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  • A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. These are 'natural' concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descendants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called formally sound and complete iff it proves all and only formulas valid in this sense. Though the step from material to formal validity and completeness may seem to be merely an unproblematic case of explication, I argue that it is not; and that mistaking the latter concepts for the former ones may lead to serious conceptual confusions.
  • A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. These are 'natural' concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descendants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called formally sound and complete iff it proves all and only formulas valid in this sense. Though the step from material to formal validity and completeness may seem to be merely an unproblematic case of explication, I argue that it is not; and that mistaking the latter concepts for the former ones may lead to serious conceptual confusions. (en)
Title
  • Two Concepts of Validity and Completeness
  • Two Concepts of Validity and Completeness (en)
skos:prefLabel
  • Two Concepts of Validity and Completeness
  • Two Concepts of Validity and Completeness (en)
skos:notation
  • RIV/00216208:11210/10:10057547!RIV12-GA0-11210___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA401/06/0387)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 293851
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11210/10:10057547
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • completeness; validity; formal logic (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [95A8A4BFE451]
http://linked.open...i/riv/nazevZdroje
  • Acta Universitatis Carolinae. Philosophica et Historica
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2007
http://linked.open...iv/tvurceVysledku
  • Peregrin, Jaroslav
issn
  • 0567-8293
number of pages
http://localhost/t...ganizacniJednotka
  • 11210
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