**PL
120 Symbolic Logic I
**

**Glossary
of Terms
**

**A proposition** In categorical logic, an A proposition is a
universal affirmative proposition.

**Abbreviated Truth Table**
In constructing a reverse truth table, *assume *that all the premises are
true and the conclusion is false, then consistently assign truth values to the
components in an attempt to show that your assumption is correct. If the
argument is invalid, this method allows you to construct one line of a truth
table that demonstrates the invalidity. If the argument is valid, it** **is
impossible consistently to assign truth values on the assumption that the
argument is invalid.

**Absorption (Abs.)** In
propositional logic, absorption is a rule of inference in which a conditional
statement is given as a premise; you conclude a conditional statement with the
same antecedent, and the consequent is a conjunction of the antecedent and
consequent of the given proposition. The form of the rule is: p →
q ⊢ p →
(p · q)

**Accent** The fallacy of accent rests upon the ways in which
you emphasize the words in a statement or by quoting passages out of context.

**Accident** An argument commits the fallacy of accident if it
applies a general rule in a case in which that rule does not apply.

** Ad hoc Hypothesis **An

**Addition (Add.)** In
propositional logic, addition is a rule of inference which, given any statement
as a premise, allows you to conclude that statement disjoined to *any *other
statement. The form of the rule is: p
⊢ p v q

**Affirmative** If you claim that members of the first class
named are members of the second class, the proposition is affirmative in
quality.

**Ambiguous** A word is ambiguous if it has more than one
meaning.

**Ampersand **The
symbol (&) for the conjunction operator.

**Amphiboly** Amphibolies are arguments based on loose sentence
structure. In an argument that commits the fallacy of amphiboly, the referent of
a word or phrase is left unclear and the meaning of the phrase shifts in the
course of the argument.

**Analogy** Analogies are claims of similarity. Analogies can be
used to illustrate, to explain, and to argue.

**Antecedent** The antecedent of a
conditional statement is the phrase following 'if; in symbolic form, it is the
statement to the left of the arrow or horseshoe.

**Appeal to Force** The fallacy of appeal to force occurs if you
appeal to force or the threat of force to convince someone to accept a
conclusion.

**Arguing in a Circle** One argues in a circle when one propose
a series of arguments in which the conclusion of the last argument was accepted
as a premise in an earlier argument.

**Argument
form
**A general logical pattern or structure that many arguments may have
in common. More specifically, a set
of two or more statement forms, one of which is designated as the conclusion and
the other (or others) designated as a premise (or premises).
An argument form may be expressed by writing the formulas for its
component statement forms and designating the conclusion and the premise or
premises.

**Argument** An argument is a set of
propositions in which one or more propositions (the premises) are said to
provide reasons or evidence for the truth of another proposition (the
conclusion).

**Argumentum ad Baculum** See Appeal to Force.

**Argumentum ad Hominem** See Personal Attack.

**Argumentum ad Populum** See Mob Appeal.

**Aristotelian Interpretation of Categorical Logic** The
Aristotelian interpretation of categorical logic is an interpretation of
categorical logic that ascribes existential import to universal propositions.

**Aristotle** A Greek philosopher who lived in

**Arrow** **( **→** )**In
the symbolic language for propositional logic, the arrow represents the relation
of material implication. It is also known as the single arrow. See also
Horseshoe.

**Association (Assoc.)** In
propositional logic, association is an equivalence falling under the Rule of
Replacement that allows you to reposition parentheses in a Statement in which
the only connectives are either wedges or ampersands. The two forms of this
equivalence are: [p ·(q
· r)] :: [(p ·
q) ·r] and [p v
(q v r)] :: [(p v
q) v r]

**Average** See Mean, Median, Midrange, and Mode.

**Bandwagon** A bandwagon argument is a form of the fallacy of
mob appeal--basically, "Everyones doing it,** **so you should
do it** **too."

**Begging the Question** You commit the fallacy of begging the
question if the conclusion of your argument is nothing more than a restatement
of one of the premises.

**Biased Sample** A survey is based on a biased sample if the
population surveyed is not representative of the population the survey purports
to represent.

**Biconditional
**A compound statement of the form
“p if, but only if, q.” See
also: material equivalence.

**Binary Relation** A binary relation is a two-place relation.
Also called a dyadic realtion.

**Boole, George** George Boole was the nineteenth-century
British logician and philosopher who is credited with resolving the controversy
over the existential import of universal propositions in favor of holding that
universal propositions *do not *have existential import.

**Boolean Interpretation of Categorical Logic** The Boolean
interpretation of categorical logic is an interpretation of categorical logic
that ascribes existential import *only *to particular propositions.

**Bound Variable** A bound variable is a variable within the
scope of a quantifier. See also Quantifier

**Categorical Syllogism** A
categorical syllogism is a special kind of syllogism in which both the premises
and the conclusion are categorical propositions, and in which there are three
terms, each occurring twice, with each term assigned the same meaning throughout
the argument.

**Ceremonial Function of Language** The ceremonial function of
language is the use of language in various ceremonies, including greetings.

**Class** A class is a collection of objects that have at least
one characteristic in common, namely, the class-defining characteristic.

**Classical Theory of Probability** The classical theory of
probability was developed by the seventeenth-century mathematicians Blaise
Pascal and Pierre de Fermat. The classical theory is *a priori *insofar
as it** **does not depend on empirical data. It assumes that all
possibilities are taken into account and that all possibilities are equal. The
mathematical basis for probability theory developed by Pascal and Fermat is also
used in the relative frequency theory of probability and the subjective theory
of probability.

**Collective Use of a Word** A word is used collectively if it**
**applies to a class itself--as a whole.

**Commissive Function of Language** The commissive function of
language is to use language to make vows and promises.

**Commutation (Comm.) **In
propositional logic, commutation is a statement of logical equivalence found
under the Rule of Replacement that allows you to switch the places of statements
around a common ampersand or wedge. The two versions of the equivalence are: (p · q) :: (q · p) and (p
v q) :: (q v
p)

**Complementary Class** For any class C, a complementary class
is a class containing all the objects not in C. The complement of the class of
green things is the class of nongreen things.

**Complex Question** The fallacy of complex question involves
implicitly asking two questions at once, one explicitly and one implicitly, and
an answer to the explicit question allows you to draw a conclusion regarding the
implicit question.

**Composition** The fallacy of composition occurs if either (1)
you attribute characteristics true of a part to a whole or (2) you claim that
something that is true of each member of a class of objects is true of the class
as a whole.

**Compound Statement** A
compound statement is any statement that has another statement as a component.

**Conclusion** In an argument, the conclusion is the statement
whose truth the argument is attempting to establish.

**Conclusion indicators
**Words or expressions used in the context of an argument to signal the
conclusion.

**Conclusion Indicators** Conclusion indicators are words such
as 'thus, 'therefore, and 'so that are used to indicate that a statement is the
conclusion of an argument.

**Conditional
**In sentential logic a
compound statement of the form “If p then q.”
See also: material implication. A conditional statement is a
statement expressing the relation of material implication. A conditional
statement is true except when its antecedent is true and its consequent is
false.

**Conditional Proof** In
propositional and predicate logic, you construct a conditional proof by assuming
a statement as an additional premise, working out the consequences of this
assumption, and discharging the assumption by constructing a conditional
statement in which the antecedent is the assumption for conditional proof and
the consequent is the conclusion reached in the previous line of the proof.

**Confirmation of a Hypothesis** If an experimental procedure
based on a hypothesis yields the predicted consequence, the experiment *tends
*to confirm the hypothesis, that is, it** **provides *some *evidence
that the hypothesis is true.

**Conjunct** A conjunct is a statement in
a conjunction.

**Conjunction
(Conj.)** In propositional logic, conjunction is a rule of inference
in which two premises are given and the conclusion is a conjunction of the two
premises. The form of the rule is: p,
q ⊢ p ·
q

**Conjunction** In propositional
logic, conjunction is represented by the ampersand (&) or dot ( ·
). A** **statement of the form
(p · q) is true if and only if
both p and q are true.

**Consequent** In a
conditional statement, the consequent is the statement following the word 'then;
in symbolic form, it is the statement to the right of the arrow or horseshoe.

**Constructive Dilemma (C.D.**)
In propositional logic, constructive dilemma is a rule of inference in which the
first premise is a conjunction of two conditional statements, the second premise
is a disjunction of the antecedents of the conditionals in the first premise,
and the conclusion is a disjunction of the consequents of the conditionals in
the first premise. The form of the rule is:
(p → q), (r →
s), p v r ⊢
q v s

**Consistency
**A set if statements is consistent if an only if it is possible for all of
the members of the set to be
simultaneously true.

**Constant
**A symbol that stands for a specifically identified thing.
In QL, *individual* constants such as a, b, c are symbols that
abbreviate singular terms and *predicate*
constants are symbols such as, A, B, and C that abbreviate predicates.

**Constant
**A symbol that stands for one specified thing.

**Constituent
element
**In a negation, the constituent element is the component that is negated,
the statement whose truth value is “flipped” by the negation.

**Contingent Proposition** The truth value of a contingent
proposition is determined by whether the proposition corresponds to the world.
All simple propositions are contingent.

**Contingent
statement **(in truth-functional
logic) A statement with the
following feature: the final column of its truth-table show at least one **T**
and at least one **F**.

**Contradiction
**(in truth-functional logic) A
statement with the following feature: the final column of its truth-table shows
all F's.

**Contradiction, Contradictories** In categorical logic, two
statements are contradictories if they are formally related to one another in
such a way that if one is true the other must be false. In propositional logic,
a contradiction or self-contradiction is a statement that is false solely in
virtue of its form.

**Contradictory
statement form. **A statement form
all of whose instances are contradictions. All
contradictory statement forms are equivalent to p ·
~p.

**Contrapositive, Contraposition** The contrapositive of a given
categorical proposition is formed by replacing the subject term with the
complement of the predicate term, and replacing the predicate term with the
complement of the subject term. A and 0 propositions are logically equivalent to
their contrapositives; E and I propositions are *not *logically
equivalent to their contrapositives.

**Contrariety, Contraries** In Aristotelian logic, contrariety
is the formal relationship between two universal propositions with the same
subject and predicate terms but opposite qualities such that it** **is
possible for both to be false but not for both to be true. Two propositions so
related are known as *contraries.*

**Conventional Connotation of a Term** The conventional
connotation of a term consists of the properties of a thing that the members of
a certain linguistic community consider common to the things a term denotes.

**Converse, Conversion** The converse of a given categorical
proposition is formed by reversing the position of the subject and the predicate
term. Only E and I propositions are logically equivalent to their converses.

**Convertand** A convertand is a proposition that is to be
converted. Copula The copula is a form of the verb 'to be.

**Criterion, Criteria** A criterion is a standard for judging on
a certain topic or subject matter.

**Crucial Experiment** A crucial experiment is an experiment
that provides strong evidence that one of two opposing hypotheses is correct by
showing that the predictions of one hypothesis correspond to the observational
data whereas the predictions of the other do not.

**DeMorgan, Augustus. A
**brilliant mathematician noted for his advances in algebra and
logic. He was a friend of Charles Babbage (inventor of the Analytical Engine,
forerunner of the modern computer), coined the term 'mathematical induction',
and, with George Boole, he was a founder of symbolic logic as it developed in

**De Morgans Theorems (DeM).**
In propositional logic, a pair of equivalences falling under the Rule of
Replacement specifying (1) that the denial of a conjunction of two propositions
is equivalent to the disjunction of the denial of each proposition, and (2) that
the denial of the disjunction of two propositions is equivalent to the
conjunction of the denial of each proposition. The forms of these two
equivalences are: ~(p v q) :: (~p · ~q)
and ~(p ·q) :: (~p v ~q)

**Decision
procedure **(or
algorithm") A problem-solving
method that has the following features: (a)
the method has precisely specified steps; (b) following the steps is a matter of
following exact rules requiring no creativity or ingenuity; and (c) the method
is guaranteed to give a definite solution in a finite number of those steps.

**Deductive Argument** A sound
deductive argument provides conclusive evidence for the truth of its conclusion.

**Deductive Counterexample** You construct a deductive
counterexample to an argument of a given form by constructing an instance of the
same form with true premises and a false conclusion. This shows that the
argument form is invalid.

**Deductively
sound argument **A deductive
argument that is valid and that also has true premises

**Deductive-Nomological Explanation** A deductive-nomological
explanation tells why a phenomenon is as it** **is by showing that
the truth of a description of the phenomenon follows deductively from a
statement of a natural law and an initial state description (statement of
antecedent conditions).

**Definiendum** The definiendum is the word defined in a
definition.

**Definiens** The word or words that define the definiendum are
known as the definiens.

**Definite Description** A definite description is a phrase of
the form "the so and so." A definite description is a complex
linguistic expression that picks out exactly one thing.

**Definition by Genus and Difference** A definition by genus and
difference is a connotative definition in which the definiendum is treated as
the name of a class; in which the definiens identifies a more general class of
which it is a part (the genus) and the properties that are unique to that
species; and in which the definiens *differentiates *that species from
other members of the genus.

**Definition by Subclass** A definition by subclass is a
denotative definition in which you name the subclasses of a class denoted by a
term.

**Denotative Definition** A denotative definition defines a word
by reference to objects in the terms denotation.

**Denotative Meaning; Denotation** The denotative meaning of a
term consists of all the things to which a term is correctly applied. Also known
as the *extension *of a term.

**Dichotomy** A dichotomy is a division of a class into two
mutually exclusive and exhaustive subclasses, that is, a division of a class
such that every member of the original class is a member of one of the two
subclasses and no member of the original class is a member of both subclasses.

**Directive Function of Language** The directive function of
language is the use of language to request information, plead for action, and
issue orders.

**Disjunct** A disjunct is a statement in
a disjunction.

**Disjunction **Disjunction is
represented by the wedge, or vee ( v ) or the

**Disjunctive Syllogism (D.S.)**
In propositional logic, disjunctive syllogism is a rule of inference in which
the first premise is a disjunction, the second premise is the negation of the
first disjunct in the first premise and the conclusion is the second disjunct in
the first premise. The form of the rule is: p v q, ~p ⊢
q

**Distribution
(Dist.)** In propositional logic, distribution is an equivalence
falling under the Rule of Replacement that specifies the relationship between a
statement conjoined to a disjunction and a conjunction of disjunctions, or a
statement conjoined to a disjunction and a disjunction of conjunctions. The two
forms of distribution are:

[p · (q v r)] :: [(p · q) v (p · r)] and [p v (q · r)] :: [(p v q) · (p v r)]

**Distribution** A term in a categorical proposition is
distributed if and only if it refers to all the members of the class denoted by
the term.

**Distributive
Use of a Word** A word is used distributively if it** **applies
to each and every member of a class taken individually.

**Division**
The fallacy of division occurs if either (1) you attribute to a part
characteristics that are true only of the corresponding whole or (2) you
attribute to a member of a class a property that is true of a class of objects
as a whole.

**Domain
of a variable**
The set of things the variable
can take as values. The values of a
variable are just the entities represented by the singular terms that can
replace the variable. The domain of
a variable is also known as the *universe of discourse* for the statement
containing the variable**.
**

**Domain
of Discourse** A domain of discourse is a set of objects that are *assumed
*to exist for the sake of the argument.

**Double
Arrow** In the symbolic language for propositional logic, the double
arrow ( « ) represents material
equivalence. See also Triple Bar (º).

**Double
Negation (D.N.)** In propositional logic, double negation is an
equivalence falling under the Rule of Replacement indicating that any statement
is equivalent to its double negative. The form of the rule is: p :: ~~p

**Drawing an Affirmative Conclusion from a Negative Premise (ACNP)**
In categorical logic, a syllogism commits the fallacy of drawing an affirmative
conclusion from a negative premise if its conclusion is an affirmative
proposition and at least one of its premises is a negative proposition.

**Dyadic connective
**(or "dyadic operator")
A connective that joins together two statements to form a compound
statement.

**Dyadic Relation** A dyadic relation is a two-place relation.

**E Proposition** In categorical logic, an E proposition is a
universal negative proposition.

**Element A
member of a universe of discourse. The
elements in a universe of discourse are the individual or objects that may have
or lack the properties used in a quantified formula.
**

**Emotive Function of Language** The emotive function of
language is the use of language to express or evoke emotions.

**Empirical Evidence, Empirical Data** Empirical evidence is
evidence drawn from experience; empirical data is data based on empirical
experience.

**Empty Denotation** A term has an empty denotation if there is
nothing** **it** **denotes.

**Enthymeme, Enthymematic Argument** An enthymeme is an argument
in which one of the premises or the conclusion is not stated.

**Enumerative Definition** An enumerative definition is a
denotative definition in which the definiendum is defined by naming objects in
the denotation of the term.

**Epithet** An epithet is a descriptive word or phrase used to
characterize a person, thing, or idea. You can commit the fallacy of begging the
question by ascribing an epithet to a person, thing, or idea that assumes what
you are trying to establish.

**Equivocate** If you shift from one meaning of a word to
another within a piece of discourse, you equivocate.

**Equivocation** An argument commits the fallacy of equivocation
if the meaning of a word shifts in the context of the argument and the
persuasive force of the conclusion depends upon that shift.

**Evidence** Evidence is that which tends to prove or disprove
the truth of a statement.

**Exceptive Proposition** An exceptive proposition is a
proposition beginning with 'All except or 'All but. Exceptive propositions are
complex. "All except S are P"* *means *both *"All
non-S are P"* *and "No S is P*.*"

**Exclusive Premises (EP)** In categorical logic, a syllogism
commits the fallacy of exclusive premises if both of its premises are negative.

**Existential Fallacy (EF)** In categorical logic under the
Boolean Interpretation, a syllogism commits the existential fallacy if its
conclusion is a particular proposition and both of its premises are universal
propositions.

**Existential Generalization (EG)** In predicate logic, the rule
of existential generalization allows you to introduce the existential quantifier
*given that a statement is true of some individual.*

**Existential Import** Existential import is the property of a
proposition if its truth entails the existence of at least one object.

**Existential Instantiation (EI)** In predicate logic,
existential instantiation is a rule that allows you to eliminate the existential
quantifier by introducing a *hypothetical *name to represent the "at
least one thing of which the statement is true. The name introduced must be new
to the proof.

**Existential Quantifier** In predicate logic, the quantifier in
a *particular* proposition. The symbol of the backward E ( ∃x)
is the existential quantifier.

**Explanation** An explanation is a discourse that answers the
question why something is as it is.

**Explicit
contradiction **A statement of the form **P
**& ~ **P**.

* *[(p
· q) →
r] :: [p → ( q → r)].

**Extension** The extension of a term consists of all the things
to which a term is correctly applied. Also known as the *denotation *of a
term.

**External Consistency **Experimental evidence is externally
consistent with accepted scientific theories when the accepted theories help
explain the evidence.

**Fallacy** A fallacy is an error in reasoning. It is an
argument that seems to be sound but is not. Invalid deductive arguments are
formally fallacious: the form of the argument does not guarantee that if the
premises are true, the conclusion is also true. Informal fallacies rest on the
content of the argument.

**Fallacy of Four Terms (4T)** In categorical logic, an argument
commits the fallacy of four terms if either there are more than three terms in
the argument, or a term is assigned different meanings at different points in
the argument. If an argument commits the fallacy of four terms, by definition it
is *not *a categorical syllogism.

**False Cause** An argument commits the fallacy of false cause
if it** **misidentifies the cause of an event and draws a
conclusion.

**False Dichotomy** An argument commits the fallacy of false
dichotomy if it presents two alternatives as the only alternatives with respect
to an issue when in fact there are other options, and rejects one of the
alternatives and concludes that you must accept the other. What the argument
claims is a dichotomy is not.

**False, Falsehood** A proposition is false if and only if it**
**does not correspond with the world. Falsehood is a characteristic of a
statement or proposition.

**Falsifying Interpretation An
assignment of values to the elements
in a universe of discourse that makes a particular formula false in that
universe under that interpretation.
**

**Fermat, ****Pierre**** de** Pierre de Fermat was the seventeenth-century French
mathematician who, with Blaise Pascal, developed the classical theory of
probability.

**Figure of a Categorical Syllogism** The figure of a
categorical syllogism specifies the position of the middle in the syllogism in
standard form.

**Form of an Argument** The form of an argument is the
structural pattern of an argument. It is like the design of a house insofar as
there may be many arguments of the same form.

**Formal Fallacy** A formal fallacy is an error in reasoning
based solely on the form of the argument, not on its content.

**Free Variable** In predicate logic, a free variable is any
variable not bound by a quantifier.

**General Conjunction Rule** In the probability calculus, the
general disjunction rule allows you to calculate the probability of the second
event on the assumption that the first event occurred. Where *A *and *B
*are two events, the formula for the general conjunction rule is:

**General Disjunction Rule** In the probability calculus, the
general disjunction rule allows you to calculate the probability of either of
two *independent *events whether or not they are mutually exclusive.
Where *A *and *B *are two events, the formula for the general
disjunction rule is: *P(A *or *B) *= P(A or B) = P(A) + P(B) - P(A
and B).

**Guide Columns** In a truth table, guide columns specify the
truth values of each of the different simple statements in the argument.

**Hasty Generalization** An argument commits the fallacy of
hasty generalization if a general conclusion--a conclusion pertaining to all or
most things of a kind--is based on an atypical case or cases.

**Horseshoe ( ⊃ ) **In the
symbolic language for propositional logic, the arrow represents the relation of
material implication. It is also known as the single arrow. See also Arrow.

**Hypothesis** A hypothesis is an educated guess or hunch
regarding a necessary or sufficient condition for a particular phenomenon or
kind of phenomenon.

**Hypothetical Syllogism**
In propositional logic, the rule of hypothetical syllogism states that given two
premises that are conditional statements in which the consequent of the first is
the antecedent of the second, the conclusion is a conditional statement in which
the antecedent is the antecedent of the first premise and the consequent is the
consequent of the second premise.
The form of the rule is: p → q, q →
r ⊢ p →
r. Sometimes called Chain Argument.

**I Proposition** In categorical logic, an I proposition is a
particular affirmative proposition.

**Identity
**To say that is identical with y is to say that x and y are one and
the same entity.

**Ignoratio Elenchi** See Irrelevant Conclusion.

**Illicit Process of the Major Term (IMa)** In categorical
logic, a syllogism commits the fallacy of illicit process of the major term
(illicit major) if the major term is distributed in the conclusion but not in
the major premise.

**Illicit Process of the Minor Term (IMi)** In categorical
logic, a syllogism commits the fallacy of illicit process of the minor term
(illicit minor) if the minor term is distributed in the conclusion but not in
the minor premise.

**Immediate Inference** An immediate inference is an inference
you can correctly draw regarding the truth value of a proposition given nothing
more than the truth value of one other proposition.

**Implication
A logical
relation that obtains between two statements whenever it is impossible for the
first of the two to be true while the second is false.
**

**Incomplete Truth Table** An incomplete truth table is a truth
table in which you construct the guide columns and the column for the
conclusion, and, proceeding from the upper right corner to the lower left, you
fill in *only *those rows in which the conclusion is false. Further, you
assign truth values to the statements in a row *only *until you find a
false premise, and you continue assigning truth values on the table *only *until
you find a row in which all the premises are true and the conclusion is false.
See also Abbreviated Truth Table and Truth Value Analysis

**Inconsistency
**A set of statements is inconsistent if and only if it is
impossible that all of the statements in the set are true together.

**Inconsistent; Inconsistency** Two propositions are
inconsistent with one another if one asserts what the other denies.

**Independent Events** In probability theory, two or more events
are independent if and only if the occurrence of any one of them has no
influence on the occurrence of any of the others.

**Indirect Proof** In propositional
and predicate logic, an indirect proof is constructed by assuming the *denial
*of the proposition you want to prove as an additional premise and showing
that this enlarged set of premises yields a pair of contradictory statements.
This procedure shows that the proposition you wanted to prove follows from the
original premises.

**Inductive Arguments** Inductive arguments provide some, but
not conclusive, evidence for the truth of their conclusions..

**Inference
**A person "draws an inference" when he or she asserts a
conclusion on the basis of one or more premises.
Inferring is a psychological act that a person undertakes.

**Informal Fallacy** An argument commits an informal fallacy if
it** **is psychologically persuasive but not logically persuasive,
and its logical error rests on the material presented in the argument.

**Informative Function of Language** The informative function of
language is the use of language to convey information.

**Intension** The intension of a term consists of all the
characteristics or properties that are common to all the members of the class
denoted by a term. Also known as the *connotation *of a term.

**Internal Consistency** A theory is internally consistent if
the statements in the theory do not entail self-contradictory statements.

**Interpretation
of a Universe of Discourse****
A specification of the properties of and relations between the elements of a
universe of discourse.
**

**Invalid, Invalidity**
Invalidity is a characteristic of an argument form. An argument form is invalid
if and only if the truth of the premises do not guarantee the truth of the
conclusion.

**Irrelevant Conclusion** You commit the fallacy of irrelevant
conclusion if your premises seem to lead you to one conclusion and you draw an
entirely different conclusion.

**Justification
**(of an inference) In a
proof, a citation of the rule used in drawing the inference and the lines to
which the rule was applied.

**Law
of Noncontradiction ** The
principles that contradictions are impossible.

**Legal Realism (American) American
Legal Realism is a theory of law which holds that the behavior of judges is far
more important to understanding what law is than are the abstract verbal
formulations of written rules. The
most extreme version of the theory holds that "The law is what the judge
says it is." Less extreme
versions treat written rules as predictions of what judges will do in concrete
cases. The view is associated with
Jerome Frank, Karl Llewellyn, Wesley Newcomb Hohfeld and Oliver Wendell Holmes.
Also called Rule Skepticism.
**

**Lexical Definition** A lexical definition states the
convention governing the use of a word.

**Logical Equivalence** Two
statement forms are logically equivalent if they express the same proposition
and if they are true under exactly the same conditions.

**Logical
truth **A statement that
can be known on the basis of logical theory alone, without investigating the
physical world.

**Major Premise** In a categorical syllogism, the major premise
is the premise containing the major term.

**Major Term** In a categorical syllogism, the major term is the
predicate term of the conclusion.

**Margin** **of Error** In a survey, the margin of
error is the percentage by which past experience suggests actual behavior might
deviate from the results of the survey within a certain "level of
confidence," which is typically 95 percent. So if the results of a survey
show that a certain presidential candidate can expect 48 percent of the votes
and the survey has a 2 percent margin of error, this indicates that there is a
95 percent chance that the candidate will receive between 46 and 50 percent of
the votes.

**Material Equivalence (Equiv.)**
In propositional logic, material equivalence is a statement of logical
equivalence falling under the Rule of Replacement that allows you to introduce
or replace a statement containing a double arrow or triple bar. The two forms of
the equivalence are: (p ↔ q)
:: [(p→q) ·(q→p)]
and (p ↔ q) ::[(p·q)
v (~p ·~q)].

**Material Equivalence** In propositional logic, material
equivalence is represented by the double-arrow (
) or the triple bar ( ≡)*. *A
statement of material equivalence is true whenever the truth values of p and q
are the same; otherwise it is false.

**Material Implication (Impl.)**
In propositional logic, material implication is a statement of logical
equivalence falling under the Rule of Replacement that allows you to replace a
conditional statement with a disjunction consisting of the denial of the
antecedent of the conditional and the consequent or to replace such a
disjunction with a conditional statement. The two forms of the equivalence are:
(p→ q) :: (~p v q) and (~p→
q) :: (p v q).

**Material Implication** In propositional logic, material
implication is represented by the single arrow (→
) or horseshoe ( ⊃). A statement
of the form "p ® q" is
true except when p is true and q is false.
Sometimes called “material conditional” or merely ‘the
conditional.”

**Matrix In
QL the body of a formula following the quantifier(s).
**

**Mean** The mean is the arithmetic average. It is calculated by
dividing the sum of the individual values by the total number of individuals in
the reference class.

**Mechanical Jurisprudence A
theory of legal reasoning which holds that a valid legal decision must be the
conclusion of a logically sound deductive argument.
The task of the judge is to apply the law, as set down by the
legislature, to the facts, as found by the jury, in a logically rigorous,
mechanical way. This theory
eliminates discretion on the part of the judge.
**

**Median** The median of a set of numerical data is the middle
value when arranged in ascending order: there are as many values above as below.
'Median is one of the meanings of 'average.

**Metaphor** A
metaphor is an analogy in which an implicit comparison is made between two
things. The statement "Language is a picture of the world" is a
metaphorical statement.

**Middle Term**
In a categorical syllogism, the middle term is the term that is in both premises
but not in the conclusion.

**Midrange** The
midrange is the point in the arithmetic middle of a range, and** **it**
**is determined by adding the highest number in the range to the lowest
number and dividing by two. 'Midrange is one of the meanings of 'average.

**Minor Premise**
In a categorical syllogism, the minor premise is the premise containing the
minor term.

**Minor Term**
In a categorical syllogism, the minor term is the subject term of the
conclusion.

**Mob Appeal**
You commit the fallacy of mob appeal by appealing to the emotions of the
crowd--the desire to be loved, accepted, respected, etc.--rather than to the
relevant facts.

**Mode** In a
set of numerical data, the mode is the value that occurs most frequently. 'Mode
is one of the meanings of 'average.

** Modus
Ponens (M.P.)** In
propositional logic,

** Modus
Tollens (M.T.)** In
propositional logic,

**Monadic
connective **(or
"monadic operator") A
connective that is joined to just one statement to form a compound statement.

**Monadic
predicate **A predicate phrase
that contains one blank and is used attribute a property to just one thing.

**Mood of a Syllogism**
In categorical logic, the mood of a syllogism consists of the kinds of
propositions of which the syllogism is composed. In stating the mood of a
syllogism, you state the letter representing the major premise first, then the
letter representing the minor premise, and finally the letter representing the
conclusion..

**Mutually Exclusive
Events** In probability theory, two or more events are mutually exclusive
if and only if they are distinct and the occurrence of one of the events
precludes the occurrence of any of the others.

**Natural
deduction method **A
method in which we deduce a conclusion from a set of premises through a series
of valid inferences corresponding to more or less natural patterns of reasoning.

**Natural
deduction system **A
system consisting of (a) a formal language that can be used to symbolize
information; and (b) a set of natural deduction rules that can be used to deduce
conclusions from premises.

**Necessary and Sufficient Condition** A necessary and
sufficient condition is a condition in whose absence a given phenomenon will not
occur and in whose presence the phenomenon occurs. A necessary and sufficient
condition is expressed by a biconditional.

**Necessary Condition** A necessary condition is a condition is
whose absence a given phenomenon will not occur. A necessary condition is
expressed by the consequent of a conditional.

**Negation Rule** In the probability calculus, the negation rule
tells you that the probability that some event *A *occurs is equal to one
minus the probability that *A *does not occur. The form of the rule is:

**Negative** If you deny that members of the first class named
are members of the second, the proposition is negative in quality.

*Non Causa Pro Causa** *("not the cause for
the cause") This is a variety of the false cause fallacy. If you
incorrectly take something to be the cause of something else without any
reference or allusion to the temporal order of events, you commit the fallacy of
*non causa pro causa.*

**Normal Probability Distribution** A normal probability
distribution is the mark of a random survey. You have a normal probability
distribution if the mean, the mode, the median, and the midrange are the same.

**O Proposition** In categorical logic, an 0 proposition is a
particular negative proposition.

**Objective Connotation** The objective connotation of a term
consists of all the characteristics common to all the things a term denotes.

**Obverse, Obversion** In categorical logic, the obverse of a
categorical proposition is obtained by changing the quality of a given
categorical proposition from affirmative to negative and replacing the predicate
term with its complement. Every categorical proposition is logically equivalent
to its obverse.

**Obvertend** The obvertend is a proposition to be obverted.

**Open
sentence **An incomplete sentence
that is lacking a subject expression and that has a space where a subject
expression may be placed.

**Operational Definition** An operational definition is a
connotative definition in which the definiens specifies an experimental
procedure or operation that provides a criterion for the application of a term.

**Oppositions** In categorical logic, oppositions are immediate
inferences among categorical propositions.

**Ostensive Definition** An ostensive definition is a denotative
definition in which the definiendum is defined by pointing to objects denoted by
the word.

**Overlapping
quantifiers **In a sentence with
overlapping quantifiers, one quantifier appears within the scope of another
quantifier.

**Parameter** A parameter is a word or phrase that is added to a
statement to specify its domain of discourse.

**Particular Affirmative Proposition** In categorical logic, a
particular affirmative proposition asserts that there is at least one member of
the subject class and** **it is also a member of the predicate
class. A particular affirmative proposition can be stated in standard form as
"Some S is(are) P."

**Particular Negative Proposition** In categorical logic, a
particular negative proposition asserts that there is at least one member of the
subject class and it is *not *a member of the predicate class. A
particular negative proposition can be stated in standard form as "Some S
is(are) not P."

**Particular Proposition** A particular proposition is a
proposition that is true of at least one individual.

**Pascal, Blaise** Blaise Pascal was the seventeenth-century
French philosopher and mathematician who, with Pierre de Fermat, developed the
classical theory of probability.

**Personal Attack** You commit the fallacy of *personal
attack *if you attempt to *refute *the conclusion of another persons
argument by attacking the person who presented the argument rather than the
argument itself.

**Polyadic predicate A
relational predicate that involves at least two variables.
**

*Post Hoc Ergo Propter Hoc** *("before
that, therefore because of that") *Post hoc ergo propter hoc *is a
variety of the false cause fallacy. If you assume that one event is the cause of
another *simply because it occurs first, *you commit the fallacy of *post
hoc ergo propter hoc.*

**Precising Definition** A precising definition is offered to
set limits to the definiendum and thereby reduce vagueness.

**Predicate Term** In a
categorical proposition, the predicate term is the term in the predicate place;
it is the second term that names a class.

**Premise**
In an argument, a premise is a statement used to provide evidence for the truth
of another statement, namely, the conclusion.

**Premise Indicators** Premise indicators are words such as
'since, 'because, and 'given that, which are used to indicate that a statement
is a premise of an argument.

**Prenex Normal Form** In predicate logic, a statement is in
prenex normal form if all the quantifiers are placed to the left of the entire
propositional function over which they range. If the quantifier is in the
antecedent of a conditional, moving the quantifier outside the farthest left
parentheses requires changing the quantity of the quantifier: universal to
particular or particular to universal.

**Principal (or Main)
Connective** In symbolic logic, the principal or main connective is
the connective that holds an entire complex statement together. For example, in
the statement "p ® (q v
r)," the arrow is the principal connective. In "(p® q) v (r®
s)," the wedge is the principal connective. The principal
connective is sometimes called the dominant operator in a formula.

**Principle of Indifference** In the probability calculus, the
principle of indifference is the assumption that all possible events in the
class under consideration are equally probable.

**Principle
of Self-Identity **Each thing is
identical with itself.

**Principle
of the Indiscernibility of** **Identicals**
If x is identical with y, then whatever is true of x is true of y and
whatever is true of y is true of x.

**Probability Calculus** The probability calculus consists of
those mathematical formulae used to calculate the probability of an event. The
probability calculus is common to the classical, relative frequency, and
subjective theories of probability.

**Proof A
proof is a finite series of formulas, beginning with the premises of an argument
and ending with the conclusion, in which each line following the premises is
justified according to accepted rules of inference and equivalence.
A proof is a formal demonstration that the conclusion of the argument
follows from the premises. Any
argument for which a proof can be constructed is valid.
**

**Proof procedure
One half of a
decision procedure, the half which provides affirmative answers to the question
“Is this argument valid?” A
proof procedure is any accepted method for constructing proofs.
**

**Proposition** A proposition is the information expressed by a
declarative sentence or statement.

**Propositional
Function** In predicate logic, a propositional function is a predicate
with a variable as its subject.

**Propositional Logic** Propositional logic is a system of logic
in which simple propositions are the fundamental elements of a logical schema.

**Quality** In categorical logic, the quality of a proposition
is either affirmative or negative.

**Quantifier Negation** In predicate logic, quantifier negation
is a rule that allows you to move the tilde across a quantifier. Moving the
tilde across a quantifier changes an existential quantifier to a universal
quantifier and changes a universal quantifier to an existential quantifier.

**Quantifier** The
quantifier of a categorical statement tells you how many things the statement
refers to. In categorical logic, the universal quantifiers are 'All and 'No, and
the particular quantifier is 'Some. In predicate logic, the universal
quantifier--all--is as upside down 'A' followed by variable in parentheses ("x),
and the existential quantifier is the backward 'E' followed by a variable ∃x.

**Quantity** In categorical logic, the quantity of a proposition
tells you how many members of the first class named are or are not members of
the second.

**Quaternary Relation** A quaternary relation is a four-place
relation.

**Quine, Willard van Orman**.
One of the most influential American philosophers and logicians of the
20th century. Sometimes referred to as the "philosopher's
philosopher", Quine is the quintessential model of an analytic philosopher.
His major writings include "Two Dogmas of Empiricism", which
influentially attacked the logical positivists' conception of analytic and
synthetic propositions, and *Word and Object*.

**Random Sample** The sample on which a survey is taken is
random if every person or object in the population surveyed has an equal chance
of being chosen for the survey.

**Red Herring** The fallacy
of shifting away from the issue
under consideration to something different and then drawing a conclusion.

*Reductio ad Absurdum** *A *reductio ad
absurdum *is literally a reduction to absurdity. It is a proof technique in
which an assumption is added to a set of premises, and it is shown that adding
the assumption yields a pair of contradictory statements. This shows that the
original assumption was false. See also Indirect Proof.

**Reflexive
relation **A relation that
possesses the following feature: if one thing (A) has the relation to something
(B) or B has the relation to A, A has that relation to itself.

**Reflexive Relation** A relation is reflexive if and only if an
object can stand in that relation to itself. The relation of "being the
same age as" is an example of a reflexive relation.

**Refutation of a Hypothesis** If an experimental procedure
based on a hypothesis fails to yield the predicted consequence, the experiment
refutes the hypothesis, that is, it** **provides conclusive
evidence that the hypothesis is false.

**Relation** A relation is a predicate of two or more places.
For example, the predicates "to the left of" and "between"
are relational predicates.

**Relative Frequency Theory of Probability** The relative
frequency theory of probability is based on empirical data. This theory of
probability is used in calculating such things as insurance rates.

**Restricted Conjunction Rule** In the probability calculus, the
restricted conjunction rule is used to calculate the probability of two *independent
*events. For the events A and B, the probability of both A and B is: P(A and
B) = P(A) **× **P(B).

**Restricted Disjunction Rule** In the probability calculus, the
restricted disjunction rule is used to calculate the probability that either of
two or more *mutually exclusive *events occurs. For the events A and B,
the probability of either A and B is: P(A or B) = P(A) +** **P(B).

**Rule of Law Model
A theory of
law derived from natural law traditions according to which the law is there for
all, including government officials, to obey.
This theory holds that no one is above the law, that the law checks the
power of government. Frequently
associated with the claim that "Ours is a government of laws, not of
men." According to this model,
the law provides a neutral playing field within which citizens are free to
pursue their own ends.
**

**Rule of Replacement** In
propositional logic, the rule of replacement is the rule that logically
equivalent expressions may replace each other wherever they occur in a proof..

**Rules of Inference** The
rules of inference are rules that allow valid inferences from statements assumed
as premises.

**Rule of Passage A
rule governing expanding or contracting the scope of a quantifier or governing
moving a negation from one side of a quantifier to the other.
**

**Rule Skepticism See
Legal Realism
**

**Sample** A sample is a portion of a certain population of
objects or people on which a poll or survey is based.

**Satisfying Interpretation An
assignment of values to the elements
in a universe of discourse that makes a particular formula true in that universe
under that interpretation.
**

**Scope of a Quantifier** The scope of a quantifier is the
propositional function whose variables are so grouped that they are bound by the
quantifier.

**Scope
of an operator **The operator
itself along with the part of the statement that the operator applies to or
links together.

**Semantics
**The theory of meaning for a language.
The semantics supplies the meanings for the various expressions of the
language.

**Sentential
Variable **A lower case letter used in a statement form to represent a statement
(either simple or compound).

**Simile** A simile is an analogy in which the word 'like makes
the comparison between two things explicit.

**Simple
statement **A statement that
does not contain within itself one or more shorter statements.
A simple statement expresses exactly one fact about the world and
contains no logical operations.

**Simplification (Simp.)**
In propositional logic, simplification is the rule of inference in which the
premise is a conjunction and the conclusion is the first conjunct. The form of
the rule is: p·q ⊢
p

**Singular Proposition or Singular Statement** A singular
proposition (statement) makes a claim about an individual, exactly one thing.

**Singular
sentence **A sentence that
is made up of two parts (1) a singular subject expression in which one specific
thing is singled out for discussion by a singular
term; (2) a predicate expression that contains a general term attributing a
property to the specific thing designated by the subject expression

**Singular
term **An expression that refers to
or describes one specifically identified thing.
In general, a singular term is used to single out a specific thing so
that we may say something about it.
This text addressed two types of singular term.

**Slippery Slope Argument** A slippery slope argument has the
following structure. There is a slope--a chain of causes. It is slippery.
Therefore, if you take even one step on the slope, you will slide all the way to
the bottom. But the bottom is a bad place to be. So, you should not take the
first step.

**Slippery Slope Fallacy** An argument commits the slippery
slope fallacy when (and only when) at least one of the causal relations
constituting the slope in a slippery slope argument does not hold.

**Some** As used in logic, the word 'some means at least one.

**Sorites** A sorites is a chain of enthymematic syllogisms in
which the unstated conclusion of one syllogism is a premise for the next
syllogism.

**Sound Argument** Sound arguments
are valid deductive arguments with premises that are all true. The
conclusion of a sound argument must be true.

**Square**** of ****Opposition**

**Standard-Form Categorical Statement** In categorical logic, a
statement is a standard-form categorical statement if and only if: (a) it
expresses a categorical proposition; (b) its quantifier is either 'All, 'No, or
'Some; (c) it has a subject and a predicate term; (d) its subject and predicate
terms are joined by a copula, a form of the verb 'to be; and (e) the order of
the elements in the statement is: quantifier, subject term, copula, predicate
term.

**Standard-Form Categorical Syllogism** A syllogism is a
standard-form categorical syllogism if and only if it** **fulfills
each of the following criteria: (a) it** **is a categorical
syllogism; (b) the premises and conclusion are standard-form categorical
statements; (c) the syllogism contains three different terms; (d) each of the
terms appears twice in the argument; (e) each term is used with the same meaning
throughout the argument; (f) the predicate term of the conclusion appears in the
first premise; (g) the subject term of the conclusion appears in the second
premise.

**Statement** A statement is a sentence that is true or false in
virtue of the proposition it expresses.

**Statement Abbreviation** In propositional logic, the uppercase
letters (A, B, C, . . .) are statement abbreviations and represent statements in
ordinary language.

**Statement
connective **(or "statement
operator") A word or phrase
that can be connected to one or more statements to produce a compound statement.

**Statement
forms
**A general logical pattern or structure that many statements may have
in common. A statement form is
expressed using a combination of variables and operators.

**Statement
letter **A capital letter used to represent a simple statement.
It is important to remember that a statement letter stands for a
completer statement, a full idea, and not for a single word.

**Statement Variables** In
propositional logic, the lowercase letters beginning with p (p, q, r, . . .) are
statement variables. Statement variables can be replaced by statements of any
degree of complexity. Also called sentential variables.

**Stipulative Definition** A stipulative definition is used to
assign a meaning to a new word, to assign a new meaning to a word already in
use, or to specify the meaning of a word in a particular context.

**Straw Person** You commit the straw person fallacy if, in
replying to an argument, you either distort the original argument by suggesting
that the first arguer accepted a premise that was not explicitly stated and
argue that the premise is implausible, or distort the conclusion, argue against
the conclusion as you have restated it,** **and hold your
criticisms to apply to the original argument.

**Subaltern** In Aristotelian logic, a subaltern is a particular
proposition with the same subject and predicate terms and the same quality as a
given universal proposition.

**Subalternation** In Aristotelian logic, subalternation is an
immediate inference between a universal categorical proposition and the
corresponding particular proposition of the same quality that allows you to
infer the truth of the particular given the truth of the universal or the
falsehood of the universal given the falsehood of the particular.

**Subcontrariety, Subcontraries** In Aristotelian logic,
subcontrariety is a formal relationship between two particular propositions with
the same subject and predicate terms but opposite qualities such that it**
**is possible for both to be true but it** **is not possible
for both to be false. Two propositions so related are known as *subcontraries.*

**Subject Term** In a categorical proposition, the subject term
is the term in the subject place; it** **is the first term that
names a class.

**Subjective Connotation** The person-to-person differences in
the connotations assigned to a term are known as subjective connotations.

**Subjective Theory of Probability** The subjective theory of
probability is based on individual beliefs. This theory of probability is used
in calculating such things as the outcome of sporting events. Also called
Bayesian probability. See also, Bayes, Thomas.

**Substitution
instance
**(of an argument form) An
argument is a substitution instance of an argument form if and only if the
argument can be generated from the form by replacing *only the variables*
in the form with TL statements and, in addition, making any necessary
parenthetical adjustments.

**Sufficient Condition** A condition is a sufficient condition
for some phenomenon if whenever that condition holds, the phenomenon in question
occurs. A sufficient condition is expressed by the antecedent of a conditional.

**Suppressed Evidence** An argument that commits the fallacy of
suppressed evidence is enthymematic. It states a premise that is true but
presupposes an additional premise, a false premise, the truth of which must be
assumed as grounds for accepting the conclusion.

**Syllogism** A syllogism is a deductive argument consisting of
two premises and a conclusion.

**Symmetrical Relation** A relation *R *is symmetrical if
and only if when it is true that *a *stands in relation *R *to *b,
*it** **is also true that *b *stands in relation *R *to
*a. *The relation of "being a sibling" is a symmetrical
relation: if John is a sibling of Mary, then Mary is a sibling of John. The
relation of "being older than" is not a symmetrical relation (it is an
asymmetrical relation): if John is older than Mary, then it** **is
false that Mary is older than John.

**Synonymous Definition** A synonymous definition is a
connotative definition in which the definiens is a single word that has the same
connotation as the definiendum..

**Syntax
**The vocabulary and rules
of grammar of a language. Essentially,
the vocabulary gives us the elements to construct expressions of the language,
and the rules of grammar tell us how to construct properly formed expressions of
the language.

**Tautology (Taut.)** In
propositional logic, a tautology is a logical equivalence falling under the rule
of replacement that indicates (1) that any statement is logically equivalent to
a disjunction of that statement with itself and (2) that any statement is
logically equivalent to a conjunction of that statement with itself. The two
forms of the equivalence are: a ⊢(a ·a
) and a ⊢(a v a). Sometimes called
the property of idempotence.

**Tautology** In propositional logic, a
tautology is a statement that is true solely in virtue of its form.

**Term** A term is a word or phrase that can be the subject of a
sente nce.

**Ternary Relation** A ternary relation is a three-place
relation.

**Tetradic Relation** A tetradic relation is a four-place
relation.

**Theorem
**A formula that can be proven true without the use of premises.
A theorem of TD is a formula that can be proven true using a premise-free
proof in TD.

**Theory** A scientific theory consists of a number of general,
well-confirmed hypotheses that will explain why specific phenomena are as they
are.

**Tilde (~) **In the symbolic language for propositional logic,
the tilde represents negation. The tilde is the only one-place connective in our
system.

**Transitive Relation** A relation *R *is transitive if
and only if given that *a *is in relation *R *to *b, *and *b
*is in relation *R *to *c, *it follows that *a *is in
relation *R *to *c. *A transitive relation possesses the
following feature: if one thing bears the relation to a second thing bears the
relation to a third thing, the first must bear the relation to the third.

**Transposition (Trans.)**
In propositional logic, transposition is an equivalence falling under the rule
of replacement that a conditional is logically equivalent to another statement
in which the denial of the consequent of the first is the antecedent and the
denial of the antecedent of the first is the consequent. The two forms of the
equivalence are: (p → q) :: (~q → ~p) and
(~p → q) :: (~q → p). Sometimes called contraposition.

**Triadic Relation** A triadic relation is a three-place
relation.

**True, Truth** Truth is a characteristic of a statement or
proposition. A proposition is true if and only if it** **corresponds
with the world.

**Truth
function
**A logical rule that relates one set of truth-values to another set of
truth-values. A truth function takes
a set on truth values as inputs and returns a unique truth value as the output.

**Truth Functional Compound ** A
truth functional compound is a
compound statement in which the truth of the entire statement is determined
wholly by the truth values of its component statements.

**Truth Functional Expansion
**In QL a method for
determining the truth value of a quantified proposition by assigning properties
to the elements of the universe of discourse and then comparing that assignment
to a known interpretation of the universe.

**Truth
Functional Operator
**An operator that forms a truth-functional compound statement when
attached to one or more component statements.

**Truth Table** A truth table represents
all logically possible truth values of a statement.

**Truth Tree** The truth-tree technique is a purely mechanical
method of determining whether an argument in propositional logic is valid and
demonstrating that an argument in predicate logic is valid. The truth-tree
technique operates by the method of *reductio ad absurdum*

**Truth Value** Truth value is a
property of a proposition. The truth value of a proposition is its truth or
falsehood.

**Undistributed Middle** In categorical logic, a syllogism
commits the fallacy of undistributed middle if the middle term is undistributed.

**Universal Affirmative Proposition** In categorical logic, a
universal affirmative proposition claims that all the members of the subject
class are included in the predicate class. A universal affirmative proposition
can be stated in standard form as "All S is(are) P."

**Universal domain **Everything
in the universe. When the domain is
everything in the universe, the domain is unrestricted or universal.

**Universal Generalization (U.G.)** In predicate logic, the rule
of universal generalization allows you to conclude the truth of a universal
proposition on the basis of propositions instantiated in terms of variables.

**Universal Instantiation (U.I.)** In predicate logic, the rule
of universal instantiation allows you to eliminate the universal quantifier by
replacing each variable in the scope of the quantifier by a constant or a
variable.

**Universal Negative Proposition** In categorical logic, a
universal negative proposition holds that no members of the subject class are
included in** **the predicate class. A universal negative
proposition can be stated in standard form as "No S is P.

**Universal Quantifier** In predicate logic,
the universal quantifier is symbolized by the upside down A ( "
), or by a variable placed in parentheses.

**Universal Statement** A universal statement makes a claim
about every member of its subject class.

**Universe of discourse
**The collection of things that the statement or statements are making
a claim about. Essentially, the
collection of things we are talking about on an occasion is our universe of
discourse on that occasion

**Unsound argument
An
unsound argument is one which is either non-valid or one which, if valid, has
false premises.
**

**Use** A word is used if the truth or falsehood of a statement
depends upon the meaning of that word.

**Vague** A word is vague if its meaning is unclear or
imprecise.

**Valid,
Validity** Validity is a characteristic of an argument form. An
argument form is valid if and only if the truth of the premises guarantees the
truth of the conclusion.

**Variable
**A symbol that stands for anything from a specified group of things.
In QL, a symbol such as x, y, or z that serves a placeholder for
individual constants. A variable in
QL performs the function that is performed by the word "thing" within
English

**Venn Diagram** The Venn diagram is
a pictorial means of representing categorical propositions understood according
to the Boolean interpretation.

**Venn, John** John Venn was a nineteenth-century logician who
developed a pictorial means of representing categorical propositions understood
according to the Boolean interpretation.

**Verbal Disputes** Verbal disputes are disputes that rest on
alternative meanings of terms rather than a genuine disagreement about the
facts.

**Wedge** In the symbolic language for
propositional logic, the wedge (or vee) represents disjunction.

**Well-Formed Formula (WFF) **I.
In propositional logic, a formula is a well-formed formula in our language under
the following conditions:

(1) any statement letter or simple proposition is a WFF;

(2) a tilde followed by a WFF is a WFF;

(3) if p and q are WFFs, then so are the following:

(p · q), (p v q), (p →
q), (p º
q) and formulas using alternative symbols for the binary connectives;

II. In predicate logic, a formula is a well-formed formula in our language under
the following conditions

(1) atomic expressions: a. individual variables: *x, y, z; *b.
individual constants: *a, b, c, *. . ., *w; *c. predicate letters:
*A, B, C, . . . Z*; d. Connectives: i. one-place: ~; ii. two-place: , , ,
; e. grouping indicators: ( ), [ ], { }; f. quantifiers: ("x),
∃x;

(2) well-formed formulae (WFFs): a. atomic WFFs: i. where R is a predicate
letter and x is either an individual constant or an individual variable, then Rx
is an atomic WFF; ii. where R is a predicate letter and x and y are either
individual constants or individual variables, then Rxy and Ryx. are atomic WFFs;
iii. since predicates can be predicates of any degree, where R is a predicate
letter followed by any number of individual constants or individual variables,
x, y, z. . ., Rxyz is an atomic WFF; b. molecular WFFs: where and are WFFs, so
are: ~, , , , ; c. general WFFs: where R is a predicate letter and x* *is
an individual variable, the following are WFFs: ("x)Rx
is a WFF ∃xRx is a WFF; d. nothing is a WFF unless it** **can
be constructed by a finite number of applications of rules a - c.

**Whole** An object is treated as a whole relative to the
various parts of which** **it** **is composed.