Quote: necessary and contingent propositions; what is (so) either is or is not (so) vs. something exists [»leibGW_1666]

Quote: possible truths are those that do not lead to contradiction; contingent truths lack resolution even if continued to infinity [»leibGW_1686]

Quote: absolute and hypothetical truths have the same laws; syllogisms are categorical

Quote: a necessary fact is true in all possible worlds; e.g., if the Goldbach conjecture is true, it is necessarily true [»kripSA_1980]

Quote: the principles of eternal things are necessarily true; they explain the being of other things; e.g., fire is why things are hot [»aris_322a]

Note: list of modal forms--necessarily, possibly, not; behaves like forAll and thereExists; be careful of secondary occurrences [»kripSA_1980, OK]

Quote: 'Necessarily' and 'Possibly' are referentially opaque; depends on wording; e.g., "number of planets = 9" and "9 is necessarily greater than 7" [»quinWV_1947]

Quote: with strict modality, quantification does not make sense, nor does modal logic; necessity becomes a synonym for analytic [»quinWV_1947]

Quote: knowledge of an unconditioned necessity must itself be an unconditioned necessity and hence unknowable

Quote: necessary truths are those that reduce to identity; impossibles are those that lead to contradiction [»leibGW_1686]

Quote: the necessary reduces to an identity; the impossible reduces to a contradiction; the possible is not impossible

Quote: to argue, every word must indicate one definite thing, a necessary connection; opposite statements are impossible [»aris_322a]

Quote: if a language contains intension adverbs (necessarily) then interchanging equivalent predicates can demonstrate cognitive synonymy; analytic already [»quinWV1_1951]

Quote: analytical propositions are necessary because they record our determination to use words in a certain fashion [»ayerAJ_1956]

Quote: necessary truths and contingent truths differ as rationals differ from irrationals; the former reduces to identity while the later leads to infinite regress [»leibGW_1679]

Note: X and Y have the same sense when X and Y necessarily have the same reference in all possible situations [»fregG_1892, OK]

Quote: all truths can be explained by numbers [»leibGW_1686]

Quote: for every true universal, affirmative, categorical proposition the predicate is contained numerically in the subject [»leibGW4_1679]

Quote: consider Neptune before it was ever seen; its description was an a priori truth but not a necessary one [»kripSA_1980]

Note: consider Nextperson as a proper name; its description fixes its reference but does not give its meaning; i.e., contingent, a priori truth [»kripSA_1980, OK]

Quote: for proper names, sense is necessary but reference is contingent; they look like shorthand or a vague description [»searJR_1958]

Quote: scientific properties are necessary but not a priori, e.g., gold has atomic number 79, but was still gold beforehand [»kripSA_1980]

QuoteRef: russB_1912 ;;17 Plato: have pure ideas (e.g., justice and whiteness) of which reality is but a reflection.

Quote: blind necessity could produce no variety of things; diversity is due to the ideas and will of a Being necessarily existing [»newtI_1685, OK]

Quote: freewill must arise from something other than collisions of atoms; it is not bowed by necessity; nothing can emerge from nothingness [»lucr_55]