The knowledge on standpoint theory is critical in analyzing inter-subjective communication. Standpoint theorists underline the use of a naturalistic concept of knowing to analyze facts. Two standpoints that philosophers deal with are the modern standpoint and the traditional standpoint. The modern standpoint (or modern square of opposition) is usually based on the Boolean standpoint to assess validity of propositions. The square of opposition permits readers to analyze the relationship that exist between propositions. On the other hand, the traditional standpoint (or the traditional square) is based on the Aristotelian standpoint, which revolves around deduction of logic. The Boolean and Aristotelian standpoints differ from each other in terms of universal proposition concerning existing things.
The traditional standpoint implies that all universal propositions indicate existing things. Just like the modern standpoint, the traditional standpoint entails arrangement of lines that exemplifies logically necessary relations, which involve four kinds of definite propositions. Aristotelian standpoint identifies universal propositions concerning existing things as having existential imports (Hurley 227). For instance,
All bears are brown.
The above statement indicates that, in reality, bears exist. This implies that Aristotelian standpoint has existential import. While interpreting Aristotle standpoint, every claim is supposed to either confirm or refute a single predicate in a single subject. The word ‘universal’ in Aristotle standpoint literary means ‘whole,’ hence, its opposite should be ‘particular.’
Aristotelian standpoint recognizes that the traditional square sustains more presumptions than the modern square. The representation of Aristotelian standpoint is characterized by the four relations as follows:
- Contradictory – opposite truth value
- Contrary – at least one is false
- Sub contrary – at least one is true
- Sub alternation – truth flows downward while falsity flows upwards
Boolean standpoint does not offer support for universal claims as having existential import. For example,
All lions are hungry.
This statement does not indicate that lions really exist. Hence, the statement lacks existential import. It is through universal propositions that the Boolean standpoint becomes relevant. Adopting the Boolean standpoint implies that a person can ignore any evidence concerning the existence conveyed by universal statements.
The Boolean standpoint is represented through four categorical proposals in a Venn diagram. A Venn diagram entails an array of overlapping circles where each circle signifies the class indicated by a term within the categorical proposition (Hurley 208). Since every categorical proposition incorporate two terms, a single categorical proposition must have two overlapping circles as illustrated below in Figure 1.
Figure 1: Venn Diagram
The members of categories expressed by each term are indicated inside each circle. Thus, members that are indicated where the circles overlaps are perceived to belong to both groups while those outside the circles do not belong to any group.
The emergence of Modern Square of Opposition happens when there is a contradictory relation. Contradictory relations imply that there exist opposite truth values in every proposition. For instance, a statement that “All bats are mammals” contradicts another statement that “Some bats cannot be mammals.” According to Hurley, if two suggestions are related through the contradictory relation, then they automatically have opposite truth value (211). Figure 2 below illustrates Modern Square of Opposition.
Figure 2: The Modern Square of Opposition
Adopting either modern standpoint or traditional standpoint makes an individual to accept ground rules that are utilized in interpreting the significance of universal propositions. An individual can opt for either standpoint while arguing about categorical propositions. Any categorical syllogism or reasoning that goes against the four relation characteristics is void from the Aristotelian standpoint. One of the implications of existential import is that if this import is denied for a universal proposition, then the relations within the square becomes unacceptable since they are no more valid (Chatti and Schang 104). The Boolean standpoint is simpler than Aristotelian standpoint due to its closeness to existence. Aristotelian standpoint attracts existential implications.
In the traditional standpoint, a proposition is perceived as a spoken assertion, rather than the meaning of assertion, as demonstrated through the modern standpoint. For Aristotelian standpoint, every affirmation has to correspond with a negation. The confirmation and the negation have to oppose each other since one of the statements is deemed to be true while the other is false. In modern standpoint, it is logical to highlight the opposition of a given claim, instead of insisting that each claim holds several different opposites. Contradictory relations indicate that Boolean standpoint can support Aristotelian standpoint in opposing a given statement.
Both traditional and modern standpoints are fundamental in inferring the truth value concerning a proposition that has existential implication. Assuming that a subject term cannot be indicated by an empty set, the Aristotle standpoint incorporates four relations that include contradictory, contrary, sub contrary, as well as implication. The Boolean standpoint diverges from the Aristotelian standpoint in regard to how it construes the existence of individuals in universal statements. In the Boolean standpoint, the only rational relation is the contradictory connection. Contrariwise, accepting the Boolean standpoint may lead to ignoring evidences that the universal statement could have held about existence. While the Boolean standpoint illustrates ‘closed’ proposition of existence, the Aristtelian standpoint indicates ‘openness’ to existence.
Chatti, Saloua, and Fabien Schang. “The Cube, The Square And The Problem Of Existential Import.” History & Philosophy of Logic 34.2 (2013): 101-132. Academic Search Premier. Web. 16 Apr. 2016.
Hurley, Patrick J. A Concise Introduction to Logic. Boston, MA: Wadsworth Cengage Learning, 2012. Print.