Understanding Arguments and Their Structure in Logic

Logic

The organized body of knowledge, or science, that evaluates arguments.

Purpose of logic

To evaluate arguments, to develop methods and techniques that allow us to distinguish good arguments from bad.

Argument

A group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (conclusion).

Good arguments

Those in which premises really do support the conclusion.

Bad arguments

Those in which premises do not support the conclusion, even though they are claimed to.

Statement

A sentence that is either true or false.

Truth values

Either true or false; questions, proposals, suggestions, commands, and exclamations usually cannot have a truth value.

Premises

The statements that set forth the reasons or evidence.

Conclusion

The statement that is claimed to support or imply.

Typical conclusion indicators

Words or phrases such as therefore, accordingly, entails that, wherefore, we may conclude, hence, thus, it must be that, it follows that, consequently, for this reason, implies that, we may infer, so, as a result.

Claimed evidence

What is claimed to follow from the evidence.

Typical premise indicators

Words or phrases such as since, in that, seeing that, as indicated by, may be inferred from, for the reason that, because, as, in as much as, for, given that, owing to.

Intended conclusion

Typically stated first, then the premises follow.

Implicit claim

Exists if there is an inferential relationship between the statements in a passage, but the passage contains no indicator words.

Simple Noninferential passages

Unproblematic passages that lack a claim that anything is being proved.

Expository passage

A kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence.

Genetic engineering

Can introduce unintended changes into the DNA of the food-producing organism, and these changes can be toxic to the consumer.

Illustrations

An expression involving one or more examples that is intended to show what something means or how it is done.

Arguments from example

Illustrations that can be taken as arguments.

Explanations

An expression that purports to shed light on some event or phenomenon, usually accepted as a matter of fact.

Explanandum

The statement that describes the event or phenomenon to be explained.

Explanans

The statement or group of statements that purports to do the explaining.

Conditional statement

An if..then statement, NOT an argument.

Antecedent

The statement following the 'if..'.

Consequent

The statement following the '..then'.

Sufficient reason

A is said to be sufficient reason B whenever the occurrence of A is all that is needed for the occurrence of B.

Necessary condition

B is said to be a necessary condition for A whenever A cannot occur without the occurrence of B.

Necessary condition

Being an animal is a necessary condition for being a dog.

Indicator words

Words that signal the presence of an argument.

Inferential relationship

A connection where one statement is claimed to be supported by another.

Nonarguments

Statements that do not present an argument, such as warnings, reports, and opinions.

Warnings

Statements that alert someone to a potential problem or danger.

Reports

Statements that provide information without arguing for a conclusion.

Pieces of advice

Suggestions offered to someone about what they should do.

Expository passages

Text that explains or informs without arguing a point.

Statements of belief

Expressions of personal convictions or faith.

Illustrations

Examples used to clarify or explain a point.

Statements of opinion

Personal views that are not necessarily backed by evidence.

Explanations

Clarifications that describe why something is the case.

Loosely associated statements

Statements that are related but do not form a coherent argument.

Conditional statements

Statements that express a condition and its consequence.

Standard form of an argument

A format that exhibits the logical structure of an argument.

Premise

A statement that provides support for a conclusion.

Subpremise

A premise that supports another premise in the argument.

Rebuttal premise

A statement used to counter objections to the argument.

Subargument

An argument that supports one of the premises of the main argument.

Standard-form reconstruction

A clear and concise representation of an argument's structure.

Conclusion

The statement that follows from the premises in an argument.

Statement

Claims that have truth value (true or false).

Argument

A claim supported by other claims.

Premises

Statements that offer evidence or support for the conclusion.

Conclusion

The statement that is supported by the premises.

Standard form of an argument

The evaluation of an argument.

Reconstructing the argument

The first step in evaluating an argument to display its logical structure.

Premise

A statement that supports the conclusion.

Sub-premise

Supports another premise.

Subargument

A situation where a subpremise is used to support one of the premises of the main argument.

Implicit Premise

Something not explicitly stated, but implied.

Rebuttal premise

A premise that addresses possible issues with the argument.

Deductive argument

An argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true.

Inductive argument

An argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true.

Irrelevant material

Material that should be excluded from the argument.

Essential meaning

The core meaning of the argument's original features.

Meerkat example (deductive)

The meerkat is a member of the mongoose family. All members of the mongoose family are carnivores. Therefore, it necessarily follows that the meerkat is a carnivore.

Meerkat example (inductive)

The meerkat is closely related to the suricat. The suricat thrives on beetle larvae.

Questions

Statements that do not have truth value.

Imperatives

Commands that do not have truth value.

Mere opinions

Statements that do not have truth value.

Heated dispute

A discussion that involves anger.

Indicator words

Words that signal the type of reasoning being used, such as 'probably', 'likely', 'certainly'.

Inductive

A form of reasoning that draws general conclusions from specific examples.

Deductive

A form of reasoning that draws specific conclusions from general premises.

Deductive Argument Forms

Structures of arguments where the conclusion necessarily follows from the premises.

Argument based on mathematics

An argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement.

Argument from definition

An argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion.

Categorical Syllogism

A syllogism in which each statement begins with one of the words 'all', 'no', or 'some'.

Pure Hypothetical syllogism

A syllogism having a conditional 'if..then'.

Disjunctive syllogism

A syllogism having a disjunctive 'either... or'.

Inductive Argument Forms

Structures of arguments where the conclusion likely follows from the premises.

Prediction

An argument that proceeds from our knowledge of the past to a claim about the future.

Argument from analogy

An argument that depends on the existence of an analogy, or similarity, between two things or states of affairs.

Generalization

An argument that proceeds from the knowledge of a selected sample to some claim about the whole group.

Argument from authority

An argument that concludes something is true because a presumed expert or witness has said that it is.

An argument based on signs

An argument that proceeds from the knowledge of a sign to claim about the thing or situation that the sign symbolizes.

Causal Inference

An argument that proceeds from knowledge of a cause to a claim about an effect, or conversely, from knowledge of an effect to a claim about a cause.

Particular statement

One that makes a claim about one or more particular members of a class.

General statement

Makes a claim about all of the members of a class.

Modus Ponens

If p, then q; P; Therefore, q.

Modus Tollens

If p, then q; Not p; Therefore, not q.

Constructive Dilemma

If p then r, and if q then s; Either p or q; Therefore, R or S.

Valid deductive argument

An argument in which it is impossible for the conclusion to be false given that the premises are true.

Invalid deductive argument

An argument in which it is possible for the conclusion to be false given that the premises are true.

Sound argument

A deductive argument that is valid and has all true premises.

Unsound argument

A deductive argument that is invalid, has one or more false premises, or both.

Strong inductive argument

An inductive argument in which it is improbable that the conclusion be false given that the premises are true.

Weak inductive argument

An argument in which the conclusion does not follow probably from the premises, even though it is claimed to.

Cogent argument

An inductive argument that is strong and has all true premises.

Uncogent argument

An inductive argument that is weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these.

Strong argument

An inductive argument in which the conclusion follows probably if we assume that the premises are true.

Weak argument

An inductive argument in which the conclusion does not follow probably from the premises, even though it is claimed to.