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Aristotelian Logic


By: S. I. Odia and A. A. Asekhauno


 Some thinking and all of philosophical discourse require some justification, foundation or validation. Logic is concerned with the Science of justification and correct reasoning. From the time of Classical Greece, Logic has been recognized as a fundamental and important element of Philosophy because nearly all of us, ordinary persons and scholars alike, engage in the process of reasoning about all sorts of topics. Everyone this employ Logic in one form or the other.

    This section offers an introduction to the main themes in Aristotlian (traditional) Logic. It is so called because Aristotle was the first philosopher to produce a systematized study of the methods and principles of correct reasoning. What then is Logic? What are propositions? What are arguments? What are categorical propositions and the Laws of Thought? These and other related questions are addressed in this chapter.


    In our daily life, we need to formulate and determine principles and rules to ensure that correct reasoning which proceeds from true premised will not lead to false conclusion. Logic, then, can be defined as the philosophical study of what counts as sound reasoning. This should not be construed as describing human psychology, i.e, the process of thinking, remembering or imagining. It should rather be seen as normative; how people ought to reason to avoid mistakes. Logic is concerned with the study of the Laws of reasoning, reflecting upon the nature of thinking itself. It is also concerned with the principle of valid inference.

    The aim of Logic is to make explicit the rules by which inferences may be drawn, rather than the study of actual reasoning processes that people use, which may or may not conform to those rules. From a given set of premises, Logic furnishes us with rules for arriving at justifiable conclusions. In this wise, Logic does not only equip us with skills for correct, persuasive and valid reasoning, it also fortifies our sensitivity to scrutinize the reasonableness of others’. In legal trials, such reasoning is key in determining grounds for accepting or rejecting a charge. There is thus clearly a difference between good and bad reasoning. A bad reasoning can lead to invalid results, and in a legal contest this may be a matter of life and death. Again in the present Century, Logic is enormously important in all technical fields, from the operation of computers to analyzing complex weather patterns.


    A proposition is a declarative statement that is capable of being true or false. We have different kinds of statements: Interrogative (“why did you do that?”), imperative (“go away!”), exclamation (“Oh, how I love you!”), indicative (“Tunde is a Nigerian”), etc. It is about the information given or the content of the statement. The statement must have a truth value, that is, capable of being true or false. A proposition could be simple or complex.


(a) Simple Proposition:

    A simple proposition is a proposition which contains only one piece of information and thus cannot be further split into other propositions. As in simple sentences, a simple proposition is neither co-joimrd with another nor does it always have more than one subject or predicate. “Mary is tall”, “All Nigerians are intelligent”, are examples of simple propositions, also known as atomic propositions.

(b) Compound Proposition:

    A compound proposition is one which comprises two or more atomic propositions rolled into one. In other words, a Compound Proposition can be split into two or more simple propositions.

    There are various ways of asserting Molecular Propositions. Firstly, it is possible that the subject class can be split so that we have two subjects performing the same or similar act. An example of such is “Bola and Jide are coming.” This could be split to mean “Bola is coming” and “Jide is coming“. Secondly, it is possible for the predicate class to be split as in “John is tall and smart.” This could be split into two thus: “John is tall” and “John is smart.” Thirdly, it is possible for both the subject and the predicate to be split as in “John and Mary are decent and Christians“. This means that “John is decent; “John is a Christian”; ” Mary is decent”; “Mary is a Catholic”.

   Often, Molecular Propositions are formed by joining three simple propositions by the terms, “and”, “if”, “then”, “or”, “but”, etc. These are called logical connectives.

 In the next post, we will look at what arguments are. Anticipate.