I. Arguments
A. Argument - a form of thinking in which certain statements (reasons) are offered in support of another statement (a conclusion).
B. Definitions
1. Synonym - flighty-nervous. Problems: few exact synonyms, defining the synonym
2. Example (ostensive - to show): cat
3. Stipulative - for the purposes of this argument z means
4. If and only If: necessary and sufficient conditions
C. Deductive - If premises are true, the conclusion must be true. Necessary rather than probable conclusions. Often involves reasoning from the general to the particular, from whole to part. Conclusion valid, if premises true.
1. Syllogism is typical deductive argument. A general syllogism contains two premises joined by a middle term.
Initial universal premise: All men are mortal.
Minor premise on particular subject: Socrates is a man.
Conclusion: Therefore: Socrates is mortal.
Mortal
Men
Socrates
2. Hypothetical Syllogisms
a. Modus ponens - affirming the antecedent
If A, then B.
A.
Therefore, B.
b. Modus tollens - denying the consequence
If A (premise), then B.
Not B (premise).
Therefore not A.
3. Reductio ad absurdum or reductio proof
If some proposition p "reduces to" or entails some other proposition that is absurd, nonsensical, or just patently false, then not-p must be true.
p, because if not p, then q, and q is absurd.
4. Disjunctive Syllogism
Premise. Either A (My keys are in my pocket) or B (I left them at home).
Not A.
Therefore B.
C.Inductive Argument: The conclusion does not follow with logical necessity from the premises. Probable rather than necessary conclusion. Often involves reasoning from the particular to general, part to whole, individual to universal. From representative sample to a general conclusion, that is, arriving at a conclusion about all members of a class from what is known about some members. Conclusions are probable rather than necessary.
Problem of Induction: All swans are white.
1. Inductive Generalization or Survey, sometimes called Empirical Generalization - terms already defined.
2. Defining concepts and categories - generalize by asking what attributes define a concept and use examples of what fits in that category. "CAT" What are essential characteristics and what non-essential?
3. Examples
a. Analogy
b. Real events
c. Hypotheticals - Invented Instances
d. Counter-examples
5. Causal Reasoning - conclusion that one event causes another
a. Develop Hypothesis:
Hypotheses should have explanatory power, economy, and predictive power.
b. Test the hypothesis
c. Evaluate hypothesis
ex. Your car won't start. or You have a stomach ache.
E. Fallacies - unsound arguments, often persuasive
1. False generalizations
i. hasty generalization
ii. sweeping generalizations
iii. false dilemma
2. False analogies
3. False causes -
i. misidentification of cause
ii. post hoc ergo propter hoc
iii. slippery slope - domino theory
4. False appeals or fallacies of relevance - appeal for support to irrelevant factors.
i. appeal to authority
ii. appeal to pity or fear
iii. appeal to ignorance
iv. appeal to personal attack - ad hominem or ad feminam
5. Fallacy of Begging the Question - reaching a conclusion from premises that are themselves in question, and must be proved true. Also, arguing in a circle.