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Reasoning, Logic, and Position Statements. First, some Vocab. Logic: the science that investigates the principles governing correct or reliable inference; a particular method of reasoning or argumentation Premise: a proposition supporting or helping to support a conclusion
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First, some Vocab • Logic: the science that investigates the principles governing correct or reliable inference; a particular method of reasoning or argumentation • Premise: a proposition supporting or helping to support a conclusion • Syllogism: an argument wherein the conclusion is supported by two premises. A typical form is “All A is C; all B is A; therefore all B is C.”
Deductive Logic (large to small/general to specific) • Deductive logic reasons from universal truths to particular conclusions. This is the kind of logic the student encounters when he studies arguments such as: • All men are mortalSocrates is a manTherefore, Socrates is mortal • The argument begins with a universal truth, “All men are mortal,” and ends up with a particular truth: “Socrates is mortal.”
All oranges are fruitsAll fruits grow on treesTherefore, all oranges grow on trees • All bachelors are singleJohnny is single,Hence, Johnny is a bachelor All dogs are mammals. All mammals have kidneys. Therefore all dogs have kidneys.
Inductive Logic (small to large/specific to general) • Inductive logic reasons from particular facts to universal conclusions. Here is an example: • Every mammal that has ever been examined has hair,Therefore, all mammals have hair • Here, specific instances of mammals being found with hair is said to justify the general conclusion that all mammals have hair.
Since Chris is a good athlete, Chris's sisters must be good athletes also. • That cat is black. That other cat is black. All cats must be black. • My grandmother died. Your grandmother died. Therefore, all grandmothers must die.
Valid vs. Sound • A valid argument is an argument whose conclusion follows logically from the truth of the premises. It is impossible for the premises to be true and the conclusion false. An example of a valid argument is: 1. If Thales was right, then everything is made of water. 2. It's not the case that everything was made of water. 3. So, Thales wasn't right. This argument has the form: If P then Q, ~Q, therefore ~P. All of the premises are true, and so is the conclusion. However, the validity of an argument does not entail the truth of its conclusion. Consider another example of a valid argument: 1. If Socrates was a philosopher, then Socrates was a happy alligator. 2. Socrates was a Philosopher. 3. So, Socrates was a happy alligator. This argument is valid: it is of the form If P then Q, P, therefore Q. However, the conclusion is false. Because it is valid, one of the premises must also be false: and, we can see, premise 1 is the culprit. If we replace it with a better premise, such as "If Socrates was a Philosopher, then Socrates existed," we derive a different and true conclusion (that Socrates existed).
Valid vs. Sound • A sound argument is an argument with two features: (i) it is valid, and (ii) its premises are all true.
Position Statements • Describes one side of an arguable point (for/against something) • Topic • Viewpoint (your side) • Counterclaim (other side) • Example (pulls together all information and makes a clear statement of purpose/position to the audience)
Logical Fallacies • Problems in logic that invalidate your argument/position. • See handout—there are tons!
Hasty Generalization • draws conclusions from scanty evidence. • Example: I wouldn’t eat at that restaurant—the only time I ate there, my entree was undercooked.
