Deductive reasoning.

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Presentation transcript:

Deductive reasoning

What is an argument? a series of statements consisting of a premise (or premises) and a conclusion which should follow from premises An argument never opens with a question or command, as neither states facts

Deductive Reasoning continued… Premise: - a factual statement or proposition - provides a reason for believing the conclusion Logical Consistency: - follows Aristotle’s 3 Laws of Thought - refers to statements that do not contradict each other Eg.: My mother is 45 years old. My mother is married. These are logically consistent because they do not contradict each other.

Logical contradiction (or inconsistency) Exists when statements cannot co-exist Eg.: My mother is 45 years old. My mother is 25 years old.

Forms of Deductive Reasoning: SYLLOGISMS. a basic form of argument introduced by Aristotle contains two premises and a conclusion

How do we ‘evaluate’ syllogism: TRUTH AND VALIDITY. Logicians distinguish between truth and validity. Validity refers to the correctness of the reasoning. Truth refers to the truth of the content of the statements. Logicians are more concerned with an argument’s validity than with the truth of its statements.

Applying Deductive Reasoning The goal of deductive reasoning is to produce a SOUND argument that is VALID (the form is correct) and that the premises are TRUE. There are 3 kinds of syllogisms: 1. Categorical 2. Disjunctive 3. Hypothetical

Categorical Syllogisms: States whether things belong or don’t belong in categories. E.g: All humans are mortal. Socrates is human. Therefore Socrates is mortal. The argument moves from a general statement to a specific conclusion. The argument is both VALID and SOUND because its form is correct and its premises are true.

Therefore Garfield is a canary. Example 2: All cats are canaries. Garfield is a cat. Therefore Garfield is a canary. This syllogism is VALID because its form is correct, but it is not SOUND as one of the statements is untrue.