Midterm Exam

Deductive Argument

An argument that provides evidence in such a way that makes it impossible for the latter to be true

Inductive Argument

An argument based on probability by providing evidence that makes the conclusion more porbable

Determination of Deductive Validity

If and only if it’s impossible that every premise is true and the conclusion is false

Determination of Deductive Soundness

if and only if the argument is deductively valid and every premise is true

Proof

Evidence to support a claim

Disproof

Evidence to oppose a claim

Contradiction

a person, thing, or situation in which inconsistent elements are involved

Token-Reflexive

Terms that change definition depending on the context

Vacuous Terms

Terms that do not refer to anything or refer to something that doesn’t exist

Negation

┐

Conditional Implication

→

Negation definition

not

Conditional Implication definition

if-then or if and only if

Conjunction

⌃

Conjunction definition

and

Disjunction

⌄

Disjunction definition

or

Terms

(a,b,c) describes something or someone involved in the sitation

Predicates

(F,G,H) assigns a property or an adjective to a term

Quantifiers

(𐆗,  Ǝ) Express a large number of individuals

𐆗 Definition

everyone

Ǝ Defintion

someone

The predicate language for “everyone is happy”

𐆗xH(x)

Axiom

A self-evident claim

Axiomatic Theory

Using axioms as evidence for a theory

Set Theory

The theory that everything belongs to a set and that there is a set for everything

{}

A set

∋ (backwards)

Set membership

∅

Empty Set

Grelling Paradox

Heterological vs. Autological

The Barber Paradox

If the barber only cuts the hair of the villagers that do not cut their own hair, does the barber cut his own hair?

Russel Paradox

The set of non-self-membered members

The Liar Paradox

“This statement is a lie” is it?