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Introduction to Logic and Critical Analysis Final exam study guide
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Gravity
Terms in this set (84)
anchoring and adjustment
Making an estimate by starting from an initial value (the anchor) and
adjusting from there. People often adjust insufficiently, resulting in their final guess being closer
to the anchor than it would be otherwise
availability
Heuristic used when we need to assess the frequency of a class or the probability of
an event. We'll ask ourselves how easy it is to think of instance or occurrences and/or if it's
easy to think of examples is something more or less likely. People tend to heavily weigh their
judgments toward more recent information, making new opinions biased toward that latest
news
completeness
Ls is complete if and only if for every set of sentences, gamma, and any
sentence phi, if gamma logically implies phi, then gamma deductively yields phi
conjunction rule (probability theory)
Lp is complete just in case, if a sequence is valid, a derivation can be given
for it in Lp: if a set of sentences, gamma, logically implies a sentence, phi, then gamma
deductively yields phi
contingent sentence
A sentence, p, is contingent, if and only if there is at least one model of p
and at least one interpretation that is not a model of p. (That is p is true under some
interpretations and false under others.)
contradictory sentence
A sentence, p, is contradictory, if and only if, p has no model. (That is p
is false under every interpretation)
deductive reasoning
Starts with a general statement to reach a specific, logical, conclusion
disjunction rule (probability theory)
A disjunction effect occurs when people prefer X over Y
when they know what event A obtains, and they also prefer x over y when they know that event
A does not obtain, but they prefer y over x when it is unknown whether or not A obtains. The
disjunction effect amounts to a violation of STP, and hence of consequentialism
domain/universe of discourse
The set of individuals over which the variables in a sentence (or
a collection of sentences, or a language) range, is the domain of discourse for that sentence
(collection of sentences, language)
heuristic
A rule of thumb, a principle that can prove useful in the solution of a problem, but that
does not guarantee a solution
inductive reasoning
inductive reasoning makes broad generalizations from specific
observations
interpretation
Ls Interpretation: An interpretation of Ls is 1) an assignment of truth values to sentential
constants and 2) the use of truth table characterizations of connectives to produce a truth value
for every sentence.
Lp Interpretation: An interpretation, I, consists of 1) a nonempty, finite or infinite, domain of
objects, D; 2) an assignment to each individual constant a member of D; and 3) an assignment
to each monadic predicate a set of objects, and to each n-adic predicate a set of ordered ntuples
of objects.
invalidity (invalid sequence)
Ls Invalidity (Invalid Sequence): A sequence is invalid if an assignment of truth values to its
atomic components results in its premises being true and its conclusion false.
Lp Invalidity (Invalid Sequence): A sequence is invalid if there is an interpretation - any
interpretation - under which its premises are true and its conclusion false
logical consequence
When Γ logically implies Φ, then Φ is said to be a logical consequence of Γ.
logical equivalence (logically equivalent sentences)
Sentences are logically equivalent when
they have identical truth conditions
logical implication
A set of sentences, gamma, logically implies a sentence phi, if and only if
phi cannot be false if gamma (i.e. every sentence in gamma) is true
logical truth (logically true sentence)
A sentence, p, is logically true, if and only if every
interpretation is a model of p. (That is, p is true under every interpretation)
model
An interpretation, I, is a model of a sentence, p, if and only if, I(P) is true. If gamma is a
set of sentences, then I is a model of gamma if and only if every sentence in gamma is true
under I
object language/metalanguage
Object Language: A language under discussion
Metalanguage: The language in which discussion of some object language is conducted
representativeness
Used when faced with problems of the form: What's the probability that
object A belongs to class B? B generates A? etc... These questions are replaced by: To what
degree does object A resemble a stereotypical B? The problem is that people overestimate its
ability to accurately predict the likelihood of an event
sentence of Ls
Cs: sentential constants, {A, B, C,... Z};
Cc: logical constants (truth functional connectives), {negation, conjuc,disjunc, cond, bicond};
P: left and right Parentheses, { (, ) }.
1) Every member of Cs is a sentence of Ls;
2) If P is a sentence of Ls, then negation P is a sentence of Ls;
3) If P and Q are sentences of Ls, then (P^Q) is a sentence of Ls;
4) If P and Q are sentences of Ls, then (PdisjunctQ) is a sentence of Ls;
5) If P and Q are sentences of Ls, then (PcondQ) is a sentence of Ls;
6) If P and Q are sentences of Ls, then (PbicondQ) is a sentence of Ls;
7) Nothing is a sentence of Ls that is not constructed in accord with rules 1-6
singular term
A singular term purports to designate a unique object. Singular terms include
proper names, descriptions, and define descriptions
soundness
Ls Soundness: Ls is sound if and only if for every set of sentences, gamma, and any sentence
phi, if gamma deductively yields phi, then gamma logically implies phi. (1 then 2)
Lp Soundness: Lp is sound just in case every derivation expressible in Lp is valid: where
<gamma, phi> is a sequence, if a set of sentences, gamma, deductively yields a sentence, phi,
then gamma logically implies phi
truth functional language
Ls is a truth functional language: The truth value of every sentence
in Ls is a function of the truth values of its constituent sentences. Given any Ls sentence, p, we
can precisely determine its truth value if we know the truth values of its constituent sentences
and the definitions of the truth functional connectives
validity
A derivation, <gamma, phi>, is valid if and only if gamma logically
implies phi
active sentence occurrence
...
all the time (always)
...
arbitrary individuals (in EI, UG)
...
at least / at most / exactly n
...
atomic sentence
...
base rate (prior probability)
...
Bayes' theorem
describes the probability of an event, based on conditions that might be related to the event
P(A|B) = P(A|B)/((P(B|A) x P (A))/P(B)
bound and free variables
...
cognitive bias
...
cognitive illusion
...
comparatives, superlatives, exceptives
...
complex term
...
conditional probability
...
connective (truth functional connectives)
...
definite description
...
discharging supposition
...
dominance
...
expected value
...
gambler's fallacy
...
general term
...
hot hand phenomenon
...
identity
...
illusory correlation
...
inactive sentence occurrence
...
inclusive and exclusive disjunction
...
individual constant
...
individual term
...
individual variable
...
law of small numbers
...
logical constant
...
meaning
...
Merkle's Principle
...
molecular sentence
...
n-place predicate
...
name
...
Newcomb's Problem
...
porcus mendax
...
porcus verus
...
possible world
...
predicate
...
quantification
...
quantifier scope
...
quantifier transformation (QT)
...
quasi-magical thinking
...
random sequence
...
recursive rule
...
retrievability bias
...
semantics
...
sentential constant
...
sentential variable
...
similarity vs. selfsameness
...
some of the time (sometimes)
...
supposition
...
sure-think principle (STP)
...
syntax
...
term
...
theorem
...
truth conditions
...
truth functional connective
...
;