## glossary of terms

*The content within each set of parentheses following each entry of this Glossary points to a Study (1-6) in which a fuller discussion may be found.*

(See end of glossary page for links to all of the Studies and Exercises.)

**A Form.**This form of a standard proposition states that All a is b, or A(ab) (Study 1)

**affirmative quality**is a form that does not distribute its predicate. (Study 1)

**affirming the consequent**the fallacy of asserting the consequent of an implication in order to infer the antecedent as conclusion. (Study 1)

**argument**is a series of connected reasons in support of a position or a conclusion. (Preview)

**axiom**is a first principle or premise. (Study 3)

**conclusion**is the proposition deduced from a previous proposition or set of propositions. (Preview)

**contradiction**the opposition between two propositions such that they cannot both be false together and cannot both be true together.( Study 2)

**contraposition**interchanging the contradictories of both subject and predicate terms; valid for

*A*and

*O*, but not for

*I*;

*E*by limitation. (Study 2)

**contraries**are two propositions which cannot be both true together, but could be both false. (Study 2)

**conversion**interchanging the subject and predicate of a proposition; valid for

*E, I*but not for

*O*,

*A*

*per accidens*, or by limitation. (Study 2)

**copula**is the present tense of the verb

*to be*; connects the subject and predicate. (Study 1)

**deduction**reasoning in which the conclusion follows necessarily from the premises presented. (Study 3)

**definiendum**the portion of a definition that is to be defined. (Study 6)

**definiens**that portion of a definition that explains or describes the word or phrase being defined. (Study 6)

**definitions by method**genus & difference, genetic, causal, functional, analogical, antonymous, and operational definitions distinguished according to the method used to define a term or phrase. (Study 6)

**definitions by purpose**lexical, stipulative, precising, theoretical, persuasive definitions distinguished according to the intended purpose. (Study 6)

**denying the antecedent**a fallacy when from the denial of the antecedent of an implication, one infers the denial of the conclusion. (Study 4)

**diagrams**Euler circles or Venn circles used to demonstrate the validity (invalidity) of an inference in deductive argument. (Study 2 , Study 3)

**dilemma**symbolized as

*(a < b) (c < d) (a + c) < (b + d),*[constructive]

*valid when conditions of form, valid implications, and complete disjunction are met; also symbolized as*

*(a < b) (c < d) (b' + d') < (a' + c')*[destructive]. (Study 4)

**disjunctive hypothetical syllogism**Symbolically: Either

*a*or

*b*,

*not-a*; therefore,

*b*. (Study 4)

**distribution**a distributed term in a proposition is one modified by

*All*, or

*No*. (Study 1)

**E Form**The form of a standard proposition symbolized as No a is b, or E(ab). (Study 1)

**enthymeme**is an argument in which one or more of the propositions is suppressed or taken for granted. (Study 3)

**euler circles**See diagrams. (Study 2 , Study 3)

**exceptive proposition**are 2 propositions in one form as

*all except x is y:*(1) All non-x is y; (2) No s is y. (Study 1)

**exclusive propositions**have the form

*only x is y*translated to the A Form: All y is x. (Study 1)

**fallacy**is a mistake in reasoning. (Study 4)

**fallacy of ambiguity**the formulation of an argument in ambiguous words or phrases. (Study 6)

**fallacy of relevance**an argument in which the premises do not logically imply or are not logically relevant to the truth of a conclusion.

**(**Study 6)

**figure**in a syllogism is the relative position of the middle term in the premises; there are 4 positions or 4 figures.( Study 1; Study 3)

**form**the subject-predicate arrangement in a proposition. There are four forms: All a is b; No a is b; Some a is b; and Some a is not b. (Study 3)

**formal property of forms**the three properties of distribution, quantity, and quality shared by the four standard form propositions.(Study 1)

**frame**the form of a syllogism, determined by the positions of the terms in the premises and conclusion; the mood and figure of a syllogism. (Study 3)

**grammatical subject**syntactic unit of sentence referring to one performing an action or being in the state expressed by the predicate; the subject of the verb is the grammatical subject.(Study 1)

**I Form**The form of a standard proposition symbolized as Some a is b, or I(ab). (Study 1)

**immediate inference**is an argument of one premise and a conclusion. (Study 2)

**indicator words or phrases**words or phrases that indicate the presence of premises or conclusion of an argument. (Study 3)

**inference**is the forming of a conclusion from premises by logical methods. (Preview)

**informal fallacy**reasoning with illogical or misleading argument; a counterfeit of a genuine deductive argument.(Study 6)

**invalid inference**when the conclusion of an argument does not follow from premises according to the rules that establish validity.

**(**Study 6)

**law of contradiction**states that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect: symbolized:

*Not both a and not-a*; or (aa')'. (Preview; Study 4)

**law of excluded middle**states that everything must either be or not be; symbolized:

*a or not-a*; or (a + a'). (Preview; Study 4)

**law of identity**states: If any proposition is true, then it is true; symbolized:

*a < a*. (Preview; Study 4)

**logic**is the science of necessary inference. (Preview)

**logical connective**is the part that joins simple propositions to form compound propositions; "and," "or," "not," and "implies" symbolized. (Study 5)

**logical subject**the subject causing the action, what the statement is about. (Study 1)

**logic quiz**a 25 Item True/False test to evaluate logic knowledge and skill. (Study 1)

**major premise**is the premise that contains the major term. (Study 3)

**major term**is the predicate of the conclusion of a syllogism or an inference. (Study 3)

**mediate inference**See syllogism. (Study 3)

**middle term**is the term which one finds in each of the premises of a syllogism, but not in the conclusion. (Study 3)

**minor premise**is the premise that contains the minor term. (Study 3)

**minor term**is the subject of the conclusion of a syllogism or an inference.( Study 3)

**modus ponens**means "a way of constructing;" symbolically: "If

*p*, then

*q*;

*p*; therefore,

*q*." (Study 4; Study 5)

**modus tollens**means "a way of destroying;" symbolically: "If

*p*, then

*q*;

*not-q*; therefore,

*not-p*. (Study 3, Study 4)

**mood**refers to the forms of a syllogism designated by

*A, E, I, or O*; the major premise comes first, followed by the the minor, then the conclusion. (Study 3)

**necessary inference**when a conclusion follows logically, strictly from premises. (Preview)

**negation**The law that states that every proposition is either true or false. (Study 5)

**negative quality**is a form that distributes its predicate. (Study 1)

**nonstandard categorical proposition**is a categorical other than

*A, E, I,*and

*O.*(Study 1, Study 3)

**nonstandard syllogism**a syllogism that contains more than 3 standard terms or is expressed as an enthymeme. (Study 3)

**O Form**The form of a standard proposition symbolized as Some a is not b. or O(ab). (Study 1)

**obversion**change the quality of the form and replace the predicate by its complement; valid for all 4 forms. (Study 2)

**parameter**a word or phrase in both subject and predicate to translate nonstandard into standard form propositions.(Preview)

**particular quantity**is a form that does not distribute its subject. (Study 1)

**per accidens**means conversion of

*A form*to

*I form*. (Study 3)

**premise**is the proposition of an argument from which a conclusion is drawn; reason(s) intended to support a conclusion. (Preview)

**proposition**the meaning expressed by a declarative sentence in which the predicate is affirmed or denied of the subject. (Preview)

**quality**two types: affirmative (A & I forms) and negative (E & O forms). (Study 1)

**quantity**two types: universal (A & E forms) and particular (I & O forms). (Study 1)

**reductio ad absurdum**Also

*reductio ad impossible*. Deducing by valid inference a conclusion you know to be false. (Study 3)

**reflexive**is a relationship between one of its objects and the object itself. (Study 2)

**sorites**a chain of propositions in which the predicate of each is the subject of the next, the conclusion consists of the first subject and last predicate. (Study 3)

**sound**a quality of valid deductive arguments in which all its propositions are true. (Study 1, Study 2, Study 3)

**square of opposition**refers to a scheme for displaying the four relationships of contrariety, subcontrariety, subalternation, and contradiction among the forms

*A, E, I, and O*. (Study 2)

**subalterns**propositions opposed in quantity, both alike in quality; the propositions may both be true together or both false together. (Study 2)

**subcontraries**the propositions

*I and O*which cannot both be false together, but could both be true. (Study 2)

**syllogism**is an argument of three propositions, two premises and a conclusion, with the conclusion's subject term in one of the premises, the predicate of the conclusion in the other premise, and a third term only in both premises. (Study 3)

**symmetrical**is a relationship which if it holds between two objects,

*a*and

*b*, also holds between

*b*and

*a*. (Study 2)

**theorem**is a proposition deduced from an axiom and/or other theorems. (Study 3)

**transitive**is a relationship which if it holds for

*a*and

*b*, and also for

*b*and

*c*, holds as well between

*a*and

*c*. (Study 2)

**transitive hypothetical syllogism**See transitive. (Study 4)

**truth table**a scheme for analyzing forms and relations among them. (Study 5)

**undistributed term**a term of a proposition not modified by the adjectives All or No. (Study 1)

**universal quantity**is a form that distributes its subject. (Study 1)

**univocal**having one meaning, not equivocal. (Study 1, Study 2, Study 3)

**unsound**a quality of valid deductive arguments in which one or more of the propositions are false. (Study 1, Study 2, Study 3)

**valid**a property of arguments in which the conclusion necessarily follows from the premises; an argument is valid if the form of the conclusion is true every time the forms of the premises are true. (Preview; Study 1, Study 2, Study 3)

**valid inference**whenever the form of the conclusion is true every time the forms of the premises are. (Study 1, Study 2, Study 3)

**validity**When a conclusion is a necessary consequence of premise(s) in an argument. (Study 1, Study 2, Study 3)

**venn diagram**See diagrams.(Study 2, Study 3)

Note: The Logic Quiz. ALL of the 25 True or False Items are FALSE. (Transform each Item to a TRUE value.)

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