Logic

Indefinite Extensibility

Indefinite extensibility describes collections, like the set of all sets, that cannot be fully listed. Any enumeration attempt can always…

5 days ago

Indefinite Descriptions

An indefinite description refers to any member of a class, not a specific individual. It's used when the identity of…

5 days ago

Inconsistent Arithmetic: When Logic Fails

Inconsistent arithmetic refers to a mathematical system where contradictions can be proven, violating the fundamental principle of consistency. This makes…

5 days ago

Gödel’s Incompleteness Theorems

Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that any consistent system powerful enough for arithmetic will…

5 days ago

Incompleteness in Logic and Mathematics

The property of a logical or mathematical system where not all true statements can be proven within the system's own…

5 days ago

Inclusive OR: Understanding Logical Disjunction

The inclusive OR, a fundamental logical operation, evaluates to true if at least one of its operands is true. It's…

5 days ago

Inclusive First-Order Logic Explained

Inclusive first-order logic is a flexible variant that permits empty domains, unlike standard first-order logic which mandates at least one…

5 days ago

Inclusive Disjunction (Logical OR)

Inclusive disjunction, also known as logical OR, is a fundamental operation in logic and computer science. It yields true if…

5 days ago

Impredicative Definitions in Mathematics and Logic

An impredicative definition defines an object in terms of a totality to which the object itself belongs. This can lead…

5 days ago

Impossible World in Modal Logic

A hypothetical construct in modal logic, the impossible world represents a state of affairs that cannot possibly exist. It's a…

5 days ago