The Difference between Aristotelian and Boolean Propositions
The variation between the Boolean illustrations and the Aristotelian illustrations is in the approaches each uses to draw the general statements. According to Boolean, the universal statements are made with no assumptions concerning the existence of the objects that were being talked about while Aristotle’s point of argument on propositions was that universal propositions about the existing things have existential import. For example, all rhinos are mammals denote that rhinos exist. Aristotelian argument is receptive on existence of the subjects. The chart below shows the traditional square (adopted from Barian, 198)
Existential import refers to a situation where a proposition asserts the reality of the subject. Boolean argument is unreceptive of existence as the cited subjects may not exist and therefore do not bear any existential import. Boole logic seems to take a neutral position on existential import. The traditional square logical associations and those apply in four quantifiers. Those are; all, no, not all, as well as some. The quantifier all bears existential import, an argument that is not held by the modern squares. The modern square shows a contradictory relation as showed in the diagram below. Contradictory relation to each other means that when one of the subjects is true, the additional must be opposite and if the additional is false, the original is the truth.
Syllogistic form is considered to be unconditionally valid despite of situations when the premises are considered to be having existential import. On the other hand, fallacies occur when the rules of the square are violated making the syllogism invalid. When no rules are broken, the syllogism remains valid.
The first fallacy is the one of undistributed middle in which the middle predicate is not spread to either premises. For example: All dogs are fierce
All cows are fierce
All cows are dogs
This commits the fallacy of the undistributed middle. The middle phrase provides a middle view between the subject and the predicate.
The second fallacy is the one of illicit major, illicit minor. In this case, the term spread in a end should also be circulated in a premise and rule two cannot be violated. When analyzing this rule, focus is given on the conclusion. In situations where the term distributed in the conclusion exits in the middle, the rule is usually violated.
The fallacy of exclusive premises cites that no two negative grounds are allowed. This is because no conclusion can be authentically be made from two negatives premises. This is despite the fact that the two classes involved are identical or distinct whether in whole or a portion. The two suggestions are contradicted as the two can’t be true at the same occasion but can be false. This is to say that if one of them is true, the other should be opposite. For example, all animals from the cat family cannot be fierce and some of them not fierce at the same time.
The fourth fallacy is that of drawing a negative conclusion from affirmative premises. In this case, the arguments tend to prove that no negative premises can lead to affirmative conclusion. Existential fallacy; exists when the fifth rule is applied. Here, if both premises are universal, the conclusion cannot be particular. Existential fallacy arises when the subject is imaginary. This is evident in cases when the contrary, sub-contrary, or sub-alteration is used on premise that subject terms refer to nonexistent things. This is to say that the logic in the traditional square when the sub-alterations are restricted. This fallacy would only be avoided when and only when the traditional logic would be modified so as to remove the existential fallacy. These modifications on the traditional square lead to the modern square. Boole appreciated the syllogistic argument that very category referred to be non-empty but it is possible to denote an empty class
The assumption that any subject cited has inferences is valid according to Aristotle, a concept that Boole is against. Aristotle logic understood universal claims hold each mentioned exited in at least one class. From the sentence “all animal from the cat family are fierce” inferring that “some animal from the cat family are fierce” commits are existence fallacy.
Barian B.P. an intro to syllogistic logic. Goodwill Trading Co., Inc. (n.d). print.