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.