Critical Thinking Final

Logic

The systemic use of methods and principles to analyze, evaluate, and construct arguments.

Argument

A group of statements with one being a conclusion, supported by the premise(s). Cannot be true or false.

Indicators

Indicates what point you are trying to make with your argument.

Not arguments

A series of sentences that express beliefs or opinions by themselves.

Conclusion

The claim being made in an argument. Supported by the premise(s).

Premise

Statements that explain why to believe or follow the conclusion.

Statement

A sentence that is either true or false.

Truth Value

Either true or false. Every statement has one.

Proposition

What a statement actually means.

Sentences with Truth Value

Statements

Sentences without Truth Value

Questions, commands, requests, proposals.

Conclusion and Premise Indicators.

Helps get the point across more clearly by showing what the premises are and the conclusion is.

Inferential Claim

How we use the premise to lead to the conclusion through reasoning.

No inferential claim

Occurs when someone provides advice or words of wisdom.

Warnings

No inferential claim.

Explanation

Use “because” to provide reasons for how an event occurred. (Already accepted fact.)

Deductive argument

Impossible for a conclusion to be false assuming the premises are true.

Inductive

Improbable that conclusion is false assuming premises are true.

Deductive argument examples

Math, geometry, definitions.

Inductive argument examples

Analogical, legal, moral, statistical, scientific.

Argument form

An arrangement of logical vocabulary and letters that stand for class terms such that a uniform substitution of class terms for the letters result in an argument.

Argument validity

Based on logical form, not the subject matter.

Statement form

An arrangement of logical vocabulary and letters that stand for class terms for the letters in results in a statement.

Substitution instance of a statement

Occurs when a uniform substitution of class terms for letters results in a statement.

Substitution instance of an argument

Occurs when a uniform substitution of class terms for the letters results in an argument.

Truth Analysis

Tells us whether a deductive argument is sound or unsound. A statement is either true or false.

Logical Analysis

Tells us whether a deductive argument is valid or invalid. Uses relationship between the premise(s) and conclusion.

Valid deductive argument

True premises make it impossible for conclusion to be false.

Invalid deductive argument

Even if all premises are true, it is possible for the conclusion to be false.

Validity

Valid or invalid, it is still a categorical distinction.

Sound argument

The argument is valid and the premises are, in fact true.

Unsound argument

The argument is invalid or at least one of the premises are false.

Logical Form

Helps to separate logical analysis from truth analysis.

Counterexample to a statement

Provides evidence that a statement is false.

Counterexample to an argument

Shows that true premises do not make the conclusion necessarily true. (Argument is invalid).

Strong inductive argument

True premises make it probable that the conclusion is true.

Weak inductive argument

True premises make it improbable that the conclusion is true.

Cogent inductive argument

The argument is strong and the premises are true.

Uncogent inductive argument

The argument is weak or has at least one false premise.

Incomplete arguments

Consists of enthymemes and principle of charity.

Enthymemes

Arguments with missing premises, missing conclusions, or both.

Principle of charity

Giving as much evidence for the premises to support the conclusion. “Benefit of the doubt”

Rhetorical Language

Speaking or writing for dramatic/exaggerated effect, often uses language that implies things not explicitly said.

Rhetorical question

A statement disguised in the form of a question. The answer is usually obvious.

Rhetorical conditionals

A conditional statement used to imply an argument.

Ambiguity in an Argument

Occurs when words, phrases, or sentence structures have multiple meanings that can lead to confusion and invalid conclusions.

Vagueness in an Argument

Occurs when terms lack clear meaning, creating “borderline cases” where it is unclear if something applies, weakening the argument’s validity.

Imprecision in an Argument

Occurs when the language, data, or logic used is too vague, ambiguous, or over-generalized to adequately support the conclusion.

Term

A single word or a group of words that can be subject of a statement; it can be a common name, a proper name, or even a descriptive phrase.

Using vs. Mentioning a word

Using a word is incorporating it into a sentence, while mentioning a word is more about describing the word and its use.

Intension

Specified by listing the properties or attributes to the term’s literal meaning.

Extension

The class or collection of objects to which the term applies. What the term references.

Increasing extension

Each term denotes a set of objects with more members than the previous term.

Decreasing extension

Each term denotes a set of objects with less members than the previous term.

Increasing intension

Each term connotes more attributes than the previous term.

Decreasing intension

Each term connotes fewer attributes than the previous term.

Relationship between intension and extension

All statements have an intension, but not all statements have an extension. Fictional things, like Santa, have no extension.

Intensional definition

Assigns a meaning to a term by listing the properties shared by all the objects that are denoted by the term.

Synonymous definitions

Assigns a meaning to a term by providing another term with the same meaning.

Word Origin Definitions

Assigns a meaning to a term by investigating its origin.

Etymology

The study of history, development, and sources of words.

Operational Definitions

Defines a term by specifying a measurement procedure.

Definition by Genus and Difference

Assigns a meaning to a term (the species) by establishing a genus and combining it with the attribute that distinguishes the members of that species.

Extensional (denotative) definition

Assigns meaning to a term by indicating the class members denoted by the term.

Ostensive Definitions

Involves demonstrating the term.

Required for ostensive definitions

Nonverbal behaviour like pointing, gesturing, drawing a picture, or showing a photograph.

Enumeration definitions

Assigns meaning to a term by naming the individual members of the class denoted by the term.

Complete enumeration

Gives every single member of the class.

Partial enumeration

Leaves out many members of the class.

Definition by subclass

Assigns meaning to a term by naming subclasses of the class denoted by the term.

Complete definition by subclass

Includes all members of the class in one definition.

Partial definition by subclass

Does not include all members of the class.

Stipulative Definitions

Introduces a new meaning to a term or symbol. Both intensional and extensional.

Lexical Definitions

A definition based on the common use of a word, term, or symbol. Dictionaries often use both intensional and extensional definitions.

Functional Definitions

Specifies the purpose or use of the objects denoted by the term. Intensional.

Precising Definitions

Reduces the vagueness and ambiguity of a term by providing a sharp focus, often a technical meaning for a term. It is very precise and leaves no room for confusion.

Theoretical Definitions

Assigns a new meaning to a term by providing an understanding of how the term fits into a general theory.

Persuasive Definitions

Assigns a new meaning to a term with the direct purpose of influencing attitudes or opinions. Doesn’t provide info, but influences thinking about emotionally charged issues.

Informative Definitions

Extremely informative and detailed.

Cognitive meaning

Language used to convey information.

Emotive meaning

Language used to express emotion or feelings.

Factual dispute

Occurs when people disagree over facts. May involve different emotional attitudes towards the facts.

Verbal dispute

Occurs when people disagree over the meaning of a vague or ambiguous term, may involve emotive meanings, political or religious divisions, and value judgements, making it difficult to agree on a definition.

Diagramming an argument

Allows us to visualize the connections between the premise(s) and the conclusion.

Convergent Diagram

A premise is independent when the falsity of one does not nullify any support the others would give to the conclusion.

Linked Diagram

Premises are dependant when they act together to support a conclusion.

Divergent Diagram

Shows a single premise supporting independent conclusions.

Serial Diagram

Shows that the conclusion from one argument is a premise in a second argument.

Diagramming Extended Arguments

Combining two or more diagramming techniques.

Formal Fallacy

A logical error in a deductive argument that occurs in the form or structure of an argument.

Informal Fallacy

A mistake in reasoning that occurs in ordinary language concerning the content of the argument rather than its form.

Fallacies based on personal attacks

Occurs when an argument is rejected solely on an attack against the person making the argument, not the merits of the argument itself.

Fallacies based on emotional appeals

Occurs when an argument relies solely on the arousal of a strong emotional or psychological reaction to get a person to accept the conclusion.

Ad Hominem Abusive

When a claim is rejected based on alleged character flaws or a negative stereotype of the person making the claim.

Ad Hominem Circumstantial

When a claim is rejected based on the life circumstances of the person making the claim.

Positioning the well

When a person is attacked before having a chance to present a case.