Table of Contents

  • TOK and Areas of Knowledge (AOKs)
  • What is Mathematics? Definitions and Perspectives

1. TOK and Areas of Knowledge (AOKs)

This section explores the topic in detail. It covers key TOK concepts and connects them to real-life situations relevant to mathematics. It addresses the nature, scope, and limitations of mathematical knowledge.

2. What is Mathematics? Definitions and Perspectives

In its simplest form, knowledge is often defined as “justified true belief,” which means that for someone to “know” something, they must believe it to be true, have good reasons for that belief, and the belief must indeed be true. However, as we will explore, this classical definition has been criticized, especially by the philosopher Edmund Gettier, who demonstrated that it is not always sufficient. As such, knowledge is a complex and multifaceted concept that extends beyond simple definitions.

Types of Knowledge

This paper aims to answer the question: What is knowledge? By examining various definitions, theories, and critiques of knowledge, we will explore how knowledge is acquired, its limitations, and its ethical implications. We will look at knowledge through the lens of different philosophical traditions, from empiricism to rationalism to constructivism, and consider how language and power play roles in shaping knowledge.

2. Classical Definitions of Knowledge

Justified True Belief (JTB)

The classical definition of knowledge, “justified true belief,” holds that for a person to know something, three conditions must be met:
1. Belief: The individual must believe the proposition to be true.
2. Truth: The proposition must be true.
3. Justification: There must be sufficient evidence or justification for the belief.
This definition was widely accepted for centuries, but it faces significant challenges. The most famous critique came from Edmund Gettier in 1963, who showed that it is possible for someone to have a justified true belief without actually having knowledge. This led philosophers to reconsider the classical definition and seek a more robust understanding of knowledge.

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