@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Field,Hartry}, subject = {Consistency}, note = {I 96 Def Strong Consistency/strong consistent/Field: a mathematical theory M is strong consistent, if it causes that the conjunction with a consistent non-mathematical theory T is still consistent. - T + M = consistent. Punch line: although strong consistency does not follow from truth, it follows from necessary truth. - However strong consistency is weaker than necessary truth because strongly consistent theories need not be true. Purely mathematical theories (without mathematical entities): for them consistency involves strong consistency. >Mathematical entities. Non-pure: E.g. set theory with basic elements. Urelement: Element of the lowest level, e.g. real numbers. I 240 Consistency/consistent/Mathematics/FieldVs: consistency is untenable as a condition for the quality of mathematics: a consistent mathematical theory can be largely inadequate. - Consistent (without contradiction) here means semantically consistent, i.e. satisfiable. >Satisfaction, >Satisfiability.}, note = { Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich, Aldershot 1994 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=284961} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=284961} }