Challenge B Introductory Logic

Terms in this set (148)

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

deals directly with reasoning, by considering the means of distinguishing between proper and improper modes of reasoning

deals with operations of thinking that are indirectly related to reasoning such as defining terms, relating terms, determining relationships between sentences

arguments of likelihood and probability By induction we draw conclusions from facts or experience

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

a concept expressed precisely in words

a statement that gives a meaning to a term

when a term is defined properly the definition gives us some idea of the relationships which the term has with other terms

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

more general, broad, or abstract than the term itself

a type, kind, or example of the term

mutually exclusive

when species do not overlap

when no other species of a term exist

the sum of all the individual objects to which the term applies

the sum of the common attributes of a term

what makes a term different from all the other terms

a message that can be stated true or false

question, command, nonsense

a message that cannot be stated true or false

a statement by a person concerning their desires, beliefs, or feelings

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

a source of information

experience, observation

other sources of information

when two statements can be true at the same time

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

when the truth of one statement does not depend on the truth of another statement

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

the term being described, or about which something is asserted

the term that describes or asserts something about the subject

identifies whether the statement is universal or particular

identifies whether the statement is affirmative or negative

universal affirmative statements

universal negative statements

particular affirmative statements

particular negative statements

square of opposition

the square of opposition demonstrates the relationships between A, E, I, and O statements

the relation between A and O statements

the relation between A and E

both statements cannot be true but they can both be false

both statements can be true but they cannot both be false

superimplication

the implication of falsity

a set of statements, one of which appears to be implied or supported by the others

the statements that support or imply the conclusion

the point or terminus of the argument, the statement that appears to be supported

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.

the subject term of the conclusion

the predicate term of the conclusion

the term that is in both premises but is not in the conclusion at all

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

a representation of a syllogism, having statements in standard order with standard abbreviations of its terms

a three letter description of the types of categorical statements it contains with arranged in standard form

a number from 1 to 4 identifying the placement of its middle term

the mood and figure of the syllogism

when the conclusion of a syllogism is true given that the premises are true

when a syllogism has true premises and a false conclusion

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

fallacy of the undistributed middle

fallacy of the illicit major/minor

fallacy of two negative premises

fallacy of a negative premise and an affirmative conclusion

fallacy of two affirmative premises and a negative conclusion

immediate inferences

a statement that can be inferred directly from another statement

a statement that reverses the subject and predicate, only valid for E and I statements

a statement of the opposite quality with a negated predicate, valid for all statements

the set of all terms not included in the given term

a statement that reverses and negates both the subject and predicate of the original, valid for A and O

a word, often relative pronoun or adverb, that often refers to a broad range of things or times

words that set boundaries referring only to a limited class of things

a syllogism with one assumed statement

a statement that affirms and outcome based on a condition

pure hypothetical syllogism

an argument that uses only hypothetical statements

the condition the part following the "if"

mixed hypothetical syllogisms

an argument that uses both hypothetical and categorical statements

If P then Q.
P.
Therefore, Q.

If P then Q.
Not Q.
Therefore, not P.

affirming the consequent

If P then Q.
Q.
Therefore, P.

"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

an illegitimate appeal to authority

an illegitimate appeal to majority

an illegitimate appeal to force

a verbal attack on a person rather than his/her argument

attacking a position by pointing out how the arguer came to hold that position

points out an inconsistency between a person's argument and their behavior

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

a vagueness of grammar that disguises or alters the meaning

the fallacy of transferring attributes from parts to whole

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

a hasty generalization

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

the logical operator that denies or contradicts a proposition

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

a logical operator that joins two propositions

a logical operator that joins two propositions

asserts that one component implies the other

true only when both component operators have the same truth value

logically equivalent

if two propositions have identical truth values

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

the premises are true and the conclusion has to be true

the premises are true and the conclusion dose not have to be true

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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