If 'sure loss' were taken as foreseeable loss, then an agent could violate the axioms by attaching positive probability to a necessary falsehood, where there is no foreseeable loss given the current state of knowledge concerning the proposition in question.
Concerning these propositions, Leibniz approvingly remarks, "What Descartes says here is most beautiful and worthy of his genius, namely, that every motion in filled space involves circulation and that matter must somewhere be actually divided into parts smaller than any given quantity" (L 393).
The second one concerns the proposition of a general adaptation phase to reuse case solving diagnostic problems in a different context.
A final point here concerns the proposition that, absent legalised/institutional torture, unlawful endemic torture in the security agencies of contemporary liberal democracies confronting terrorism is inevitable.
The truth of this proposition concerning the mental state of an agent (Peter, who believes it is raining) need not be affected by the truth of the embedded proposition (it is raining), which may be false [ 6, 7].
This was a common view concerning indefinite propositions when they are read generically, such as 'A dodo is a bird', which (arguably) can be true now without there being any dodos now, because being a bird is part of the essence of being a dodo.
A further development of Leibniz's views, revealed in a text written in 1686 but long unpublished, was his generalization concerning propositions that in every true affirmative proposition, whether necessary or contingent, the predicate is contained in the notion of the subject.
In proceeding this way, however, we would have to face serious problems concerning purely logical propositions, i.e., propositions all of whose parts are purely logical ideas.
The very concept of an independent film – one financed outside the traditional system, usually with little to no guarantee of distribution – is a concerning proposition in Australia.
