LOGIC LECTURE #3: DEDUCTION AND INDUCTION Source: A Concise Introduction to Logic, 11 th Ed. (Patrick Hurley, 2012)
Deductive Vs. Inductive If the conclusion is claimed to follow with strict certainty or necessity, the argument is said to be deductive; but if it is claimed to follow only probably, the argument is inductive.
Deductive Arguments DEDUCTIVE ARGUMENT: An argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. Deductive arguments are those that involve necessary reasoning.
Deductive Argument Example The meerkat is a member of the mongoose family. All members of the mongoose family are carnivores. Therefore, it necessarily follows that the meerkat is a carnivore.
Inductive Arguments INDUCTIVE ARGUMENT: An argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true. Inductive arguments involve probabilistic reasoning.
Inductive Argument Example The meerkat is closely related to the suricat. The suricat thrives on beetle larvae. Therefore, probably the meerkat thrives on beetle larvae.
Deductive Vs. Inductive In deciding whether an argument is inductive or deductive, we look to certain objective features of the argument: 1. the occurrence of special indicator words 2. the actual strength of the inferential link between premises and conclusion 3. the form or style of argumentation.
Deductive Argument Indicator Words Necessarily Certainly Absolutely Definitely
Inductive Argument Indicator Words Probably Improbable Plausible Implausible Likely Unlikely Reasonable to Conclude
Inductive Vs. Deductive Indicator Words Inductive and deductive indicator words often suggest the correct interpretation However, if they conflict with one of the other criteria (discussed shortly), we should probably ignore them. Arguers often use phrases such as it certainly follows that for rhetorical purposes to add impact to their conclusion and not to suggest that the argument be taken as deductive. Similarly, some arguers, not knowing the distinction between inductive and deductive, will claim to deduce a conclusion when their argument is more correctly interpreted as inductive.
Deductive Argument Forms Many arguments have a distinctive character or form that indicates that the premises are supposed to provide absolute support for the conclusion. Five examples of such forms or kinds of argumentation are: arguments based on mathematics arguments from definition categorical syllogisms hypothetical syllogisms disjunctive syllogisms
Arguments Based on Mathematics ARGUMENT BASED ON MATHEMATICS: An argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement. Since all arguments in pure mathematics are deductive, we can usually consider arguments that depend on mathematics to be deductive as well. A noteworthy exception, however, is arguments that depend on statistics.
Arguments From Definition ARGUMENT FROM DEFINITION: An argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion.
A syllogism, in general, is an argument consisting of exactly two premises and one conclusion.
Categorical Syllogisms CATEGORICAL SYLLOGISM: A syllogism in which each statement begins with one of the words all, no, or some..
Categorical Syllogisms Example All ancient forests are sources of wonder. Some ancient forests are targets of the timber industry. Therefore, some sources of wonder are targets of the timber industry.
Hypothetical Syllogisms HYPOTHETICAL SYLLOGISM: A syllogism having a conditional ( if... then ) statement for one or both of its premises.
Hypothetical Syllogisms Examples If estate taxes are abolished, then wealth will accumulate disproportionately. If wealth accumulates disproportionately, then democracy will be threatened. Therefore, if estate taxes are abolished, then democracy will be threatened. PURE HYPOTHETICAL SYLLOGISM
Hypothetical Syllogisms Examples If Fox News is a propaganda machine, then it misleads its viewers. Fox News is a propaganda machine. Therefore, Fox News misleads its viewers. MIXED HYPOTHETICAL SYLLOGISM
Disjunctive Syllogisms DISJUNCTIVE SYLLOGISM: A syllogism having a disjunctive ( either... or... ) statement.
Disjunctive Syllogisms Examples Either global warming will be arrested, or hurricanes will become more intense. Global warming will not be arrested. Therefore, hurricanes will become more intense.
Inductive Argument Forms In general, inductive arguments are such that the content of the conclusion is in some way intended to go beyond the content of the premises.
Inductive Argument Forms The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about. Such an argument may take any of several forms: Predictions about the future Arguments from Analogy Inductive Generalizations Arguments from Authority Arguments based on Signs Causal Inferences
Predictions PREDICTION: An argument that proceeds from our knowledge of the past to a claim about the future.
Argument from Analogy ARGUMENT FROM ANALOGY: An argument that depends on the existence of an analogy, or similarity, between two things or states of affairs.
Generalization GENERALIZATION: An argument that proceeds from the knowledge of a selected sample to some claim about the whole group.
Arguments from Authority GENERALIZATION: An argument that concludes something is true because a presumed expert or witness has said that it is.
Arguments Based on Signs ARGUMENT BASED ON SIGNS: An argument that proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes.
Causal Inferences ARGUMENT BASED ON SIGNS: An argument that proceeds from knowledge of a cause to a claim about an effect, or, conversely, from knowledge of an effect to a claim about a cause.
Particular Vs. General Statements PARTICULAR STATEMENT: A statement that makes a claim about one or more particular members of a class. GENERAL STATEMENT: A statement that makes a claim about all the members of a class.
General Vs Particular Examples Three is a prime number. Five is a prime number. DEDUCTIVE Particular General Seven is a prime number. Therefore, all odd numbers between two and eight are prime numbers.
General Vs Particular Examples Gabriel is a wolf. Gabriel has a tail. DEDUCTIVE Particular Particular Therefore, Gabriel s tail is the tail of a wolf.
General Vs Particular Examples All emeralds previously found have been green. Therefore, the next emerald to be found will be green. INDUCTIVE General Particular