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1

Logic

Study of methods for evaluating arguments

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Argument

set of statements, one of which, called the conclusion, is affirmed on the basis of the others, which are called the premises

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Statement

sentence that is either true or false

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True Values

truth and falsehood are the two possible outcomes

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Premises

the statements on the basis of which the conclusion is affirmed

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Conclusion

the statement that is affirmed on the basis of the premises

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Valid argument

it is necessary that if the premises are true, then the conclusion is true

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Invalid argument

It is not necessary that if the premises are true, then the conclusion is true

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Sound Argument

It is valid and all its premises are true

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Unsound Argument

Is an argument that either is invalid or has at least one false premise

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deductive logic

Part of Logic that is concerned with tests for validity and invalidity

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Substitution Instance

an argument that results from uniformly replacing letters with terms in an argument

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Argument form

pattern of reasoning

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Counterexample

Is a substitution instance whose premises are well known truths and whose conclusion is a well-known falsehood

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Antecedent

the if-clause of a conditional

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Consequent

the then-clause of a conditional

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logically equivalent

two statements are this if each validity implies the other

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Modus Ponens

If A, then B.
A.
Therefore, B.
means “the mode of positing” (sometimes called the way of affirmation) because the second premise posits the antecedent of the conditional (first) premise.

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Modus Tollens

If A, then B.
Not B.
Therefore, not A.
means “the mode of removing” (sometimes called “way of denial”) because the second premise removes or denies the truth of the consequent of the first (conditional or major) premise.

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Negation

Denial

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Fallacy of denying the antecedent

If A, then B.
Not A.
Therefore, Not B.
invalid and is confused with modus tollens

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Fallacy of affirming the consequent

If A, then B.
B.
Therefore, A.
invalid and is confused with modus ponens

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hypothetical syllogism

If A, then B.
If B, then C.
Therefore, If A, then C.
In Greek, “syllogism” means “to reason together.”
The argument is called “hypothetical” because it involves only conditional statements.

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disjunctions

statements of the form "either A or B"

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disjunctive syllogism

Either A or B.
Not A.
Therefore, B.
The two parts of the major premise are called “disjuncts.”
There are two senses of “or.”
The inclusive sense basically means “at least one of A or B (or both).”
The exclusive sense means “either A or B (but not both).”

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constructive dilemma

Either A or B.
If A, then C.
If B, then D.
So, either C or D.
combines both conditional and disjunctive statements

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Strong Argument

It is probable (but not necessary), that if the premises are true, then the conclusion is true

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Weak argument

It is not probable that if the premises are true, then its conclusion is true

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Arguments from authority

R is a reliable authority regarding S
R sincerely asserts that S.
So S

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Arguments from analogy

Object A is similar to object B in certain relevant respects
B has property P
So A has property P also