Logic Exam Notes

Meaning and Importance of Logic

Logic derived from Greek word “Logos” meaning speech, thought, study, discourse, or theory.
Logic is the study of methods and principles distinguishing correct from incorrect reasoning.
Reasoning involves constructing and evaluating arguments.
Correct reasoning is a solid foundation for reliable judgments.

Core Concepts

Proposition: A statement that asserts something is or is not the case; it's either true or false.
Propositions are the building blocks of arguments.
Questions, commands, and exclamations are not propositions.
Argument: Affirming a proposition based on other propositions, drawing an inference.
Inferences can be warranted (correct) or unwarranted (incorrect).

Importance of Logic

Logic helps to consciously apply rules of correct reasoning.
It makes one acutely conscious of correct arguments and inferences.
Aims to develop a system of methods, rules, and principles for evaluating arguments, leading to critical thinking.
Critical thinking involves understanding the structure of an argument, recognizing issues, and examining evidence.
Good reasoning skills are fundamental to various disciplines (business, science, law).
Logic serves as a canon of sciences, appraising understanding's correctness.
Logic is key to all learning, providing standards to evaluate information.
It stimulates thought capacity, combats incorrect thinking, and promotes definite, systematic procedures.
Logic is essential to free thought, opening minds to possibilities and liberating from prejudices.
It fosters fair-mindedness, empathy, and respect for differing opinions, aiding civilization to embrace freedom.

Laws of Thought

Fundamental axiomatic rules for rational discourse.
Guide and underlie everyone's thinking and expression.
Associated with three ambiguous expressions: law of identity, law of non-contradiction, and law of excluded middle.
Law of Identity: 'Whatever is, is.' For all a: $a = a$ .
Law of Non-Contradiction: ‘Nothing can both be and not be.’ $¬(A . ¬A)$ .
Law of Excluded Middle: 'Everything must either be or not be.’ $A ∨ ¬A$ .

Argument: Meaning and Components

Argument: A group of propositions where one is claimed to follow from the others.
It's a structured cluster of propositions exhibiting an inference.
Conclusion: The proposition affirmed based on other propositions.
Premises: Propositions supporting the conclusion.

Key Components of Argument

Proposition: A statement that is either true or false.
Premise: A proposition providing evidence for the conclusion.
Conclusion: The proposition supported by the premises.
Inference: The process of arriving at and affirming a proposition based on others.

Recognizing Arguments

Identifying argumentative passages requires understanding language and recognizing argument indicators.
Conclusion Indicators: Words or phrases signaling the conclusion (e.g., therefore, hence).
Premise Indicators: Words or phrases marking the premises (e.g., since, because).

Types of Arguments

Deductive Argument: Aims to provide conclusive evidence; premises necessitate the conclusion.
Inductive Argument: Premises provide some support for the conclusion, but not with certainty; probability-based.
Abductive Argument: Inference to the best explanation; reasoning from data to a hypothesis.

Deductive Argument

Claims its premises provide a totally sufficient guarantee of the conclusion.
Aims to establish its conclusion with certainty.

Inductive Argument

The relationship between premises and conclusion is based on probability, not necessity.
Truth of premises doesn't guarantee truth of conclusion.
Requires empirical observation to confirm or falsify the conclusion.

Abductive Reasoning

Inference to the best explanation.
Reasoning from data to a hypothesis that best explains the data.
Medical diagnoses are examples of abductive processes.

Evaluating Arguments

Logicians focus on sentences to which truth or falsity can be applied (propositions).
Deductive arguments: evaluated as valid or invalid.
Inductive arguments: evaluated as strong or weak, sound or unsound.

Deductive Arguments: Validity and Invalidity

Validity and invalidity apply solely to deductive arguments.
Truth and falsity apply to propositions.
Valid Argument: Premises and conclusion are related such that the premises can't be true and the conclusion false.
Validity depends on the logical form, not the subject matter.
Invalid Argument: Has true premises and a false conclusion.
Proving invalidity can be done through refutation by logical analogy.

Soundness and Unsoundness

Terms associated with arguments.
Sound Argument: Valid argument with all true premises.
Unsound Argument: Valid argument with false premises or a mixture of true and false premises.

Inductive Arguments: Correct and Incorrect

Evaluated as strong/sound (correct) or weak/unsound (incorrect).
Strength is determined by how well the premises justify the inductive claim.
Additional premises can strengthen or weaken an inductive argument.

Fallacies

Mistakes in logical reasoning, distorting the process from premises to conclusion.
Result in false, invalid, or unsound arguments.

Types of Fallacies

Formal Fallacies: Occur in the structure of the argument.
Informal Fallacies: Occur in the content of the argument; categorized into fallacies of relevance, weak induction, presumption, ambiguity, and grammatical analogy.

Fallacies of Relevance

Premises are logically irrelevant to the conclusion.
Examples: Argumentum ad baculum (appeal to force), Argumentum ad misericordiam (appeal to pity), Argumentum ad populum (appeal to the people), Argumentum ad hominem (argument against the person), Fallacy of Accident, Strawman Fallacy, Ignorantio Elenchi (missing the point).

Fallacies of Weak Induction

Connection between premises and conclusion is weak.
Examples: Argumentum ad verecundiam (appeal to unqualified authority), Argumentum ad ignorantiam (appeal to ignorance), Fallacy of Hasty Generalization, Fallacy of False Cause.

Fallacies of Presumption

Presume what they seek to prove.
Examples: Fallacy of Begging the Question (petitio principii), Fallacy of Complex or Loaded Question.

Fallacies of Ambiguity

Include Fallacy of Equivocation and Fallacy of Amphiboly.
Arise from the ambiguous use of words or phrases.

Fallacies of Grammatical Analogy

Include Fallacy of Composition and Fallacy of Division.
Involve incorrect transfer of attributes between parts and wholes.

Definitions

Definition: Explaining the meaning of a word, thing, or symbol to enhance proper application.
Definiendum: Term to be defined.
Definiens: Defining term.
Types: Lexical definitions and stipulative definitions.

Scope of Definitions

Definition should not be too broad or too narrow.
Definition should not be incomprehensible.

Defining Characteristics

A word designates the name of the characteristics a thing must have for the word to apply to it.

Rules of Definition

The definition must be clearer than the term being defined.
The definition must not contain the term being defined.
The definition must be convertible with the term being defined.
The definition must not be negative but positive whenever possible.

Kinds of Definition

Contextual, Lexical, Nominal, Ostensive, Persuasive, Precising, Real, and Stipulative Definitions.