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Logic

Logic is the science and art of reasoning well

The law of the excluded middle

Any statement is either true or false

The law of identity

If a statement is true, then a statement is true

The law of non contradiction

A statement cannot be both true and false

Formal logic

Formal logic deals with the proper modes of reasoning

Informal logic

Informal logic deals with operations of thinking that are indirectly related to reasoning

Induction

Induction is reasoning with probability from examples or experience to general rules

Deduction

Deduction is reasoning with certainty from premises to conclusions

Term

A term is a concept that can be expressed precisely

Definition

A definition is a statement that gives the meaning of a term

Ambiguous

An ambiguous word has more than One definition

Vague

A vague word is one who's extent is unclear

Genus of a term

A genus of a term is a term that is more general, broad, or abstract then the original term and includes it

Species of a term

A species of a term is a term that is more specific, narrow or concrete than the original term and is included by it

Extension of a term

The extension of a term is the sum of all the individual objects described by it

Intension of a term

The intention of a term is the sum of all the common attributes denoted by the term

Statement

A statement is a sentence that is either true or false

Self-supporting statement

A self-supporting statement is a statement whose truth value can be determined from the statement itself

Tautology statement

A tautology is a statement which is always true because of its logical structure

Self-contradiction

A self-contradiction is a statement that is false due to its logical structure

Supported statement

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

Consistent statements

Two statements are consistent if they can both be true at the same time

Implication

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

Logically equivalent

Two statements are logically equivalent if they imply one another

Independent statements

Two statements are independent if the truth of falsity of one has no effect on the truth or falsity of the other

Real disagreement

A real disagreement is an actual inconsistency between two statements: they cannot both be true at the same time

Apparent disagreement

An apparent disagreement is a difference of opinion or perception

Verbal disagreement

A verbal disagreement is a misunderstanding due to differing definitions for one or more words

Subject of a statement

The subject of a statement is the term being described, or about which something was asserted

Predicate term

The predicate is the term that describes or asserts something about the subject

Quantity of a statement

The quantity of a statement is the scope of its claim about the extension of the subject: universal (entire extension) or particular (partial)

Quality of a statement

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

Square of opposition

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

Contrary statements

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

Subcontrary statements

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

Subimplication

Subimplication is 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

Superimplication is the relationship between a universal and particular statement of the same quality

Argument

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

Conclusion of an argument

The conclusion of an argument is the statements which appears to be implied by the other statements in the argument, which are called premises

Categorical syllogism

A categorical syllogism is a deductive argument consisting of three statements in categorical form that together use only three terms, called the major, minor, and middle

Major term

The major term of a syllogism is the predicate of the conclusion and is used in one premise

Minor term

The minor term is the subject of the conclusion and is used in the other premise

Middle term

The middle term is found once in each premise

Major premise

The major premise of a syllogism is the premise containing the major term

Minor premise

The minor premise contains the minor term

Schema of a syllogism

The schema of a syllogism is a representation of it, having statements in standard order with standard abbreviations of its terms

Mood of a syllogism

The mood of a syllogism is a three-letter description of the types of categorical statements it contains when arranged in standard order

Figure of a syllogism

The figure of a syllogism is a number from 1 to 4 identifying the placement of its middle term

A valid syllogism

A syllogism is valid if the conclusion is necessarily true given that the premises are true

A sound syllogism

A sound syllogism is valid and has true premises

Counterexample of a syllogism

The counterexample of a syllogism is a syllogism of the same form as the original, but with obviously true premises and false conclusion, in order to show the original to be invalid

Distributed term

A distributed term is a term that, within a statement, refers to all the members of its class

Immediate inference

The immediate inference is a statement which can be inferred directly from another statement

Converse of a statement

The converse of a statement is a statement that reverses the subject and predicate. it is only valid for E and I

Obverse of a statement

The obverse of a statement is a statement of the opposite quality with a negated predicate. It is valid for all statements

Complement of a term

The complement of a term is 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

The contrapositive of a statement is a statement that reverses and negates both the subject and predicate of the original. It is valid for A and O

Enthymeme

An enthymeme is an arguement in which a statement is unstated and assumed. Specifically, it is a syllogism with one assumed statement

Hypothetical

A hypothetical is a statement that affirms an outcome based on a condition. It has the form If P then Q

Puere hypothetical syllogism

A pure hypothetical syllogism is an argument that uses only hypothetical statements

Antecedent of a hypothetical statement

The antecedent of a hypothetical statement is the condition, the part following the "if." The consequent is the result of the condition, the part after the "then"

The Latin phrase non sequitur

The Latin phrase non sequitur means "it does not follow"; i.e., that an arguement is invalid

Informal fallacy

An informal fallacy is a popular but invalid (or unhelpful) form of arguement

Fallacy of a distraction

A fallacy of a distraction is an argument that confuses the issue by pointing to information that is actually irrelevant to the conclusion

Ipse dixit

Ipse dixit is an illegitimate appeal to authority

Ad populum

Ad populum is an illegitimate appeal to authority

Ad baculum

Ad baculum is an illegitimate appeal to force

Ad hominim

Ad hominim is a verbal attack on a person rather than his arguement

Bulverism

Bulverism is attacking a position by pointing out how the arguer came to hold it

Tu quoque

Tu quoque points to an inconsistency between a person's argument and behavior

Ad ignorantiam

Ad ignorantium is an argument from lack of evidence

Chronological snobbery

Chronological snobbery is an argument based merely on the passage of time

Fallacies of ambiguity

Fallacies of ambiguity are arguments that confuse the real issue with multiple, vague, or otherwise uncleat meanings

Equivocation

Equivocation is changing the definition of a term in the middle of an arguement

Fallacy of the accent

The fallacy of the accent alters the meaning of a statement through changed emphasis

Amphiboly

Amphiboly is a vagueness of grammar that disguises or alters meaning

Composition

Composition is the fallacy of transferring attributes from part to whole

Division

Division is the fallacy of transferring attributes from whole to part

Fallacies of form

Fallacies of form are arguments that fail to establish their conclusions because of a weakness in logical structure

Circular reasoning

Circular reasoning is secretly assuming what you are trying to prove

Post hoc ergo propter hoc

Post hoc ergo propter hoc is improperly assuming that a sequence in time implies a cause and effect

Either/or

Either/or is making an argument based on a false dilemma

A complex question

A complex question is a question crafted to exclude any possible legitimate response

Apriorism

Apriorism is a hasty generalization