Sentence examples for necessary propositions from inspiring English sources
According to a traditional view, all true necessary propositions are analytic (tautologous) and knowable a priori (knowable independently of experience).
Moreover, the Renaissance enthusiasm for mathematics had resulted in a profound interest in rational principles, necessary propositions, and innate ideas.
Necessary propositions are sometimes said to be true or false (as the case may be) in all possible worlds.
According to Kripke, the view that all necessary propositions are a priori relies on a conflation of the concepts of necessity and analyticity.
Because all analytic propositions are both a priori and necessary, most philosophers have assumed without much reflection that all necessary propositions are a priori.
Some philosophers recognize a second category of "metaphysically" necessary propositions that are not analytic and generally not a priori; examples include identity statements such as "Water is H2O".
L is intended to be interpreted as "It is necessary that," so that Lp will be true if and only if p is a necessary proposition.
According to Aristotle, possibility is to be understood in relation to necessity: whereas a necessary proposition predicates something of a thing's essence (as in "All humans are mortal"), a possible proposition predicates something of a thing that is merely accidental (as in "Some humans are tall").
By convention, he sets the value of the necessary proposition at 0 the necessary proposition is no news at all!
Indeed, unstructured propositionalism entails that there is exactly one necessary proposition.
The problem is that the Russellian analysis seems to turn a contingent proposition into a necessary proposition.
