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Challenge B Introductory Logic
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Terms in this set (148)
Logic
The science and art of reasoning well
The Law of Excluded Middle
The law that states that every statement is either true or false
The Law of identity
The law that states that if a statement is true then it is true
The Law of Noncontradiction
The law that states that a statement cannot be both true and false
formal logic
deals directly with reasoning, by considering the means of distinguishing between proper and improper modes of reasoning
informal logic
deals with operations of thinking that are indirectly related to reasoning such as defining terms, relating terms, determining relationships between sentences
induction
arguments of likelihood and probability By induction we draw conclusions from facts or experience
deduction
arguments of valid or invalid
categorical logic
deals with syllogisms which are a type of deductive argument in which the conclusion connects one category with another
propositional logic
connects entire propositions together in arguments
term
a concept expressed precisely in words
definition
a statement that gives a meaning to a term
relationship
when a term is defined properly the definition gives us some idea of the relationships which the term has with other terms
ambiguous
when a word has more than one possible meaning
lexical definition
a definition that you might find in a dictionary
precising definition
a definition that clarifies
stipulative definition
a definition for a new word
theoretical definition
a theory about the term being defined
persuasive definition
a definition used to manipulate one's thoughts about a term
genus
more general, broad, or abstract than the term itself
species
a type, kind, or example of the term
mutually exclusive
when species do not overlap
exhaustive
when no other species of a term exist
extension
the sum of all the individual objects to which the term applies
intension
the sum of the common attributes of a term
difference
what makes a term different from all the other terms
statement
a message that can be stated true or false
question, command, nonsense
a message that cannot be stated true or false
self reports
a statement by a person concerning their desires, beliefs, or feelings
tautology
a statement that is true by logical nature
self contradiction
a statement that is false by logical nature, i.e. Jesus is the Son of God and he is not the Son of God
statements that are true or false by definition
a statement that is true or false by definition
supported statement
requires evidence from the outside
authority
a source of information
experience, observation
other sources of information
consistent
when two statements can be true at the same time
implication
when the truth of the first of two statements requires the truth of the second
logically equivallent
if two statements are logically equivalent then the first must imply the second and vise versa
independence
when the truth of one statement does not depend on the truth of another statement
disagreement
when there is inconsistency
Real disagreement
actual inconsistency both statements cannot be true
apparent disagreement
the result of disagreeing opinions or perception
verbal disagreement
when different definitions are used for the same word
categorical statements
statements that affirm or deny something about a given subject
subject
the term being described, or about which something is asserted
predicate
the term that describes or asserts something about the subject
quantity
identifies whether the statement is universal or particular
quality
identifies whether the statement is affirmative or negative
A statements
universal affirmative statements
E statements
universal negative statements
I statements
particular affirmative statements
O statements
particular negative statements
square of opposition
the square of opposition demonstrates the relationships between A, E, I, and O statements
contradiction
the relation between A and O statements
contrary
the relation between A and E
Contrariety
both statements cannot be true but they can both be false
subcontrariety
both statements can be true but they cannot both be false
superimplication
the implication of falsity
argument
a set of statements, one of which appears to be implied or supported by the others
premise
the statements that support or imply the conclusion
conclusion
the point or terminus of the argument, the statement that appears to be supported
syllogism
a particular form for organizing categorical statements into an argument
categorical syllogism
categorical syllogisms are made up of three statements. the first two are premises, and the last is a conclusion. i.e. all red plants are living things. all roses are red plants. therefore all roses are living things.
minor term
the subject term of the conclusion
major term
the predicate term of the conclusion
middle term
the term that is in both premises but is not in the conclusion at all
major premise
the premise that contains the major term
to put an argument in standard form follow these steps
1. find the conclusion
2. find the major term
3. find the major premise
4. find the minor premise
5. write the syllogysm
schema
a representation of a syllogism, having statements in standard order with standard abbreviations of its terms
mood
a three letter description of the types of categorical statements it contains with arranged in standard form
figure
a number from 1 to 4 identifying the placement of its middle term
schematize
to schema
form
the mood and figure of the syllogism
valid
when the conclusion of a syllogism is true given that the premises are true
invalid
when a syllogism has true premises and a false conclusion
sound
when a syllogism is valid and the premises are true
counterexamples
a syllogism of the same form as the original but w/ true premises and a false conclusion in order to show the original to be invalid
distributed term
a term that within a statement refers to all members of its category
rule 1
fallacy of the undistributed middle
rule 2
fallacy of the illicit major/minor
rule 3
fallacy of two negative premises
rule 4
fallacy of a negative premise and an affirmative conclusion
rule 5
fallacy of two affirmative premises and a negative conclusion
immediate inferences
a statement that can be inferred directly from another statement
converse
a statement that reverses the subject and predicate, only valid for E and I statements
obverse
a statement of the opposite quality with a negated predicate, valid for all statements
complement
the set of all terms not included in the given term
contrapositive
a statement that reverses and negates both the subject and predicate of the original, valid for A and O
inclusives
a word, often relative pronoun or adverb, that often refers to a broad range of things or times
exclusives
words that set boundaries referring only to a limited class of things
enthymemes
a syllogism with one assumed statement
hypothetical
a statement that affirms and outcome based on a condition
pure hypothetical syllogism
an argument that uses only hypothetical statements
antecedent
the condition the part following the "if"
mixed hypothetical syllogisms
an argument that uses both hypothetical and categorical statements
modus ponens
If P then Q.
P.
Therefore, Q.
modus tollens
If P then Q.
Not Q.
Therefore, not P.
affirming the consequent
If P then Q.
Q.
Therefore, P.
non sequitur
"it does not follow"
denying the antecedent
If P then Q.
Not P.
Therefore, not Q.
informal falacies
a popular but invalid form of an argument
fallacy of distraction
an argument that confuses the issue by pointing to the information that is actually irrelevant to the conclusion
Ispe dixit
an illegitimate appeal to authority
Ad populorum
an illegitimate appeal to majority
Ad baculum
an illegitimate appeal to force
Ad hominem
a verbal attack on a person rather than his/her argument
Bulverism
attacking a position by pointing out how the arguer came to hold that position
Tu quoque
points out an inconsistency between a person's argument and their behavior
Ad ignorantum
an argument from lack of evidence
Chronological snobbery
an argument based on the passage of time
fallacies of ambiguity
arguments that confuse the real issue with multiple, vague, or otherwise unclear meanings
amphiboly
a vagueness of grammar that disguises or alters the meaning
composition
the fallacy of transferring attributes from parts to whole
division
the fallacy of transferring attributes from whole to part
fallacies of form
arguments that fail to establish their conclusions because of a weakness in logical structure
circular reasoning
secretly assuming what you are trying to prove
Post ergo propter hoc
improperly assuming that a sequence in time implies a cause and effect
complex questions
question crafted to exclude any possible legitimate responce
apriorism
a hasty generalization
proposition
a sentence with truth value
truth functional proposition
a proposition whose truth value depends on the truth value of its component parts
simple proposition
a proposition with only one component part
compound proposition
a proposition with more than one component part
logical operators
words that combine or modify simple proposition to make compound propositions
propositional constant
an uppercase letter that represents a single given proposition
propositional variable
a lowercase letter represents any proposition
negation, conjunction, disjunction
three fundamentals logical operators
negation
the logical operator that denies or contradicts a proposition
truth table
a listing of the possible truth values for a set of one or more propositions
defining truth table
displays the values produced by a logical operator modifying a minimum number of variables
conjunction
a logical operator that joins two propositions
disjunction
a logical operator that joins two propositions
conditional
asserts that one component implies the other
biconditional
true only when both component operators have the same truth value
logically equivalent
if two propositions have identical truth values
tautology
a preposition that is true for every row in the truth table is called a
self contradiction
a preposition that is false for every row in the truth table is called a
valid
the premises are true and the conclusion has to be true
invalid
the premises are true and the conclusion dose not have to be true
dilemma
a valid argument which presents a choice between two conditionals
constructive dilemma
an argument that works like a modus ponens
destructive dilemma
and argument that works like a modus tollens
go between the horns
deny the disjunctive premise and provide a third alternative
grasp it by the horns
reject one of the conditionals in the conjunctive premise
rebut the horns
make a counter-dilemma
the rules of replacement
forms of equivalent statements
conditional proof
a special rule in a formal proof which allows us to assume the antecedent of a conditional and, once we deduce the consequent to conclude the entire conditional
reduction ad absurdum
a special rule which allows us to assume the negation of a proposition deduce a self contradiction the conclude the proposition
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