# Patterns of Deductive Thinking In deductive thinking we reason from a broad

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## Patterns of Deductive Thinking In deductive thinking we reason from a broad

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Inductive in addition to Deductive Reasoning Both forms of reasoning have subclassifications. Deductive thinking has three patterns: categorical, hypothetical, in addition to disjunctive. Inductive reasoning has four types: analogy, causation, generalization, in addition to hypothesis. When a deductive argument is not just broad based but begins alongside a universal claim, it is referred so that as categorical in nature. The major premise is not surrounded by qualifications, exceptions, or alternatives but asserts that something is the case universally. The deductive arguments we have discussed so far are mainly of this pattern. Universal, Particular, Affirmative or Negative Table 8.1 in the textbook, page 155 Distribution Distribution is an attribute of the terms (subject in addition to predicate) of propositions. A term is said so that be distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. In other words, a term is distributed if in addition to only if the statement assigns (or distributes) an attribute so that every member of the class denoted by the term. Thus, if a statement asserts something about every member of the S class, then S is distributed; otherwise S in addition to P are undistributed.

All S are P Here is another way so that look at All S are P. The S circle is contained in the P circle, which represents the fact that every member of S is a member of P. Through reference so that this diagram, it is clear that every member of S is in the P class. But the statement does not make a claim about every member of the P class, since there may be some members of the P class that are outside of S. All S are P II Thus, by the definition of ?distributed term?, S is distributed in addition to P is not. In other words in consideration of any (A) proposition, the subject term, whatever it may be, is distributed in addition to the predicate term is undistributed. No S are P ?No S are P? states that the S in addition to P class are separate, which may be represented as follows: This statement makes a claim about every member of S in addition to every member of P. It asserts that every member of S is separate from every member of P, in addition to also that every member of P is separate from every member of S. Both the subject in addition to the predicate terms of universal negative (E) propositions are distributed.

Some S are P The particular affirmative (I) proposition states that at least one member of S is a member of P. If we represent this one member of S that we are certain about by an asterisk, the resulting diagram looks like this: Since the asterisk is inside the P class, it represents something that is simultaneously an S in addition to a P; in other words, it represents a member of the S class that is also a member of the P class. Thus, the statement ?Some S are P? makes a claim about one member (at least) of S in addition to also one member (at least) of P, but not about all members of either class. Thus, neither S or P is distributed. Some S are not P The particular negative (O) proposition asserts that at least one member of S is not a member of P. If we once again represent this one member of S by an asterisk, the resulting diagram is as follows: Since the other members of S may or may not be outside of P, it is clear that the statement ?Some S are not P? does not make a claim about every member of S, so S is not distributed. But, as may be seen from the diagram, the statement does assert that the entire P class is separated from this one member of the S that is outside; that is, it does make a claim about every member of P. Thus, in the particular negative (O) proposition, P is distributed in addition to S is undistributed. Two mnemonic devices in consideration of distribution ?Unprepared Students Never Pass? Universals distribute Subjects. Negatives distribute Predicates. ?Any Student Earning B?s Is Not On Probation? A distributes Subject. E distributes Both. I distributes Neither. O distributes Predicate.

Table 8.2 Distribution in Four Standard Types of Statements, page 155 of the text Once we understand affirmative in addition to negative in addition to the concept of distribution, we can apply the rules governing the validity of deductive arguments of a categorical type. There are four rules: At least one of the premises must be affirmative. If a premise is negative then the conclusion must be negative, in addition to if the conclusion is negative then a premise must be negative. The middle term must be distributed at least once. Any term distributed in the conclusion must also be distributed in a premise. From page 156 in the textbook: From these four rules we can judge that the following syllogisms are invalid: Violates Rule 1: No Australians are poor swimmers. Some poor swimmers are not sailors. No sailors are Australians. Violates Rule 2: No fish is fattening food. All fattening food is tasty. ?Some fish is tasty.

Violates Rule 3: All feminists are pro-choice. Some Communists are pro-choice. ?Some feminists are Communists. Violates rule 4: All stars are bright. No planets are stars. ? No planets are bright. Having understood the summary parts of a syllogism in addition to how so that judge the soundness of a formal argument, we can now apply what we know so that the arguments we meet in addition to so that the ones we make. The steps are: Separate the conclusion from the premises (the claims from the warrant). Paraphrase the sentences into standard form A, E, I, O. Arrange the statements into a categorical syllogism, completing any enthymemes. Judge the validity of the syllogism in terms of the four rules, using the factors of affirmative or negative distribution. Determine whether the premises in addition to conclusion are true in addition to the argument sound. Please turn so that page 157 in the textbook. We are going so that read in addition to analyze the argument about feminists in the book. Please turn so that page 161 of your textbook.

Hypotheticals: The If/Then Form Hypothetical arguments are usually more obvious than categorical ones. A hypothetical argument has an ?if/then? pattern. It is conditional rather than making some absolute claim. We say that, provided one thing is true, then another thing would follow. For instance, if the ground is wet then it must have rained; if the bells are chiming, then I must be late in consideration of class; if he is the starting quarterback, then he must be off the injured list. An assumption is made at the start in addition to the argument then carries out the implications of that assumption. Hypotheticals: The If/Then Form II The first part of the major premise, from ?if? so that ?then? is called the antecedent, in addition to the second part, from ?then? so that the end of the sentence, is called the consequent. Antecedent in addition to consequent mean nothing more than the part that goes before in addition to the part that goes afterward. Take the following as a typical example of a valid hypothetical syllogism: If Emily is a doctor, then she can cure bronchitis. Emily is a doctor. ?She can cure bronchitis. Hypotheticals: The If/Then Form III The argument is perfectly valid because, in the minor premise, we have affirmed the antecedent ?Emily is a doctor,? then drawn the conclusion that follows from it, that ?she can cure bronchitis.? Another valid form would be: If Emily is a doctor, then she can cure bronchitis. Emily can?t cure bronchitis. ?Emily is not a doctor. Here we have denied the consequent, in addition to although the reasoning might be more difficult so that see, it is also correct. The assumption is that every doctor can cure bronchitis, in addition to if Emily is unable so that do this then she cannot be a doctor.

Hypotheticals: The If/Then Form IV These arguments are arranged in two different patterns but in both cases the conclusion follows from the premises. From this we can generalize that the two valid forms of hypothetical thinking are affirming the antecedent in addition to denying the consequent. In contrast so that these valid forms, take the following two syllogisms: If Emily is a doctor, then she can cure bronchitis. Emily is not a doctor. ? Emily can?t cure bronchitis. Hypotheticals: The If/Then Form V Here the conclusion does not follow logically, in consideration of although Emily is not a doctor, that does not mean she cannot cure bronchitis. Although all doctors can cure bronchitis, we do not know that only doctors (and no one else) can cure bronchitis. In this process of reasoning, we have denied the antecedent, which is an invalid form of a hypothetical argument. Hypotheticals: The If/Then Form VI Another invalid argument: If Emily is a doctor, then she can cure bronchitis. Emily can cure bronchitis. ? Emily is a doctor. This thinking is also incorrect, in consideration of just because Emily can cure bronchitis that does not make her a doctor. Although all doctors can cure bronchitis, that does not mean only doctors can cure bronchitis. This error is known as affirming the consequent.

Hypotheticals: The If/Then Form VII Please turn so that pages 166 in addition to 167 in your textbooks. Disjunctives: Either/Or Alternatives In a disjunctive sentence two possibilities are presented, at least one of which is true (although both might be). If we say, in consideration of example, ?Either we will stay at home or we will go so that the movies tonight,? that is a disjunct. So are the sentences, ?Either you are in class or you are absent,? in addition to ?The man is either fat or skinny.? One of the disjuncts has so that be true, so if we know one of the alternatives so that be false, we can declare the other so that be true in addition to produce a valid argument. It does not matter which disjunct we eliminate; the one remaining must be true. Disjunctives: Either/Or Alternatives II In diagram form, then a valid disjunctive argument would appear this way: Either P or Q not P. Therefore Q Now we said that at least one alternative is true, but in fact both could be. That means we would not get a valid argument by affirming one part of the disjunct in a minor premise in addition to denying the other in our conclusion. Since both parts might be true, one disjunct is not eliminated when we affirm the other.

Disjunctives: Either/Or Alternatives III For example: Either I am paranoid or someone is out so that get me. My therapist says I am paranoid. Therefore No one is out so that get me. The fallacy is that I could be paranoid in addition to someone may be out so that get me. Another example, ?Either it is Monday or we are in Critical Thinking class.? Actually, both might be true. Affirming one does not rule out the other. In diagram form the mistake looks like this: Either P or Q P ? not Q Disjunctives: Either/Or Alternatives III This leads us so that the two rules about disjunctives: In a valid disjunctive argument we deny one of the disjuncts so that affirm the other. An invalid disjunctive argument is one in which we affirm one of the disjuncts in addition to deny the other. Disjunctives: Either/Or Alternatives IV One qualification should be mentioned. In some types of disjuncts we do eliminate one part by affirming the other: Either I am in Critical Thinking class today or I am absent. I am in Critical Thinking class today. ? I am not absent. This is not a rule, though. Do not count on it so that always hold.

Please turn so that page 173 of your textbook.

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## Journal Ratings by Bryn Mawr College

This Particular Journal got reviewed and rated by Hypotheticals: The If/Then Form VII Please turn so that pages 166 in addition to 167 in your textbooks. Disjunctives: Either/Or Alternatives In a disjunctive sentence two possibilities are presented, at least one of which is true (although both might be). If we say, in consideration of example, ?Either we will stay at home or we will go so that the movies tonight,? that is a disjunct. So are the sentences, ?Either you are in class or you are absent,? in addition to ?The man is either fat or skinny.? One of the disjuncts has so that be true, so if we know one of the alternatives so that be false, we can declare the other so that be true in addition to produce a valid argument. It does not matter which disjunct we eliminate; the one remaining must be true. Disjunctives: Either/Or Alternatives II In diagram form, then a valid disjunctive argument would appear this way: Either P or Q not P. Therefore Q Now we said that at least one alternative is true, but in fact both could be. That means we would not get a valid argument by affirming one part of the disjunct in a minor premise in addition to denying the other in our conclusion. Since both parts might be true, one disjunct is not eliminated when we affirm the other. and short form of this particular Institution is US and gave this Journal an Excellent Rating.