# Traditional Logic I by Martin Cothran

(Louisville: Memoria Press, 2000), 150

The kiln tests the potter's vessels; so the test of a man is in his reasoning.
-Sir-27-6

"Mom?"
"Yes?"
"What's lodge-ick?"
"Logic? Why, dear, logic is knowing what things are true and not true."
Ray Bradbury, The Illustrated Man ("Zero Hour", 260)

# Notes

Contents

## Introduction: What is Logic?

Definitions

• Josiah Royce: "The science of order."
• Raymond McCall: "Logic in general is the science of right thinking."
• Jacques Maritain: "Logic is the art which enables us to proceed with order, ease, and correctness in the act of reason itself."
• Irving Copi: "The distinction between correct and incorrect reasoning is the central problem with which logic deals."

History of Logic

• Aristotle (384-322 BC) is the "father of logic"
• Chrysippus (279-206 BC) laid the foundation for symbolic logic, which was picked up by Leibniz (1646-1716)
• John Stuart Mill (1806-1873) pioneered induction

Two Branches of Logic

• Formal (minor) Logic: concerned with the *form or structure of reasoning, or the method of deriving one truth from another
• Material (major) Logic: concerned with the content of argumentation and the truth of the terms

You can only find truth with logic if you have already found truth without it.
G.K. Chesterton

Truth, Validity, Soundness

• A statement is either true or false. A true statement corresponds to reality.
• The structure of an argument is valid if its conclusion follows logically from its premises, otherwise it is invalid.
• An argument as a whole is sound if all premises are true and the argument is valid.

Components of an Argument

• Term: the verbal expression of the mental act of simple apprehension
• Proposition: the verbal expression of the mental act of judgment, whereby we affirm that something is something, or deny that something is not something
• Syllogism: the verbal expression of the mental act of deductive inference, whereby we make the logical connections between the terms in the argument in a way that shows us that the conclusion either follows or does not follow from the premises
Mental Act Verbal Expression
Simple Apprehension Term
Judgment Proposition
Deductive Inference Syllogism.

# Simple Apprehension (Term)

## Chapter 1: What Is Simple Apprehension?

• Sense Perception: the act whereby your senses present an object to your mind; you perceive an object by means of your senses
• Mental Image: the image of an object formed in the mind as a result of a sense perception of that object
• Simple Apprehension: is an act by which the mind grasps the general concept of an object without affirming or denying anything about it.
• Abstraction: is the process by which a simple apprehension is derived from a sense perception and mental image.

## Chapter 2: Comprehension and Extension

• The two properties of simple apprehension (concepts) are comprehension and extension
• Comprehension is the completely articulated sum of the intelligible aspects or elements (or notes) represented by a concept.
• A comprehension answers the question, "What is a <blank>?"
• A Note is the simple (atomic) concept that cannot be broken into simpler parts
• The Porphyrian Tree (invented by third-century logician Porphyry) allows us to identify the notes associated with a concept
graph TD

a(<strong>Category:</strong> Substance)
b(Material)
c(Non-Material)
d(<strong>Remote Genus:</strong> Body)
e(Living)
f(Non-Living)
g(<strong>Remote Genus:</strong> Organsm)
h(Sentient)
i(Nonsentient)
j(<strong>Proximate Genus:</strong> Animal)
k(Rational)
l(Nonrational)
m(<strong>Logical Species:</strong> Man)

classDef r fill:#f96

a:::r --> b
a --> c
b --> d:::r
d --> e
d --> f
e --> g:::r
g --> h
g --> i
h --> j:::r
j --> k
j --> l
k --> m

• Extension tells us to which things an essence applies.
• An extensions answers the question, "To what does the concept <blank> refer?
• The greater number of notes a concept has, the less extension it has (something more specific is less applicable).

## Chapter 3: Signification and Supposition

• A Term is the verbal expression of a concept.
• The two properties of terms are signification and supposition.
• Signification is a way of dividing terms:
• Univocal terms are terms that have exactly the same meaning no matter when or how they are used.
• Equivocal terms have different and unrelated meanings.
• Analogous terms are applied to different things but have related meanings.
• →Logic requires an accurate and consistent use of terms (which is an issue with equivocal and analogous terms).
• Supposition is a way of dividing terms:
• Material supposition is when a term refers to something as it exists verbally
• Logical supposition is when a term refers to something as it exists logically or mentally
• Real supposition is when a term refers to something as it exists in the real world

# Judgment (Proposition)

## Chapter 4: What is Judgment?

• Judgment is the act by which the intellect unites the subject and predicate by affirming, or separates them by denying.
• Judgment is a mental act whose verbal expression is a proposition.
• A Proposition is a statement which expresses truth or falsity. A proposition consists of three elements: the subject-term (S), the predicate-term (P), and the copula (c, usually "is" or "are"), which must be arranged in logical form.
• $\text{(Man)}^S \text{ (is)}^c \text{ (an animal)}^P$
• "The little brown-haired boy screams very loudly" becomes: $\text{(The little brown-haired boy)}^S \text{ (is)}^c \text{ (a child who screams very loudly)}^P$

## Chapter 5: The Four Statements of Logic

• The Four Statements of Logic
• A: All S is P (affirmo)
• I: Some S is P
• E: No S is P (nego)
• O: Some S is not P
• Quantifiers include: all, some, no, some...not
• The Quality of a proposition is affirmative or negative
• The Quantity of a proposition has to do with whether it is universal or particular (or singular, treated as universal). Statements are assumed to be universal unless stated otherwise.
• A: Affirmative-Universal
• I: Affirmative-Particular
• E: Negative-Universal
• O: Negative-Particular
↓Quantity/Quality→ Affirmative Negative
Universal A (All S is P) E (No S is P)
Particular I (Some S is P) O (Some S is not P)

## Chapter 6: Contradictory and Contrary Statements

• Categorical statements can be related in Opposition or in Equivalence
• Opposition: statements in opposition affirm and deny the same predicate of the same subject
• Contrary
• Subcontrary
• Subaltern
• Equivalence
• Obversion
• Conversion
• Contraposition
• Rule of Contradiction: Contradictory statements are statements that differ in both quality and quantity. Same colors (opposites) are contradictory:
↓Quantity/Quality→ Affirmative Negative
Universal A (All S is P) E (No S is P)
Particular I (Some S is P) O (Some S is not P)
• The Rule of Contraries: Two statements are contrary to one another if they are both universals but differ in quality. A (red) and E (purple) are contrary:
↓Quantity/Quality→ Affirmative Negative
Universal A (All S is P) E (No S is P)
Particular I (Some S is P) O (Some S is not P)
• First Law of Opposition: Contradictories cannot at the same time be true nor at the same time be false.
• The Second Law of Opposition: Contraries cannot at the same time both be true, but can at the same time both be false.

# Deductive Inference (Syllogism)

## Chapter 14: Review

Topic: Logic

Source

Created: 2024-07-06-Sat
Updated: 2024-08-27-Tue