Step 1: Understanding the Concept of Creation.
Visistadvaita Vedanta, a philosophy developed by Ramanuja, asserts that Brahman, the ultimate reality, is personal and that the world originates as an extension of Brahman. This system views the world as real, not illusory, and creation as God's manifestation of the diverse world from within Himself.
Step 2: Analyzing the Options.
- 1. Carvaka: A materialist philosophy denying God and asserting the world is based on physical elements. - 2. Samkhya: A dualistic philosophy that rejects a creator God, positing instead the interaction of Purusha (consciousness) and Prakriti (matter). - 3. Visistadvaita: Correct. In Visistadvaita, God (Brahman) is considered both the material and efficient cause of creation. - 4. Advaita: Advaita Vedanta, by Adi Shankaracharya, teaches that the ultimate reality is non-dual (Brahman is everything) but does not describe the world as originating from God.
Step 3: Conclusion. The correct answer is 3. Visistadvaita.
Final Answer: \[ \boxed{\text{The correct answer is 3. Visistadvaita.}} \]