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005 20160413122649.0
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008 121205s2013 ne | s |||| 0|eng d
020 _a9789400753013
_9978-94-007-5301-3
024 7 _a10.1007/978-94-007-5301-3
_2doi
050 4 _aBC1-199
072 7 _aHPL
_2bicssc
072 7 _aPHI011000
_2bisacsh
082 0 4 _a160
_223
100 1 _aGeldsetzer, Lutz.
_eauthor.
245 1 0 _aLogical Thinking in the Pyramidal Schema of Concepts: The Logical and Mathematical Elements
_h[electronic resource] /
_cby Lutz Geldsetzer, Richard L. Schwartz.
264 1 _aDordrecht :
_bSpringer Netherlands :
_bImprint: Springer,
_c2013.
300 _aXLIV, 140 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
520 _aThis new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual  expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.
650 0 _aPhilosophy.
650 0 _aLogic.
650 0 _aMathematical logic.
650 1 4 _aPhilosophy.
650 2 4 _aLogic.
650 2 4 _aMathematical Logic and Formal Languages.
650 2 4 _aMathematical Logic and Foundations.
700 1 _aSchwartz, Richard L.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789400753006
856 4 0 _uhttp://dx.doi.org/10.1007/978-94-007-5301-3
912 _aZDB-2-SHU
942 _2Dewey Decimal Classification
_ceBooks
999 _c48553
_d48553