Which of the following philosophies does not believe in the material world?

The correct option is Idealism.

To understand why this is the correct answer, let's break down the core principles of the philosophical positions mentioned in the options:
1. Idealism: This philosophy asserts that reality is fundamentally mental, spiritually constituted, or immaterial. According to idealists, the material world either does not exist independently of the mind, or is subordinate to consciousness and ideas. Therefore, it does not believe in an objective, independent material world.
2. Rationality/Logic: This is a methodological framework rather than a metaphysical belief about the existence of the material world. It focuses on reasoning, validity, and truth-seeking methods.
3. Pragmatism: This philosophy holds that the truth or value of an idea lies in its practical consequences and utility. Pragmatists generally accept the existence of the material world as a practical reality within which human actions take place.
4. Conservatism: This is primarily a political and social philosophy that favors traditional values and institutions. It is not a metaphysical theory concerning the nature of material reality.

Consequently, Idealism is the only philosophy among the choices that rejects the fundamental reality or independent existence of the material world, making it the correct answer.