Sentence examples for frequency of a proposition from inspiring English sources
That they will be rational numbers follows from the definition of the relative frequency of a proposition at a world.
For this, we need the notion of the limiting relative frequency of truths amongst propositions of a certain sort.
We should distinguish between a property of a proposition, and a property that is a constituent of a proposition.
Like Tarski, Bolzano defines the validity of a proposition in terms of the truth of a family of related propositions.
propositions that are "merely thought" (bloß gedacht); a "merely thought proposition" is in fact a subjective idea of a proposition, i.e. a mental phenomenon which grasps an idea whose object is a proposition (WL I, 155).
But an adequate understanding of a proposition does not make that proposition more probable, so is not evidence for it.
Coherentists do not believe that the truth of a proposition consists in coherence with any arbitrarily chosen set of propositions.
Then there is a single unique number \(\mathrm{Freq}(\mathcal{F}', A, \sim', w)\) that gives what the relative frequency of truths amongst propositions like \(A\) would be were there all the propositions in \(\mathcal{F}'\) and where the relation of similarity amongst them is given by \(\sim'\), where this counterfactual is evaluated at the world \(w\).
The idea is that, for each proposition \(A\) in \(\mathcal{F}\), there is not just a fact of the matter about what the frequency of truths amongst propositions like \(A\) actually is; there is also a fact of the matter about what the frequency of truths amongst propositions like \(A\) would be if there were more propositions like \(A\).
