Modern Classification of Propositions

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Traditional Classification

Basics

Aristotle

Perceived

Every Prop affirmes or denies something of something else

Meaning : Subject - Predicate form

Defects

As perceived

Contrarily

4 prop in Traditional Classification

are general prop

Exception of Singular Prop

Closer Look

Traditional Logician

Failed in analysis

Lacked the distinguishing capabilities between singular proposition from propositions whose subject term is a class.

Aims and Basis

Classification as devised

Separating a proposition from other proposition which do not contain another proposition (s) as a component from those proposition which contain

Simply Stating - Simple prop ( for the former eg ) and Compound Proposition ( latter eg)

Simple Proposition

Defined as

Prop

Not having

Other Prop as a component

Kinds Of

Subjectless

Subject - Predicate

Relational

Class Membership

Asserts

Concept🎶

Assertion made

Exclamatory

Fires!

Impersonal

It rains.

States -

Individual 👉

Possess 👉

Quality

👆 Is a singular term

'Subject 'is a singular term

Symbolically : S-P

Relation

Between

2 or more constituents

Term of relation are Subject and Predicate

Terminology

'Sense or direction of relation'

WHERE relation proceeds from something to something

Referent - term from which relation proceeds

Relatum - term to which relation proceeds

Symbolically

R (x,y) ; x- referent , y- relatum

But Nothing Expressed

Concept 🎶

Asserts

Individual

Is a member of

Class

Symbolized

a ε F

a - Individual ; F - 'any class'

Distinctions

Make a note for this in 10 min. ❤

Compound Proposition

Note: All the above example were of affirmative type, denial of simple proposition gives us compound proposition

Negative Proposition

Any Proposition

Negated

We get

Negative Proposition

Propositional

Connectives

~ :Tilde or curl

Variables

'' ~p''

Conjunctive Proposition

Combination

Of any 2 proposition

Truth Functional

"and "

Components

Called

As Conjuncts

Propositional

Connective

"."

Variable

"p.q"

Truth value

Disjunctive Proposition

word

"or"

combines 2 prop

Components

Called as

Disjuncts

Use of "or"

Inclusive

Exclusive

Both Disjuncts can be True

One Disjunct True other False

[weak]

[strong]

Apt Example for this is in book.

Logic Considers "or " in inclusive sense

Propositional

Connective

v - wedge

Variable and connective

p v q

Implicative Proposition

Combination

2 proposition

words "if....then......."

Component

Between

If...then - antecedent

After "then..." - consequent

Propositional

Connective

⊃

Form

p ⊃ q

Note : Implicative prop false only when antecedent is true, and the consequent is false.

Equivalent prop

Combination

2 component prop

'if and only if'

materially implying e.o

Propositional

Variable

triple bar

form = 'p triple bar q'

Read some end 2-3 para of this context from book.

True it is only if both conjuncts are true

Number of Times Revised