P HILOSOPHICAL F OUNDATIONS OF QUALITATIVE S PATIAL R EASONING ACASE FOR BERTRAND RUSSELL Adam Trybus [email protected]Institute of Philosophy University of Zielona Gora History and Philosophy of Computing Bergamo 2019 Adam Trybus [email protected]University of Zielona Gora Russell and QSR
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A CASE FOR BERTRAND RUSSELL...I Bertrand Russell wrote only two major works where geometry plays an important role: An Essay on The Foundations of Geometry (EFG, 1897) and Philosophy
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PHILOSOPHICAL FOUNDATIONS OF
QUALITATIVE SPATIAL REASONINGA CASE FOR BERTRAND RUSSELL
I Bertrand Russell wrote only two major works wheregeometry plays an important role: An Essay on TheFoundations of Geometry (EFG, 1897) and Philosophy ofMathematics (PoM, 1903)
I His contribution in that respect is, for the most part,forgotten
I These two works are different in many aspects: what iscommon to them is the focus on a special type of geometry
I In fact, this geometry can be seen to underpin all his majorphilosophical works!
I Bertrand Russell wrote only two major works wheregeometry plays an important role: An Essay on TheFoundations of Geometry (EFG, 1897) and Philosophy ofMathematics (PoM, 1903)
I His contribution in that respect is, for the most part,forgotten
I These two works are different in many aspects: what iscommon to them is the focus on a special type of geometry
I In fact, this geometry can be seen to underpin all his majorphilosophical works!
I Bertrand Russell wrote only two major works wheregeometry plays an important role: An Essay on TheFoundations of Geometry (EFG, 1897) and Philosophy ofMathematics (PoM, 1903)
I His contribution in that respect is, for the most part,forgotten
I These two works are different in many aspects: what iscommon to them is the focus on a special type of geometry
I In fact, this geometry can be seen to underpin all his majorphilosophical works!
I Bertrand Russell wrote only two major works wheregeometry plays an important role: An Essay on TheFoundations of Geometry (EFG, 1897) and Philosophy ofMathematics (PoM, 1903)
I His contribution in that respect is, for the most part,forgotten
I These two works are different in many aspects: what iscommon to them is the focus on a special type of geometry
I In fact, this geometry can be seen to underpin all his majorphilosophical works!
logical independence of projective geometry can onlybe maintained by a purely descriptive definition (EFG,p. 122)
“Projective Geometry deals only with quality — forwhich reason it is called descriptive — and cannotdistinguish between two figures which are qualitativelyalike” (EFG, p. 33)
“quantities, as used in PG, do not stand for spatial mag-nitudes but are conventional symbols for purely quali-tative spatial relations” (EFG, p. 36)
logical independence of projective geometry can onlybe maintained by a purely descriptive definition (EFG,p. 122)
“Projective Geometry deals only with quality — forwhich reason it is called descriptive — and cannotdistinguish between two figures which are qualitativelyalike” (EFG, p. 33)
“quantities, as used in PG, do not stand for spatial mag-nitudes but are conventional symbols for purely quali-tative spatial relations” (EFG, p. 36)
logical independence of projective geometry can onlybe maintained by a purely descriptive definition (EFG,p. 122)
“Projective Geometry deals only with quality — forwhich reason it is called descriptive — and cannotdistinguish between two figures which are qualitativelyalike” (EFG, p. 33)
“quantities, as used in PG, do not stand for spatial mag-nitudes but are conventional symbols for purely quali-tative spatial relations” (EFG, p. 36)
’In Geometry, von Staudt’s quadrilateral constructionand Pieri’s work on Projective Geometry have shownhow to give points, lines and planes an order inde-pendent of metrical considerations of quality, while De-scriptive Geometry proves that a very large part of Ge-ometry demands only the possibility of serial arrange-ment. Moreover the whole philosophy of space andtime depends upon the view we take of order’ (PoM, p.201)
“. . . these differences are not very important for ourpresent purpose and it will therefore be convenient tospeak of projective and descriptive Geometry togetheras non-quantitative Geometry.” (PoM, p 425)
Descriptive Geometry applies to Euclidean and hyper-bolic but not elliptic (PoM, p. 405)
“. . . these differences are not very important for ourpresent purpose and it will therefore be convenient tospeak of projective and descriptive Geometry togetheras non-quantitative Geometry.” (PoM, p 425)
Descriptive Geometry applies to Euclidean and hyper-bolic but not elliptic (PoM, p. 405)
I Speaking in modern terms, I claim that both projective andaffine geometry informed Russell’s philosophical ideas
I This can be seen from The Problems of Philosophy (1912),to On Our Knowledge of the External World (1914) even toHuman Knowledge (1948)
I Because of the emphasis he put on the notion of quality ingeometry, Bertrand Russell should be considered one ofthe forefathers of Qualitative Spatial Reasoning paradigm,a subfield of Knowledge Representation and Reasoning
I Speaking in modern terms, I claim that both projective andaffine geometry informed Russell’s philosophical ideas
I This can be seen from The Problems of Philosophy (1912),to On Our Knowledge of the External World (1914) even toHuman Knowledge (1948)
I Because of the emphasis he put on the notion of quality ingeometry, Bertrand Russell should be considered one ofthe forefathers of Qualitative Spatial Reasoning paradigm,a subfield of Knowledge Representation and Reasoning
I Speaking in modern terms, I claim that both projective andaffine geometry informed Russell’s philosophical ideas
I This can be seen from The Problems of Philosophy (1912),to On Our Knowledge of the External World (1914) even toHuman Knowledge (1948)
I Because of the emphasis he put on the notion of quality ingeometry, Bertrand Russell should be considered one ofthe forefathers of Qualitative Spatial Reasoning paradigm,a subfield of Knowledge Representation and Reasoning