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logic

the science and art of reasoning well

term

a concept that can be expressed precisely

Law of the Excluded Middle

Any statement that is either true or false

Law of Identity

If a statement is true, then it is true.

Law of Non-contradiction

When a statement cannot be both true and false.

Formal Logic

Deals withe the proper modes of reasoning.

Informal Logic

Deals with operations of thinking that are indirectly related to reasoning.

Induction (Inductive Reasoning)

Is reasoning with probability from examples or experiences to heneral rules

Deduction (Deductive Reasoning)

Is reasoning with certainty from premises to conclusions.

ambiguous

When a word has more than 1 definition.

vague

When a word is one whose extent is unclear.

Genus of a term

That is more general, broad or abstract than the original term and includes it.

Species of a Term

A term that is more specific, narrow, or concrete than the orginal term and is included by it.

Extension

The sum of all the individual objects described by it.

Intension

The sum of all the common attributes denoted by the term.

Definition

A statement that gives the meaning of a term.

Lexical Definition

Shows relationships or reduces ambiguity by providing a single established meaning of a term.

Stipulative Definition

A definition which supplies the meaning of a new term.

Persuasive Definition

Defined to influence the attitudes and emotions of the audience.

Precising Definition

Definition which reduces the vagueness of a term in a given situation.

Theoretical Definition

The word may be familiar, but not understood. For ex.: H2O for water.

statement

a sentence which is either true or false

self-supporting statement

a statement whose truth value can be determined from the statement itself

tautology

a statement which is always true because of its logical structure

self-contradiction

a statement that is false due to its logical structure

supported statement

a statement whose truth value depends on evidence or information from outside itself

consistent statements

they can both be true at the same time

implication (statements related by)

two statements are related by implication if the truth of one requires the truth of the other

logically equivalent statements

if they imply one another

independent statements

the truth or falsity of one has no effect on the truth or falsity of the other

disagreement

when there appears to be inconsistency

real disagreement

an actual inconsistancy between two statements: they cannot both be true at the same time

apparent disagreement

difference of opinion or perception

verbal disagreement

a misunderstanding due to differing definitions for one or more words

subject

the term being described, or about which something is asserted

predicate

is the term that describes or asserts something about the subject

quantity of a statement

the scope of its claim about the extension of the subject: universal (entire extension) or particular (partial)

quality of a statement

is the positive or negative nature of its claim about the subject: affirmative (asserts something) or negative (denies something)

3 ways to determine truth value of a supported statement

authority; experience; deduction

Requirements of Standard Categorical Form

1. Statements must begin w/ all, no, or some. 2. Verb must be a verb of being: is, are, etc. 3. Both subject and predicate must be a noun or a noun phrase.

square of opposition

a diagram of the basic relationships between statements with the same subject and predicate

contradiction

two statements are in contradiction if and only if they always have opposite truth values

contrary

two statements are contrary if and only if they can both be false but cannot both be true

subcontraries

two statements are subcontraries if and only if both can be true but both cannot be false

subimplication

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

superimplication

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.

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