By Swami Harshananda
Aliñga literally means ‘without sign’.
The Sāṅkhya system of philosophy posits two fundamental realities as follows :
Aliñga is one of the synonyms of this prakṛti. Etymologically the word ‘liṅga’ signifies a characteristic mark or an object that dissolves back in its cause. ‘Aliñga’ therefore is that which is the opposite of ‘liṅga’. Prakṛti or primordial nature with its three constituent guṇas in a state of perfect equilibrium is so subtle, that there is absolutely no manifest sign by which it can be perceived. It can only be inferred. Hence it is called ‘avyakta’ (the unmanifest) and ‘aliñga’ (without characteristic signs).
Being the original cause and the substratum of dissolution of all its products, it has no dissolution itself. Even in this sense it is ‘aliñga.’ The word is used in some of the Upaniṣads  to indicate Ātman or Brahman since the latter has no lingas or signs by which it can be perceived. It cannot be perceived by the senses or even the mind.
- The Concise Encyclopedia of Hinduism, Swami Harshananda, Ram Krishna Math, Bangalore