1. OVERVIEW OF LOGIC

Outline

 

James Fieser, UT Martin

updated 1/1/2020

 

A. WHAT IS AN ARGUMENT?

 

1. 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.

 

2. Propositions and Non-Propositional Statements

Utterance: The most general form of verbal expression

 which conveys meaning. Statements include questions (“who am I?”), commands (“get that porcupine out of my face!”), expressions of feelings (“three cheers for old glory!”), and propositions (see next definition).

Proposition: An either true or false statement about the world, such as, “The door is brown”

 

3. 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

 

4. Argument Diagrams

Joint inference: 1+2 |→ 3

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

 

B. INFORMAL FALLACIES

 

1. 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.

 

2. 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

 

1. 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”)

P, but Q

P, although Q

P; Q

P, besides Q

P, however Q

P, whereas Q

Conditional Clue Words (“If-Then”)

If P, it follows that Q

P implies Q

P entails Q

Whenever P, Q

P, therefore Q

Q follows from P

Q, since P

 

2. Nested Logical Connectives

 

D. PROPOSITIONAL LOGIC

 

1. 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

 

2. 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

 

3. Sound and Unsound Arguments

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

 

E. INDUCTIVE LOGIC

 

1. 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.

2. Inductive Argument Forms

Simple Enumerative Induction: drawing a generalized conclusion about an entire class of things based on a few observations about members of that class.

premise (1) Item x has attribute A

premise (2) Item y has attribute A

concl.    (3) Therefore, all items of the same type as x and y probably have attribute A

Fallacy of hasty generalization: drawing a general conclusion based on one or several atypical instances.

Statistical induction: drawing a conclusion about a population based on a statistically acceptable 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.

Statistical syllogism: drawing a conclusion about an item based on statistics about 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.

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.