I 23
Content/Schurz: A proposition is the more substantial, the more consequences it has. Probability and content of hypotheses are often opposite. >
Stronger/weaker, >
Strength of theories, >
Theories, >
Probability,
>
Truth.
I 89
Content/stronger/weaker: The content strength decreases during the transition from all-phrases via singular phrases to existential phrases.
E.g. A universal sentence (x)Fx is logically stronger than its singular Fa instances and these are stronger than the corresponding existential sentence (Ex)Fx).
>
Stronger/weaker, >
Generalization/Schurz, >
Falsification/Schurz.
I 97
Def Logical Content/Schurz: the logical content of a proposition (or set of propositions) S is the set of all propositions or consequences logically following from S.
Def Empirical Content/Schurz: only the set of empirical (and thus verifiable) propositions or consequences logically following from S, which are not already analytically true.
Def Observational content/Schurz: is even narrower than empirical content: only the observational propositions that follow from S. This notion has very limited applicability: Only for purely universal law hypotheses.
Observation proposition/Schurz: no observation propositions follow from an allexistence hypothesis Ex H:= (x)(Fx > (Ey)(Gxy).
Schurz: From H follows by universal instantiation only Fa > Gay and this is no observation theorem, because (Ey)Gay is a spatiotemporally restricted existence theorem.
Such allexistence hypotheses are therefore also not falsifiable. However, they are confirmable. But this is weaker than falsifiable.
>
Observation, >
Observation sentences.
Def Probabilistic content/statistics/probability/Schurz: Let S be a set of statistical hypotheses, this logically does not imply any observational propositions, but at best gives them a belief probability.
Wrong: to assume that the content would be the set of propositions with a certain minimum probability. Because this set can be contradictory! Even if r is still so close to 1.
Conjunction probability: the conjunction of many highly probable sentences can be very improbable on their part!
Solution/Schurz: probabilistic content is the set of all probability propositions which follow from S according to the axioms of probability.
>
Probability, >
Subjective propability.
I 109
Def relevant content/relevance/logic/Schurz:
(a) the relevant logical content of a proposition or set of propositions S is the set of its relevant consequence elements.
Notation: Cr(S)
b) the relevant empirical content of S is the set of those relevant consequence elements of S that are empirical and not analytic true propositions.
Notation: Er(S).
Each set of sentences is L equivalent to the set of its relevant consequence elements.
>
Relevance/Schurz.
