The Syntax of Propositional Logic

Stripping Down the Rhetoric

Fundamentals of Propositional Logic | Lesson 1

The Rhetorical Challenge

"It is not merely that the subject is difficult, but rather that the very nature of human perception precludes a direct apprehension of the thing-in-itself, unless one is willing to abandon the comforts of empirical certainty."

— Kantian-style fragment

The Question

Which parts of this sentence carry truth value? Which are purely stylistic or rhetorical?

Natural vs. Formal Language

Natural Language

Ambiguous, context-dependent, nuanced, and rich with connotation. (English, French, etc.)

Formal Language

Precise, rigid, context-independent. Defined by explicit syntax rules. (Logic, Math, Python.)

Logic is the abstraction of content to reveal structure.

The Atomic Proposition

A proposition is a declarative statement that is either True or False.

"The cat is on the mat."

"π is an irrational number."

"Close the door!" (Command)

"Are you hungry?" (Question)

Syntax Rule #1

If it cannot be assigned a truth value, it is not a proposition in our system.

Symbolizing Content

P

The economy is growing.

Q

Inflation is decreasing.

Standard Practice

Use Capital Letters (P, Q, R, S) to represent atomic propositions.
Ensure the letter represents the entire positive statement.
Avoid negations in the atomic form (e.g., let P = "It is raining" not "It is not raining").

Workshop: Distillation

In your groups, take the provided abstract and highlight the core propositions. Ignore the "unfortunately," the "undeniably," and the "perhaps."

Step 1

Identify the verbs and subjects.

Step 2

Check for truth-functionality.

Step 3

Assign a unique letter to each distinct fact.

Syntax of Logic

Syntax of Logic Slides

Atomic Proposition Workshop

Syntax of Logic Teacher Guide