|Connectives: connectives are also called logical connectives or logical particles. E.g. and, or, if, then, if and only if. Negation also counts as a connective. See also truth value table, truth table._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Robert Brandom on Connectives - Dictionary of Arguments
Connectives/Gentzen/Brandom: connectives are defined according to their inferential role. (epoch-making): Definition Introduction rules: sufficient conditions for the use of the connective - Definition elimination rules: necessary consequences of the use (of the connective) - E.g. in order to define the inferential role of "&" in Boole you indicate that everyone who is defined on p and q thus has to be regarded as defined on p&q as well - the first part without the connective specifies the circumstances, i.e. the sets of the premises.
Dummett transferred this to sentences, singular terms and predicates - it may be that we do not overlook all connections - conservative extension: by these two rules._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994
Expressive Vernunft Frankfurt 2000
Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001
Begründen und Begreifen Frankfurt 2001