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Hinduism acknowledges the significance of logic, known as "Tarka" in ancient texts, within the framework of Sanatana Dharma. The scriptures of Hinduism contain dedicated sections discussing the subject of logic. Our Hinduism Stack Exchange has seen several questions 1, 2, 3, 4, 5 exploring these scriptures.

Among the various forms of "pramana," or valid means of knowledge, "Anumana pramana" relies on logic. However, Sanatana Dharma also recognizes the limitations inherent in logic. Two instances come to mind where the Scriptures explicitly acknowledge these limitations.

#1: In yaksha prasna, Yudhishthira explicitly states:

The Yaksha asked,--'...What is the path?...'

Yudhishthira answered,--'O amphibious creature, ... (tarko 'pratiṣṭhaḥ) Argument leads to no certain conclusion, ...'

#2: A story from the Tripura Rahasyam illustrates the incompleteness of logic:

After hearing him, Hemalekha replied: "Listen, Prince, to what I am going to say now. "I answer your point. How is one to be judged, whether one is good or bad? Is it by reference to accepted standards? What is the authority behind such standards? Are the authors themselves worthy or unworthy? In this way, there will be no end to argument. Moreover, the observer's competence must be taken into account. (Thus, too, there will be no finality reached.) Therefore life moves by faith only. I shall tell you the rationale of reaching the Supreme Goal by means of faith. Be attentive. People will not gain anything, either during their life-time or after death, by endless discussions or blind acceptance. Of the two, however, there is hope for the latter and there is none for the former."

You can read the whole story from CHAPTER VI ON THE MERITS OF FAITH FOR GAINING THE GOAL AND ON THE HARMFULNESS OF DRY POLEMICS, Jnana Kanda of Tripura rahmasyam.

I am seeking references from the Vedas that explicitly address the limitations of logic, whether in concise statements like quote #1 or in explicit stories like quote #2.

Is there any reference from the Vedas that explicitly supports the limitations of logic?

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    idk about vedas, but brahma sutras and vedanta clearly talk about 3 - pratyaksa (perception), anumana (inference) and shabda (testimony). pratyaksha can be flawed (mistaking rope for snake in a dark room). anumana can be flawed because it is dependent on past pratyaksha (i saw a "snake" in this room, so i infer that snakes can enter this room). shabda can be flawed if the person giving testimony is wrong or liar. But here Shabda means Vedas. So far they have never been wrong. Therefore, we trust Vedas and not eyes or logic.
    – ram
    Aug 2, 2022 at 21:08

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