Basic Concepts in Logic, Inductive Logic, and Analyzing Arguments

Comprehensive vocabulary flashcards covering basic concepts in formal logic, deductive argument evaluation, famous valid forms, inductive logic, causal analysis, and the reconstruction of well-crafted arguments.

Logic (Howard-Snyder and Wasserman, 2009)

The study of methods for evaluating whether the premises of an argument adequately support (or provide good evidence for) its conclusion; roughly paraphrased as the study of methods for evaluating arguments.

Logic (Pocket Oxford English Dictionary)

The science of reasoning.

Argument

A set of statements where some of the statements, called the premises, are intended to support another statement, called the conclusion.

Premises

Statements in an argument on the basis of which the conclusion is affirmed or intended to be supported.

Conclusion

The statement in an argument that is intended to be supported by the premises.

Statement

A declarative sentence which is either true (describing things as they are) or false (describing things in ways other than they are), excluding questions, commands, or suggestions.

Deductive Argument

An argument in which the premise(s) are intended to guarantee the truth of the conclusion.

Inductive Argument

An argument in which the premise(s) are intended to make the conclusion probable, without guaranteeing it.

Valid Argument

A deductive argument in which the premises succeed in guaranteeing the conclusion; it is necessary that if the premises are true, then the conclusion is true.

Invalid Argument

An argument in which it is not necessary that, if the premises are true, then the conclusion is true; the conclusion can be true but is not guaranteed by the premises.

Sound Argument

A valid deductive argument in which all of the premises are true ($\text{Valid} + \text{All Premises True} = \text{Sound}$).

Unsound Argument

An argument that either is invalid or is valid with at least one false premise.

Argument Form

A pattern of reasoning; specifically, a group of sentence forms such that all its substitution instances are valid arguments.

Substitution Instance (SI)

An argument that results from uniformly replacing the variables in an argument form with statements (or terms).

Valid Argument Form

An argument form that has no substitution instances that are invalid; every substitution instance is a valid argument.

Invalid Argument Form

An argument form that has at least one substitution instance that is an invalid argument.

Famous Valid Forms Method

A method to evaluate deductive arguments by identifying the component statements with capital letters, eliminating stylistic variants, and comparing the resulting pattern of reasoning to five common valid forms.

Conditional Statement

An 'if-then' statement consisting of an antecedent (the 'if'-clause) and a consequent (the 'then'-clause); it constitutes a single statement rather than an entire argument.

Modus Ponens (MP)

A valid deductive argument form (affirming the antecedent) structured as: If $A$, then $B$. $A$. So, $B$.

Affirming the Consequent (AC)

A formal fallacy and invalid argument form structured as: If $A$, then $B$. $B$. So, $A$.

Modus Tollens (MT)

A valid deductive argument form (denying the consequent) structured as: If $A$, then $B$. Not $B$. So, Not $A$.

Denying the Antecedent (DA)

A formal fallacy and invalid argument form structured as: If $A$, then $B$. Not $A$. So, Not $B$.

Hypothetical Syllogism (HS)

A valid deductive argument form composed of conditional statements structured as: If $A$, then $B$. If $B$, then $C$. So, if $A$, then $C$.

Disjunctive Syllogism (DS)

A valid argument form that has two versions: (1) Either $A$ or $B$. Not $A$. So, $B$. (2) Either $A$ or $B$. Not $B$. So, $A$.

Disjunction

A compound statement formed by connecting simpler statements (disjuncts) using 'or', which can be interpreted inclusively ('$A$ or $B$ or both') or exclusively ('$A$ or $B$ but not both').

Constructive Dilemma (CD)

A valid argument form combining disjunctive and conditional statements: Either $A$ or $B$. If $A$, then $C$. If $B$, then $D$. So, either $C$ or $D$.

Counterexample

A substitution instance of an argument form in which the premises are true and the conclusion is false; a good counterexample uses well-known truths for the premises and a well-known falsehood for the conclusion.

Inductive Logic

The branch of logic concerned with the study of methods for evaluating arguments for strength and weakness.

Strong Argument

An inductive argument in which it is probable (but not necessary) that, if the premises are true, then the conclusion is true.

Weak Argument

An inductive argument in which it is not probable that, if the premises are true, then the conclusion is true.

Cogent Argument

A strong inductive argument in which all of the premises are true.

Uncogent Argument

An inductive argument that is either weak, or strong with at least one false premise.

Statistical Syllogism

An inductive argument form patterned as: $x\text{ percent of } A \text{ are } B$. $c \text{ is an } A$. So, $c \text{ is a } B$, where $x$ is greater than 50 and less than 100.

Fallacy of Incomplete Evidence (Cherry-picking)

A fallacy committed when an arguer fails to consider all available relevant evidence when choosing the reference class for a statistical syllogism, making an argument appear strong when it may be weak.

Argument from Authority

An inductive argument form structured as: $R \text{ sincerely asserts that } S$. So, $S$, where $R$ is a source of information (person or reference work) and $S$ is a statement.

Induction by Enumeration

An inductive argument form where a conclusion about all or an approximate percentage of members of a class is drawn from premises referring to an observed sample of that class.

Sufficient Condition

A condition $x$ such that if $x$ occurs, $y$ occurs (e.g., being beheaded is a sufficient condition for human death).

Necessary Condition

A condition $x$ such that $y$ occurs only if $x$ occurs; all necessary conditions must be present for the phenomenon to happen.

Method of Agreement

One of Mill's methods that identifies a common factor that is present whenever the effect is present to conclude that '$A \text{ causes } B$'.

Method of Difference

One of Mill's methods that compares two cases—one where the effect is present and one where it is absent; if a factor $C$ is absent when the effect is absent, $C$ is supported as the cause.

Joint Method of Agreement and Difference

One of Mill's methods for causal inference that combines both the method of agreement and the method of difference.

Method of Concomitant Variation

One of Mill's methods showing that as one factor varies in magnitude or intensity, another factor varies in a corresponding way.

Method of Residues

One of Mill's methods that involves 'subtracting out' those aspects of an effect whose causes are already known, concluding that the remaining effect ('the residue') is due to an additional cause.

Scientific Way of Reasoning

An inductive reasoning procedure derived from Mill's methods involving three steps: describing the problem, formulating a hypothesis, and testing the hypothesis.

Argument from Analogy (Analogical Reasoning)

An inductive argument form patterned as: $A \text{ is similar to } B$. $B \text{ has property } P$. So, $A \text{ has property } P$.

Report

A non-argumentative passage consisting of a set of statements intended to convey or provide information about a situation, topic, or event.

Illustration

A non-argumentative passage intended to provide examples that illustrate, clarify, or exemplify a claim rather than provide convincing evidence to prove it.

Explanatory Statement

A statement or passage that shows why something is the case (providing a causal or other reason) rather than seeking to prove that it is the case.

Well-Crafted Argument (WCA)

An argument that is reconstructed and stated in such a way that its important logical features and structure are made explicit.

Premise Indicators

Words or phrases (such as 'since,' 'because,' 'for,' 'follows from,' 'inasmuch as,' and 'given that') that are typically followed by a premise.

Conclusion Indicators

Words or phrases (such as 'therefore,' 'hence,' 'thus,' 'so,' 'consequently,' and 'as a result') that are typically followed by a conclusion.

Excess Verbiage

Words or statements that add nothing to the logical support of an argument, categorized into discounts, repetition, assurances, and hedges.

Discount

A type of excess verbiage that acknowledges a fact or possibility that might be thought to render the argument invalid, weak, unsound, or uncogent (signaled by words like 'although' or 'even though').

Assurance

Words or phrases (such as 'obviously,' 'clearly,' 'no doubt,' and 'the fact is that') used to indicate high confidence in the truth of the premises or conclusion.

Hedge

Words or phrases (such as 'in my opinion,' 'I think that,' 'perhaps,' and 'it seems that') indicating tentativeness about a premise or inference.

Uniform Language

The principle of well-crafted arguments requiring consistent terminology throughout the premises and conclusion to keep the logical structure clear.

Principle of Charity

The interpretive guideline directing the reader to interpret an argument fairly by choosing the interpretation that best preserves the rationality and intended meaning of the author.

Sub-conclusion

A statement within a complex argument that is supported by one or more premises and also acts as a premise supporting a subsequent or final conclusion.

Enthymeme

An argument that leaves one or more premises or the conclusion implicit rather than stated explicitly.

Argument Diagram

A visual tool where numbered statements are linked by arrows pointing from supporting premises to the conclusion, illustrating independent or interdependent support.