Logic_-_the_Traditional_Square_of_Opposition

The Traditional Square of Opposition The traditional square of opposition was developed in the fourth century BC from Aristotle’s works and has been in logic texts ever since. The traditional square of opposition is a diagram of logical relationships among the four types of categorical propositions. The traditional square of opposition has categorical propositions that can determine if an argument is valid or invalid. The standard-form categorical propositions having the same subject terms and the same predicate terms may differ from each other in quality, or in quantity, or in both. In any differing of subject and predicate it is traditionally called opposition. The four types of standard categorical propositions are universal affirmative, universal negative, particular affirmative and, particular negative. The proposition A is universal affirmative “All S are P.” The proposition E is universal negations “No S are P.” The proposition I is particular affirmative “Some S are P.” And last the O proposition is particular negations “Some S are not P.” There are four ways in which propositions may be “opposed” as contradictories, contraries, subcontraries, and as subalternators. These four propositions are used in a diagram that is called the square of opposition. Contradictories have two propositions where one is the denial or the negation of the other which means they cannot both be true and cannot both be false. Either of two propositions related in such a way make it is impossible for both to be true or both to be false. Contraries have two propositions that cannot both be true if the truth of one proves the falsity of the other. A proposition related to another in such a way that if the latter is true, the former must be false, but if the latter is false, the former is not necessarily true. Subcontraries have two propositions that have the same subject and the same predicate terms and agree in quality but differ in quantity and are called corresponding propositions. A proposition related to another in such a way that both may be true, but both cannot be false. Subalternation is when two propositions have the same subject and the same predicate terms, and agree in quality but differ in quantity. They are called corresponding propositions. The position of each proposition exhibits a relationship as it follows the square diagram illustrated on the next page. Every S is P or no S is P are propositions understood to be contraries. Two propositions are contraries if they cannot both be true but can both be false. Some S is P and some S is not P are propositions understood to be subcontraries. Two propositions are subcontraries if they cannot be false but can both be true. Every S is P and some S is P are propositions understood to be subalternations. Again no S is P and some S is not P are propositions understood to be subalternations. Every S is P or some S is not P are propositions understood to be contradictories. Two propositions are contradictory if they cannot both be true and they cannot both be false. A proposition is a subaltern of another if it must be true if its subaltern is true, and the subaltern must be false if the subaltern is false. The inferences that the propositions illustrate are true and false statements. In the traditional square of opposition there is an explanation in which it provides the logical basis for validating certain elementary forms of an argument. There are two inferences and they are immediate inferences and mediate inferences. When a conclusion is drawn from only one premise there is no such mediation, and the inference is understood to be immediate. When more than one premise is relied, because the conclusion is drawn from the first premise through the mediation of the second the inference is understood to be mediate. One can infer the following regarding the truth or falsity of the below statement if you assume “Some reptiles are not poisonous” is false' (1) All reptiles are poisonous. – True (2) No reptiles are poisonous. - False (3) Some reptiles are poisonous. - True The traditional square of opposition has been in logic for over centuries and is still used today. The traditional square of opposition is represented as a square diagram. The diagram represents a collection of logical relationships traditionally relating or not relating to one another. The diagram allows people to understand and to evaluate the relations among the four-categorical standard propositions. REFERENCES Copi M. Irving., Cohen Carl. Introduction to Logic, 2009 Custom Edition., Strayer University Custom Publishing; New York. Parsons, Terence. (2006). The Traditional Square of Opposition., Retrieved October 29,2010, from http://plato.stanford.edu/entries/square/ Pearsons Terence, (2010). Square of opposition - Wikepedia, the free encyclopedia. Retrieved October 29, 2010, from http://en.wikipedia.org/wiki/Square_of_opposition Sirswal, Raj Desh. May 4, 2009. Unit-VII: Immediate Inference-Square of Opposition, Retrieved October 30, 2010 from, http://niyamaklogic.wordpress.com/2009/05/04/unit-vii immediate-inference-square-of-opposition/ Square of opposition. (2010). In Encyclopædia Britannica. Retrieved October 29, 2010, from Encyclopædia Britannica Online: http://www.britannica.com/EBchecked/topic/430279/square-of-opposition Square of Opposition. (2010). Retrieved October 29, 2010, from http://www.tutorvista.com/math/square-of-opposition