The Mathematics and Logic of the Term “All”

 (Erico Joseph T. Canete)

THE TERM “ALL” may be classified in different parts of speech depending on its usage. As a pronoun, when the term stands alone like “All are grateful,” or as an adverb, “She cried all alone in solitude.” On top of that, the term “all” is a determiner, that is, “all” plus a plural form of the noun. It determines the quantity.

Logic classifies this determiner under Classification of Term according to Extension as a Universal Term i.e. a term applied to a class as a whole and to every member belonging to that class. When we say, “All members,” it applies to all the members and to every member of that class. Though this universal term is a unification of both single and collective terms, it should not be taken separately either individually or collectively but simultaneously, and as one. The error occurs when one totally equates universal as particular (a universal term taken partly and indeterminately) like, “All members” is the same as “Some members.” Though some is part of the all, but to equate ALL and SOME with exactly the same quantity is wrong. It’s simple logic.

How can ALL be SOME and vice versa at the same time?

To alter the comprehension, signification, thought-content, meaning and definition of “ALL” destroys the principles of knowledge. 

These disjunctive and conditional multiple hypothetical propositions in the Aristotelian logic present:

It’s either 24 or not!

If it’s 24, then it’s 24. If it’s not 24, then it’s not 24.

It is impossible for 24 and not 24 to exist simultaneously.

To unify and apply the opposites at the same time and respect to the fundamental and supreme law of the land, which per se has a nature of immutability unless duly amended or revised as provided by law, is violative to the principles of knowledge namely; Principle of Excluded Middle (A being is either is or is not), Principle of Identity (Whatever is, in so far as it is, is, and whatever is not, in so far as it is not, is not), and the Principle of Non-Contradiction (A being cannot-be and not be at the same time, manner, and respect). 

Problem is, some fellows understand the mathematics but not the logic!