this exploration emerges an understanding that the present negative attitudes towards the use of diagrams in logic and geometry owe more to implicit appeals to their history and philosophical background than to any technical incompatibility with modern theories of logical systems.
