Logic Part 1 Definitions

Front 1

An argument consists of (2):

Back 1

1. A number of sentences called the premises of the argument.

2. One sentence called the conclusion of the argument.

Front 2

A way to think about a logic is as consisting of a(n) (2):

Back 2

1. Expressive part: A Formal Language (syntax and semantics)

2. Normative part: A logical consequence (validity)

Front 3

Semantic method for checking validity of arguments is called...

Back 3

entailment

Front 4

Syntactic method for checking validity of arguments is called...

Back 4

derivability/deduction

Front 5

To discuss validity of an argument from natural language, we first have to _______ it, that is, translate it into the formal language of a logic.

Back 5

formalise

Front 6

The semantic method gives us a way to....

Back 6

check for validity

Front 7

The syntactic method gives us a way to...

Back 7

generate/derive valid conclusions given a set of premises

Front 8

A counter-example for an inference A1, ...., An/C is a situation in which...

Back 8

A1, ...., An are all true but C is false.

Front 9

The inference A1, ...., An/C is valid in and only if...

Back 9

there exist no counter-examples.

Front 10

The inference A1, ...., An/C is invalid in and only if...

Back 10

there exists at least one counter-example.

Front 11

Theorems:

Back 11

general claims that are true

Front 12

a proposition:

Back 12

any well-formed expression of a given logic

Front 13

An arbitrary proposition Z is a contradiction if and only if...

Back 13

there is no situation in which Z is true

Front 14

An arbitrary proposition Z is satisfiable if and only if...

Back 14

there is at least one situation that makes Z true

Front 15

An arbitrary proposition Z is a tautology if and only if...

Back 15

Z is true in all situations

Front 16

Classical negation:

Back 16

flips the truth value of propositions i.e. if Z is true, than "not Z" is false

Front 17

Two propositions are jointly satisfiable (consistent) if and only if...

Back 17

they can be true together, that is, there is some situation that makes both propositions true

Front 18

Two propositions are logically equivalent if and only if...

Back 18

both A -> B AND B -> A

Front 19

characteristica universalis:

Back 19

an ideal symbolic language in which reasoning can be represented so that validity of arguments is a matter of calculation

Front 20

______ arguments that have true ________ are called ________.

Back 20

Valid, premises, sound

Front 21

Classical logic underlies....

Back 21

the reasoning in mathematics and science at large

Front 22

Characteristics of a syllogism:

1) Only two ______

2) Of the form "____ A ______ B", where A and B are _______

3) The argument involve just three _______

4) One of the _______, the so-called _______, is contained in both of the _________.

5) The ________ relates the other two.

Back 22

1) premises

2) All/some, are/are not, predicates

3) predicates

4) predicates, middle-term, premises

5) conclusion

Front 23

The logic of syllogisms is _________ because there is a mechanical method for checking the validity of such arguments. When there is no such method, we say the logic is __________.

Back 23

decidable, undecidable