The subject of a proposition sometimes is a particular idea...

The subject of a proposition sometimes is a particular idea which refers to a specific existent, such as “Everest is the highest mountain in the world,” and sometimes a universal concept and applies to an infinite number of instances.

In the second case, it is sometimes a whatish concept, such as “Metals expand when heated,” and it is sometimes a philosophical concept, such as “An effect without a cause does not come into existence,” and it is sometimes a logical concept, such as “The contradictory of a universal negative is a particular affirmative.” In classical logic, propositions are divided into two forms, predications and conditionals.

Predications are composed of subjects and predicates and the relation between them is ‘unity’, such as, “Man is a thinker.” Conditionals are composed of antecedent and consequent, and the relation between them is either necessary, such as, “If a plane figure is triangular, then the sum of its angles is equal to that of two right angles,” or it is one of exclusive disjunction ( ta‘ānud ), such as “A number is either even or odd,” that is, if a number is even, it will not be odd, and if it is odd, it will not be even.

However, other forms also may be imagined for propositions, and all of them may be returned to predications.

[All propositions are composed of predicational propositions.] The relation between subject and predicate sometimes has the attribute of ‘contingency’ ( imkān ), such as in this proposition: “One human individual is bigger than another individual.” Sometimes the attribute is necessary, such as in this proposition: “Each whole is larger than its parts.” Logicians call these attributes ‘the matter of the proposition’ ( māddah qaḍiyyah ).

When these attributes are explicitly mentioned in a proposition, they are called the ‘mode of the proposition’ ( jahat qaḍiyyah ). The matter of a proposition is usually mentioned implicitly, and is not an element of it, although the predicate may be assimilated to the subject, and the matter or mode of the proposition take the form of a predicate and an element of the proposition.

For example, in the above proposition one may say, “One human individual’s exceeding the size of another is possible,” and “A whole's exceeding the size of its parts is necessary.” This kind of proposition is really a representative of the quality of the relationship of the subject and predicate of another proposition.