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The Empty Concept Principle Is False
The empty concept principle is itself false. The mere existence of any concept C does not entail the existence of what C is about. David Hume articulates this when he says that whatever we can conceive as existing, can you conceive that God exists? Well, then you can conceive that God does not exist. Some people think that things have an abstract nature and these things exist; there are arguments of necessity for those claims. So it's a matter of debate whether or not all human beings even if they stopped thinking about 2 plus 4 equaling 4 would still equal 4.