Bayes’ Theorem
Bayes' theorem is a fundamental concept in probability theory. It provides a mathematical way to update the probability of a hypothesis when new evidence is introduced, forming the basis of…
Basis Step in Mathematical Induction
The basis step, or base case, is the foundational element of a proof by mathematical induction. It establishes the truth of a statement for the smallest value in the set,…
Frege’s Basic Law V and the Foundations of Arithmetic
Frege's Basic Law V aimed to ground arithmetic in logic. It states that the extension of a concept is defined by the objects it collects, a principle that ultimately led…
Barcan Formula
The Barcan formula in modal logic states that if something exists, then it necessarily exists. It explores the relationship between existential quantification and necessity, allowing for interchangeability under certain conditions.
Barbara Syllogism
Barbara (AAA) is a standard Aristotelian syllogism with three universal affirmative propositions. It follows the structure: All M are P, All S are M, therefore All S are P.
Bad Company Objection
The bad company objection challenges mathematical abstractionism by highlighting the difficulty in separating valid from invalid abstractions, especially concerning Frege's Basic Law V and its resulting paradoxes.
Understanding Axioms: Foundational Truths in Logic and Mathematics
An axiom is a fundamental statement accepted as true without proof. It serves as the bedrock for logical reasoning and the construction of theories in fields like mathematics and philosophy.
Axiological Logic: Understanding Value in Logic
Axiological logic is a specialized branch of logic focused on the study of value, encompassing ethical and aesthetic judgments. It often integrates concepts from modal logic to analyze value-laden propositions.
Automorphism: Understanding Mathematical Symmetries
An automorphism is an isomorphism from a mathematical object to itself, preserving its structure. It represents internal symmetries within logical and algebraic systems, crucial for understanding object properties.
Automaton: Understanding Self-Operating Machines and Computational Models
An automaton is a self-operating machine or a theoretical computational model. It follows predefined rules to perform tasks, forming the basis of many computer science concepts and real-world automation.