speaker's mind, as to belief or disbelief. In its second or _objective_ aspect, it declares a truth or falsehood correlating with such belief or disbelief, for the information of the hearer. Now the Mode belonging to a proposition of this sort, in virtue of its _form_, is to be _true_ or _false_. But there are also other propositions--other varieties of speech enunciative--which differ from the Simple or Assertory Proposition having the form _is_ or _is not_, and which have distinct modes belonging to them, besides that of being true or false. Thus we have the Necessary Proposition, declaring that a thing _is_ so _by necessity_, that it _must be_ so, or _cannot but be_ so; again, the Problematical Proposition, enunciating that a thing _may or may not be so_. These two modes attach to the _form_ of the proposition, and are quite distinct from those which attach to its _matter_ as simply affirmed or denied; as when, instead of saying, John is sick, we say, John is sick _of a fever_, John is _dangerously_ sick, with a merely material modification. Such adverbs, modifying the _matter_ affirmed or denied, are numerous, and may be diversified almost without limit. But they are not to be placed in the same category with the two just mentioned, which modify the _form_ of the proposition, and correspond to a state of mind distinct from simple belief or disbelief, expressed by a simple affirmation or negation.[52] In the case of each of the two, Aristotle has laid down rules (correct or incorrect) for constructing the legitimate _Antiphasis_, and for determining other propositions equipollent to, or following upon, the propositions given; rules distinct from those applying to the simple affirmation. When we say of anything, _It may be or may not be_, we enunciate here only one proposition, not two; we declare a state of mind which is neither belief nor disbelief, as in the case of the Simple Proposition, but something wavering between the two; yet which is nevertheless frequent, familiar to every one, and useful to be made known by a special form of proposition adapted to it--the Problematical. On the other hand, when we say, _It is by necessity--must be--cannot but be_--we declare our belief, and something more besides; we declare that the supposition of the opposite of what we believe, would involve a contradiction--I would contradict some definition or axiom to which we have already sworn adherence. This again is a state of mind known, distinguishable, and the same in all, subjectively; though as to the objective correlate--what constitutes the Necessary, several different opinions have been entertained.