TY - JOUR
T1 - Reasoning with truth
AU - Roeper, Peter
PY - 2010
Y1 - 2010
N2 - The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the metalanguage and in the object language, of paradoxical and 'truth teller'-like sentences.
AB - The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the metalanguage and in the object language, of paradoxical and 'truth teller'-like sentences.
KW - Definite truth
KW - Groundedness
KW - Paradoxical sentence
KW - Tarski schema
KW - Truth
KW - Truth-preserving inference
UR - http://www.scopus.com/inward/record.url?scp=77952313922&partnerID=8YFLogxK
U2 - 10.1007/s10992-010-9124-8
DO - 10.1007/s10992-010-9124-8
M3 - Article
SN - 0022-3611
VL - 39
SP - 275
EP - 306
JO - Journal of Philosophical Logic
JF - Journal of Philosophical Logic
IS - 3
ER -