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Philosophy #2 Midterm

by: Shane Ng

Philosophy #2 Midterm Phil 103

Shane Ng

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Deductive and Inductive Arguments
PHIL 103 Critical Reasoning
Daniela Vallega-Neu
Study Guide
philosophy, critical thinking
50 ?




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This 7 page Study Guide was uploaded by Shane Ng on Sunday February 21, 2016. The Study Guide belongs to Phil 103 at University of Oregon taught by Daniela Vallega-Neu in Fall 2016. Since its upload, it has received 38 views. For similar materials see PHIL 103 Critical Reasoning in PHIL-Philosophy at University of Oregon.


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Date Created: 02/21/16
Deductive and Inductive Arguments - In a deductive argument, if the premises are true the conclusion must be true also. - In an inductive argument, if the premises are true and the logical inference strong, the conclusion may still be false. (CT, P.161) Evaluation criteria for deductive and inductive arguments - In deductive arguments, we determine whether the argument is valid or invalid (Whether the conclusion follows with necessity or not). - In inductive arguments, we determine whether the argument is strong or weak. Validity - Validity is a term used exclusively for deductive arguments not for the inductive arguments. - Validity addresses only the logical strength of the argument independently from the truth or falsity of the statements it contains. - In a deductive argument, the conclusion is followed with necessity from the premises. When this is the case, we say that the argument is valid and this independently from the truth or falsity of the statements it contains. - When a supposedly deductive argument fails to lead with necessity to the conclusion we say that it is invalid. (Note that all inductive arguments are invalid.) - If an argument is valid and the premises are true, the conclusion must be true as well. - If the argument is valid, the premises entail the conclusion Validity and Soundness - A deductive argument can have true premises and thus necessarily a true conclusion. When this is the case, the argument is not only valid, but also sound. o If p then q o If q then r o If p then r - A deductive argument can be valid with false premises and a false conclusion. In this case it is valid but not sound. o Syllogism:  All A are B  All C are A  All C are B o This argument is valid because of its form. - A deductive argument can valid with (all or some) false premises and a true conclusion. In this case it is valid but not sound. Form of a Deductive and Inductive Argument - In inductive arguments, we diagram the logical structure (as V- argument, T-arguments and using arrows to indicate the drawing of a conclusion.) - In deductive arguments, we formalize arguments, i.e. we substitute concepts with letters and then determine whether the argument form in valid. o If [this is a living thing] then [it needs nourishment in order to survive]. o [This is a living thing.] L o [It needs nourishment in order to survive.] N  If L then N  L  Therefore N. - Note that we always need to make quantifiers and negations explicit: o All dogs are mammals  All A are B o No mammals are coldblooded  No A are B o Some mammals are feline  Some A are B - We also need to make all logical function markers like “if…then” “and” “either…or” “…is false” explicit: o It is raining and it is cold  Rand C o It is either raining or cold  R or C o It is not true that it is cold  Not C o If it is cold you need a coat  If p then q Valid Deductive Argument - Often deductive arguments include conditional statements (if p then q) - This form of argument is valid because of its form: o If p then q o If q then r o Therefore, if p then r - The argument is sound because it is valid and has true premises. Truth Functional Statements - Deductive reasoning rests on truth functional statements - The truth of truth-functional statements is determined not by directly seeing whether what it says is true but by seeing whether its components are true. o Negation: “p is false.” A negation is true when its component statement is false. (CT, 166) o Conjunction: “ p and q.” A conjunction is true only when both, p and q are true  Using words such as “even thought”, “but” o Disjunction: “p or q.” A disjunction is true when p is true, when q is true, and when both p and q are true. o Implication: “If p then q.” An implication such as if p then q is false only when p is true and q is false. (CT, 166)  Implications make use of conditional statement of the form “If p then q.”  “If It rains (antecedent), then the roads are wet (consequent)”  In a true conditional statement, the antecedent is “sufficient” for the consequent to occur. Any time it rains, the roads are wet.  On the other hand, in a true conditional statement, the consequent is not sufficient for the antecedent to occur. That the roads are wet does not mean that it rains. They could be wet for another reason. However, the consequent is “necessary” for the antecedent: it is necessary that the roads are wet when it rains.  Implications (if p then q) can be expressed in many ways such that they may be harder to detect. When formalizing implications, always reformulate them into “If p then q.” Formal Validity and Soundness - When applied to deductive reasoning, the concept of logical strength has a narrower meaning than when applied to deductive arguments. - In a valid deductive argument, if the premises are true, the conclusion must be true as well. - Since a deductive argument guarantees the truth of its conclusion, it has a stricter logical strength that is called formal validity. - Validity concerns only the form of an argument and not the truth and falsity of its statements. - To show that an argument is valid, we need only to show that it has a valid argument form. - When assessing a deductive argument, you should always formalize it. Valid Argument forms 1. Affirming the antecedent: o If p then q. o P. o Therefore, q. 2. Denying the consequent: o If p then q. o Not q. o Therefore, not p. 3. Chain argument (or “hypothetical syllogism): o If p then q. o If q then r. o Therefore, if p then r. o (Note that here all statements are hypothetical.) 4. Disjunctive syllogism: o Either p or q. o Not p. o Therefore, q. o (Note that since disjuncts (in this case p and q) may both apply, we cannot affirm one disjunct (let’s say p) and arrive at the conclusion that the other disjunct is not the case (in this case not q). Reconstructing Deductive Arguments 1. We need to identify the truth-functional statements and their logical operators. 2. Symbolize the statement to bring out their truth-functional relationships. o If p Then q. o Not p. o Therefore, not q. Symbolizing Complex Deductive Arguments - Complex deductive arguments may combine a chain argument and, for example, a modus ponens. - A complex argument: o “If he tells his teacher he cheated, he will be punished by the principal. But if he doesn’t tell his teacher he cheated, he will be punished by his parents. Either way he is going to be punished.” - This is called a dilemma o P1: If p then q. o P2: If not p, then q. o MP3: Either p or not p. o C: Therefore, q. Formal Invalidity 1. Affirming the consequent: o If p then q. o q. o Therefore p. 2. Denying the antecedent: o If p then q. o Not p. o Therefore, not q. Inductive Reasoning Forms of inductive reasoning - Inductive generalization (arguments based on examples) o Uses a number of examples in order to draw a generalizing conclusion. o In scientific contexts, inductive generalization is based on sampling: a portion of a population is observed in order to draw a conclusion about the entire population.  Z percent of observed Fs are G.  Therefore, it is probable that Z percent of all Fs are G. o Two possible weaknesses (strength)  Samples might not be representative  Samples might not be large enough - Statistical syllogism o Includes a specific case under features of a general group when there are known possible exceptions to features of the group. o Inductive generalizations move from the particular to the general, statistical syllogisms move from the general to the particular.  Z percent of all Fs are G.  X is an F.  Therefore there is a Z percent probability that X is G. o OR  Most A are B  m is A  Therefore, m is B. - Induction by confirmation - Analogical reasoning - Arguments from authority - Causal reasoning (Mill’s methods) Conditions for strength of Inductive arguments - Each form of inductive argument has its own conditions for strength and needs to be assessed differently, although got any argument we need to question the acceptability of the premises, the relevance of the premises for the conclusion, and the adequacy of the premises with respect to the conclusion. Relevance of an appeal to authority depends on whether the authority we appeal to for a certain issue is an expert in that issue. Adequacy of any appeal to authority depends on the following criteria (CT, 244f): 1. The authority must be identified. 2. The authority must be generally recognized by the experts in the field. 3. The particular matter in support of which an authority is cited must lie within his or her field of expertise. 4. The field must be one in which there is genuine knowledge. 5. There should be a consensus among the experts in the field regarding the particular matter in support of which the authority is cited. Analogical Reasoning - Analogical reasoning presupposes an analogy between two things (objects, classes, of objects, situations, relationships), one of which is familiar and one unfamiliar. - In an argument by analogy, we use an analogy to provide support for a conclusion. o Strong or weak analogies The analogy compares two cases: - The subject case is that about which we are trying to draw a conclusion. - The analogue case is that which is used to draw the conclusion. - The conclusion of an analogical argument will always be about the subject case and contain a target feature which is the feature of the subject case about which the conclusion is being drawn. - This means that the analogy is provided in the premises, i.e., the conclusion does not consist in an analogy. Two Kinds of Analogical Arguments: - Analogical arguments may be either based on comparison of the properties of the subject case and those of the analogue case or it may be based on a comparison between relations. - A property is a feature that is attributable to a thing considered on its own and as a single entity. o It has the form:  X has A, B, C.  Y has A, B.  It is probable, therefore, that Y has C. o Y is the subject case. o X is the analogue case. o C is the target feature. - A relation is a feature that is attributable to the relationship between two or more things. o It has the form:  x is to y as a is to b.  x is R to y.  It is probable, therefore, that a is R to b. o a and b are related in the subject case. o x and y are related in the analogue case. o R is the target feature. - A strong argument is one in which there is a large number of relevant similarities and a small number of relevant dissimilarities between cases. - The relevance of a similarity or dissimilarity depends on the target feature of the analogy and the conclusion being inferred.


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