OVERVIEW OF LOGIC

Outline

Introduction

Fallacies of the Sophists

A. What is an Argument?

Terms

Premise: a statement which is used as evidence for a conclusion

Conclusion: a statement which is supported by at least one premise

Argument: at least one premise accompanied with a conclusion.

Propositions and Non-Propositional Utterances

Proposition: an either true or false statement about the world

Non-propositional Utterance: a verbal expression that conveys meaning, but is not a true or false statement about the world. (includes questions, expressions of feelings, and propositions)

Premise and Conclusion Indicators

Premise Indicators: since, for, because, given that, for the reason that, in view of the fact that

Conclusion Indicators: therefore, thus, hence, so, accordingly, for this reason, consequently, it follows that

Argument Diagrams

Joint inference: 1+2 |→ 3

Independent inference: 1 |→ 3 and 2 |→ 3

B. Informal fallacies

Fallacies of Relevance

Argument against the Person (argumentum ad hominem): attacking a person’s character instead of the content of that person’s argument.

Argument from Ignorance (argumentum ad ignorantiam): concluding that something is true since you can’t prove it is false.

Appeal to Pity (argumentum ad misericordiam): appealing to a person’s unfortunate circumstance as a way of getting someone to accept a conclusion.

Appeal to the Masses (argumentum ad populum): going along with the crowd in support of a conclusion.

Appeal to Authority (argumentum ad verecundiam): appealing to a popular figure who is not an authority in that area

Irrelevant Conclusion (non sequitur): drawing a conclusion which does not follow from the evidence.

Other Common Fallacies

False Cause (post hoc ergo procter hoc): inferring a causal connection based on mere correlation.

Circular Reasoning: implicitly using your conclusion as a premise.

Equivocation: an argument which is based on two definitions of one word.

Composition: assuming that the whole must have the properties of its parts.

Division: assuming that the parts of a whole must have the properties of the whole.

Red Herring: introducing an irrelevant or secondary subject and thereby diverting attention from the main subject.

Straw Man: distorting an opposing view so that it is easy to refute.

C. Propositional Statements

Complex Propositions and Logical Connectives

Logical Connectives

Conjunction: P and Q

Disjunction: P or Q

Conditional: if P then Q

Negation: not P

Conjunction Clue Words (“And”)

Conditional Clue Words (“If-Then”)

Nested Logical Connectives

D. Propositional Logic

Valid Argument Forms

Valid Argument: an argument which fits a valid argument form (such as modus ponens)

Modus Ponens

premise (1) If P then Q

premise (2) P

concl. (3) Therefore, Q

Modus Tollens

premise (1) If P then Q

premise (2) Not Q

concl. (3) Therefore, not P

Disjunctive Syllogism (two versions)

premise (1) P or Q

premise (2) not P

concl. (3) therefore, Q

Hypothetical Syllogism

premise (1) if P then Q

premise (2) if Q then R

concl. (3) Therefore, if P then R

Fallacious Argument Forms

Fallacious Modus Ponens: fallacy of affirming the consequent

premise (1) if P then Q

premise (2) Q

concl. (3) therefore, P

Fallacious Modus Tollens: fallacy of denying the antecedent

premise (1) if P then Q

premise (2) not P

concl. (3) therefore, not Q

Fallacious Disjunctive Syllogism: fallacy of asserting an alternative

premise (1) P or Q

premise (2) P

concl. (3) therefore, not Q

Sound and Unsound Arguments

Sound Argument: an argument which (a) follows a valid argument form, and (b) has only true premises.

E. Inductive Logic

Inductive vs. Deductive Arguments

Deductive argument: an argument whose conclusion follows necessarily from its basic premises.

Inductive
argument: an argument in which the premises provide reasons supporting
the *probable* truth of the
conclusion.

Inductive Probability

Inductively very strong: probability is close to certain.

Inductively strong: probability is high.

Inductively weak: probability is low.

Inductively very weak: probability is close to non-existent.

Inductive Argument Forms

Statistical Syllogism: drawing a conclusion about an individual based on the population as a whole.

premise (1) n percentage of a population has attribute A.

premise (2) x is a member of that population.

concl. (3) Therefore, there is an n probability that x has A.

Fallacy of small proportion: a conclusion is too strong to be supported by the small population proportion with the attribute.

Statistical Induction: drawing a conclusion about a population based on a sample.

premise (1) n percent of a sample has attribute A.

concl. (2) Therefore, n percent of a population probably has attribute A.

Fallacy of small sample: a conclusion is too strong to be supported by a small sample number.

Fallacy of biased sample: a conclusion is too strong to be supported by a nonrandom sampling technique.

Argument from Analogy: drawing a conclusion about one individual based on its similarities with another individual.

premise (1) Objects x and y each have attributes A, B and C.

premise (2) Object x has an additional attribute D.

concl. (3) Therefore, object y probably also has attribute D.

Fallacy of false analogy: comparing two items that have trivial points in common, but differ from each other in more significant ways.