The Square of Opposition PDF

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The Square of Opposition

Taylor Saxton-Getty West Coast University Phil 341: Critical Reasoning Professor Saeb May 17th, 2020

2 The Square of Opposition The Internet Encyclopedia of Philosophy defines the Square of Opposition as “a chart that was introduced within classical (categorical) logic to represent the logical relationships holding between certain propositions in virtue of their form” (IEP). Author Brooke Moore defines categorical logic as logic “based on the relations of inclusion and exclusion among classes or categories as stated in categorical claims”. These terms must be nouns or noun phrases, with the first being the subject noun and the second being the predicate noun so that the classes or categories are clearly defined for accurate decision making. The Square of Opposition is a helpful tool in understanding logic so that we can be more careful and precise in our thinking, Moore (2020). It is extremely reliable in helping to understand and analyze a claim that is being made and to see how two similar claims are related. The square of opposition uses logical reasoning to define the difference in A, E, I, and O Claims and propositions. Categorical logic is used to define what is or is not being claimed and to clarify the claim itself. Adjusting the wording of a claim can cause the claim to have serval different meanings. The purpose of the square of opposition is to show how similarly worded statements referring to the same subject and predicate can become contrary and contradictory. Each corner of the Square of opposition makes a claim that is A, E, I, and O. The A and E statements are contrary and will not both be true. The I and O statements are subcontrary and will not both be false. At the same time, the A and O as well as the E and I statements are contradictory and will never have the same truth value, Moore (2017). Each A, E, I, and O claim refers to its own Venn diagram form to present a categorical claim. The Venn diagrams are based on claims that have been translated into standard form for the claim type. When translating basic claims, there are keywords associated with each claim that helps identify its categorical proposition. Before being translated into standard form, Universal Affirmative or A claims will generally start with words such as; every, only, wherever,

3 and whenever. Once converted to standard form, these claims will begin with the word ‘all’. Universal Negative or E claims generally contain; no, none or not – before being translated into standard form. Once they are in the standard form they will begin with ‘no’. Particular Affirmative or I claims contain the word some and Particular Negative claims or O claims contain the phrase some are not. Each claim type requires that the claims have been translated into a standard form to apply the set rules correctly. The ordinary claim I will be translating into the standard A claim form is “Only nurse are hospital employees”. The A claim standard form reads that all of one subject are the predicate, therefore “All nurses are hospital employees”. The E claim prior to translation would read the “Nurses are not hospital employees”. By following the form that none of the subjects are the predicate, the E claim standard form would be that “No nurses are hospital employees”. With the I claim, the phrase before translation would be that “There are nurses who are hospital employees” as the subject can sometimes be the predicate. This then will read that “Some nurses are hospital employees” in standard form. Finally, the O claim in its ordinary form would say that “there are nurse who are not hospital employees”. By showing that the subject sometimes is not the predicate, standard form of this will be “Some nurses are not hospital employees”. The A and E claims are universal categorical claims that cannot both be true at the same time, however, they can both be false. This shows how the statement all nurses cannot be hospital employees is true while no nurses are hospital employees is false. The I and O claims can both be true, but cannot both be false. With this example, we have validated the claim as it is probable that some nurses are hospital employees while others are not. At the same time, the A and O statements are contradictory as the A claim universally asserts that all nurses are hospital employees while the O claim states that some nurses are not hospital employees. These statements cannot have the same truth value as the A encompasses all

4 nurses while the O can only ever cover some nurses. This is seen as well in the E and I claims, as the universal claim cannot have the same truth value as the particular claim. The Square of Opposition allows for logical analysis of similar claims so that it can be determined how the phrases relate and should be interpreted. By identifying categorical claims and comparing them within the square, we can understand how claims that universally encompass a broad range have similar meanings or are intended to be interpreted differently. With the goal of helping a reader understand how a claim relates to different subjects we are able to make more well thought out critical decisions and practice our analytical reasoning.

5 Citations International Encyclopedia of Philosophy. (n.d.). Retrieved from https://www.iep.utm.edu/sqr-opp/ Moore, B. N., & Parker, R. (2020). Critical thinking (Twelfth). New Yo4k, NY, United States of America: McGraw-Hill Education....