Imperfect Syllogisms
Shortened and lengthened forms of the syllogism: the Enthymeme, Epichirema, Polysyllogism, Sorites, and Dilemma; followed by a note on Argument from Analogy and Argument from Hypothesis.
Several abbreviated or extended forms of the syllogism are treated. The Enthymeme suppresses one premise (the most common form of actual argument: 'He is mortal, for he is a man' — the universal major is suppressed). The Epichirema is a syllogism in which one or both premises carry their own supporting reasons appended to them. The Polysyllogism is a chain of syllogisms in which the conclusion of one becomes a premise of the next. The Sorites is a compressed polysyllogism with all intermediate conclusions suppressed, yielding only the final conclusion from the chain of premises. The Dilemma presents a conditional major with a disjunctive minor: whatever horn of the dilemma is chosen, the conclusion follows. An Argument from Analogy transfers a property from a known case to a relevantly similar unknown case; it is never demonstrative but may be highly probable.
An imperfect syllogism is a shortened or lengthened syllogism — usually having fewer or more than three propositions, or having an explanatory clause attached to one or both premisses.
1. The Enthymeme
The Enthymeme is an abbreviated syllogism in which one of the premisses is unexpressed but clearly understood.
God is holy; therefore, He hates sin.
Fully expressed:
He who is holy hates sin. God is holy. Therefore God hates sin.
Other examples:
- “It rains; therefore, my friend will not come.”
- “John is a good son; therefore, he will take care of his aged parents.”
Law for the Enthymeme: Supply the missing premiss, and judge by the Laws of Syllogisms.
This law must be carefully observed. Faulty enthymemes usually conceal their error in the unexpressed premiss. Always supply it before evaluating the argument.
2. The Epichirema
The Epichirema is a syllogism that adds an explanation or justification to one or both premisses:
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.
The italicised clauses are Enthymemes embedded in the premisses. The Epichirema may be made into a simple syllogism by removing these explanatory clauses:
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 embedded Enthymeme-premisses, must all meet the Laws of Syllogisms.
Law for the Epichirema: Reduce the Epichirema to the simple syllogisms involved in it and criticise these by the Laws of Syllogisms.
3. The Polysyllogism
The Polysyllogism is a series of syllogisms so connected as to form an unbroken chain of argument. The conclusion of each syllogism becomes the major premiss of the next:
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 to syllogisms fully expressed, and judge by the Laws of Syllogisms.
4. The Sorites
The Sorites 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; the conclusion then connects the predicate of the last premiss with the subject of the first:
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.
- No premiss may be negative but the last.
- In other words: the first premiss may be A or I; the last premiss may be A or E; all other premisses must be A.
The reason: two negatives or two particulars in the premisses (when the Sorites is expanded into its constituent syllogisms) would make conclusion impossible.
5. The Dilemma
The Dilemma (“the horned syllogism”) is a form of argument consisting of:
- a disjunctive proposition (the major premiss), and
- two conditional propositions (each a horn), both leading to the same practical conclusion.
Example:
The skeptical doctrine that we can have no certainty of anything is either true or false. If true, we cannot accept the skeptical doctrine itself as certain. If false, then we cannot accept it. Therefore, in no case can we accept the skeptical doctrine.
Another example:
The Catholic Religion was propagated either with the aid of miracles, or without miracles. If with miracles, it is true (miracles certify truth). If without miracles, its rapid spread in the face of superhuman difficulties 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.
A Dilemma improperly constructed may be retorted — turned back upon the person who uses it. The famous exchange between Protagoras and his student Eualthus illustrates this: each party constructed a Dilemma that seemed to prove the opposite conclusion from the same facts. The judges dismissed the case; the student may consider how they might have decided it.
A Dilemma with three possibilities is called a Trilemma; with four, a Quadrilemma; but the general term Dilemma is used for any argument of this character.
A Note on Two Further Forms of Argument
Argument from Analogy
An Argument from Analogy deduces a fact from another because of resemblance between them. Its principle: 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 affords only probability, not certainty.
Three forms:
- Similitude: draws a parallel between two situations to illuminate one by the other. “When a man builds a temple, he clears away loose soil and lays his foundation on solid rock. So every Christian must clear away the passions and base the soul’s structure on faith and love.”
- Example: a historical parallel. “Be patient, brave, and hopeful, as the great Father of his Country was.” (Always historical, never fictional.)
- Parable: a fiction constructed to point a moral or illustrate a truth.
Argument from Hypothesis
Hypothesis is the assuming of an unproved proposition as the provisional explanation of facts under investigation — a starting-point and working-basis. The investigator’s task is then to try to upset the hypothesis, not to justify it.
If the hypothesis withstands all tests and is found to explain all the facts it was assumed to explain, it becomes a theory. If the theory survives sufficient and careful testing, it becomes a scientific fact or scientific law.
A hypothesis should have initial probability — it must look like the right explanation. If it cannot explain all the data, it is to be rejected as inadequate.
Summary of the Article
We have learned how to construct and criticise the Enthymeme (supply the missing premiss), the Epichirema (reduce to simple syllogisms), the Polysyllogism (reduce to fully expressed syllogisms), the Sorites (first premiss may be particular; last may be negative; all others must be A), and the Dilemma (complete disjunction; strictly drawn consequents). We have also studied the nature and limits of Argument from Analogy and Argument from Hypothesis.