The Powers and Limitations of Logic

Warning. This is one of those more theoretical blog posts.

From a drop of water
a logician could infer the
possibility of an Atlantic or a Niagara
without having seen or heard of one or the other.
~ Sir Arthur Conan Doyle

Appeal to logos (logic) is rooted in reasoning. We study logic to understand the nature of language and thinking; to define terms, to make distinctions, to judge correctly, and to validate truth. Logic study encourages systematic and disciplined thinking.

As the rules of phonics are the structure behind the sounds of words, as the rules of grammar comprise the structure behind the writing of sentences, so are the rules of logic the structure behind coherent and correct argumentation.

In the case of phonics and grammar, we have long ago learned the rules, and we can read and write, but rarely do we formally refer to the rules of phonics or grammar when we read or write.

Likewise, the formal rules of logic, while they are used directly and carefully in constructing syllogisms, when it comes to rhetorical argumentation we do not directly refer to the rules of logic very often.

Formal Logic

We study formal logic as a means of acquiring certainty about the validity and soundness of an argument. The methods of formal logic work well in math and science. But this is not so when it comes to historical, religious, or philosophical questions.

Most political, philosophical, and historical questions are not simple to start with. Definitions of the basic terms are often complex and not agreed on. Any stated premise that is clearly defined is usually under a great deal of dispute, but worse than that, the answers to historical and political questions are usually not binary (meaning, they are not an either-or case).

Syllogisms

In most human arguments there are a multiplicity of answers interwoven with each other, tangled and attached in funny ways that make formal logic impractical as a vehicle for argumentation. In most cases where we can indeed write a simple essay and use a formulary syllogistic approach, the argument is so simple that the premises or the conclusion are not really subject to dispute to start with. For example in the classic syllogism:

All men are mortal.
Socrates is a man.
Therefore Socrates is moral.

This syllogism states the obvious and undisputed in its two premises, and it proceeds to conclude the obvious in its conclusion. There is no startling new information here. It is merely a rearrangement of the terms yielding an answer we were all too familiar with. In fact, most of us, even without the syllogism, would have reached that conclusion on our own. This would make a most uninteresting essay.

In matters of persuasion we are not dealing with the obvious. We are trying to reason about that which is disputed amongst men, and that alone implies that the answers are not obvious, the premises are not agreed on, and often the terms or the use of the terms are under dispute as well.

What is an essay, but a written answer to a complex question that requires PERSUASION because the answer is not agreed on, simple, or obvious? If the answer were obvious and certain, there would be no need for argumentation; everyone would be able to SEE it logically.

The many questions we ask in history, philosophy, and literature are questions that require persuasion precisely because they are not obvious. Therefore, the direct vehicle of employing formal syllogistic logic is often not a good way to answer those questions.

Formal logic and its vehicle, the syllogism, mostly seem to be useful in questions that debate whether something ‘is or isn’t X’. In other words, syllogisms are good at asking yes/no questions because you can formulate a syllogism that says:

All things that are clear are Y.
X is Y.
Therefore X is clear.

So the thesis of the essay is X is Y… and you spend the body paragraphs of your essay showing that X is Y (by definition, by example, by analogy, by testimony, by cause and effect etc… whatever invention topic fits your case.)

But in most essay questions we are asking more complex questions, like

Why did the League of Nations fail?

or

Was slavery the cause of the Civil War?

In those cases, YES, we use reasoning to dig up arguments and to support our answers, but to dig down to extract a syllogism as a framework for the thesis proposition we are trying to support seems unnecessarily cumbersome, and in some cases, not at all helpful.

If we take the time to construct a syllogism with each premise in standard logical form that looks like this:

All human institutions that fail are human institutions that do not have the power to enforce what they stand for.
The League of Nations is a human institution that does not have the power to enforce what it stands for.
Therefore the League of Nations is an institution that failed.

… how helpful is that? I already knew that, and so did the prospective readers of my essay. What I need to show is that the League of Nations did not have the muscle to enforce what it stood for, so my essay is actually more or less enthymemic in that it suppresses the obvious and jumps straight to the interesting point.

Nowhere in Aristotle’s Rhetoric, Quintillian’s Institutes, or Cicero’s De Oratore do we see a classical model for constructing syllogisms to come up with all available means of persuasion in a speech or an essay. We are more likely to dig into Cicero’s topics of invention and define, differentiate, compare, exemplify, and so forth, to generate persuasive support for our work.

A SYLLOGISM is really meant as a slam dunk proof of certainty, and that we cannot generate in the context of disputable issues. The best we can do on disputable issues is to lean one way or another and try to persuade.
Rhetoric is the art of being persuasive in cases where certainty is not possible. Rhetoric is ‘second best’ in terms of certainty, but so many issues in life—in fact, most of the issues that matter most to us—are issues that people and cultures differ on and therefore matters of persuasion. (This of course does not mean that YOU cannot personally be certain about something. It is merely asserting that mankind as a whole does not agree on many of the issues that matter.) The areas where we would love to be most certain are the ones that are the hardest to be certain about.
So to conclude, in the case of Confirmation and Refutation in this book, syllogisms can be useful, simple devices but so simple that while their structure is inherent in the work we do, they are so simple we hardly need to call attention to their existence.

In the progymnasma Confirmation basically we say that

• All narratives that contain the following features
(list the features you are going to discuss here) are clear.
• This narrative is a narrative that contains the following features (list the same features here).
=> Therefore, this narrative is clear.

Example 1

• All narratives that tell the story in a straightforward manner using simple words are clear.
• This narrative is a narrative that tells the story in a straightforward manner using simple words.
=> Therefore this narrative is a clear narrative.

The same structure of argument could be presented for the narrative being possible, plausible, etc.

In the case of Refutation we would say that

• All narratives that contain the following features
(list them here) are narratives that are not possible.
• This narrative is a narrative that does contain the following features (list the same features here).
=> Therefore, this narrative is not possible.

Example 2

• All narratives that contain legendary and mythological creatures are narratives that are not physically possible.
• This narrative contains legendary and mythological creatures.
=> Therefore, this narrative is not physically possible.

In the case of writing a Commonplace essay (as in Essay 4) we basically choose a person who has committed a crime and say:

• All persons who have committed this particular crime are persons who deserve the following punishment.
• This person has committed this particular crime.
=> Therefore this person deserves that punishment also.

The logic, as in most judicial rhetoric cases, should be simple and clear. It ought to be. It is meant to be clear and easy for a jury to see the issues and render a verdict. Furthermore, the matter of sentencing also should be clear so that justice has been served. We do not, in judicial rhetoric, want to render a nebulous judgment or pronounce an unfair sentence.

About Lene Jaqua

Co-author of Classical Writing books
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