Logic - Week 1 aug Wed,Th,Fr

Formal Logic

The study of the form or structure of reasoning.

Material Logic

The study of the content and truthfulness of arguments.

Deductive Reasoning

Reasoning from general → specific, using logical rules to reach a specific, certain conclusion.

Inductive Reasoning

Reasoning from specific observations/examples → general conclusion.

Logic Box

A tool for mentally organizing statements.

Categorical Statements Types

A, E, I, O.

A

All S are P — Universal Affirmative.

E

No S are P — Universal Negative.

I

Some S are P — Particular Affirmative.

O

Some S are not P — Particular Negative.

A, E, I, O mnemonic

A = All; E = No; I = Some; O = Some…not.

Subject Term (S)

The first group in a statement; usually a noun or noun phrase.

Predicate Term (P)

The second group in a statement; usually a noun or noun phrase.

Copula

The verb that connects the Subject and Predicate terms: is, are, am.

Quantifiers

Words that tell us the number/range of the group and whether the connection is positive or negative.

Logical Quantifiers

All, No, Some, Some…not.

Quality

Whether a statement is Affirmative or Negative.

Quantity

Whether a statement is Universal or Particular.

Universal

The statement refers to the whole group.

Particular

The statement refers to part of the group.

Distribution

The status of a term regarding its extension/range—how much of the term is being referred to.

When is a term Distributed?

When it refers to all members of the class.

Subject-Term distribution rule

Universal = Distributed; Particular = Undistributed.

Predicate-Term distribution rule

Affirmative = Undistributed; Negative = Distributed.

Distribution pattern for A

A = D U — Subject Distributed, Predicate Undistributed.

Distribution pattern for E

E = D D — Subject Distributed, Predicate Distributed.

Distribution pattern for I

I = U U — Subject Undistributed, Predicate Undistributed.

Distribution pattern for O

O = U D — Subject Undistributed, Predicate Distributed.

Complete distribution code

A = DU | E = DD | I = UU | O = UD.

“All dogs are animals.” type

A — Universal Affirmative.

“No dogs are reptiles.” type

E — Universal Negative.

“Some dogs are friendly.” type

I — Particular Affirmative.

“Some dogs are not friendly.” type

O — Particular Negative.

“All students are learners.” Subject (S)

Students.

“All students are learners.” Predicate (P)

Learners.

“All students are learners.” Copula

Are.

“All students are learners.” distribution

S = Distributed; P = Undistributed.

“No students are robots.” distribution

S = Distributed; P = Distributed.

“Some students are athletes.” distribution

S = Undistributed; P = Undistributed.

“Some students are not athletes.” distribution

S = Undistributed; P = Distributed.

“D” in distribution

Distributed — referring to all members of the class.

“U” in distribution

Undistributed — not referring to all members of the class.

Identify Subject's distribution

Look at the quantity: Universal = D; Particular = U.

Identify Predicate's distribution

Look at the quality: Affirmative = U; Negative = D.

Complete A-E-I-O cheat code

A DU — E DD — I UU — O UD.