Logical Reduction

‘A propositions’ are Universal Affirmative Statements where the entire Subject category is contained in the category of the Predicate. For example: All men are mortal. In ‘A proposition’ we are talking about each and every thing in the world and essentially use words such as ‘all’, ‘every’, ‘each’, ‘any’, ‘always’, ‘whatever’, ‘invariable’, ‘necessarily’, ‘absolutely’. Further, Statements containing ‘Only’, ‘Alone’, ‘None But’ (Exclusive terms) should be considered ‘A proposition’. For example, when we say, “Only Logic students are present” we mean “All those who are present are Logic students”. Also, if in a proposition an exception is definite then that proposition should be considered as A proposition. When we say, “All students except Leo are present” we mean “All students are present”. If singular term is definite then such proposition should be considered as A proposition. For example: Everest is the highest mountain.

‘E propositions’ are Universal Negative Statements where the entire Subject category is mutually exclusive from the category of the Predicate. For example: No man is hungry. In the ‘E proposition’ we are talking about each and every thing in the world and use words such as ‘no’, ‘never’, ‘not at all’, ‘not a single’, ‘not even one’.

‘I propositions’ are Particular Affirmative Statements where some part of the Subject is contained in the Predicate. For example: Some men are tall. In ‘I proposition’ we are talking about only some things in the world and use words such as ‘most’, ‘many’, ‘a few’, ‘certain’, ‘all most all’, ‘several’, ‘mostly’, ‘generally’, ‘frequently’, ‘often’, ‘perhaps’, ‘nearly’, ‘always’, ‘sometimes’, ‘occasional’.  Further, if in a proposition an exception is indefinite then that proposition should be considered as I proposition. For example, when we say, “All students except one are present”, we mean, “Some students are present”. Also if singular term is indefinite then that proposition should be considered I proposition. For example, when we say, “Asians are Buddhists” we mean “Some Asians are Buddhists”.

‘O propositions’ are Particular Negative Statements where some part of the Subject is not contained in the Predicate. For example: Some men are not tall. In ‘O propositions’ we are talking about only some things in the world and use words such as ‘few’, ‘seldom’, ‘hardly’, ‘scarcely’, ‘rarely’.

When I propositions are negated, we get O propositions. When A proposition is denied we get O proposition.