Glossary

"All S are P."

Attacking the person making an argument instead of the argument.

From P, conclude "P or Q" for any Q.

A categorical statement that includes members in the predicate class (A or I).

The invalid form: P or Q; P; so not Q.

The invalid form: if P, then Q; Q; so P.

An argument that relies on a sentence's ambiguous grammar.

The "if" part of a conditional.

Citing someone whose expertise doesn't cover the question.

Using feelings such as pity or fear in place of reasons.

Using a threat in place of reasons.

Concluding something is true because it hasn't been disproved, or false because it hasn't been proved.

Treating "lots of people believe it" as a reason to think it's true.

Reasons offered to support a claim.

A picture showing which claims support which in an argument.

Regrouping a chain of "and"s, or a chain of "or"s, doesn't change its truth value.

A sentence supposed for the sake of argument at the start of a subproof.

A sentence with no connectives: just one sentence letter.

Assuming, in the premises, the very conclusion you are trying to prove.

An "if and only if" claim: both parts have the same truth value.

From A ↔ B and one side, write the other side.

From two subproofs, A to B and B to A, write A ↔ B.

The reading on which "all" and "no" statements make no claim that anything exists.

The responsibility of whoever makes a claim to support it.

A statement about how two classes are related.

A two-premise argument made of three categorical statements that share three terms.

A group of things picked out by some shared feature.

One thing bringing about another.

A step-by-step rewrite of a sentence, each step justified by a named law.

The truth table that defines a connective.

An argument whose conclusion reappears among its own premises.

The rule name and line numbers written beside a proof line to justify it.

An inductive argument is cogent if it is strong and all its premises are actually true.

A third factor that produces both of two correlated things.

The order of the two sides of an "and" or an "or" doesn't matter.

Everything that is not in a given class.

A sentence built from smaller sentences with connectives.

The claim an argument is trying to support.

A word or phrase that usually signals the conclusion is coming.

An "if … then" claim.

From A → B and A, write B: modus ponens as a proof rule.

From a subproof that assumes A and reaches B, write A → B.

One of the parts of an "and" claim.

An "and" claim, or the argument form that builds one.

From A ∧ B, write A (or B).

From A and B on separate lines, write A ∧ B.

An "and" of "or"s of literals.

A word or symbol that builds a sentence from other sentences.

The "then" part of a conditional.

Two conditionals plus "one condition or the other" give "one result or the other."

A sentence that is true on some rows and false on others.

A sentence that is false on every row of its truth table.

Two statements that always have opposite truth values.

Swapping subject and predicate and replacing both with their complements.

The conditional "if not Q, then not P," which is equivalent to "if P, then Q."

Two statements that cannot both be true but can both be false.

A factor that makes an outcome more likely without guaranteeing it.

Comparing groups that differ only in the suspected cause.

The conditional you get by swapping the if-part and the then-part.

Swapping the subject and predicate terms of a categorical statement.

The linking verb "are" or "are not" in a categorical statement.

Two things tending to vary together.

A possible situation where an argument's premises are all true and its conclusion is false.

A row that makes every premise true and the conclusion false.

Negating an "and" gives an "or" of negations, and vice versa.

An argument meant to guarantee its conclusion.

Able to be weakened by new information, the way an inductive argument can be.

The invalid form: if P, then Q; not P; so not Q.

A shortcut rule that could always be replaced by basic-rule steps.

Two conditionals plus "one result fails or the other does" give "one condition fails or the other does."

Closing a subproof, so its assumption is no longer in force.

One of the parts of an "or" claim.

An "or" claim.

From A ∨ B and two subproofs reaching the same C, one from A and one from B, write C.

From A, write A ∨ B for any B.

An "or" of "and"s of literals.

From "P or Q" and not P, conclude Q.

A term the statement says something about every member of.

"And" distributes over "or," and "or" distributes over "and."

An "or" with a tautology is a tautology; an "and" with a contradiction is a contradiction.

"Not not A" is equivalent to A.

"No S are P."

A rule for using a sentence whose main connective is a given connective.

Premises entail a conclusion when no row makes them all true and the conclusion false.

An argument with an unstated premise or conclusion.

Switching between two meanings of the same word within an argument.

An "or" that means one or the other, but not both.

A syllogism with two negative premises.

Drawing a "some" conclusion from premises that are all "all" or "no" statements.

Whether a statement commits you to its subject class having members.

Reasons why something is true, given to someone who already accepts that it is.

From ⊥, write any sentence at all.

A common pattern of bad reasoning.

Applying a sound general rule to an exceptional case it was never meant to cover.

A fallacy that works only because a word or sentence can be read two ways.

Reasoning that what is true of each part must be true of the whole.

Reasoning that what is true of the whole must be true of each part.

A fallacy that quietly assumes something it has no right to assume.

A fallacy whose premises, true or not, have nothing to do with the conclusion.

Claiming a cause on evidence that doesn't support one.

Presenting two options as the only ones when there are others.

The position of the middle term in a syllogism's two premises, numbered 1 to 4.

An invalid argument form that looks like a valid one.

A step-by-step derivation of a conclusion from premises using stated rules.

The rules that say which strings of symbols count as sentences.

Judging a claim by where it came from instead of by the evidence for it.

Drawing a general conclusion from too few or unrepresentative cases.

A truth-table column for a smaller piece of a sentence, filled in first to make the main column easy.

From "if P, then Q" and "if Q, then R," conclude "if P, then R."

"Some S are P."

Repeating a sentence with "and" or "or" adds nothing: "A and A" is just A.

Joining a sentence to a tautology with "and," or to a contradiction with "or," leaves it unchanged.

A syllogism whose major term is distributed in the conclusion but not in its premise.

A syllogism whose minor term is distributed in the conclusion but not in its premise.

An "or" that is still true when both parts are true.

Premises that each support the conclusion on their own.

Assume "not A," reach a contradiction, and conclude A.

An argument meant to make its conclusion likely, not certain.

How likely an argument's premises, if true, would make its conclusion.

The step from premises to a conclusion.

A reasoning mistake found in what an argument says, not in its form.

A claim that is supported by premises and then supports something further.

A rule for writing a new sentence whose main connective is a given connective.

An argument is invalid if its premises could all be true while its conclusion is false.

The conditional "if not P, then not Q" formed from "if P, then Q."

Premises that support the conclusion only when taken together.

Able to be true together on at least one row.

A puzzle about islanders who always tell the truth (knights) or always lie (knaves).

Every sentence of the form "A or not A" is a tautology.

No sentence and its negation are both true: "not (A and not A)" is a tautology.

A sentence letter or the negation of one.

A question that smuggles in an assumption, so any direct answer accepts it.

The study of what makes reasons actually support a conclusion.

A table used to solve puzzles by recording what each clue rules out.

Two sentences that have the same truth value on every row.

The pattern of an argument, left over when you blank out what it is about.

The final claim an argument is trying to establish.

The connective whose scope is the whole sentence.

The premise of a syllogism that contains the major term.

The predicate term of a syllogism's conclusion.

The truth-functional "if … then": false only when the antecedent is true and the consequent false.

The equivalence "if A then B" ≡ "not A, or B."

The term that appears in both premises of a syllogism but not in the conclusion.

The premise of a syllogism that contains the minor term.

The subject term of a syllogism's conclusion.

An unstated claim an argument needs in order to work.

From "if P, then Q" and P, conclude Q.

From "if P, then Q" and not Q, conclude not P.

The three letters (A, E, I, O) naming a syllogism's statement types, in order.

A proof system with an introduction rule and an elimination rule for each connective.

Something that must hold for another thing to happen.

A claim that says another claim is false.

From A and ¬A, write ⊥.

From a subproof that assumes A and reaches ⊥, write ¬A.

"A or not A" is always true; "A and not A" is always false.

A categorical statement that excludes members from the predicate class (E or O).

"Some S are not P."

Changing a categorical statement's quality and replacing its predicate with the complement.

Introduces the consequent: "P only if Q" means "if P, then Q."

Naming one cause for an outcome that had several.

Restating a claim in clearer words without changing what it says.

A truth table with only the rows needed to settle a question.

A categorical statement about at least one member of its subject class (I or O).

A bracket-free notation that writes each connective before its parts.

A way things could be, whether or not they actually are that way.

Concluding that A caused B only because B came after A.

A convention that lets some brackets be left out by ranking the connectives.

The class a categorical statement relates its subject to.

A statement offered as a reason in an argument.

A word or phrase that usually signals a reason is coming.

Rebuild an argument in its most reasonable form before judging it.

The claim a sentence makes, apart from the words used to make it.

Whether a categorical statement includes or excludes.

Whether a categorical statement is about all or only some of its subject class.

Deciding by chance which subjects get a treatment, so the groups differ only by luck and the treatment.

Changing the subject to something that sounds related but isn't.

Copying an available earlier line.

Swapping a part of a sentence for something equivalent keeps the whole equivalent.

The cause running the opposite way from the one claimed.

A question asked to make a point rather than to get an answer.

A rule saying which new line may be written from which earlier lines.

Five checks a categorical syllogism must pass to be valid on the Boolean reading.

The part of a sentence that a connective applies to.

An English sentence that can be bracketed two ways with different meanings.

A capital letter that stands for one particular simple sentence.

A letter, like P or Q, that stands for any whole claim in a form.

The logic of whole sentences joined by "not," "and," "or," "if," and "if and only if."

Testing validity by assuming the conclusion false and every premise true, then working backward.

From "P and Q," conclude P (or Q).

Claiming one step will set off an unstoppable chain of worse ones, without support.

An argument is sound if it is valid and all its premises are actually true.

A diagram of the logical relations among A, E, I, and O statements with the same terms.

An argument rewritten as a numbered list of premises with the conclusion at the bottom.

A categorical statement written exactly as "All/No/Some S are/are not P."

A sentence that is either true or false.

Attacking a distorted, weaker version of someone's position.

On the traditional square, the inference from "all" down to "some."

Two statements that cannot both be false but can both be true.

The class a categorical statement is about.

An indented stretch of a proof that begins with an assumption.

An argument you get by filling in a form's blanks with actual claims.

Something that is enough, on its own, for another thing to happen.

Another name for the fallacy of accident.

A list saying which English sentence each sentence letter stands for.

A sentence that is true on every row of its truth table.

A sentence that can be proved from no premises at all.

The older reading on which every categorical statement assumes its subject class has members.

A table listing a sentence's truth value on every possible valuation.

Whether a statement is true or false.

Depending only on the truth values of the parts.

Checking validity by looking for a row with true premises and a false conclusion.

Dismissing a claim because the person making it doesn't follow it.

An inductive argument is uncogent if it is weak or has a false premise.

A syllogism whose middle term is not distributed in either premise.

A categorical statement about every member of its subject class (A or E).

"P unless Q" means "if not Q, then P," which is the same as "P or Q."

An argument is unsound if it is invalid or has at least one false premise.

A conditional that is true only because its antecedent is false.

An argument is valid if its premises being true would guarantee its conclusion is true.

An assignment of true or false to every sentence letter.

Overlapping circles that picture classes: shading means empty, an X means something is there.

A string of symbols that counts as a sentence of the formal language.

One truth-table row that shows something is possible, such as every sentence in a set being true at once.