Unformatted text preview: Deductive and Inductive Arguments Deductive The conclusion follows from the premises as a matter of necessity. Inductive The conclusion follows from the premises as a matter of probability. Deductive Inductive Argument from definition Argument from mathematics Hypothetical syllogisms Disjunctive syllogisms Categorical syllogisms Inductive generalizations Argument from authority Argument from signs Causal inference Argument from analogy Prediction Argument from definition Since there is a necessary connection between a word and its definition, any argument based on a definition is deductive. Claudia is mendacious therefore she tells lies. Argument from mathematics Since mathematics is a deductive science any argument based on mathematics is deductive. Just because an argument does not contain numbers doesn't mean it's not a mathematical argument. Just because an argument contains numbers doesn't mean it is a mathematical argument. The Matterhorn is higher than Mount Whitney, and Mount Whitney is higher than Mount Rainer. The obvious conclusion is that the Matterhorn is higher than Mount Rainer. 83% of St. Stephen's students are Episcopalian. Beatrice is a St. Stephen's student. So, Beatrice is probably Episcopalean. Syllogisms Any argument with two (2) premises and one (1) conclusion is a syllogism. Three syllogisms are ALWAYS deductive.
Categorical (all, no, some) Hypothetical (if. . .then. . .) Disjunctive (either/or) Categorical syllogism Every statement within the syllogism must be a categorical statement. All cats are mammals. All mammals are animals. Therefore all cats are animals. Hypothetical syllogism At least one statement must be a conditional statement. It is possible that all the statements be conditional statements. If it rained last night, then the streets will be wet. The streets are wet. Therefore, it rained last night. Disjunctive syllogism Only one statement is a disjunction (either/ or). Either today is Saturday or Sunday. Today is not Saturday. Therefore today is Sunday. Inductive generalization whole part Inductive generalization Involves reasoning from part of a group to the whole group. This includes statistical arguments. All dinosaur bones so far discovered have been more than 65 million years old. Therefore, probably all dinosaur bones are more than 65 million years old. Argument from authority Any argument based on an authority is best considered inductive. According to world famous physicist Stephen Hawking, there may be a black hole at the center of our galaxy. Therefore, it is likely that such a black hole exists. Argument from sign Any reasoning based on a sign (label) is best considered inductive. The label on this bag of chips says that they are fat free. Therefore, there must be no fat at all in these chips. Causal inference Any reasoning based on cause/effect is best considered inductive. I left a bottle of wine in the freezer last night. So, it is likely that it is frozen now. Argument from Analogy Item one Attribute a Attribute b Attribute c Attribute x Item two Attribute a Attribute b Attribute c Attribute x I have a car with four doors, leather interior, silver in color and it gets excellent gas mileage. Therefore, your new silver car with four doors and leather interior, also must get excellent gas mileage. Predictions Involves reasoning from past/present to future. There are several tropical storms in the Gulf of Mexico right now. Therefore, it is quite likely that we will be getting some rain in the next week. Other considerations Scientific arguments can be either deductive or inductive. Phrases such as "it must be the case" and "it necessarily follows" are not always indicators of deductive reasoning. Phrases such as "it probably follows" are reliable indicators of inductive reasoning. ...
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 Spring '07
 D.C.
 Logic, Deductive and Inductive Arguments, Inductive generalizations Argument

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