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|Field II 252/296
Material Conditional/Adams Conditional/Field: (Lit. Adams 1975): (outside of mathematics): few of us would agree with the following conclusion: E.g. from Clinton will not die in office to 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. - In other words: If A then B does not seem to have the same truth conditions as ~A v B - 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).
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.
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.
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.
Truth conditions/nonfactualism/conditional/(s): if there are no facts, then ther 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.
Field: ditto, but the main thing is that one cannot explain the acceptance conditions without the truth conditions in terms of the truth conditions.
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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980
Die Identität von Körper und Geist Frankfurt 1989
Konventionen Berlin 1975
Philosophical Papers Bd I New York Oxford 1983
Philosophical Papers Bd II New York Oxford 1986
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991