Quick preface, Stirner was arguing against the seemingly religious and secular modes of thought of his time. This is when Hegelianism was hot-hot-hot, and thought was very lofty and unconcerned with the material.
So, the bedrock of Stirner's thought can be pretty simply summed up as 'people act in their self interest'.
As such, there are two modes of life, in which we are either consciously of this, or act on it unconsciously.
While people may argue that in moments of altruism or sacrifice, we are not acting in our own self interest, Stirner counters that we are taking the moralistic/ethical course of action which we hold to be good, right, or true.
Further, Stirner argues that above beliefs of sacrifice, altruism and other moralistic goods are fixed ideas, or in meme parlance, "Spooks".
A "Spook" is at best an assumption about reality reinforced by cultural, religious or philosophical thought (i.e. Familial honor, Christian repentance, the categorical imperative, Rand saying homosexuality is bad and so on).
While we may be able to find compelling rationalizations to think such things, Stirner claims that if we were to look closer, in reality, these thoughts are merely products of our own mind.
Stirner held that truths are material, and thus,
The Individual is above concept.
As such, another large proponent of Stirner's thought is revealed.
"I do not step shyly back from your property, but look upon it always as my property, in which I respect nothing. Pray do the like with what you call my property!"
He also critiques rights and property, rejecting the powers of authority, whether State, Divine, or other Individuals.
At this point, some people may come to understand him.
When considered, it seems that he has done away with a great deal of philosophic thought, and has left nothing but an Ockham's Razor of reality. Few assumptions are made beyond the material.
Sometimes called an end of philosophy, it is rather a new beginning.
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