Introducing the Syllogism - Introduction to “Logic: The Art of Defining and Reasoning” by John Oesterle

Stephen Alexander Beach 

(933 Words) 

Oesterle begins his introduction by pointing to the Aristotelian notion that all men desire to know, and yet it is a particular kind of knowledge that is unique to humans, that of rational knowledge. This, he says, is the knowledge of why things happen, or why something is so. 1 Like the desire to know, knowledge also proceeds from our wonder of the world around us. We desire to understand causally how such things are possible. “Now logic is nothing else that the art that guides us in coming to know something previously unknown to us. Logic, then, is an instrument for helping us to find out why things are as they are.” 

An Introduction to the Syllogism

To reason with logic is to reason in a syllogistic manner. This means that there are implicit truths in the world around us that we can bring out when we begin to think coherently about our knowledge of the world. 2 This is a demonstrative type of knowledge [as we are revealing something that is hidden]. The syllogism is made up of parts. The act of reasoning through two statements and a conclusion is made up of judgments or propositions, i.e. each statement. These propositions are made up on concepts, i.e. the words in the statement. To complete this process successfully, we must know what the words mean that we are using, know if the statements are true, and then the correct means by which to relate the statements to one another to produce the implicit truth we did not know before. 3

“There are three main topics to be considered: (1) definition, (2) proposition, and (3) syllogism. Each of these belongs to a different act of the human intellect.” 

The Definition - “Definition is known by the act of simple apprehension. The act of simple apprehension is the way in which we grasp a simple object, such as a man or dog or horse. This is the first act of the human intellect, and we express these simple notions by definitions.”

The Proposition - “The proposition (also called an enunciation) is known by the intellectual act of composition and division of terms, in which truth or falsity appears. If we combine or compose two terms, as in Every dog is an animal, we have an affirmative proposition. If we divide or deny two terms of each other, as in No horses are dogs, we have a negative proposition.” 

The Syllogism - “The syllogism is known by the act of reasoning, in which we proceed from one thing to another. More specifically, by knowing two propositions as true and as related in a certain way to each other, we reason to a third proposition concluding from them. Thus, by knowing Every mammal is an animal and Every cow is a mammal, we arrive at the reasoned knowledge Every cow is an animal.”

Oesterle talks about two types of the unknown, the simple and the complex. The simple unknown refers to the defining of a thing by the first act of the intellect. The complex unknown is when begin to say more about that thing or its connection to other things, this being done by the second act of the intellect. And if the complex unity is not self-evident [Meaning that the predicate is not necessarily contained in the subject - like a triangle having three sides -], then we must resort to the third act of the intellect which makes it clear and necessary through argumentation. 4 

Formal and Material Logic 

Oesterle makes a brief introduction to the distinction to the difference between formal and material logic. Material logic deals with the content of the this particular syllogism, while formal deals with the structure or manner in which the content is arranged and related. “Formal logic deals with the manner of ordering terms and propositions in a syllogism.” These forms of reasoning can be abstracted and represented with individual letters. 5 Material logic, however considers the nature of the things signified. “The use of words, however, brings out the matter of the syllogism, matter in the sense of the things signified, which material logics considers.” 

While syllogisms may be formally correct, if there is ambiguity in the material logic, such as unknown elements of the things considered, then the conclusion may not have the same weight. For example, if we talk about swans always being white, and then realize that there are black swans, our concept of swans, or our material logic was incomplete, and thus the conclusion will be affected. There can be no formal logic as such, as we are always reasoning about aspects of the real world. And so even when formal logic creates these templates, they still have specific meanings. For example, “Thus, in the syllogism that we have expressed formally above, the symbols, A,B, and C still imply matter, or things signified, to the extent that the symbol A has to be some object that can stand as the subject of the conclusion of the syllogism, the symbol B has to signify some object that can stand as the middle term of the syllogism, and the symbol C has to signify some object that can stand as the predicate of the conclusion. Furthermore, as we shall see later, the symbol C has to signify an object more universal than B, and B an object more universal than A.” 6

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1 - Oesterle, John. Logic: The Art of Defining and Reasoning. Englewood Cliffs, NJ: Prentice Hall, 1955. Pg. xiii

2 - xiv 

3 - xv 

4 - xvi 

5 - xvii 

6 - xviii