Tag Archives: Aristotle

Reasoning by Analogy

Classical Education, Logic, Rhetoric, Why learn logic?, ,

I have been thinking about analogies lately, and finding them fascinating. There appear to be three basic uses for the term analogy.

Comparisons

First, almost any comparison, especially one in which a familiar, simpler, or concrete thing is used to clarify or illuminate something that is unfamiliar, complex, or abstract, can be called an analogy. For example, this excerpt from George Orwell’s essay “A Hanging” is considered an analogy:

They crowded very close about him, with their hands always on him in a careful, caressing grip, as though all the while feeling him to make sure he was there. It was like men handling a fish which is still alive and may jump back into the water.

The manner in which the guards handled the prisoner is compared to men handling a fish. Most people have tried to handle a live fish just pulled from the water that wants back in, so this comparison gives the reader a vivid mental picture of the less familiar situation Orwell is describing.

Ordered-pairs

Second, we see analogies in what can be called ordered-pair form: A is to B as C is to D, or more briefly A : B :: C : D. Typically these appear in the vocabulary or reasoning section of standardized tests, like this sample question from the GRE. Choose the analogous pair:

APPRENTICE : PLUMBER ::
A. player : coach
B. child : parent
C. student : teacher
D. intern : doctor

The best answer is D. Just as an apprentice is training to be a plumber, so an intern is training to be a doctor. A child does not formally study to become a parent, and a player or student is not necessarily studying to become a coach or teacher (respectively).

Illustrative parallels

Third, we see analogies being used for the purposes of persuasion, called arguments by analogy, or what Aristotle calls illustrative parallels. Here is an example from Aristotle’s Rhetoric II.20:

Public officials ought not to be selected by lot. That is like using the lot to select athletes, instead of choosing those who are fit for the contest; or using the lot to select a steersman from among a ship’s crew, as if we ought to take the man on whom the lot falls, and not the man who knows most about it.

Illustrative parallels use both inductive and deductive reasoning. We use inductive reasoning to mentally move from the source (e.g. we ought not use the lot to select athletes) to a more general, unspoken intermediate conclusion (we ought not randomly select someone for a skilled position). We then use deductive reasoning to move from this intermediate conclusion to our specific conclusion, the target (we ought not select public officials by lot).

In my next post, I will explain how to construct illustrative parallels.

A Brief History of Validity #1

Introductory Logic, , , ,

Which forms of categorical syllogisms are valid? Logicians have disputed the answer for centuries, a dispute that can give us insight into the meaning of validity, the central concept of formal logic. This will be the first of a few posts in which I will briefly discuss the history of syllogistic validity.

Aristotle’s 16

It all started with Aristotle, who in his Prior Analytics, Book I, chapters 4-7, detailed sixteen valid forms:

Figure 1: AAA, EAE, AII, EIO
Figure 2: EAE, AEE, EIO, AOO
Figure 3: AAI, EAO, IAI, AII, OAO, EIO
Figure 4: EAO, EIO

If you read Prior Analytics (which is no trivial task), Aristotle presents only the first three figures as figures, omitting any mention of a fourth figure. But in chapter 7 he admits in passing the forms of EAO-4 and EIO-4 as valid, saying,

If A belongs to all or some B, and B belongs to no C … it is necessary that C does not belong to some A.

It is not difficult to see why Aristotle omits AAI-1, EAO-1, AEO-2, and EAO-2. These four forms are his AAA-1, EAE-1, AEE-2, and EAE-2 with the subimplication of the conclusion. Aristotle apparently saw no need to include syllogism forms with particular conclusions when the premises could imply the universal.

Aristotle and Figure 4

It is rather more difficult to understand why Aristotle does not admit the fourth figure, though logicians have argued that it has to do with how he defines a syllogism. We learn from Bertrand Russell, in his Cambridge Essays, that

The fourth figure…was added by Aristotle’s pupil Theophrastus and does not occur in Aristotle’s work, although there is evidence that Aristotle knew of fourth-figure syllogisms.

Theophrastus apparently recognized three more valid forms of figure 4: AAI, AEE, and IAI, bringing the total to 19. These were given Latin names by medieval scholars, but that will be the topic for my next post.

Paul Echoes Aristotle on Friendship

Rhetoric, ,

24__Paul_the_ApostleReading Aristotle’s Rhetoric II.4 on “friendship” is like reading an expanded version of  the Apostle Paul’s 1 Corinthians 13:4-7, which reads:

Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It does not dishonor others, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres.

2__AristotleIt is not hard to show that every single phrase in this Bible passage alludes to some portion of that section from Aristotle’s Rhetoric. Read more here: Rhetoric 2.4 & I Cor 13.

Either the Apostle Paul knew his Aristotle, or they have a nearly identical understanding of the love between friends.

Rhetoric-2.4-I-Cor-13

Genus & Species Bonus

Introductory Logic, Why learn logic?, ,

Lessons about genus and species charts often emphasize the capability of these charts to show relationships between terms (i.e. this is a kind of that). This is one benefit, but we should also note the benefit they provide in helping to develop arguments. Two classic examples should help to demonstrate this.

In C. S. Lewis’s The Lion, The Witch, and The Wardrobe, Susan and Peter are concerned with Lucy, who insists that she has gotten into the land of Narnia through a magic wardrobe. The Professor proceeds to develop an argument based off of this genus and species chart: Continue reading Genus & Species Bonus →

The extreme right

Classical Education

“I am no enemy of the classics. I have read the Aeneid through more often than I have read any long poem; I have just finished re-reading the Iliad; to lose what I owe to Plato and Aristotle would be like the amputation of a limb. Hardly any lawful price would seem to me too high for what I have gained by being made to learn Latin and Greek. If any question of the value of classical studies were before us, you would find me on the extreme right.”

— C. S. Lewis, The Idea of an ‘English School’

 

The Philosopher and the Apostle

Classical Education, Old Western Culture, Rhetoric, ,

Aristotle presents the general line of argument “That if it is possible for one of a pair of contraries to be or happen, then it is possible for the other: e.g. if a man can be cured, he can also fall ill; for any two contraries are equally possible, in so far as they are contraries” (Rhetoric II.19).

I was wondering if anyone would really argued this way, when I recalled an argument from Paul about the resurrection: “For since death came through a man, the resurrection of the dead comes also through a man. For as in Adam all die, so in Christ all will be made alive” (1 Cor. 15:21-22).

Paul either knows his Aristotle, or Aristotle knows how people think.

Paul Preaching to the Ephesians
Paul Preaching at Athens