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One such deductive consequence is the arbitrary statement.
By the innocuous point, E confirms any deductive consequence of the conjunction.
It was a large ultra-Uranian planet that had approximately the mass and orbit predicted by Leverrier". We treated Huygens's conclusion as a strict deductive consequence of his principles.
It is presumably true that an ideally rational thinker will have a set of beliefs that are closed under defeasible, as well as deductive, consequence.
There is one relation of deductive consequence, and different formal systems do a better or worse job of modelling that relation.
Deductive consequence is monotonic: if a set of premises logically entails a conclusion, than any superset (any set of premises that includes all of the first set) will also entail that some conclusion.
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Mathematical logic supplied a clear conception: a theory is a collection of statements (the axioms of the theory) and their deductive consequences.
Since it restricts empirical knowledge to observation sentences and their deductive consequences, scientific theories are reduced to logical constructions from observables.
Hypothetico-Deductive (HD) confirmation theorists propose that observational evidence argues for the truth of theories whose deductive consequences it verifies, and against those whose consequences it falsifies (Popper 1959, 32 34).
These considerations suggested that the logical relationship between scientific theories and empirical evidence cannot be exhausted by means of observation sentences and their deductive consequences alone, but needs to include observation sentences and their inductive consequences as well (Hempel 1958).
The assumption that degrees of belief satisfy the probability laws implies omniscience about deductive logic, because the probability laws require that all deductive logical truths have probability one, all deductive inconsistencies have probability zero, and the probability of any conjunction of sentences be no greater than any of its deductive consequences.
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