Bolzano's semantic notion of entailment requires that from the smallest number of premises the largest number of conclusions follow, none of which has simple components not also contained in the premises
Semantic notion of entailment(the core concept being explained)
A way of understanding how conclusions logically follow from starting statements based on what those statements actually mean, rather than just following formal logical rules.
Simple components(describing what elements make up a statement's meaning)
The basic, irreducible parts or building blocks of a statement—like the individual concepts or ideas that make it up.
entailment(Conceptualist framework)
Understood in terms of truth at a world
premises(as used in logic and philosophical arguments)
Starting statements or assumptions that are used to support a conclusion—like the opening claims in an argument that lead to a final point.
The relation of entailment between (sets of) conceptual truths has the characteristic feature that, according to it, from the smallest number of premisses the largest number of conclusions will follow none of which has simple components which are not also contained in its premisses (WL II, 386). Ideas such as these sound akin to Gerhard Gentzen’s characterization of normal proofs: “They do not make a detour. They do not introduce concepts which are not contained in its final result and must ther