most of logic 🤓😖🙂
Terms in this set (110)
the science and art of reasoning well
Law of the Excluded Middle
any statement is either true or false
Law of Identity
if a statement is true, then it is true
Law of Noncontradiction
a statement cannot be both true and false
deals with the proper modes of reasoning
deals with operations of thinking that are indirectly related to reasoning
reasoning with probability from examples or experience to general rules
reasoning with certainty from premises to conclusions
a type of deductive argument in which the conclusion connects one category (or term) with another
a concept that is expressed precisely in words
a statement that gives the meaning of a term
when a term is defined properly, the definition often gives some idea
words that have more than one possible meaning
a single, established meaning of a term
a definition that you would find in a dictionary
a definition that reduces vagueness
given to a newly discovered or invented word
increased the vocabulary of the language to which they are added
accepting a theory about the term being defined
a definition given in a way to persuade the listener one way or another
a term that is more general, broad, or abstract than the original term and includes the original as well
a term that is more specific, narrow, or concrete than the original term
Genus and Species Hierarchy
clearly showing the relationships between genus and species
informal and formal logic are this thus they do not overlap
informal and formal logic are this
meaning no other types of logic exist
the sum of all the individual objects described by it
Example: book is all novels, dictionaries, textbooks, manuals, etc.
the sum of all the common attributes denoted by the term
Example: helmet- fitting on the head, resisting impact, made of protective material, and so on
Definitions give meaning for terms. Definitions can show relationships between terms, remove ambiguity, reduce vagueness, increase vocabulary, explain concepts theoretically, and influence attitudes. Along with these purposes are the five types of definitions: lexical, precising, stipulative, theoretical, and persuasive.
Summary for Lesson 1
Terms can be organized into genus and species charts. A genus is a category into which a given term fits. A species is a type,kind or example of a given term. Species should be mutually exclusive, and may be an exhaustive list.
Summary for Lesson 2
The extension of a term is the sum of all the individual things to which a term applies. The intension of a term is the sum of the common attributes of the term. Extension and intension are inversely related; as extention increases, intension decreases, and vice versa.
Summary for Lesson 3
L4--Definining by Synonym
words with the same or similar meaning
Good way of defining but not all words have a close synonym or synonym at all.
Example: oxygen has no real synonym
L4--Defining by example
when an example is given to describe or show a term and/or its definition
L4--Defining by Genus and Difference
when a term is defined by naming its genus, and then adding descriptive words that distinguish that term from every other species under that genus--that is, by providing the difference.
Usually the clearest method of defining.
Terms may be defined by synonym, by example, or by genus and difference. Terms are defined by genus and difference by stating the genus of the term along with words distinguishing that term from every other species under the genus.
Summary for Lesson 4
1. A definition should state the essential attributes of the
2. A defintion should not be circular.
3. A defintion should not be too broad nor too narrow.
4.A definition should not be unclear or figurative.
5. A definition should be stated positively, if possible.
6. A definition should be of the same part of speech as the
Lesson 5 Definition Rules
When terms are defined by genus and difference, certain rules should be followed.
Summary for Lesson 5
a sentence which is either true or false.
3 types of sentences that are not statements
1. question 2. command 3. nonsense
a statement whose truth value can be determined from the statement itself
3 types of self-supporting statements
1. self-reports 2. true or false by logical structure 3. true of false by definition
a statement by a person concerning his own desires, beliefs or feelings.
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 (e.g., Jesus is God OR Jesus is not God.) A or ~A
a statement which is always false because of its logical structure (e.g., Jesus is God AND Jesus is not God) A and ~A
true or false by definition
a statement which is necessarily true or false because of the definitions of the words in the sentence
a statement whose truth value depends on evidence or information from outside itself
3 ways to determine the truth value of supported statements
1. authority 2. experience 3. deduction
a trustworthy, authoritative source (e.g., scripture, encyclopedia)
trusting our own senses to determine truth value
reasoning to some conclusion based on other statements, whose truth value we know
4 relationships between statements
1. consistency/inconsistency 2. implication 3. logical equivalence 4. independence
when 2 statements can both be true at the same time
when there is a conflict between 2 statements so they cannot time both be true at the same
when the truth of 1 statement requires the truth of the other.
when 2 statements imply each other (the statements must both be true or both be false)
when the truth or falsity of 1 statement has no effect on the truth or falsity of the other
3 kinds of disagreements
1. real 2. apparent 3. verbal
an actual inconsistency between 2 statements; they cannot both be true at the same time (e.g.: Jesus is God. Jesus is not God.)
a difference of opinion or perception (e.g., Ann: I think logic is easy; Bob: I think logic is hard)
a misunderstanding due to differing definitions for one or more words
Rules for Changing Statements into Standard Form
1. Identify and write down the entire subject
2. Choose the proper "to be" verb.
3. Rewrite the entire predicate as a predicate nominative.
Statements that affirms or denies something about a given subject.
Term being described, or about which something is asserted.
Term that describes or asserts something about the subject.
Positive or negative nature of its claim about the subject: affirmative (asserts something) or negative (denies something)
the scope of its claim about the extension of the subject: universal (entire extension) or particular (partial)
Categorical Statement Forms
1. All S are P.
2. No S are P.
3. Some S are P.
4. Some S are not P.
Square of Opposition
A diagram of the basic relationships between categorical statements with the same subject and predicate.
Universal affirmative statements.
Universal negative statements.
Particular affirmative statements.
Particular negative statements.
Two statements are in contradiction if and only if they always have opposite truth values.
Both statements cannot be true, but they can both be false.
Both statements can be true but they cannot both be false.
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.
A set of statements, one of which appears to be implied or supported by the others
2 Statements in an Argument
A deductive argument with two premises and three terms
A syllogism consisting of three statements in categorical form
The predicate of the conclusion. Also used in one premise.
The subject of the conclusion. Also used in the other premise.
A term that is in both premises but is not in the conclusion at all.
A premise containing the major term.
A premise containing the minor term.
Rules for Changing Syllogisms into Standard Form
1. Find the Conclusion
2. Find the Major Term
3. Find the Major Premise
4. Find the Minor Premise
5. Write the Syllogism out in Standard Order
The ------ of a syllogism is a representation of it, having statements in standard order with standard abbreviations of its terms.
The ---- of a syllogism is a three letter description of the types of categorical statements it contains when arranged in standard order.
The ------ of a syllogism is a number from 1 to 4 identifying the placement of its middle term.
In ---------, the middle term is the subject of the major premise and the predicate of the minor premise.
In ---------, the middle term is the predicate of of both premises.
In ---------, the middle term is the subject of both premises.
In ----------, the middle term is the predicate of the major premise and the subject of the minor premise.
To set out the syllogism's schema.
The ---- of the syllogism is the mood and figure of the syllogism.
Conclusion Identifier Examples
Therefore, thus, so, consequently (etc.)
Common Word Identifier Examples
Since, because, for, given that (etc.)
Words that introduce the conclusion in an argument.
Common Word Identifiers
Words that generally follow the conclusion.
When the premises in a syllogism imply the conclusion
When a syllogism has true premises and a false conclusion
When a syllogism is valid and has true premises
A syllogism of the same form as the original, but with obviously true premises and an obviously false conclusion, in order to show the original to be invalid
A term that is within a statement and refers to all members of its category
Rules for Testing the Validity of Syllogisms
1.) In at least 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
Fallacy of the Undistributed Middle
The middle term must be distributed at least once
Fallacy of an Illicit Major
The major term is distributed in the conclusion, but not in the premise.
Fallacy of an Illicit Minor
The minor term is distributed in the conclusion, but not in the premise
Fallacy of Two Negative Premises
A valid syllogism cannot have two negative premises
Fallacy of a Negative Premise and an Affirmative Conclusion
A valid syllogism cannot have a negative premise and an affirmative conclusion
Fallacy of Two Affirmative Premises and a Negative Conclusion
A valid syllogism cannot have two affirmative premises and a negative conclusion
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