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.)
(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)
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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