Imperfect Syllogisms
The shortened or lengthened forms of the syllogism — Enthymeme, Epichirema, Polysyllogism, Sorites, and Dilemma — each with its law of correctness and worked examples, plus a note on Argument from Analogy and Argument from Hypothesis.
An imperfect syllogism is shortened or lengthened relative to the perfect three-proposition form. The Enthymeme abbreviates by leaving a premiss unexpressed (supply it before judging). The Epichirema adds an explanatory clause to a premiss (reduce to the simple syllogisms it conceals). The Polysyllogism chains syllogisms, each conclusion becoming the next major premiss; the Sorites compresses this into a single chain of propositions, governed by its own law (only the first premiss may be particular, only the last may be negative). The Dilemma argues from a disjunction plus two conditionals converging on one conclusion — illustrated by the Protagoras-Eualthus legal dispute and the Calif Omar's justification for burning the Library of Alexandria — and must be checked for a genuinely complete disjunction, since a faulty dilemma can be 'retorted' upon its user. Finally, Argument from Analogy (similitude, example, parable — yielding probability, not certainty) and Argument from Hypothesis (a provisional explanation tested by attempts to upset it, becoming a theory and eventually scientific law if it survives and explains all the data) are distinguished from strict syllogistic reasoning, with the evolution hypothesis discussed as a worked case.
Article 4. Imperfect Syllogisms
An imperfect syllogism is a shortened or lengthened syllogism. It usually has less or more than three propositions, or has an explanatory clause attached to one or both premisses. Important types of imperfect syllogisms are the following:
1. The Enthymeme
This is an abbreviated syllogism, one of the premisses being unexpressed but clearly understood. Example:
God is holy; therefore, He hates sin.
As a syllogism fully expressed, this argument would be:
He who is holy, hates sin God is holy Therefore God hates sin.
Other examples of the Enthymeme:
It rains; therefore, my friend will not come. John is a good son; therefore, he will take care of his aged parents. Prudent men praise this method of business; therefore, it is a sound one.
Law for the Enthymeme: Supply the missing premiss, and judge by the Laws of Syllogisms.
It is important that this law be carefully observed. Precipitation often leads to false conclusions through failure to observe the law. A faulty Enthymeme is usually the result of error in the unexpressed member. Therefore, always supply the missing premiss before evaluating this form of argument. Criticize the following:
I don’t understand this; therefore, it isn’t true. This method of doing business is praised; therefore, it is a good one. I saw it in the paper; hence it must be true.
2. The Epichirema
This is a syllogism which adds an explanation or justification to one or both of the premisses. Example:
Man has a spiritual soul, for he can reason; A spiritual soul is immortal, since what is spiritual cannot corrupt; Therefore, man has an immortal soul.
We see at once that there are Enthymemes involved in the premisses of the Epichirema. In the illustration we find the following:
Man can reason; therefore he has a spiritual soul.
(Full syllogism: If man can reason, he has a spiritual soul; Man can reason; Therefore, he has a spiritual soul.)
A spiritual being cannot corrupt; therefore, it is immortal.
(Full syllogism: Whatever is spiritual cannot corrupt; Man’s soul is spiritual; Therefore, man’s soul cannot corrupt.)
The Epichirema may be made into a simple syllogism by lopping off the explanatory clauses from the premisses. Thus the example here given, minus its explanations or justifications, is the following:
Man has a spiritual soul A spiritual soul is immortal Therefore, man has an immortal soul.
This simple syllogism, plus the syllogisms developed from the Enthymeme-premisses, must all meet with the requirements of the Laws of Syllogisms to insure correctness in the Epichirema. Therefore we state the following law:
Law for the Epichirema: Reduce the Epichirema to the simple syllogisms involved in it and criticize these by the Laws of Syllogisms.
3. The Polysyllogism
This is a series of syllogisms so connected as to form an unbroken chain of argument. The conclusion of one syllogism becomes the major premiss of the next. Example:
He who is prudent is temperate He who is temperate is constant Therefore, he who is prudent is constant;
He who is constant is imperturbable Therefore, he who is prudent is imperturbable;
He who is imperturbable is without sadness Therefore, he who is prudent is without sadness;
He who is without sadness is happy Therefore, he who is prudent is happy.
Law for the Polysyllogism: Reduce the Polysyllogism to syllogisms fully expressed, and judge by the laws of Syllogisms.
4. The Sorites
This is a shortened form of Polysyllogism. It consists of a number of propositions so connected that the predicate of one becomes the subject of the next, and so on to the last premiss inclusive; then the conclusion connects the predicate of the last premiss with the subject of the first. Example:
He who is prudent is temperate He who is temperate is constant He who is constant is imperturbable He who is imperturbable is without sadness He who is without sadness is happy Therefore, he who is prudent is happy.
Law for the Sorites: No premiss may be particular but the first, and no premiss may be negative but the last. In other words:
- The first premiss may be an A- or I-proposition;
- The last premiss may be an A- or an E-proposition;
- All other premisses must be A-propositions.
The reason for this rule is found in the Laws of Syllogisms, for two negatives or two particulars in the premisses would make conclusion impossible.
Examples for criticism:
A ton of hay is a weight A wait is a short stop A short-stop is a ball-player Therefore, a ton of hay is a ball-player.
A good man has a good conscience He who has a good conscience enjoys peace He who enjoys peace is happy Therefore, a good man is happy
Three dogs are more than two dogs Two dogs are more than one dog One dog is more than no dog No dog is more than seven dogs Therefore, three dogs are more than seven dogs.
5. The Dilemma
This is a form of argument consisting of a disjunctive proposition and two conditional propositions (connective type), each of which leads to the same practical conclusion. It is sometimes called “the horned syllogism,” and the two conditionals are the “horns” designed to gore an adversary. Yet the Dilemma must be constructed in the most accurately correct manner, else it may easily be retorted upon the person who uses it. Examples:
The skeptical doctrine that we can have no certainty of anything is either true or false; If it is true, we cannot accept the skeptical doctrine itself as certain; If it is false, then we cannot accept it; Therefore, in no case can we accept the skeptical doctrine.
The Catholic Religion was propagated either with the aid of miracles, or without miracles; If propagated with the aid of miracles, it is true; for miracles are a certain evidence of truth in that which they are performed to support; If propagated without miracles, then its rapid spread in the face of superhuman difficulties and furious opposition is the greatest miracle; Therefore, in any case, the Catholic Religion is true.
Law for the Dilemma: Let the major premiss be a complete disjunction, and let the consequents of the conditional premisses be strictly drawn.
Examples for criticism:
Eualthus studied law under Protagoras, agreeing to pay for the teaching when he should win his first case. After finishing his studies, Eualthus took up a business other than law, and so defended no cases. Protagoras brought suit to recover his fees. Then came the following exchange of Dilemmas:
Protagoras: “Judges, you will presently decide this case. Eualthus will be told that he has won or lost it. If he loses it, he must pay me by your order; and if he wins it, he must pay me by the terms of our agreement. Therefore, in any case, he must pay me.”
Eualthus: “Judges, if I win the case, I am absolved from obligation to pay by your order; if I lose, I am absolved by the terms of our agreement. Therefore, in no case must I pay Protagoras.”
The judges dismissed the case. How would you decide it? Why?
An Athenian was dissuaded from seeking office by the following argument: “Do not seek for this office. If you achieve it and rule well, you will displease the bad citizens; and if you rule ill, you will displease the good citizens. Therefore, in any case, your rule will occasion displeasure, and you should not seek the place.” Let the student construct this argument in strict Dilemma-form. Then let him criticize it by the Law for the Dilemma, and construct its “retort.”
The Calif Omar justified the burning of the Library of Alexandria in the following manner: “Either these books agree with our Koran or they are in opposition to it. If they agree, they are useless; if they are in opposition to it, they are dangerous. Therefore, in any case, they should be destroyed.” Let the student criticize this dilemma, and “retort” it.
If there is such a thing as a cause, it cannot be known as such. For a cause would have to occur at one of three possible points of time, viz., before its effect, after its effect, or simultaneously with its effect. But if it occur before its effect, it is a cause before it is a cause! If it occur after its effect, it is no cause at all, since that which it supposedly produced existed before the so-called cause. If it occur simultaneously with its effect, it is impossible to know which of the concurring events is cause, and which is effect. Therefore, in no case can a cause be known as such.
The last example should be called a “Trilemma,” since its disjunctive premiss involves three possibilities. One with four possibilities should be called a “Quadrilemma,” and so on. But the term “Dilemma” is generally used to indicate any argument of this character.
A Note on Two Further Forms of Argument
Here, at the end of our study of Imperfect Syllogisms, it may be well to add a note concerning two forms of Argument which the Dialectician must notice, viz., Argument from Analogy, and Argument from Hypothesis.
i. Argument from Analogy
An Argument from Analogy is one in which a fact is deduced from another because of resemblance that exists or appears to exist between them. Pathology, for example, employs analogy in tracing the causes of various diseases, concluding from the like character of certain diseases to their common nature. The principle of analogy is: “Whatever prevails in one member of a class of similar things probably prevails in the other members also.”
Analogy often opens the way for valid induction, but in itself it affords mere probability, not certainty, in its conclusions.
Arguments from analogy are called similitude, example, and parable. To illustrate:
i. Similitude: “When a man builds a temple, he clears away the loose surface soil and lays his foundation upon the solid rock beneath. Now every Christian must make his soul the temple of God. Hence he must clear away the loose soil of the passions, the mere emotions, and base the structure solidly upon faith and love.”
ii. Example: “Be patient, brave, and hopeful, as the great Father of his Country was.” Example is regularly historical, never a fiction.
iii. Parable is a fiction constructed to point a moral, or illustrate a truth.
ii. Argument from Hypothesis
Hypothesis is the assuming of an unproved proposition as the provisional explanation of facts investigated. It affords the investigator a starting-point and a working-basis. Suppose an investigator wishes to know whether steam has motive-power. He assumes that it has such power; and this is his hypothesis. Then he tries to upset his own hypothesis, not to find justification for it. It is his starting-point, his working-basis, and if it cannot stand assault, it is to be abandoned. Suppose the hypothesis that steam has motive-power stands up under all the tests and experiments. It looks more and more like the right explanation of observed facts. It is now a theory. If the theory stands the careful and sufficient tests to which it is then subjected, if it be found to explain all the facts that the investigator assumes it to explain, then it becomes a scientific fact, a scientific law. The hypothesis of the motive-power of steam may be subjected to this process, and it emerges a scientific fact and law.
Suppose evolution is assumed as a hypothesis for explaining the data of geology and biology. It looks like a probable explanation of the gradation observed in the life-forms on earth, in the earth’s strata, and in the fact that certain species of plant and animal life are now extinct, and that other species now exist which did not exist formerly. Thus it is a hypothesis. It is subjected to test. If it tries to explain development of the earth and life as gradual and continuous, it faces the fact that there is not a trace of true intermediate forms, of stages of passage from one species of life-form to another; it has not one Missing Link to find, but ten million. This fact prevents the hypothesis from developing into a theory. But if evolution is content to explain development by “jumps,” sudden changes, it need not look for intermediate forms; still, this explanation seems contrary to the ordinary development of individuals and of classes of life-forms as we know them. Analogy at least is against this assumption. Therefore, the evolution hypothesis remains a hypothesis. In our day, many teachers and writers assert it as a theory, and some even assert it as scientific fact. The honest scientist, however, never makes unsupported claims — and such a claim as we have mentioned is absolutely without support. Still, it is a hypothesis. As regards man, the Catholic finds it in conflict with truth which he knows by Divine Science, and he is right to reject it. But in the lower life-forms, it may be found true; and so it is still the working-basis, the hypothesis of many scientists.
For a hypothesis to be worthy of its name it should have probability to begin with; it should look like the explanation of data investigated. In the second place, it must be found to explain all the data, else it is to be rejected as inadequate, and useless scientifically.
Summary of the Article
In this Article we have learned how to construct and to criticize the arguments known as the Enthymeme, the Epichirema, the Polysyllogism, the Sorites, and the Dilemma. We have studied the matter of argument from analogy and from hypothesis.