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Conditional: A conditional in logic is a statement that asserts a relationship between two propositions, typically in an "if-then" format. It states that if the antecedent is true, then the consequent must also be true. In contrast to (purely formal) implication, the conditional refers to the content of the propositions. See also Implication.
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.

Author Concept Summary/Quotes Sources

Robert Adams on Conditional - Dictionary of Arguments

Field II 252/296
Material Conditional/Adams Conditional/Field: (Lit. Adams 1974): (outside of mathematics): few of us would agree with the following conclusion: E.g. from

Clinton will not die in office


If Clinton dies in office, Danny de Vito will become President.

That suggests that here the equivalence between A > B and ~(A v B) does not exist.
, >Counterfactual conditional.
In other words: If A then B does not seem to have the same truth conditions as ~A v B.
>Truth conditions.
Adams-conditional: it may only be used as a main operator. - The degree of belief of A > B is always the conditional belef degree (B I A).
>Operators, >Conditional probability.
II 253
In the case of the indicative conditional, the premise is always required. - Adams: intuitively, conclusions with conditionals are correct. Problem: then they will say less about the world.
Indicative conditional sentence/material implication/truth/field: further considerations have however led many to doubt that there are truth conditions here at all.
>Material implication.
Conditional/Field: A > B: here the premise A is always required when concluding. That is, we accept conditional B relative to premise A.
Adams: the idea of contingent acceptance justifies our intuitive beliefs according to which conclusions with conditionals are correct.
Cf. >Presuppositions, >Principle of Charity.
But then it is anything but obvious that conditionals say something about the world. For example, there must not be a statement C whose probability in all circumstances is the same as the conditional (contingent) probability of (B I A). That is, the conditional A > B is not such a C.
N.B.: this shows that we do not have to assume "conditional propositions" or "conditional facts". This is the nonfactualist view.
((s) Truth conditions/nonfactualism/conditional/(s): if there are no facts, then there are also no truth conditions.)
Borderline case: If the conditional (contingent) probability is 0 or 1, it is justifiable that the assertibility conditions (acceptance conditions) are the same as those of the material conditional.
Vs: one could argue that a sentence without any truth conditions is meaningless.
>Assertibility, >Assertibility conditions.
Field: ditto, but the main thing is that one cannot explain the acceptance conditions without the truth conditions in terms of the truth conditions.
>Truth conditions.

1. R. Adams (1974). Theories of Actuality. Nous, 5: 21-231.
Lewis V 133
Conditional/Adams/Adams-conditional/Lewis: is an exception to the rule that the speaker usually expresses nothing that is probably untrue. - Then the assertibility goes rather with the conditional subjective probability of the consequent.
>Subjective probability, >Conditional probability, >Probability.

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 [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

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
Theories of Truth, Paul Horwich, Aldershot 1994

Lewis I
David K. Lewis
Die Identität von Körper und Geist Frankfurt 1989

Lewis I (a)
David K. Lewis
An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966)
Die Identität von Körper und Geist, , Frankfurt/M. 1989

Lewis I (b)
David K. Lewis
Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972)
Die Identität von Körper und Geist, , Frankfurt/M. 1989

Lewis I (c)
David K. Lewis
Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980
Die Identität von Körper und Geist, , Frankfurt/M. 1989

Lewis II
David K. Lewis
"Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35
Handlung, Kommunikation, Bedeutung, Georg Meggle, Frankfurt/M. 1979

Lewis IV
David K. Lewis
Philosophical Papers Bd I New York Oxford 1983

Lewis V
David K. Lewis
Philosophical Papers Bd II New York Oxford 1986

Lewis VI
David K. Lewis
Convention. A Philosophical Study, Cambridge/MA 1969
German Edition:
Konventionen Berlin 1975

Clarence Irving Lewis
Collected Papers of Clarence Irving Lewis Stanford 1970

LewisCl I
Clarence Irving Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991

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