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The Jonathan Dolhenty Archive |
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DEDUCTION: Part 5 by Jonathan Dolhenty, Ph.D.
A syllogism is a deductive argument consisting of two premises and a conclusion. There are different kinds of syllogisms, taking their names from the kinds of propositions they contain. The categorical syllogism is so called because it contains categorical propositions exclusively. We have so far discussed the categorical syllogism and its various types. The propositions contained with a categorical syllogism consist of a direct assertion between the subject and the predicate of a sentence. There is another type of proposition called hypothetical propositions which are totally different from categorical propositions. Hypothetical propositions do not involve a direct assertion of agreement or disagreement between the subject and the predicate. Instead, they express the dependence of the truth or falsity of one statement upon the truth or falsity of another statement. The truth of a hypothetical judgment is involved with the truth of the dependence, a logical relation, between one statement upon another statement. If the dependence actually exists, the statement is true. If the dependence doesn't exist, the statement is false. Consider the following propositions stated in hypothetical form:
Notice that in the first proposition, it is not asserted that it is, in fact, raining outside. Nor is it asserted that we will not go to the auto races. What is being asserted is a dependence of "we will not go to the auto races," on the statement "If it is raining outside." If the relation of dependence of the former statement on the latter statement is as stated, the judgment is true. We can use hypothetical propositions as the major premise of a syllogism. If the minor premise can affirm or deny one part of the hypothetical proposition, the conclusion may possibly affirm or deny the other part. A syllogism which has a hypothetical proposition as its major premise is called a hypothetical syllogism. There are three types of hypothetical syllogisms: conditional, disjunctive, and conjunctive. Conditional Syllogisms We can define a conditional syllogism as a hypothetical syllogism which contains a conditional proposition as its major premise. Conditional propositions are "if" statements. The first part of the proposition contains the condition and is introduced by the word "if." The truth of the second part is dependent on the fulfillment of the condition stated in the second part of the proposition. Consider these simple conditional propositions:
Only when the first part of the proposition is true, can the the truth of the second part also be stated. The first part is called the antecedent. The second part is called the consequent. The antecedent gives the ground or the reason or the cause. The consequent gives the result or the dependent or the effect. In the above propositions, these parts are as follows:
A pure conditional syllogism consists entirely of conditional propositions. A mixed conditional syllogism consists of one premise that is a conditional proposition and one premise that is a categorical proposition. Consider these examples: Pure conditional syllogism:
Mixed conditional syllogism:
Notice that in the pure conditional syllogism, the conclusion is also a conditional proposition. The conclusion does not state a clear agreement or disagreement between two ideas. The argument leads to no definite result as far as truth is concerned. The mixed conditional syllogism, on the other hand, does assert in its conclusion a definite result since it is a categorical proposition. There are two possible way of getting a valid conclusion from the premises in a mixed conditional syllogism:
If we assert that the condition in the antecedent is realized, we must also assert the truth of the consequent since the truth of the consequent is dependent on the realization of that condition. The reverse is also true. If the consequent did not happen, then we know that the condition in the antecedent could not have been realized. Otherwise the consequent must also have happened. Consider these two arguments:
These are valid arguments. Notice, however, that the antecedent is accepted in the first argument and the consequent is rejected in the second argument. The consequent, "he is seriously ill," depends entirely on the truth of the condition stated in the antecedent, "If Peter has leukemia." This is a cause and effect relationship. If the cause has been operational, "Peter has leukemia," the effect must follow, "he is seriously ill." If the effect did not follow, then the cause was not operational. We then arrive at a double principle:
If we reject the antecedent, however, must we reject the consequent? Also, if we accept the consequent, must we accept the antecedent? Consider these two arguments:
These arguments obviously are not valid. The fact that Peter doesn't have leukemia does not permit the conclusion that is not seriously ill. Peter may be seriously ill from some other disease or cause. The conclusion of the second syllogism is also inconsistent. The fact that Peter is seriously ill does not mean that its cause is leukemia. Peter could have some other disease. It may be true that "if Peter has leukemia," he certainly is seriously ill. The reverse, however, is not necessarily true: "If Peter is seriously ill, he must have leukemia." His illness could have causes other than leukemia. It may be true that "Peter doesn't have leukemia," but we cannot exclude the possibility that his serious illness has other causes. The conditional proposition simply gives one of the possible causes which might produce the same effect. It would be inconsistent to exclude all other possible causes since there is nothing in the antecedent to restrict the effect to one single cause. Here, then, is the Law of the Conditional Syllogism:
From an understanding of this law, we can see that there are only two valid moods for the conditional syllogism. If the minor premise accepts the antecedent, the conclusion must accept the consequent. If the minor premise rejects the consequent, the conclusion must reject the antecedent. The two valid moods for the conditional syllogism are called the constructive mood and the destructive mood. Each of these moods can appear in form forms:
The Constructive Mood The mood in which the minor premise accepts the antecedent and the conclusion accepts the consequent is called the constructive mood. Here are examples of the four valid forms for the constructive mood: (1)
(2)
(3)
(4)
The Destructive Mood The mood in which the minor premise rejects the consequent and the conclusion rejects the antecedent is called the destructive mood. Here are examples of the four valid forms for the destructive mood: (1)
(2)
(3)
(4)
Fallacies To Watch For It is easy to fall into fallacious reasoning when using conditional propositions in syllogisms. Inconsistency enters into this type of argument when we try to conclude from the falsity of the antecedent to the falsity of the consequent, or from the truth of the consequent to the truth of the antecedent. The potential for fallacious reasoning when using conditional propositions is very great. Fallacious arguments of this type are a frequent source of error, even in academic writing and speaking. This type of error occurs often in political discourse. Consider this argument:
This argument may be true enough, but it is not consistent. We cannot draw a correct conclusion by passing in this way from the consequent to the antecedent. Though it may be true in some cases, it is not true in all cases, and we can't be sure of our conclusions. Consider this argument:
This is a common argument but it is fallacious. There may be many other reason for a movie to be popular than artistic merit. The fact that the movie is popular gives us no information about its artistic merit. The movie might be popular because it contains pornographic scenes which have nothing to do with artistic merit. Here is an example of a commonly accepted fallacious argument regarding that controversial topic "evolution." This is argued even in academic and scholarly circles by philosophers and scientists. They should know better. Here it is:
The conclusion "Evolution occurred" does not necessarily follow. The result in the consequent will be the effect of either evolution or creation. The mere fact that the consequent is true, does not prove that evolution is the cause. Evolution may be the cause, but it need not be. The result in the consequent could be caused by creation just as well. We get a similar fallacy when we reject the antecedent in the minor premise and then go on to reject the consequent in the conclusion. Consider this argument:
The fact that there is no progress doesn't necessarily mean there is no possibility of change in the opposite direction, that is, toward deterioration. Change, after all, may go in two directions: toward progress and toward deterioration. Consider this argument and the fallacious reasoning will be clear:
The conclusion that "The grass is not wet" does not necessarily follow from the premises. We may have taken the hose out and watered the lawn. We need to be very careful when dealing with conditional propositions. We need to be aware of antecedents and consequents and the proper relationship between them. Disjunctive Syllogisms The disjunctive syllogism is one in which the major premise is a disjunctive proposition. The following are examples of disjunctive propositions:
It can easily be seen that a disjunctive proposition has an "either-or" construction. There are two types of disjunctive propositions and each produces its own distinctive syllogism. They are called the proper disjunction and the improper disjunction. Syllogisms With Proper Disjunctive Propositions The component parts of a proper disjunctive proposition can neither be true nor false together. The general rule here is: If one is true, the other must false, and if one is false, the other must be true. This rule leads us to the fact that the two-part disjunctive syllogism will have two valid moods:
Because the parts may be affirmative or negative, there are four possible forms for each type of syllogism:
The "Accepting" Two-Part Disjunctive Syllogism Here are examples of the four forms of this syllogism: (1)
(2)
(3)
(4)
The "Rejecting" Two-Part Disjunctive Syllogism Here are examples of the four forms of this syllogism: (1)
(2)
(3)
(4)
Syllogisms With Improper Disjunctive Propositions The improper disjunctive proposition differs from the proper disjunctive because the members of the improper disjunctive are not mutually exclusive. In other words, all parts of the proposition cannot be false, but some or all may be true together. If one part of the disjunction is accepted, we are not permitted to reject the other. This would be fallacious because the others may also be true. If, however, one part is rejected in the minor premise, the other parts must again be accepted with an improper disjunction. This is the only legitimate conclusion that can be drawn. Consider this example:
It would be fallacious to argue:
It is possible that all the parts of this improper disjunction might all be true. Of course, if we know all the facts and can by a process of elimination to reject all part of the disjunction except one, the conclusion can legitimately accept this one remaining part of the proposition. The reason is that at least one of the parts must be true. The following conclusion would be legitimate:
Conjunctive Syllogisms A conjunctive proposition is a hypothetical proposition which expresses a judgment that two alternative assumptions are not or cannot be true simultaneously. Consider these examples:
In the major premise of a syllogism, the conjunctive proposition states that two or more things are impossible at the same time. No two of the parts can be true at the same time, but they all may be false together. The general rule for this type of proposition is: From the truth of one part follows the falsity of the others but from the falsity of one part the truth of the other part(s) does not follow. Consider the following proposition:
If we can make the further statement that, "It is a reptile," we can certainly conclude that, "It is not a mammal." But if we say, "It is not a reptile," we cannot necessarily conclude that "It is a mammal." It is possible that the thing is neither a reptile nor a mammal, but something else entirely, say a bird or amphibian. We can only reject one part when we can accept the other part as true. We cannot, however, when rejecting one part, accept the other part since both parts could be false together. The only valid mood for the conjunctive syllogism is the following: If the minor premise accepts one part of the conjunctive major premise, the conclusion must reject the other part(s). Here are examples of valid conjunctive arguments:
Fallacious reasoning can slip into this type of argument when we reject a part of the conjunctive major premise and then accept the other part(s) in the conclusion. Consider this argument:
The conclusion does not necessarily follow. Jane may be in Los Angeles, but she could also be in some other city. Incidentally, this type of argument is often used in criminal cases when defense lawyers need to establish an alibi for their client. The argument goes this way:
The prosecutor may attempt to argue against this alibi by stating that "The defendant was not in Los Angeles at the time of the crime." If he did this, however, it would not automatically place the defendant in Dallas. The prosecutor would still have to find evidence which would prove that the defendant was, in fact, in Dallas at the time of the crime. NEXT - Part 6: Arguments in Ordinary Language
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