Introduction to Logic Vocab Challenge B
Terms for Fall term Introductory Logic by James Nance
Terms in this set (135)
The science and art of reasoning well.
The Law of the Excluded Middle
Any statement is either true or false.
The Law of Identitiy
If a statement is true, then it is true.
The Law of Non-contradiction
A statement cannot be both true and false
Logic dealing with the proper modes of reasoning.
Logic dealing with operations of thinking that re indirectly related to reasoning
Reasoning with probability from examples or expercience to general rules.
Reasoning with certainty from premises to conclusions.
A concept that can be expressed precisely.
A statement that gives the meaning of a term.
Describes a word that has more than one definition
Describes a word whose extent is unclear
A definition that seeks to make more precise what was previously vague or fuzzy.
A definition given when a new word is invented, or an existing word is applied in a new way.
What are the purposes of Definitions?
give meanings for terms, show relationships between terms, remove ambiguity, reduce vagueness, increase vocabulary, explain theoretically, influence attitues
What are the five types of Definitions?
lexical, precising, stipulative, theoretical, persuasive
A definition which shows relationships or reduces ambiguity by providing a single, established meaning of a term. (The definition you would find in a dictionary.)
Definition to explain concepts that are often scientific or philosophical in nature.
Definition that aims at persuading the listener one way or another toward the term being defined.
Genus of a Term
A Category into which a given term fits. It is more general, broad, or abstract than the original term and includes it.
Species of a Term
A type, kind, or example of a given term. It is more specific, narrow,or concrete than the original term and is included by it. ***It should be mutually exclusive, and may be an exhaustive list.
--do not overlap
--no other types exist
Extension of a Term
The sum of all the individual objects described by it.
Intension of a Term
The sum of all the comor attributes denoted by the term.
Extension and Intension are __________ related.
What are the methods of defining a term?
by synonym, by example, by genus and diference
How do you define a term by genus and species?
State the genus of the term along with words distinguishing that term from every other species under the genus.
A definition should state the essential _________of the term.
A definition should not be ____________.
A definition should not be too _________nor too __________.
A definition should not be _________or _________.
A defitintion should be stated ____________, if possible.
A definition should be of the same__________as the term.
part of speech
What are the rules when defining a term by genus and difference?
state the essential attributes, not be circular, not be too broad or too narrow, not be unclear or figurative, be stated postitively, if possible, be of the same part of speech
A sentence which is wither true or false.
_________,__________, and ___________are not statements because they do not have a truth value.
questions, commands, nonsense sentences
A statement whose truth value ccan be determined from the statment itself.
What are the three categories of self-supporting statements?
self-reports, statements which are true or false by logical structure, statements which are true or false by definition
A statement by a person concerning his or her own desires, beliefs, or feelings. We usually take such statements as true.
Statements which are true or false by logical structure
A statement which can be seen to be true or false by how the sentence is put together
A statement which is always true because of its logical structure.
A statement which is false by logical structure.
Statements which are true or false by definition
A statement which is necessarily true or false because of the definition of the words in the sentence.
A statement whose truth value depends on evidence or information from outside itself.
What are the ways to determine a supported statement's truth value?
authority, experience, deduction
Consistency of Statements
Two statements are consistent if they can both be true at the same time.
Two statements are related by implication if the truth of one requires the truth of the other.
Two statements are logically equivalent if they imply one another.
Two statements are independent if the truth or falsity of one has no effect on the truth or falsity of the other.
What are the four basic relationships between statements?
consistency, implication, logical equivalence, independence
An actual inconsistency between two statements: they cannot both be true at the same time.
A difference of opinion or perception.
A misunderstanding due to differing definitions for one or more words.
What are the three types of disagreements between statements ?
real disagreements, apparent disagreements, vergal disagreements
To analyze statements using categorical logic, translate them into a form that uses the verb of __________.
How do you translate statements so that they use the verb of being?
1. identify and write down the entire subject, 2. choose the "to be" verb that matches the subject and predicate 3. rewrite the entire predicate as a predicate nominative
Subject of a Statement
The term being described or about which something is asserted.
Predicate of a Statement
The term that describes or asserts something about the subject.
What are the four basic forms of categorical statements?
All S are P.
No S are P.
Some S are P.
Some S are not P.
What are the names of the four categorical statements?
Quantity of a Statement
The scope of its claim about the extension of the subject: universal or particular.
Quality of a Statement
The positive or negative nature of its claim about the subject: affirmative or negative.
Square of Opposition
A diagram of the basic relationships between statements with the same subject and predicate.
How do we abbreviate the four basic categorical statements in the square of opposition?
Contradiction of Statements
Two statements are in contradictions if and only if they always have opposite truth values.
In the square of opposition the statements in the _____________corner are contradictory statements.
opposite A,O and I,E
Contrarariety of Statements
Two statemtents are contrary if and only if they can both be false but cannot both be true.
In the square of opposition, satements ___ and ___ have a relationship of contrariety.
Subcontrarriety of Statements
Two statements are subcontraries if and only if both can be true but both cannot be false.
In the square of opposition, statements ___and____have a relationship of subcontrariety.
The relationship between a universal and particular statement of the same quality in which the truth of the universal necessitates the truth of the particular.
The relationship between a universal and particular statement of the same quality, in which the falsity of the particular necessitates the falsity of the universal.
Which pairs of statements in the square of opposition have a relationship of superimplication?
I & A and O & E
An argument is a set of statements, one of which appears to be implied or supported by the others.
The statement which appears to be implied by the other statements in the argument, which are called premises.
A deductive argument consisting of three statements in categorical form that together use only three terms, called the major, minor, and middle.
The predicate of the conclusion of a syllogism.
The subject of the conclusion of a syllogism.
The term found in each of the premises of a syllogism.
The premise containing the major term.
The Premise containing the minor term.
What are the steps in putting a syllogism in standard form?
1. Find the conclusion 2. Find the major term 3. Find the major term 4. Find the minor premise 5. Write the syllogism out in standard form
schema of a syllogism
A representation of a syllogism having statements in standard order with standard abbreviations of its terms.
mood of a syllogism
A three-letter description of the types of categorical statements it contains when arranged in standard order.
What is the abbreviation of the major term in a syllogism?
What is the abbreviation of the minor term in a syllogism?
What is the abbreviation of the middle term in a syllogism?
figure of a syllogism
A number from 1-4 identifying the placement of its middle term.
When is a syllogism valid?
A syllogism is valid if and only if the conclusion is necessarily true given that the premises are true.
When is a syllogism sound?
A sound syllogism is valid and has true premises
counterexample to a syllogism
A syllogism of the same form as the original, but with obviously true premises and false conclusions, in order to show the original to be invalid.
A term that, within a statement, refers to all member of its class.
What are the five rules for testing the validity of a syllogism?
1. In at lease one premise, the middle term must be distributed.
2. If a term is distributed in the conclusion, it must also be distributed in its premise.
3. A valid syllogism cannot have two negative premises.
4. A valid syllogism cannot have a negative premise and an affirmative conclusion.
5. A valid syllogism cannot have two affirmative premises and a negative conclusion.
A statement which can be inferred directly from another statement. Use them to translate arguments with complementary terms into standard form syllogisms for analysis.
converse of a statement
A statement that reverses the subject and predicate. It is only valid for E and I.
obverse of a statement
A statement of the opposite quality with a negated predicate. It is valid for all statements.
complement of a term
The set of all terms not included in the given term. Thus the complement of the term P is non-P.
contrapositive of a statement
A statement that reverses and negates both the subject and predicate of the original. It is valid for A and O.
Name the three types of equivalent immediate references:
converse, obverse, contrapositive
In logic, a word that refers to a bread range of things or times.
In logic, words that set boundaries, referring only to alimited class of things.
An argument in which a statement is unstated and assumed. Specifically, it is a syllogism with one assumed statement.
A statement that affirms an outcome based on a condition. It has the form if P then Q.
pure hypothetical syllogism
An argument that uses only hypothetical statements.
antecedent of a hypothetical statement
The condition, the part following the "if."
consequent of a hypothetical statement
The result of the condition, the part after the "then."
mixed hypothetical syllogism
An argument that uses both hypothetical and categorical statements.
A Latin phrase meaning "it does not follow"; that an argument is invalid.
How do you establish the truth of a statement?
1. Put the statement into categorical form 2. Find a valid argument form that has that type of statement as a conclusion 3. Place the statement as the conclusion of the selected form of syllogism and fill in the known terms 4. Find a middle term that makes the premises both true and completes the argument
A popular, informal form of reasoning that are invalid or unhelpful.
fallacy of distraction
An argument that confuses the issue by pointing to information that is actually irrelevant to the conclusion.
Latin for "he has said it himself" it is an illegitimate appeal to authority
Latin for "to the masses", an illegitimate appeal to a majority
Latin for "to the stick", an illegitimate appeal to force
Latin for "to the man", a verbal attack on a person rather than his argument
attacking a position by pointing out how the arguer came to it
points to an inconsistency between a person's argument and behaviour ("you do it too")
an argument from lack of evidence
an argument bases merely on the passage of time
Name the fallacies of distraction
ipse dixit, ad populum, ad baculum, ad hominem, bulverism, tu quoque, ad ignorantiam, chronologial snobbery
fallacies of ambiguity
arguments that confuse the real issue with multiple, vague, or otherwise unclear meanings
changing the definition of a term in the middle of an argument
fallacy of accent
altering the meaning of a statement through changed enphasis
a vagueness of grammar that disguises or alters meaning
fallacy of composition
the fallacy of transferring attributes from part to whole
fallacy of division
transferring attributes from whole to part
fallacies of form
arguments that fail to establish their conclusions because of a waekness in logical structure
secretly assuming what you are trying to prove
post hoc ergo propter hoc
Latin for "after this, therefore because of this", improperly assuming that a sequence in time implies a cause and effect
fallacy of either/or
making and argument based on a false ilemma
a question crafted to exclude any possible legitimate response
Name the fallacies of form
circular reasoning, post hoc ergo propter hoc, either/or, complex question, apriorism
a hasty generalization
Name the fallacies of ambiguity
equivocation, accent, amphiboly, composition, division