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Mini-Course in Philosophy The Logical Question |
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Section 4: Reasoning and Argument Topics:
a) Reasoning Reasoning, the third and most complex of the major operations of the mind, is a roundabout or mediate way of reaching a judgment that cannot be made immediately. It is an operation of the mind in which the relation of two ideas (as agreeing or disagreeing) is inferred from their respective relation to a common third idea. The man who realizes that one and one make two does so immediately. His comparison of the ideas "one and one" and "two" shows him that these are identical. But the man who proves that the angles of any triangle come to a sum of 180 degrees has reached his final judgment after a long series of connected judgments, each of which was arrived at by comparing two ideas with a common third. He has reached the final conclusion by a process of sustained reasoning or mediate inference or discursive thought. Each step of the reasoning process by which we "think things out" consists, implicitly or explicitly, of three judgment. In the first of these, one of the two ideas which we seek to bring together in final judgment is compared with a common third; in the second, the other idea is compared with the common third. These two judgments constitute the antecedent element of reasoning. The judgment which is latent in the antecedent is explicitly rendered as the consequent element of reasoning. The antecedent thus consists of two judgments called the premises. The consequent is a single judgment called the conclusion. Thus the reasoning process proceeds in this fashion: Antecedent:
Consequent:
The three judgments are the "matter" of reasoning; the "form" of reasoning is the logical connection or sequence (known technically as consequence) which show that the final judgment (the conclusion) is inevitably to be drawn from the other two (the premises). Certain general laws of reasoning are to be noticed:
Reasoning is deductive when its course is from the more general to the less general; it is inductive when its course is from the less general to the more general. Deductive reasoning is called deduction; inductive reasoning is called induction. These are not opposed methods of reasoning; they are supplementary. To argue from the fact that all metals are heavier than water to the fact that this metal or these several metals are heavier than water is deduction. To argue from the fact that this or these metals are heavier than water is induction. Pure reasoning, as in most mathematical sciences, is deductive; reasoning based on experiment and observation of data is inductive.
b) Expression of Reasoning - Argument
Argument or argumentation is therefore a formula of terms and propositions which gives outer expression to the reasoning process and its result. The most perfect form of argument is the syllogism.
The propositions express the antecedent and the consequent elements of the reasoning process, and they are known by the same names. The antecedent element of the syllogism conists of two propositions called the premises (the first of which is the major premise, and the second the minor premise); the consequent element consists of a single proposition called the conclusion. There are two main types of the syllogism, the categorical syllogism, and the hypothetical syllogism. The categorical syllogism consists of three categorical propositions. The hypothetical syllogism consists of one hypothetical proposition and two categorical propositions. Examples: Categorical syllogism:
Hypothetical syllogism:
Although fundamentally the laws governing the syllogism are the same for all types, it is a convenience for the student to have definite regulations for the forming and judging of each type, and so we shall presently discuss two sets of laws, one for the categorical syllogism, and one for the hypothetical syllogism. The material element or "matter" of the syllogism consists of three propositions, and ultimately of three terms each of which occurs twice. We have already learned that the propositions are called major premise, minor premise, and conclusion. We must now learn that the terms are called major term, minor term, and middle term. The major term is the term which serves as the predicate of the conclusion. The minor term serves as the subject of the conclusion. The middle terms is that with which the major term and the minor term (called the extremes) are compared in the premises; it does not occur in the conclusion. In the first premise, that is, the major premise, one of the extremes is compared with the mean or middle term; in the other premise, that is, the minor premise, the other extreme is compared with the mean or middle term; in the conclusion, the extremes are brought together as subject and predicate of an affirmation or denial. Hence, the middle term (called the mean in contrast to the extremes) is the term which is found in each premise but not in the conclusion.
c) The Laws of Argument The laws of argument are the reasoned rules which must be observed if the syllogism is to be correct and legitimate. Since there are two main types of argument, viz., the categorical syllogism and the hypothetical syllogism, we set forth two sets of laws.
Here we have eight laws, four of which apply to the terms of the categorical syllogism, and four to the propositions of the syllogism. Laws of Terms
Laws of Propositions
The "figure" of the categorical syllogism is determined by the position of the middle term in the premises. The middle term may be:
Hence there are four figures of the categorical syllogism. These are called simply the First, Second, Third, and Fourth Figures. If we take M to stand for the middle term, P for the major term, and S for the minor term, we may thus illustrate the four figures: Figure I
Figure II
Figure III
Figure IV
The first figure is called the most perfect figure for the reason that in it the necessity of drawing the given conclusion is most plainly evident. Hence logicians have developed an elaborate system of rules for "reducing syllogisms of the last three figures," that is, of restating these syllogisms in the shape of the first figure. We shall not pause to discuss this "reduction of syllogisms." In addition to "figure," each categorical syllogism has "mood." The mood of a syllogism is determined by the sequence of types of propositions which compose it. Since categorical syllogisms are made up of propositions of the types A-, E-, I-, O-, the mood of syllogisms is expressed in these letters. A syllogism like this...
is called AAA because it consists of three A-propositions; we say its mood is AAA. The following syllogism is in the mood AII:
There are nineteen useful moods of categorical syllogisms. Other combinations of types of propositions than these nineteen are useless, for they make up syllogisms which do not square with the laws of terms and propositions already studied; hence they make invalid syllogisms. The nineteen useful moods are these:
A hypothetical syllogism is a syllogism which has a hypothetical proposition as its major premise. Now, there are three types of hypothetical proposition: the conditional, the conjunctive, and the disjunctive.
Thus it appears that all types of hypothetical propositions are reducible to the conditional type. Still we distinguish three types of hypothetical syllogism according to the three types of hypothetical propositions, and we express rules for each. The thoughtful student will not have great difficulty in thinking out the reasons for these rules; he or she will find the basis of all of them in the fact that all hypotheticals can be reduced to the conditional type and are ultimately governed by the laws which spring from its nature. Here we briefly discuss: the conditional syllogism, the conjunctive syllogism, and the disjunctive syllogism. (a) The Conditional Syllogism The first part of the major premise (the conditional proposition in the syllogism) is called the antecedent, the second part is the consequent. Thus, in the proposition, "If it rains, there will be no game," the antecedent is found in the words "If it rains"; the consequent is found in the words, "there will be no game." The laws upon which the conditional syllogism is based are these:
Hence, the following is a valid conditional syllogism: "If it rains, there will be no game. It rains. Therefore there will be no game." But this conditional syllogism is invalid: "If it rains, there will be no game. There will be no game. Therefore, it rains." As is evident, the game may be canceled for a variety of reasons other than unsuitable weather, and we cannot conclude from the cancellation of the game that rain is falling. (b) The Conjunctive Syllogism The parts of a conjunctive or a disjunctive propositions are called members. The laws of the conjunctive syllogism are these:
Thus we have a valid syllogism in the following: "John cannot be in New York and Chicago at the same time. He is in Chicago. Therefore, he is not in New York." But the following syllogism violates its laws and is invalid: "John cannot be in Chicago and New York at the same time. But he is not in Chicago. Therefore, he is in New York." (c) The Disjunctive Syllogism The major premise must be a complete disjunctive, omitting no possible member.
"It is spring, or summer, or autumn, or winter. But it is, in fact, summer. Therefore, it is neither spring, nor autumn, nor winter." The syllogism would be invalid if the major premise were, for instance, the following: "It is spring, or summer, or autumn," for a possible member has been left out, and the disjunction is incomplete. The syllogism would be valid, as it is in the form first given, if the minor premise were negative, thus: "It is not spring. Therefore, it is summer, or autumn, or winter." Similarly, the syllogism would be valid if two or more members were denied in the minor premise: " It is neither spring nor winter. Therefore, it is either autumn or summer."
By way of postscript to our treatise on syllogisms and their laws of structure and validity, we must mention certain irregular syllogisms. The following irregular types are important to notice: 1. The Enthymeme is a shortened syllogism; one premise is omitted as easily understood. Thus: "John is a good boy; he will do his duty" tacitly supposes but does not express the major premise, viz., "Good boys will do their duty." 2. The Epicherema is a lengthened syllogism, for it adds a word of proof or explanation to one or to both of its premises. Thus: "These pupils will study hard, for they are diligent. Those who study hard will pass the examination, for hard study develops capability. Therefore, these students will pass the examination." 3. The Polysyllogism is a connected series of syllogisms (two or more) in which the conclusion of one is the major premise of the next succeeding. Thus: "The man of good life avoids evil. He who avoids evil advances in virtue. He who advances in virtue is pleasing to God. Therefore, the man of good life is pleasing to God." 4. The Sorites is a connected series of premises so arranged that the predicate of one is the subject of the next succeeding; the conclusion combines the subject of the first premise with the predicate of the last. Thus: "A worldly man has many unchecked desires. He who has many unchecked desires feels many wants. He who feels many wants is distressed in mind. He who is distressed in mind is not at peace. He who is not at peace is not happy. Therefore, a worldly man is not happy." 5. The Dilemma or horned syllogism offers, in a major disjunctive premise, two alternatives or "horns," and in two conditional premises it catches an opponent on either one horn or the other, and reaches the same conclusion by either alternative. Thus: "The Christian religion was spread through the world either with the help of miracles or without the help of miracles. If with the help of miracles, it is divine, for miracles are the incontestable mark of divine help and approval. If without miracles, its rapid spread in the face of every worldly obstacle is itself a miracle, and this miracle proves it divine. Therefore, in either case, the Christian religion is divine." If, in this type of argument, the major disjunctive premise offers three possibilities, the syllogism is called a trilemma; if four, it is called a quadrilemma, and so forth.
Another postscript must here be added to warn the student of logic against tricky arguments which may appear valid but in reality are not so. Such arguments are called fallacies. Notable fallacies are the following: 1. Equivocation consists in using a single term in two different meanings, thus making it equivalent to two terms. By equivocation a fourth term is introduced into a categorical syllogism, and this renders the argument valueless. 2. Compounding is the taking of a term or proposition in a solid or compounded sense when it is meant to be taken in a divided or distinguished sense. 3. Dividing is the taking of a term or proposition in a divided sense when it is meant to be taken in a solid or compounded sense. 4. Missing the Point or Ignoring the Issue is a fallacy which comes from a mistaken (or sly) effort to prove one thing by offering argument for another. 5. Begging the Question is a fallacy which comes from the fact that the very point to be proved is assumed as a fact and used as a basis of argument. as well as many more, Click Here.
Summary of the Section In this Section we have defined reasoning, and have discussed its antecedent and its consequent elements. We have distinguished two types of reasoning, the deductive and the inductive. We have studied the expression of reasoning in terms and propositions, and have learned that is called argument or argumentation, and that its most perfect form is the syllogism. We have noted the two chief types of syllogism, the categorical and the hypothetical, and have set down the reasoned laws that determine the structure and the value of each type. We have also noted the figures and the moods of categorical syllogisms. We have noticed certain types of irregular syllogisms, and have indicated certain fallacies which the careful thinker must avoid.
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