Note: There is also a glossary at the end of your textbook. It is a good idea to look up terms you don't understand in both glossaries. I put mine together without reference to Prof. Hurley's, so our definitions will be stated differently. Sometimes having things explained two different ways is helpful. (His glossary also more extensive!)
Select the first letter of the word from the list above to jump to appropriate section of the glossary. If the term you are looking for starts with a digit or symbol, choose the '#' link.
a universal, affirmative categorical proposition.
An informal fallacy of relevance in which a general rule is misapplied in a case where an exception should obviously be allowed.
ad hominem argument
An informal fallacy in which one arguer uses a logically irrelevant "attack" on another arguer as a reason to disregard the second arguer's argument. It is a fallacy of relevance. there are three types, Abusive, circumstantial and tu quoque.
A categorical proposition which states that some or all of the subject term is included in the predicate term.
An informal fallacy of ambiguity in which the arguer draws upon some ambiguity in the grammatical structure of a statement to draw a false conclusion from it.
A comparison between two objects or events.
The first part of a conditional statement. If the antecedent is true the consequent will have to be true as well, for the conditional statement to be true.
appeal to force
An informal fallacy in which a threat is given as a reason to believe something, rather than a premise.One of the fallacies of relevance.
appeal to ignorance
An informal fallacy of weak induction, in which the fact that we don't know whether something is or is not the case is used as a reason to believe one way or the other.
appeal to pity
An informal fallacy in which pity for the arguer is used as a reason to believe something rather than a premise. A fallacy of relevance
appeal to the people
An informal fallacy that uses the listeners' desire as a reason to believe the conclusion, rather than a premise. Can be direct or indirect.
An informal fallacy of weak induction in which an authority is appealed to when there isn't good reason to believe him/her.
a premise that is implied, or is necessary for the argument to be valid, but is unstated.
begging the question
A group of informal fallacies of presumption, in which the conclusion is actually assumed as a premise, though it looks like new information is proven.
symbolized with a tripplebar, a biconditional is a statement that says two propositions are logically equivalent. An "if and only if" statement.
Statements that deal with inclusion or exclusion of members of subject classes in predicate classes.
A deductive argument form made up of three categorical propositions.
An inductive argument drawing conclusions about causes or effects.
claim of inference
The claim of inference is an invisible but necessary part of every argument. The arguer implies that there is a link between the premises and the conclusion, such that if the premises ore true, the conclusion will be true as
A good inductive argument. Since the premises are true and the form is strong, there is good reason to believe the conclusion.
an informal fallacy of presumption in which a question is asked that has another question embedded in it, forcing the answerer to answer the embedded question as well.
A proposition or statement made out of two or more simple propositions. Also called a compound proposition or compound statement.
an informal fallacy of grammatical analogy, in which a conclusion is drawn about a whole (not a group-see hasty generalization) in the basis of irrelevant characteristics of its parts.
see complex proposition
A conclusion is a statement in an argument that indicates of what the arguer is trying to convince the reader/listener.well.
An if...then statement. The consequent is conditional upon the antecedent.
Conjoint premises work together to prove the conclusion. If one were dropped the other wouldn't support the conclusion on its own.
A complex proposition in which two propositions are asserted to both be true. An "and" statement.
Symbols used in propositional logic. See: P language.
The consequent follows the "then" in a conditional statement. Its realization is conditional upon the antecedent .
An argument is consistent if the premises are not contradictory.
dependent upon a particular state of events to be true.
When two propositions have opposite truth values.
An operation to manipulate the content of a standard form categorical proposition without changing the truth value. Preserves truth value when used on A and O statements only. subject and predicate terms are switched, as for conversion, and term compliments are substituted for both terms.
When two statements can't both be true. (they could both be false)
An operation to manipulate the content of a standard form categorical proposition without changing the truth value. Preserves truth value when used on E and I statements only. The subject and predicate terms are switched.
The word which connects subject and predicate terms in a standard form categorical proposition. The only legal ones are "are" and "are not."
A process developed to prove a deductive argument is invalid. The form of the argument is abstracted and different content is substituted in to give clearly true premises and a clearly false conclusion. Also called substitution method
An argument in which the premises are intended to provide necessary support for the conclusion. Deductive arguments are either valid or invalid.
Both halves of a disjunction are called disjuncts.
An "either/or" statement.
A deductive argument in which one of the disjuncts of a disjunctive statement, or disjunction, are denied, proving that the remaining one must be true.
A term in a categorical proposition is distributed if you know something about every member of its class.
an informal fallacy of grammatical analogy in which a conclusion is drawn about a part of a whole on the basis of irrelevant characteristics of the whole. In a sense, the opposite of composition.
" · " The logical operator that stands for "and." It is the main operator of a conjunction.
A universal, negative, standard form categorical proposition.
a syllogism in which at least one of the three propositions is unstated.
An informal fallacy of ambiguity in which a false conclusion is drawn on the basis of a synonym.
A formal fallacy in which an inference about a particular statement is drawn on the basis of universal premises, or, from the Aristotelian standpoint, when an inference is made about things that do not exist.
An extended argument is made up of more than one smaller sub-arguments, in which the premises of the main argument are themselves proven.
the part of an explanation that is being explained. This is the common knowledge.
The part of an explanation that gives new information. The conjectured reasons for the explanandum.
Explains why something is the case. An explanation is sometimes difficult to distinguish from an argument because it also involves reasons (and even "premise" indicator words) But, unlike an argument, where the conclusion is the "new" information, in an explanation, the statement being explained--the explanandum, the part of the passage that looks like a conclusion. --is usually a commonly accepted fact. The explanans, which can look like premises, are the "new" information in an explanation, whereas they are the accepted fact in an argument.
One of the implied parts of every argument. the speaker implies that the premises are true. (without this claim they wouldn't be premises, only loosely associated statements.)
fallacy of ambiguity
A group of informal fallacies in which the inferential link is faulty because of some ambiguity in the language of the argument.
A group of informal fallacies in which the inferential link is faulty even though they are grammatically analogous to other good arguments.
fallacy of presumption
a group of informal fallacies in which the information in the conclusion of an argument is actually assumed in the premises, thus not actually proving anything new.
fallacy of relevance
a group of informal fallacies pertaining to the inferential relationship in arguments. The premises are in some way logically irrelevant to the conclusion, though they may have psychological or emotional relevance.
fallacy of weak induction
a group of informal fallacies pertaining to the inferential relationship in inductive arguments. The premises are irrelevant to the conclusion, but this fact is obscured in some way.
false cause fallacy
An informal fallacy of weak inductuion in which the arguer tries to claim a causal relationship about two events that are most likely just coincidental.
An informal fallacy of presumption based on a disjunction when there are actually more than two choices.
The figure of a categorical syllogism refers to the arrangement of the middle terms in the premises. The shirt collar mneumonic device can be used to remember the four possible figures. They are used in conjunction with the mood to classify valid and invalid categorical syllogisms.
form of argument
the structure of the argument without any of the contingent content. Usually, to see the form, symbols or capital letters are substituted instead of categories or simple propositions.
An invalid argument in which the problem has to do with the form of the argument.
The study of the the form of arguments, unobscured by contingent content.
an argument in which a conclusion is drawn about a group on the basis of characteristics of a sample of the group.
An informal fallacy of weak induction in which a generalization is drawn on the basis of a faulty sample.
an extended argument in which the main pattern is of many premises supporting one conclusion. Also called scattergun argument.
" É" The logical operator that is used to symbolize conditional statements.
A deductive argument form made out of three "linked" conditional statements. (see also: syllogism)
A particular, affirmative, standard form categorical proposition.
"red flags" in an argument that signal how its components are to be interpreted. They may indicate premises, conclusions, or type of argument. (deductive or inductive)
An argument in which the premises are intended to provide probable support for the conclusion. It is conceivable, in an inductive argument, that the premises are all true but the conclusion is false, this is just unlikely. (The sun will come up in the east tomorrow morning, because it always has in the past is an inductive argument)
A jump of reasoning from known information to new information. (See inferential relationship)
see: claim of inference
The relationship between the premises and conclusion in a good argument. See modus ponens.
A bad (invalid or unsound) argument, where the problem has to do with the contingent content of the argument, and can't be detected by looking at the form itself.
A deductive argument which has something wrong with the form. It is possible for the argument to have true premises and a false conclusion. This is a bad argument, even if the premises are true.
the study of arguments.
When two propositions have the same truth value. (It does not mean that their contingent content has the same meaning)
Also called connectives, used in propositional logic. They are the tilde, dot, wedge horseshoe and tripplebar.
The logical operator in a complex proposition that is outside all parentheses.
The first premise in a standard form categorical syllogism. It contains the middle term and the major term.
The term in a standard form caregorical syllogism which is in the major premise and is the predicate term of the conclusion. Symbolized P.
The term in a standard form categorical syllogism which is in the premises but not in the conclusion. Symbolized M.
The second premise in a standard form categorical syllogism. It contains the middle term and the minor term.
The term in a standard form caregorical syllogism which is in the minor premise and is the subject term of the conclusion. Symbolized S.
missing the point
an informal fallacy of relevance in which the arguer gives premises that would support one conclusion, but substitutes a different, usually extreme one instead.
Boolean) square of opposition
A square of opposition in which no assumptions are made about the existence of the terms.
The mood of a standard form categorical syllogism is a list of the types of its three component propositions, beginning with the major premise.
Something is necessary if it is impossible to imagine it not being the case, even in a different possible world. Not contingent upon any particular state of events or set of truth values.
A categorical proposition which states that some or all of the subject term are excluded from the predicate term.
A particular, negative, standard form categorical proposition.
An operation to manipulate the content of a standard form categorical proposition without changing the truth value. The quality of the proposition is changed without changing the quantity, and the term compliment is substituted for the predicate term. Preserves the truth value of all four types of propositions.
A language in symbolic logic utilizing 5 logical operators, or connectives, capital letters to stand for simple propositions, and parentheses, brackets and braces for punctuation. Sentences of this language are called well formed formulas or WFF's.
"( )" used to enclose propositions in the language P, keeping the meaning of the statement clear.
When pertaining to a categorical proposition, it is a statement that pertains to at least one of the subject class.
Often called critical thinking, it is the study of verbal arguments, instead of focussing on the form as formal logic does.
The second term in a categorical proposition. It is a class into which the subject term is included or from which it is excluded. (ofter shortened to P term)
A Premise is a statement in an argument that provides reason or support for the conclusion. There can be one or many premises in a single argument.
A statement. Propositions are sentences or phrases that can be judged to be true or false, for example "The sky is blue" and not "please hurry!"
The formal, symbolic logic using the language P.
When referring to standard form propositions the quality is determined by whether the subject class is (affirmative) or is not (negative) included in the predicate class.
in categorical logic, the quantifier determines how much of the subject term is referred to by the predicate term. Standard form quantifiers are all, some and no.
When referring to standard form propositions the quantity is determined by the quantifier. It is either uuniversal or particular.
an informal fallacy of relevance in which the arguer leads listener astray with irrelevant statements rather than premises.
reducing the scope
when working with term compliments, narrows down the range of objects referred to.
A complex proposition that is always false due to its structure. The opposite of a tautology.
the smallest possible proposition. If it were cut into smaller parts it would no longer be a proposition.
An informal fallacy of weak induction in which the arguer gives a series of causal inferences that probably won't come about.
A "good" deductive argument. Since the conclusion actually follows from the premises, and the premises are true, the conclusion should be believed.
square of opposition
A standardized arrangement of standard form categorical propositions that portrays the relationships between the types of propositions and aids in drawing inferences on the basis of their properties.
English sentences are translated, following strict formal guidelines, which make it possible to study arguments objectively.
A statement is a sentence that is either true or false, such as "The cat is on the mat." Many sentences are not statements, such as "Close the door, please" , "How old are you?"
An informal fallacy of relevance in which an arguer presents a "straw" version of another arguer's argument, defeats it, and pretends to have defeated the real argument.
An inductive argument with a good form. The inferential relationship is such that the premises provide probable support for the conclusion.
The first term in a categorical proposition. (the term which is being talked about). It must be a class, not a singular term. (Often shortened to S term)
The relation between propositions by which it is inferred from a true universal statement that the corresponding particular statement is true; and from a false particular that the corresponding universal is false.
When two propositions can't both be false, though they could both be true.
an informal fallacy of presumption that obscures the existence of much stronger evidence that would undermine the argument.
A formal argument with two premises and one conclusion.
A type of formal logic in which symbols are used to study the properties of the form of the argument.The most elementary symbolic language is P
A complex proposition that is always true, because of the form of the statement.
A term is a simple component of a statement, with a limited and definite meaning. In a categorical proposition the term must signify a class.
A term compliment is the opposite of a term. Sometimes formed by adding "non-" to the term, sometimes formed using prefixes, with longer terms you must reduce the scope of the term.
The square of opposition developed by Aristotle which supports the maximum number of inferences. Only used when you can certify that the terms involved exist.
" º " The logical operator that stands for "if and only if." It shows that two propositions are logically equivalent. It is the main operator in a bi-conditional statement.
The set of possible truth values a formal complex proposition could have, depending on the truth of the contingent content that could be substituted into it. There is a four line truth table for each connective.
A truth table is a conventionalized arrangement of all the possible combinations of truth values for the components of a proposition or argument.
"~" The logical operator that stands for "not." It is the main operator of a negation.
a standard form categorical proposition with universal quanitfier.
A deductive argument in which the premises provide necessary support for the conclusion. It is impossible for the premises to be true and the conclusion false.
A standardized drawing to help visualize categorical propositions and categorical syllogisms. They are created with overlapping circles to symbolize the different terms.
An extendended argument in which the main pattern is one of linked sub-arguments in a chain, one conclusion being premise in the next argument.
An informal fallacy of weak induction in which a poor analogy is drawn.
An inductive argument with a poor form. Even if the premises are true they wouldn't provide much support for the conclusion.
"v" the logical operator that stands for "or". It is the main operator in a disjunction.
well formed formula (WFF)
A readable sentence of the language P. It is properly punctuated and unambiguous.