The Square of Opposition: Unlocking the Power of Categorical Logic - Essay Sample

Introduction

The square of opposition refers to a chart introduced within categorical logic to represent the relationship that holds certain prepositions about their form. Categorical logic applies to an argument that consists of three prepositions, whereby there are two premises and one conclusion. There also appear three categorical terms, with each being used twice. Additionally, there is a final premise which links the minor and middle terms, and it is referred to as a minor premise. The chart contains four corners that denote the four prepositions primary forms that are recognized. The prepositions are A, E, I and O (Thompson, 1953).

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A prepositions take the arrangement of all P are S, E prepositions usually take the procedure of no P are S, I prepositions take the procedure of some P are S. O prepositions take the formula some P are not S. A and O can be referred to as contradictory prepositions, similar to I and E prepositions. When the truth of a preposition illustrates the falsity of the other proposition, then they are known as contradictory (Thompson, 1953).Contrary prepositions are those that are not true - for example, A and E (Thompson, 1953). For instance, an A preposition can be like "all dogs are white". The proposition is not valid, just like the corresponding E proposition that states that "no dogs are white". Although the two prepositions are contrary, they are not contradicting. Although both of them cannot be true, they can be false.

Sub contrary prepositions are those that appear intolerable for both of them to be untrue, for example, I and O prepositions. For example, when one says that "some trips are free", that may be false, but "some trips are not free" must be true. However, it is possible for both the I and O prepositions to be right (Thompson, 1953).

Prepositions can be said to be subalternation when the actuality of a single preposition shows the reality of another. A preposition can be said to be in a sub alternation relation with the I preposition (Thompson, 1953). For example, it is right to say that "all human beings are warm-blooded", and it is also true to say that "some human beings are warm-blooded". However, when relating the O and the E prepositions, it is true to say that "some companies in Africa are not Chinese-based". By using the E proposition, it is not correct to say that "no company in Africa is Chinese-based".

The truth of an E or A preposition shows the truth of O or I preposition, whereas the falsity of an O or I preposition shows the falsity of the consequent E or A preposition. However, the falsity or truth of one proposition does not necessarily indicate the falsity or truth of another preposition (Thompson, 1953).

Conclusion

Recently, most logicians have abandoned the assumption made above, that all groupings have at least one entity. Current logic deals with instantiated rapports for example "ether flow" and "unicorn", just as it deals with other terms like "orangutan" and "apple". When one is dealing with empty categories, such relations of being subcontrary, subornation and contrary is no longer considered (Veloudis, 2019). For example, the statement that "all Monoceros have horns" (A), and "no Monoceros have horns" (E) are both true, so not contrary. Similarly, saying that "some Monoceros have horns" (I) and "some Monoceros do not have horns" (O) can both be regarded as false and not subcontrary.

References

Thompson, M. (1953). On Aristotle's Square of Opposition. The Philosophical Review, 62(2), 251. doi: 10.2307/2182795

Veloudis, I. (2019). Exploiting the Square of Opposition for expressive purposes. Lingua, 220, 65-75. doi: 10.1016/j.lingua.2019.01.004