Logic Chapter 1

Front 1

Logic

Back 1

Study of methods for evaluating whether the premises of an argument adequately support its conclusion

Hint 1

Evaluating

Front 2

Argument

Back 2

Set of statements where some of the statements (premises) are intended to support another (conclusion)

Front 3

Statement

Back 3

A sentence that is either true or false.

Hint 3

T or F

Front 4

Deductive Argument

Back 4

An argument in which the premises are intended to guarantee the conclusion. Deductive logic is concerned with evaluating validity.

Hint 4

Guarantee

Front 5

Inductive Argument

Back 5

An argument in which the premises are intended to make the conclusion probable. Inductive logic is concerned with evaluating strength.

Hint 5

Probable

Front 6

Valid Argument

Back 6

A deductive argument in which it is necessary that, if the premises are true, the conclusion is true.

Hint 6

Necessary

Front 7

Invalid Argument

Back 7

An argument in which is isn't necessary that, if the premises are true, the conclusion is true.

Hint 7

Unnecessary

Front 8

Sound Argument

Back 8

Valid argument in which all premises are true.

Front 9

Unsound Argument

Back 9

Argument that is either invalid OR valid with at least one false premise.

Front 10

Modus Ponens

Back 10

Famous form: If A, B. A. So, B.

Front 11

Modus Tollens

Back 11

Famous form: If A, B. Not B. So, not A.

Front 12

Hypothetical Syllogism

Back 12

Famous form: If A, B. If B, C. So, if A, C.

Front 13

Disjunctive Syllogism

Back 13

Famous form: Either A or B. Not A. So, B.

Front 14

Constructive Dilemma

Back 14

Famous form: Either A or B. If A, C. If B, D. So, either C or D.

Front 15

Argument Form

Back 15

A pattern of reasoning.

Front 16

Substitution Instance (of an Argument Form)

Back 16

An argument that results from uniformly replacing variables in in that form with statements (or terms).

Front 17

Valid Argument Form

Back 17

An argument form in which every substitution instance is valid.

Front 18

Formally Valid Argument

Back 18

An argument that is valid in virtue of its form.

Front 19

Negation

Back 19

The denial of a statement.

Front 20

Conditional (Statement)

Back 20

An "if..., then..." statement.

Front 21

Antecedent

Back 21

The "if" clause of a conditional.

Front 22

Consequent

Back 22

The "then" clause of a conditional.

Front 23

Disjunction

Back 23

An "either... or..." statement.

Front 24

Disjuncts

Back 24

The statements comprising a disjunction.

Front 25

Falacy of Denying the Antecedent

Back 25

Invalid form: If A, B. Not A. So, not B.

Front 26

Invalid Argument form

Back 26

An argument form with some invalid substitution instances.

Front 27

Counterexample (of an argument form)

Back 27

A substitution instance in which the premises are true, but the conclusion is false.

Front 28

Good Counterexample

Back 28

A counterexample in which the premises are well-known truths and the conclusion is a well-known falsehood.

Front 29

Fallacy of Affirming the Consequent

Back 29

Invalid form: If A, B. B. So, A.

Front 30

Categorical Statement

Back 30

A statement that relates two classes or categories, where a class is a set or collection of things.

Front 31

Term

Back 31

A word or phrase that represents a class of things.

Front 32

Counterexample Method

Back 32

1. Convert to argument form with variables.

2. Substitute statements/terms for conclusion that produce a well-known falsehood.

3. Substitute statements/terms for premises that are well-known truths

4. Check that the substitution instance is invalid.

Front 33

Strong Argument

Back 33

An inductive argument in which it is probable that, if the premises are true, the conclusion is true.

Front 34

Weak Argument

Back 34

An inductive argument in which it is not probable that, if the premises are true, the conclusion is true.

Front 35

Cogent Argument

Back 35

A strong argument in which all premises are true.

Front 36

Uncogent Argument

Back 36

An inductive argument that is either weak OR strong with at least one false premise.

Front 37

A & B. C. So, D.

Valid or invalid?

Example?

Back 37

Invalid;

George Washington was a US president and GW is long dead. Barack Obama was a US president. So, BO is long dead.

Front 38

If A, B. If A, C. So, if B, C.

Valid or Invalid?

Example?

Back 38

Invalid;

If Will Smith is a thoroughbred, he is a mammal. If WS is a thoroughbred, he is a horse. So, if WS is a mammal, he is a horse.

Front 39

All A are B. All B are C. So, all A are C.

Valid or invalid?

Example?

Back 39

Valid;

All presidents are humans. All humans are mammals. So, all presidents are mammals.

Front 40

All A are B. Some C are not B. So, some C are not A.

Valid or invalid?

Example?

Back 40

Valid;

All emeralds are gems. Some rocks are not gems. So, some rocks are not emeralds.

Front 41

Every A is a B. Some A are C. So, some B are C.

Valid or invalid?

Example?

Back 41

Valid;

Every sockeye is a salmon. Some sockeye are natives of the Copper River. So, some salmon are natives of the Copper River.

Front 42

All A are B. Some B are not C. So, some A are not C.

Valid or invalid?

Example?

Back 42

Invalid;

All lions are mammals. Some animals are not felines. So, some lions are not felines.

Front 43

No A are B. Some C are not B. So, some C are not A.

Valid or invalid?

Example?

Back 43

Invalid;

No closed-plane figures are Klingons. Some squares are not Klingons. So, some squares are not closed-plane figures.