Step 1: Understanding Uttara Mimamsa.
Uttara Mimamsa, also known as Vedanta, is the latter part of the Mimamsa philosophical system. It is termed "Uttara" (later) as it concentrates on interpreting the Upanishads, which follow the Vedic rituals (Karma-Kanda). Vedanta prioritizes knowledge (Jnana) over ritualistic actions and investigates the nature of the self and the ultimate reality, Brahman.
Step 2: Analyzing the Options.
- 1. Vedanta System: Correct. Vedanta is synonymous with Uttara Mimamsa, focusing on the Upanishadic philosophical teachings. - 2. Carvaka System: Incorrect. Carvaka is a materialistic philosophy that rejects Vedic and Vedanta authority. - 3. Nyaya System: Incorrect. Nyaya centers on logic and reasoning, with no direct relation to Vedanta philosophy. - 4. Jaina System: Incorrect. Jainism is an independent philosophical system and is not part of Mimamsa or Vedanta.
Step 3: Conclusion. The correct identification is 1. Vedanta System.
Final Answer: \[ \boxed{\text{The correct answer is 1. Vedanta System.}} \]