Formal Sciences
[ DOMAIN 02 ]

LOGIC

The architecture of truth. Logic strips away context, emotion, and bias, leaving only the immutable framework of valid reasoning.

Level 1: Binary States & Connectives

Before we can build complex mathematical proofs or computer algorithms, we must define the absolute basics: True and False. At this level, we only care about how simple statements combine together.

∧
AND
∨
OR
¬
NOT

The Truth Engine

Variables
2-BIT
# Binary Connectives

AND

∧
0∧0
=
0
State
FALSE

OR

∨
0∨0
=
0
State
FALSE

XOR

Exclusive
⊕
0⊕0
=
0
State
FALSE

NAND

Not AND
⊼
0⊼0
=
1
State
TRUE

IMPLIES

If P, then Q
⇒
0⇒0
=
1
State
TRUE

IFF

Biconditional
⇔
0⇔0
=
1
State
TRUE

Module: Propositional Logic

Deep dive into Boolean Algebra and Truth Tables.

Level 2: Quantifiers & Sets

Simple true/false statements aren't enough to describe the universe. "All dogs are mammals" requires a new syntax. Here, we introduce Quantifiers and begin grouping objects into overlapping Sets.

Set & Quantifier Visualizer

Module_02 // Interactive
The Universe (U)
Set A
(Circles)
Set B
(Filled)

The Universe

Welcome to a logical universe consisting of 12 objects. To make logical statements, we group objects with similar properties into Sets.

Set AContains all objects that are Circles.
Set BContains all objects that are Filled.
Notice how a single counter-example breaks a Universal (∀) statement. If you say "∀ objects in Set B are Filled", the engine immediately flags the empty circles as the reason the statement is FALSE.

First-Order Logic

Predicates and mathematical syntax.

Set Theory

The infinite and mathematical paradoxes.

Level 3: Informal Logic

Mathematical logic is perfect. Humans are not. When we attempt to apply logical structures to everyday language and debate, we frequently make structural errors known as Logical Fallacies.

Module: Cognitive Biases & Fallacies

Ad Hominem, Straw Man, and broken arguments.

[ Q.E.D. VERIFICATION ]
Proof of Comprehension1 / 5

True or False: If proposition P is False, the implication (P ⇒ Q) is ALWAYS considered True, regardless of the truth value of Q.