Logic Definitions

Question 1

Logically true sentence

Answer 1

A sentence is logically true if and only if it cannot be false.

Question 2

Logically Valid Argument

Answer 2

An argument is logically valid if and only if there is no interpretation under which the premises are all true and the conclusion is false

Question 3

Contradiction

Answer 3

A sentence is a contradiction if and only if it cannot be true.

Question 4

Contingent sentence

Answer 4

A sentence that is neither a logically true nor a contradiction is contingent

Question 5

Consistency

Answer 5

A set of sentences is consistent if and only if it is possible for all the members of the set to be true
together.

Question 6

Inconsistency

Answer 6

A set of sentences is inconsistent if and only if it is not logically consistent.

Question 7

Logical equivalence

Answer 7

A pair of sentences are logically equivalent if and only if it is not possible for one of them to be true
while the other is false. They always share the same truth-value, whatever the circumstances.

Question 8

Logical validity (in terms of consistency)

Answer 8

An argument is valid if and only if the set obtained by adding the negation of the conclusion to the
premises is inconsistent.

Question 9

Set

Answer 9

A collection of objects

Question 10

When are sets identical?

Answer 10

Iff they have the same members

Question 11

Extensional definition of sets

Answer 11

Listing the things the set contains

Question 12

Intensional definition of sets

Answer 12

Giving a rule which determines what the elements are

Question 13

When is a set a binary relation?

Answer 13

A set is a binary relation if and only if it contains only ordered pairs.

Question 14

Transitivity

Answer 14

A relation R is transitive on a set S iff for all d, e, f: if <d, e>  R and <e, f>  R, then also <d, f>  R

Question 15

Symmetry

Answer 15

A relation R is symmetric on a set S iff for all d, e: if <d, e>  R then <e, d>  R

Question 16

Asymmetry

Answer 16

For no d, e: if <d, e>  R and <e, d,>  R

Question 17

Antisymmetry

Answer 17

For no two distinct d, e: <d, e>  R and <e, d>  R

Question 18

Reflexivity

Answer 18

A relation R is reflexive on a set S iff for all d in S the pair <d, d> is an element of R

Question 19

Equivalence relation

Answer 19

A relation is an equivalence relation iff it is transitive, reflexive and symmetric

Question 20

Function

Answer 20

A binary relation R is a function iff for all d, e, f: if <d, e> ∈R and <d, f> ∈R then e=f

Question 21

Object Language

Answer 21

The language being talked about (e.g. L1)

Question 22

Metalanguage

Answer 22

The language that we are using to talk about the object language

Question 23

Use/Mention Distinction

Answer 23

Difference between a word being used to refer to something, versus the word itself being mentioned (discussed)

Question 24

Three rules for determining whether L1 symbols are a sentence of L1

Answer 24

1. All sentence letters are sentences of L1.
2. If φ and ψ are sentences of L1, then ¬ φ, (φ ∧ ψ), (φ v ψ), (φ → ψ), (φ ↔ ψ) are sentences of L1
3. Nothing else is a sentence of L1.

Question 25

Truth-functional connective (Sophie)

Answer 25

Iff the truth-value of the compound sentence that its use generates is wholly determined by the truth-values of the sentence it connects and which connective it is.

Question 26

Truth-functionality (Volker)

Answer 26

A connective is truth functional if and only if the truth-value of the compound sentence cannot be changed by replacing a direct subsentence with another sentence having the same truth-value.

Question 27

Domain of a function

Answer 27

The domain of a function R is the set {d: there is an e such that ∈ R}

Question 28

Range of a function

Answer 28

The range of a function R is the set {e: there is a d such that ∈ R}

Question 29

Function into a set

Answer 29

R is a function into the set S iff all elements of the range of the function are in S

Question 30

N-place relation

Answer 30

A set containing only n-tuples. And n-place relation is called a relation of arity n.

Question 31

Atomic formulae of L2

Answer 31

If Z is a predicate letter of arity n and each of t1,...,tn is a variable or constant, then Zt1...tn is an atomic formula of L2