Linga haven't nothing with phallic symbol fourth part, short about symbol Kudu
I hope you can very easy accept next two facts.
Crucial is what intuition have for answer, not what write in books or say any authority (I prefer only direct knowledge, or only what permanent have in conciousness as outside part non omitted conciousness).
Today we have more then 95% wrong tradition rules, and this rules can't show us Our Source, only give control this people which spread this type rules.
Do you know real manning very old symbol kudu? I find only few times in India this older symbol writing on walls few homes.
This symbol is complete describing nature of God (this is one from oldest symbolic picture of Shivalinga). Two triangles present lower nature and higher nature, tangent (line) present Son and point (circle) present Father. God not Trinity, God is Trinity and God Will (Lower Mother - lower nature - static triangle). This is very old real meaning of Shiva Linga or God, oldest then any book and knowledge.
OOXOOOOOX - Higher Mother - Holly Spirit
OOOXOOOX - Parashakti
OOOOXOX - Sat-chit-ananda
OOOXOOOX - Lower Mother - Divine Will
OOXOOOOOX - Tamas-rajas-satva
OXOOOOOOOX - Proton-Electorn-Neutron
Father make Son through Higher Nature in Lower Nature. Through changes Lower nature in Higher Nature, and then through Higher Nature Son became Father.
Now we can see deepest reality: very mportant Great Parashakti is Goddess (many call She God) as inseparable His part!
I write about main meaning Shiva Linga, but today in books and dictionaries main meaning is complete wrong, of course Shivalinga is and universal form and people can accept as want. We have many old cults, old books which spread very partial knowledge, but truth is: through sex we can't do nothing, problem is resolve intention for sex.
One way is accepting and much deeper value in life, what India have much more then all countries together.
Bibliography is book: "Technique of Opening Third Eye" - second chapter. Author is one from few Parmapara Gurus 20 century last Master of Shivayoga (which name in Veda time is Old Yoga) H.H. Mahatapasvi Shri Kumaraswamiji (1909-1995) - Karnataka, Dharwad, Tapovana