  1. ENTHYMEME.An enthymeme is a syllogism in which one of the three propositions is omitted. Suppressing the major premise gives an enthymeme of the first order; whereas if the minor premise be suppressed, the enthymeme becomes one of the second order; while omitting the conclusions gives an enthymeme of the third order. Illustrations: Complete syllogism. All true teachers are just, You are a true teacher, (Hence) You are just. Enthymeme of first order; major premise omitted. .......................... You are a true teacher, (Hence) You are just. Enthymeme of second order; minor premise omitted. All true teachers are just, .......................... (Hence) You are just. Enthymeme of the third order; conclusion omitted. All true teachers are just, (And) You are a true teacher, .......................... To argue in terms of the complete syllogism is the unusual, not the usual method. We have a way of abbreviating our remarks; expressing only the necessary and leaving the obvious to be taken for granted. Thus the enthymeme becomes the natural form of expression. But the mere fact that a part of the argument is omitted, makes it more essential for the student to think clearly and with careful continuity, that no error may intrude itself. Probably the most common enthymemes are those of the first order. This may be explained by the fact that the major premise is usually the most universal of the three propositions, and, in consequence, the one which would be the most generally understood. The following represent enthymemes of this order, gleaned from the ordinary conversation of ordinary people: (1) “Your beets won’t grow, because you are planting them in the wrong time of the moon.” (2) “You, being a member of the Sunday School, should be ashamed of such language.” (3) “Being the son of your father, you ought to have some pride in this matter.” (4) “We are going to have an open winter, because Ihave observed that the hornets’ nests are near the ground.” (5) “You had better put in lots of coal, for Ihave noticed that the squirrels have gathered in more nuts than usual.” Judging from these enthymemes, it would seem to be more natural to assert the conclusion and follow this by The enthymeme of the second order occurs only infrequently, since it seems to be an unnatural mode of expression, though sometimes it appears to lend emphasis to the conclusion; e.g., “All untrustworthy boys come to a bad end, and Ipredict that you will come to a bad end.” Enthymemes of the third order are commonly used for the sake of emphasis, as the following make evident: (1) “No business man wants an indolent boy, and you are indolent.” (2) “All successful teachers are interested in their work, and you plan to be a successful teacher.” (3) “Humility is a sign of greatness, and Lincoln possessed this quality.” 2. EPICHEIREMA.An epicheirema is a syllogism in which one or both of the premises is an enthymeme. To put it in another way: An epicheirema is a syllogism in which one or both of the premises is supported by a reason. When one premise is an enthymeme the syllogism is termed a single epicheirema; whereas when both premises are enthymemes it becomes a double epicheirema. Single epicheirema. All men are mortal, because all men die, Socrates was a man, ? Socrates was mortal. Double epicheirema. All men are mortal, because all men die, Socrates was a man, because he was a rational animal, ? Socrates was mortal. It is obvious that supporting each premise with a reason lends strength to the argument. This justifies the use of the epicheirema. 3. POLYSYLLOGISM.A polysyllogism is a series of syllogisms in which the conclusion of a preceding syllogism becomes a premise of a succeeding one. The syllogism in the series whose conclusion becomes a premise of the succeeding syllogism is termed a prosyllogism; while the syllogism which uses as one of its premises the conclusion of the preceding syllogism is called an episyllogism. Illustrations.
4. SORITES.A sorites is a series of syllogisms in which all of the conclusions are omitted except the last one. Just as the epicheirema is a combination of enthymemes of the first and second orders, so the sorites is a combination of enthymemes of the third order. If each conclusion were written, the sorites would take the form of prosyllogisms and episyllogisms. Two forms of the sorites are recognized by logicians. These are the progressive or Aristotelian, and the regressive or Goclenian. Illustrations. Progressive Symbolized. Put in Word Form. All A is B Thomas Arnold was a teacher, All B is C A teacher is a man, All C is D A man is a biped, All D is E A biped is an animal, Hence all A is E Hence Thomas Arnold was an animal. Regressive All A is B A biped is an animal, All C is A A man is a biped, All D is C A teacher is a man, All E is D Thomas Arnold was a teacher, Hence all E is B Hence Thomas Arnold was an animal. When regarded from the viewpoint of extension, the progressive sorites proceeds from the smaller to the larger while the regressive is the converse of this. The point may be illustrated by circles: FIG. 15. Circle 1 stands for Thomas Arnold. Circle 2 stands for teacher. Circle 3 stands for man. Circle 4 stands for biped. Circle 5 stands for animal. The progressive sorites proceeds from the smaller circle to the larger, thus: All of circle 1 belongs to 2 All of circle 2 belongs to 3 All of circle 3 belongs to 4 All of circle 4 belongs to 5 Hence, All of circle 1 belongs to 5 The regressive sorites proceeds from the larger to the smaller; i.e.: All of circle 4 belongs to 5 All of circle 3 belongs to 4 All of circle 2 belongs to 3 All of circle 1 belongs to 2 Hence, All of circle 1 belongs to 5 Other differences become apparent when the omitted conclusions are expressed. Progressive Symbolized Word Form All A is B T. Arnold was a teacher, (A) All B is C A teacher is a man, (A) ? All A is C ? T. Arnold was a man. (A) All C is D A man is a biped, (A) ? All A is D ? T. Arnold was a biped. (A) All D is E A biped is an animal, (A) ? All A is E ? T. Arnold was an animal. (A) In the three completed syllogisms it becomes evident that the progressive sorites uses the minor as its first premise and in consequence takes the form of the fourth figure, though the reasoning is according to the first figure. The progressive sorites must conform to the following rules: (1) The first premise may be universal or particular, all the others must be universal. (2) The last premise may be affirmative or negative; all the others must be affirmative. A violation of the first rule would result in undistributed middle; whereas a violation of the second rule would give illicit major. These rules may be illustrated by giving attention to the symbols of the foregoing completed syllogisms. The first completed syllogism of the sorites is: All A is B All B is C ? All A is C Securing a logical arrangement by interchanging the major and minor premises gives: (A) All (M) (A) All (S) (A) ? All (S) Applying the rules we find this syllogism valid, or we may recall that A Let us now make the first premise of the sorites particular and test. Some A is B All B is C ? Some A is C Arranged logically: (A) All (M) (I) Some (S) (I) ? Some (S) Proof: Since one premise is particular the conclusion must be particular. (Rule7) As there are no negatives in the argument, only one conclusion is possible; namely, a particular affirmative (I). Thus, instead of the conclusion, “All A is C,” which is an (A), it must be, “Some A is C,” or an (I). Underscoring the distributed term, it is seen that the middle term is distributed in the major premise and that no term is distributed in the conclusion. Thus the mood is valid. This is “checked” when we recall that AII is always valid in the first figure. We have now shown that the first premise of a progressive sorites may be universal or particular. Let us further Data: Given the first completed syllogism of the sorites: All A is B All B is C ? All A is C Proof: Let any other premise, such as the second, be particular; this gives the following: All A is B Some B is C ? Some A is C Arranged logically: Mood, figure, and distribution indicated. (I) Some (M) (A) All (S) (I) ? Some (S) We note at once that the middle term is undistributed, hence the mood I The truth of the first rule has been demonstrated, and now we may follow a similar plan to prove the truth of the second rule. Problem: To prove that the last premise may be negative.11 Data: Given the last completed syllogism: All A is D Let us make the last premise negative (E) and test the result. (As all but the first must be universal we cannot use an O.) All A is D No D is E ? No A is E Arranged logically and symbolized: (E) No (M) (A) All (S) (E) ? No (S) Proof: Negative premise; negative conclusion. No particulars. Middle term distributed in major premise. No term distributed in conclusion which is not distributed in premise where it occurs. Syllogism valid. We must now prove that all the other premises must be affirmative. Problem: To prove that no other premise can be negative, or that all others must be affirmative. Data: Given last syllogism of sorites with the first premise negative. (Any other may be taken.) No A is D All D is E ? No A is E Arranged logically and symbolized: (A) ? All (M) (E) No (S) (E) ? No (S) Proof: “G” is distributed in the conclusion but not in the major premise. Fallacy of illicit major. Hence no other premise can be negative. We may now consider the completed syllogisms of the regressive sorites. All A is B All C is A ? All C is B All D is C ? All D is B All E is D ? All E is B By examining the foregoing it becomes apparent that the regressive sorites, both in form and in the reasoning, adapts itself to the first figure. The rules of the regressive sorites are just the reverse of the progressive. These are: (1) The first premise may be negative; all the others must be affirmative. (2) The last premise may be particular; all the others must be universal. It would be a valuable exercise for the student to test these rules according to the plan pursued in treating the progressive sorites. 5. IRREGULAR ARGUMENTS.It has been intimated that a syllogistic argument, in order to be logical, should be made to conform to the rules of the syllogism. It must not be inferred from this, however, that all deductive reasoning is included by the logical forms here treated. There seem to be arguments which yield valid conclusions, and yet which are not logical in the strict sense of the word. The following illustrate some of these forms: (1) Quantitative Arguments. John is taller than James, Albert is taller than John, ? Albert is taller than James. Here, apparently, is a fallacy of four terms: these four terms are (1)John, (2)taller than James, (3)Albert, (4)taller than John. Yet we know that the argument is valid. There is not a particle of doubt in the mind relative to the truth of the conclusion that “Albert is taller than James.” We are consequently forced to the inference that such quantitative arguments lie outside the field of syllogistic reasoning. The argument involves this new principle, “Whatever is greater than a second thing which is greater than a third thing is itself greater than a third thing.” There are many other arguments similar to this which are not syllogistic in nature. To wit: A equals B, B equals C, C equals D; A equals D. A is a brother of B, B is a brother of C, C is a brother of D; A is a brother of D. A is west of B, B is west of C, C is west of D; A is west of D. (2) Plurative Arguments. These are arguments in which the propositions are introduced by more or most; e.g.: Most (more than half) of the team are seniors, Most (at least half) of the team are under twenty, ? Some students under twenty are seniors. Here we have an I 6. OUTLINE.INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS. (1) Enthymeme. First, second and third orders. Natural form. (2) Epicheirema. Single, double. (3) Polysyllogism. Prosyllogism, episyllogism. (4) Sorites. Progressive, regressive. Two rules of each. (5) Irregular Arguments. Quantitative, plurative. 7. SUMMARY.(1) An enthymeme is a syllogism in which one of the three propositions is omitted. Suppressing the major premise gives an enthymeme of the first order; omitting the minor gives one of the second order; while omitting the conclusion gives one of the third order. The enthymeme is really the natural form of expression. Enthymemes of the first order are the most common while those of the third order are the most emphatic. (2) An epicheirema is a syllogism in which one or more of the premises is an enthymeme. An epicheirema is said to be single when but one premise is an enthymeme, and double when both premises are enthymemes. (3) A polysyllogism is a series of syllogisms in which the conclusion of the preceding syllogism becomes a premise of the succeeding one. The one of the series whose conclusion becomes a premise is termed a prosyllogism; while the one which uses the conclusion as a premise is called an episyllogism. (4) A sorites is a series of syllogisms in which all the conclusions are omitted except the last one. The two kinds of sorites are the progressive and regressive. The progressive uses the “minor” as its first premise and adopts the form of the fourth figure, whereas the regressive uses the “major” as its first premise and adopts the form of the first figure. The two rules of the progressive sorites are, (1)“The first premise may be particular, all the others must be universal”; (2)“The last premise may be negative, all the others must be affirmative.” The two rules of the regressive are, (1)“The first premise may be negative, all the others must be affirmative”; (2)“The last premise may be particular, all the others must be universal”. (5) Irregular arguments are such as yield valid conclusions and yet do not conform to the syllogistic rules. The quantitative argument expresses quantity and contains four terms. This argument is based on the principle, “What ever is greater than a second thing which is greater than a third thing is itself greater than a third thing.” Plurative arguments are introduced by “more” or “most” and 8. REVIEW QUESTIONS.(1) Define and illustrate an enthymeme. (2) Illustrate the enthymemes of the three orders and point out their distinct uses. (3) Why should the enthymeme demand closer thought than the ordinary syllogism? (4) Define and illustrate the epicheirema. (5) Of what use is the epicheirema? Illustrate. (6) Define and illustrate a prosyllogism and an episyllogism. (7) Why are polysyllogisms so called? (8) Define and illustrate the sorites. (9) Relate the sorites and the epicheirema to the enthymeme. (10) Illustrate the two forms of sorites. (11) Explain the two forms of sorites by means of a diagram. (12) Prove the truth of the two rules of the progressive sorites. (13) Illustrate two kinds of irregular arguments and show that they are valid. (14) Complete the five enthymemes of page248 and indicate their mood and figure. 9. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.(1) Why should enthymemes of the second order be less common than those of the first? (2) You desire to make it evident to a child that a small beginning often leads to a momentous ending; do so in terms of the enthymeme of the first order. (3) Show that prosyllogism and episyllogism are relative terms. (4) When the common premise of the “pro” and “epi” syllogism is omitted what abbreviated form results? (5) From the viewpoint of your definition criticise this: “Asorites is a series of prosyllogisms and episyllogisms in which all of the conclusions are suppressed except the last.” (6) Prove the truth of the two rules of the regressive sorites. (7) Show that the prosyllogism and the episyllogism may be progressive or regressive. (8) “Reasoning from cause to effect”—is such progressive or regressive? Explain. (9) Which is inductive in nature, the progressive form of reasoning or the regressive? Explain. (10) Test the validity of the enthymemes on pages 248 and 249. (11) “A sorites is at least as immediately convincing as the chain of syllogisms into which it can be decomposed.” Discuss this. |
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