One of the names of Mahādeva Śiva (Mahadeva Shiva). In the Śiva Sahasranāma Stotra (Shiva Sahasranama Stotra; the hymn praising the thousand names of Shiva), the word acintya (achintya) is mentioned twice as one of the names of Mahādeva. The word acintya refers to the one who cannot be validated, proved or established through logic, reason or idea. Scholars opine that whatever is not limited by logic is acintya, whatever is beyond nature is acintya

acintyāḥ khalu ye bhāvā na tāñgstarkena sādhayet
prakṛtibhyaḥ paraṁ yattu tadacintyasya lakṣanam.

In Upaniṣada (Upanishada), while alluding to the characteristics of Brahma, it is said that the Supreme Being, who is inherent in all living beings as the essence of life, is smaller than the smallest atom, i.e., the particle, and at the same time vaster and more expansive than the sky—

aṇoraṇīyān mahato mahīyān
ātmāsya jantornihito guhāyām.

Therefore, he cannot be expressed through words. He cannot be sensed or felt through eyes, ears, and other sense organs, and he cannot be confined within one’s thoughts—

yanmanasā na manute yenāhurmano matam
tadeb brahma tvaṁ viddhi nedaṁ yadidamupāsate.

Based on this concept Brahma is referred to as acintya, or beyond thought. Mahādeva is addressed as acintya because he is perceived as being one with the Acintya Brahma—

acintyaḥ cintyādupāsyādanyaḥ pratyagātmāvān tadeva
brahma tvaṁ viddhi nedaṁ yadidamupāsate iti śruteśca.

Whatever is beyond the perceptible universe is referred to as acintya. The form of acintya can only be defined through discourse.