Lecture 02 Notes

Logic

Philosophical Method

Logic: A Calculus for Good Reason
Clarification, Not Obfuscation--In order to accomplish this goal, philosophers make distinctions and attempt to disambiguate concepts.
Examples and Counterexamples
1. Examples and Counterexamples are ways of engaging in hypothetical reasoning.
2. Examples and Counterexamples reveal our deepest convictions.
3. Examples and Counterexamples help us test our principles and definitions.

Logic: Primary Philosophical Tool

Logic Gives us Rules for Reasoning

Arguments and Their Parts

Sample Argument

All humans are mortals.
Socrates is a human.
Therefore, Socrates is mortal.

Premises
- Premises are the assumptions of the argument; they are not established by the argument.
- In the Sample Argument, the first two lines are premises.
Sub and Main Conclusions
- Conclusions are supposedly established by the argument.
- Sub conclusions are conclusions that will later be used as premises to establish the main conclusion.
- In the Sample Argument, the third line is the conclusion.

Note--Relation Between Premises and Conclusion Is What Matters

Logic is the study of this relation; it tells us which relations guarantee the truth of the conclusion if the premises are true.
Logic is a calculus for generating new beliefs on the basis of old ones.

Types of Argument: Two Main Forms of Inference

Deductive Inference
1. Validity: If the Premises are True, the Conclusion Must Be True
2. Distinguishing Validity From Truth
  - Validity describes the relationship between premises; truth describes the relationship between a premise and the world.
  - Arguments: Valid or Invalid; Not True or False
  - Premises: True or False; Not Valid or Invalid
  - Logicians care more about truth preservation than truth. That is, logicians are concerned with the validity of an argument not necessarily with the truth of the premises.
3. Soundness: Valid AND True Premises
4. Logical Schema
  - One can determine the validity of an argument even if one cannot determine whether or not the premises are true.
  - Symbolic Variables--Because the truth of the premises is irrelevant to validity, one can use variables to express the premises when one is examining argument forms for validity.
5. Some Common Deductive Forms:
  - Categorical Syllogism: (1) All As are Bs (2) x is an A (3) Therefore, x is a B
  - Modus Ponens: (1) If P, then Q (2) P (3) Therefore, Q
  - Modus Tollens: (1) If P, then Q (2) Not Q (4) Therefore, not P.
Non-Deductive Reasoning
1. Inductive Inference
  - Probability: If the Premises are True, the Conclusion is Probably True
  - Inference to the Next Case (Ex. All of the Big Macs I have ever eaten have been good. Therefore, the next Big Mac I eat will be good.)
  - Universal Generalization (Ex. Every instance of copper encountered is a good conductor of electricity. Therefore, all copper conducts electricity well.)
2. Inference to the Best Explanation
- Appealing to the best hypothesis.
- Sherlock Holmes mysteries employ this type of reasoning.
Fallacies
1. Begging the Question--Presupposing the conclusion (often covertly) in your premises. (Ex. All forms of murder are wrong. Abortion is always murder; Therefore, abortion is always wrong!?? The second premise begs the question by just assuming the very thing that is debated in abortion controversies.)
2. Equivocation--Using the same word in two premises but using it in different ways. (Ex. All men are dogs. All dogs have four legs. Therefore, all men have four legs?!? Equivocates on "dog".)
3. Composition--Assuming that the whole has all of the features that the parts have. (Ex. A brick weighs 5 lbs. Therefore, the wall must weigh 5 lbs.?!? The wall does not necessarily have all of the features that its parts have.)

Citation: administrator. (2006, September 19). Lecture 02 Notes. Retrieved January 09, 2009, from Notre Dame OpenCourseWare Web site: http://ocw.nd.edu/philosophy/introduction-to-philosophy-2/Lecture%2002%20Notes.html.