affirming the consequent
a formal fallacy with the following form:
P1: if P, then Q
P2: Q
C1: P
argument
any group of propositions of which one is claimed to follow from the others, which are regarded as providing support for the truth of that one; constructed with propositions; affirms one proposition on the basis of some other propositions; requires an inf
argument from ignorance
an informal fallacy in which one claims that the truth of a premise is based on the fact that it has not been proven false or proven true
argument from silence
an informal fallacy in which the conclusion is based on the absence of evidence, rather than the existence of evidence
assuring
a strategy for proving one's argument in casual conversation in which one indicates that there are backup reasons even though one is not providing them in full at the moment
atomic formula
a predicate followed by zero or more names; the number of names following predicate make it an n-place predicate
biconditional elimination
a rule of inference with the following form:
from P tribar Q, infer either P implies Q or Q implies P
biconditional introduction
a rule of inference with the following form:
from P implies Q and Q implies P, infer P tribar Q
biconditional modus ponens
a rule of inference with the following form:
from P tribar Q and P/Q, infer P/Q
biconditional modus tollens
a rule of inference with the following form:
from P tribar Q and ~P/~Q, infer ~P/~Q
compound proposition
a proposition that contains other propositions within itself; the Amazon River is long and wide
conclusion
a proposition that is affirmed on the basis of other propositions of an argument
conclusion markers
words that indicate the presence of a conclusion; therefore, thus, hence, then
conditional fallacy
an argument which may or may not be fallacious, conditional on whether or not one of its premises is true; for example, an argument from authority can be fallacious when the authority isn't authoritative, but can be valid when there's reason to trust the
conditional introduction
a rule of inference with the following form:
given a hypothetical derivation of Q from P, end the derivation and infer P implies Q
conjunction
a compound proposition containing two separate statements connected by an "and"; separate statements called conjuncts; connective is dot; both conjuncts must be true for statement to be true; truth-functional compound statement/components/connective
conjunction elimination
a rule of inference with the following form:
from P and Q, infer P or Q
also called simplification
conjunction introduction
a rule of inference with the following form:
from P and Q, infer P and Q
constructive dilemma
a rule of inference with the following form:
from (P or Q) and (P implies R) and (Q implies S), infer R or S
contingent statement form
a statement form that has both true and false statements among its substitution instances
continuum fallacy
an informal fallacy in which assuming that a continuum of possible states between two states means they are not meaningfully different; a form of equivocation; has the following form:
P1: X is one extreme and Y is another extreme
P2: there is no definable
contradiction
a statement form that has only false substitution instances
contraposition
a logical law that states that a conditional statement is logically equivalent to its contrapositive; if P, then Q is equivalent to if not Q, then not P
counterexample
a possible situation in which an argument's premises are true but its conclusion is false; must affirm premises, deny conclusion, and explain how this can be the case without contradiction
deductive argument
an argument whose conclusion is claimed to follow from its premises with absolute necessity; necessity is not a matter of degree and not depending in any way on whatever else may be the case
De Morgan's Laws
rules of inference with the following forms:
~(P or Q) tribar (~P and ~Q)
~(P and Q) tribar (~P or ~Q)
denying the antecedent
a formal fallacy of the following form:
P1: if P, then Q
P2: not P
C1: not Q
derived rules
De Morgan's Laws, material implication, commutation, association, distribution, contraposition, ex falso quodlibet, biconditional modus ponens, biconditional modus tollens, double negation, constructive dilemma
direct objection
a counterargument in which one disproves the conclusion of the original argument
discounting
a strategy for proving one's argument in casual conversation in which one anticipates criticisms and dismisses them; four components: assertion of A, assertion of B, suggestion of some opposition between A and B, indication that the truth of B is more imp
disjunction
a compound statement that separates component statements by "or"; inclusive if both components can be true (at least one); exclusive if only one of the components can be true (at least one and at most one); connective is wedge
disjunction elimination
a rule of inference with the following form:
from P or Q, P implies R, and Q implies R, infer R
disjunction introduction
a rule of inference with the following form:
from P, infer either P or Q or Q or P
disjunctive syllogism
a valid argument of the following form:
P1: either P or Q
P2: it is not the case that P
C1: Q
enthymeme
an argument used in everyday discourse that has unstated premises
equivocation
an informal fallacy that relies on the different meanings a word can have in different contexts; has the following form:
P1: X is Y (meaning 1)
P2: Y (meaning 2) is Z
C1: X is Z
existential elimination
from any existential formula ExFx, hypothesize Fb, b being any name not present in any hypothetical derivation that has not yet ended or any premise; end the derivation when the name is no longer present with the line at which the derivation ends
existential introduction
given any formula with a name in it, add an existential quantifier and replace each name with a variable
existential quantifier
for at least one, some; backwards E
explicandum (explanandum)
a term or statement that is to be explained
explicans (explanans)
the meaning of a term or statement
fallacious argument style
an argument in which one speaker uses unfair, manipulative, or disruptive tactics to prevent actual discussion of the issue
fallacy fallacy
a formal fallacy in which one claims that if an argument contains a logical fallacy, the proposition it was used to support is wrong; a true statement can be defended using false logic, so using false logic to defend an opinion is not proof of the opinion
fallacy of composition
an informal fallacy in which one assumes that something true of part of a whole must also be true of the whole
fallacy of division
an informal fallacy in which one assumes that something true of a thing must also be true of all or some of its parts
false dilemma
an informal fallacy in which two opposing views are presented as the only options, but are not
formal fallacy
an argument in which the conclusion would not be true whether or not its premises are correct, because it does not follow valid logical structure
Galileo gambit
a conditional fallacy in which one asserts that if one's ideas provoke the establishment to vilify or threaten one, one must be right; being persecuted doesn't mean you are right
Gambler's fallacy
an informal fallacy in which one believes that separate, independent events can affect the likelihood of another random event
guarding
a strategy for proving one's argument in casual conversation in which one weakens one's claims so that they are less subject to attack; weaken extent (all to most), inject probability, or reduce level of commitment (I know that to I suspect that)
hedging
a subset of guarding in which one "takes things back" or "waters down" one's claim
Hume's guillotine
an informal fallacy in which one derives prescriptive or normative statements from descriptive ones; there is no obvious, coherent method to move from is's to oughts; also called the is-ought problem or the naturalistic fallacy
hypothetical proposition
proposition that asserts no components separately; if-then statement; antecedent follows if; consequent follows then; for proposition to be false, the antecedent need be true and the consequent false; also called a conditional proposition; connective is h
hypothetical syllogism
a valid argument of the following form:
P1: if P, then Q
P2: if Q, then R
C1: if P, then R
identity elimination
from a premise of the form a = b and a formula F containing either a or b, infer any formula which results from replacing one or more of these occurrences with either of the other in F
identity introduction
where a is any name, assert a = a
implication
governs hypothetical propositions; logical, definitional, causal, decisional, and material; q is necessary condition for p; p is a sufficient condition for q; both if p, then q
indirect objection
a counterargument in which one disproves one of the premises of the original argument
inductive argument
an argument that does not make the claim that its conclusion is supported by its premises conclusively; maintains a degree of probability
inference
process that may tie together several propositions
informal fallacy
an argument in which the conclusion would be true if the premises were true, but those premises are almost always incorrect
instantiation
a valid argument of the following form:
P1: all F's are G's
P2: a is an F
C1: A is a G
intermediate conclusion
a conclusion reached in the course of an argument that serve as premises for further conclusions
invalid argument
an argument that does not establish the conclusion necessarily if the premises are true; an argument for which the premises are true and the conclusion is false
law of the excluded middle
a logical law that states that either a proposition is true or its negation is true; predicated on the principle of bivalence
logic
the study of the methods and principles used to distinguish good and bad reasoning
material equivalence
the truth-functional connective that asserts that the statements it connects have the same truth value; tri-bar; if and only if; biconditional
material implication
a rule of inference with the following form:
from P implies Q, infer ~P or Q
modus ponens
a valid argument of the following form:
P1: if P, then Q
P2: P
C1: Q
also called conditional elimination
modus tollens
a valid argument of the following form:
P1: if P, then Q
P2: not Q
C1: therefore, not P
negation
denial of a proposition; usually formed by adding "not"; connective is curl or tilde
negation elimination
a rule of inference with the following form:
from ~~P, infer P
negation introduction
a rule of inference with the following form:
given a hypothetical derivation of any formula of the form (P and ~P) from Q, infer ~Q; reductio ad absurdum
Nirvana fallacy
an ad hoc informal fallacy in which one claims that a realistic solution is useless because it is not as good as an idealized perfect solution
No True Scotsman
an ad hoc informal fallacy in which groups are redefined on the spot
not even wrong
...
one single proof
a fallacious argument style in which one dismisses all circumstantial evidence in favor of a single "smoking gun" that may not (and may not need to) exist
paralogism
a piece of illogical or fallacious reasoning, especially one which appears superficially logical or which the reasoner believes to be logical
petitio principii
circular reasoning; begging the question; premises presume conclusion
post hoc ergo propter hoc
an informal fallacy in which one assumes that because event A happened before B, A must have caused B
predicate
a statement or portion of a sentence that may be true or false depending on the values of its variables
premise
propositions which are affirmed or assumed as providing support for conclusion
presupposing
a strategy for proving one's argument in casual conversation in which one identifies shared assumptions
proposition
abstract entity that asserts that something is the case; must be true or false; must be a declarative sentence
quantifier exchange law
for any statement with an existential or universal quantifier, change the first quantifier to its reverse and negate the statement and its closest following forumla
quantifier scope ambiguity
the ambiguity arising from the use of both existential and universal quantifiers in the same sentence; e.g. something loathes everything
red herring
a logical fallacy in which a speaker attempts to distract an audience by deviating from the topic at hand by introducing a separate argument the speaker believes is easier to speak to
reason markers
words that indicate the presence of a premise; since, for, because, as
rules of inference
conditional introduction, conditional elimination, conjunction introduction, conjunction elimination, disjunction introduction, disjunction elimination, biconditional introduction, biconditional elimination, negation introduction, negation elimination; ea
sorites
a form of argument having several premises and one conclusion, capable of being resolved into a chain of syllogisms, the conclusion of each of which is a premise of the next; also polysyllogism, multi-premise syllogism, climax, or gradatio
sound argument
a valid argument with true premises
specific form
a statement form from which the statement by substituting consistently a different simple statement for each different statement variable
statement form
any sequence of symbols containing statement variables but no statements, such that when statements are substituted for the statement variables--the same statement being substituted for the same statement variable throughout--the result is a statement
straw man
a fallacious argument style in which one distorts an opponent's position for greater rhetorical flexibility
tautology
statement form that has only true substitution instances
Texas sharpshooter fallacy
an informal fallacy in which one uses the same data both to construct and to test a hypothesis; name comes from a sharpshooter who shoots at the wall of a barn, and paints a bullseye around the hole
toupee fallacy
an informal fallacy regarding silent evidence and the problem of induction; "all toup�es look fake; I've never seen one that I couldn't tell was fake
truth
attribute of a proposition that asserts what really is the case
trick of abusive assurance
a subset of assuring in which one suggests that there is something wrong with you if you ask for a reason
trick of the disappearing guard
a subset of guarding in which one begins with a "perhaps" that disappears at the end, where it is taken for granted
truth-functional component
component that when replaced in
the compound by any different statements having the same truth value as each other, the different compound statements produced by those replacements also have the same truth values as each other; truth value of component do
truth table
table representing truth values of component statements and their effect on compound statements
tu quoque
an informal logical fallacy that intends to discredit the opponent's argument by asserting the opponent's failure to act consistently in accordance with its conclusion(s).
Tu quoque "argument" follows the pattern:
Person A makes claim X.
Person B asserts
two-place predicate
a predicate with both a subject and an object; the order is predicate-subject-object
universal elimination
given any formula with a variable and a universal quantifier in it, remove the universal quantifier and replace one variable with any name
universal introduction
given any formula with a name that does not appear in any of the premises or any hypothetical derivations that have not yet ended in it, add a universal quantifier and replace the name with a variable
universal quantifier
for any, for all; upside down A
ultracrepidarianism
a conditional fallacy in which a source is quoted outside of their expertise, as if expertise in one field extends to another
valid argument
an argument whose conclusion can only be true if its premises are true