If some such view is correct, it might avoid certain (unpleasant) questions prompted by earlier Fregean views: how can a sentence indicate a proposition with a different structure; and if grammar is deeply misleading, why think that our intuitions concerning impeccability provide reliable evidence about which propositions follow from which?
In this regard, Stumpf clearly separate the question of the origins of concepts, which is a psychological question, from the logico-mathematical domain to which propositions and axioms belong.
Armstrong (1973) combines the view with an instrumentalist attitude towards propositions, on which propositions are mere abstractions from mental states and should not be taken seriously, ontologically speaking.
An axiom is simply an indemonstrable proposition from which other propositions may be deduced.
In particular, the set \ \Omega\), on which the preference ordering \ \preceq\) is defined, has to be an atomless Boolean algebra of propositions, from which the impossible propositions, denoted \ \bot\), have been removed.
Frege says that "the apodictic judgment [i.e., roughly, the judgment whose content begins with a "necessarily" governing the rest of the content] is distinguished from the assertory in that it suggests the existence of universal judgments from which the proposition can be inferred, while in the case of the assertory one such a suggestion is lacking" (Frege 1879, §4).
In fact, Poincaré's model of explanation, founded on a minimum of well-confirmed hypotheses erected into principles and from which any meaningful propositions can be deduced, is called into question by Maxwell's approach.
Even if we allow that in simple cases one's justification for a belief that follows immediately from one's understanding of simple premises from which the believed proposition follows, this sort of strategy will only work in a small class of cases.
In classic use the term "hypothesis" marked propositions from which deductions were to be made.
