When it comes to religious matters, the scriptures are of utmost importance, but in terms of the Shiva lingam, many different stories point to different meanings. Therefore, to conclude we need to consider the authoritativeness of the scriptures.
1. Cosmic Pillar of Fire: In Hinduism, Vedas have the highest authority but unfortunately, there is nothing mentioned about Shiva lingam in it. Lord Shiva, as we know him today, shares many features with the Vedic god, Rudra. The word Shiva appears in the Rigveda and Yajurveda as an adjective for Rudra as well as other gods.
“With firm limbs, multiform, the strong, the tawny adorns himself with bright gold decorations: The strength of Godhead never departs from Rudra, him who is Sovereign of this world, the mighty.”
5. In the Taittiriya Aranyaka of Yajur Veda (10.24.1), Rudra is called the Purusha (universal consciousness) and the soul of creatures.
All these verses explain why Rudra aka Lord Shiva is associated with the cosmic pillar. My point is if a story has some reference to the Vedas, then it should be considered authoritative than others.
1. The story of the cosmic pillar has a base in the hymn dedicated to the Yupa-Stambha and the Vishwakarma Suktam, and Lord Shiva is mentioned as the sovereign god in the Vedas.
2. The second point is the authoritativeness of the Linga Purana over the other Puranas in terms of the Shiva lingam.
Let us consider a hypothetical scenario. Assume that there is a case in the court that you are a judge of, and you have a doubt related to the heart condition of a victim. You have two doctors before you who have different opinions. One of those doctors is a cardiologist, and another is a neurologist. Then, whose opinion would you consider the most authoritative? I think the answer should be the cardiologist because he is a heart specialist.
The same thing applies to the Linga Purana. The Linga Purana is a dedicated book to the Shiva lingam, and it contains more information about it than other books. Therefore, in this case, we should treat the Linga Purana more authoritative than the other Puranas.
The Linga Purana clearly says that it is a cosmic pillar, and the base is the pedestal that supports it.
3. We have also seen that Lord Shiva himself has stated in the Shiva Purana that it is his formless aspect and is the column of fire.
4. It is mentioned in the Skanda Purana that the whole universe has originated from it and merges into it at the end (1.7.2).
5. The Shiva lingam is also called a Jyotirlinga. The meaning of the word Jyotirlinga also points to it being a pillar of fire.
6. Also, a soul is symbolized as a flame of a lamp that resembles a lingam. Therefore, the supreme soul is symbolized as a pillar of light.
7. Even if we assume that all the Puranas are equally authoritative and take the literal meaning of the stories in them, we can see that the story of Lingodbhava happened before other stories.
8. This assumption also explains the shape of the Banalinga and swayambhu lingams.
Therefore, calling the Shiva lingam the column of fire is a very strong argument.
2. Purusha and Prakriti: We have seen that in some verses in the Vedas, Rudra is called Purusha. In the Katha Upanishad, it is mentioned that Purusha is the size of a thumb, and the thumb looks like a lingam. Many swayambhu lingams also look like a thumb. Therefore, it is quite possible that the lingam is a symbolic representation of Purusha.
According to Brihadaranyaka Upanishad, Purusha is like a grain of rice or barley. It could be the reason behind the worship of the Banalinga.
It is possible that later on, as the meaning of the words Purusha and linga changed to “male” and “sexual organ” respectively, some people might have started looking at it as the sexual organ of Lord Shiva, but the people who knew the correct meaning continued to think otherwise. Therefore, there are two streams of thoughts about the meaning of the Shiva lingam.
Prakriti is a Vedic era concept, which means "making or placing before or at first, the original or natural form or condition of anything, original or primary substance. It means "nature, body, matter, phenomenal universe" in Hindu texts.
The Samkhya School of philosophy associated the concept of Purusha with the masculine principle and Prakriti with the feminine principle.
The Puranas further declare that Lord Shiva and Goddess Parvati (Uma) are Purusha and Prakriti respectively.
In the Vishnu Purana, it is said that Lord Vishnu and Goddess Lakshmi are Purusha and Prakriti respectively. Like Ardhanarishwara form of Lord Shiva, Vaikuntha-Kamalaja is a composite form of Lord Vishnu and Goddess Lakshmi, but she is not associated with Shaligram in the way Goddess Parvati is with the Shiva lingam.
The reason behind this could be that Hindus do not pour the liquid over Lord Vishnu as they do over Lord Shiva. Hence, there was no need to add a pedestal. It implies that originally the Shiva lingam was associated with Lord Shiva only and for cleanliness purposes its shape was changed to the contemporary one.
The Star of David and the Christian cross also imply the masculine and feminine principles.
Therefore, the Shiva lingam as Purusha and Prakriti is also a very strong argument.
3. Hiranyagarbha: As discussed previously, this assumption is also very appropriate and answers most of the questions.
So we have three things based on the scriptures that could be the Shiva lingam, viz. cosmic pillar of fire, Purusha and Prakriti, and Hiranyagarbha.