"the proposition asserts" is correct and usable in written English.
It is commonly used in formal or academic writing to introduce a statement or claim that is being made. Example: The proposition asserts that poverty can be alleviated through increased access to education and job opportunities.
These assumptions can be represented by the set of worlds at which they are jointly true, which Stalnaker calls the 'context set.' The point of assertion is to add the proposition asserted to the set of background assumptions and thereby eliminate worlds where it is not true from the context set.
To achieve this, every assertion needs to conform to the rule that the proposition asserted is false in some of the worlds that were in the context set before the utterance (otherwise there are no worlds to eliminate) and true in others (since the audience cannot eliminate all worlds from the context set).
Though "self-evident" and "universally valid," the proposition asserting this tripartite character of consciousness is, according to Reinhold, not analytic but synthetic.
What explains the impression that a sentence like (1) expresses an a posteriori claim is the fact that the proposition asserted by a typical utterance of the sentence is not the one that is semantically expressed by it, but a different proposition that is contingent and can only be known empirically.
The following proposition asserts the correctness of the algorithm.
The following proposition asserts that, for fixed (rho ), when the constraint (0 ;< S ; le ; S_0) is ignored, the point ((Q^), (S^)) is the optimal solution such that the expected total cost (hat{Pi }) has minimum value.
The following proposition asserts that, for fixed (m) and (L in left[ {L_{i},L_{ii - 1}} right]), the point (Q^) is the optimal solution such that the integrated total cost has minimum value.
"Admission to the nation's top universities and colleges is a zero-sum proposition," asserts the brief from the 80-20 Nationel Asian American Educatiofal Foundathen, one of the groups opposed to affirmative action.
Or, as Stout writes in his Preface to Jones (1911), "every affirmative proposition asserts, and every negative proposition denies, the union of different attributes within the unity of the same thing" (Stout 1911, v).
Nor does the universal proposition assert that some class relation holds between A and B – the assertion of a class relation is just a way of saying that certain propositions are true.
