As the title indicates, this thesis is a critical exposition of Armstrong's theory of universals. But at a deeper level it is also an argument against one of the main tenets of traditional realism since Plato: the claim that the nature of physical properties, and objects in general, are ontologically independent of any mind or belief system. Armstrong's attempt to argue for a non-relational immanent realism epitomizes this claim. Armstrong's main argument for his position is an indirect one. He argues for the untenability of all theories opposing his and then attempts to show how his theory does not suffer from the same problems. Against theories opposing his (all forms of nominalism and transcendent Platonic realism) he puts forth four arguments: (1) the relation-regress, (2) the object regress, (3) the thought experiment, and (4) causality. These are all various attempts to show that nothing external to an object is relevant to the nature of the object. Against (1) and (2) I argue that the regresses are not infinite and that even if they were they would not be vicious. Concerning (3) and (4) I argue that Armstrong sets up a straw man and that therefore these two arguments are just irrelevant to his general claim. The conclusion then is that he has not given us any reason not to believe that there is no mind-dependent element in ontology. The site having thus been cleared, I then give positive reasons for believing that there are mind-dependent components in ontology. These reasons come mainly in the form of examples for which Armstrong's theory cannot account. My primary examples are artifacts. There seems to be a certain mind-dependent element in the nature of artifacts even though they are external to us. My argument then basically is a challenge to Armstrong's theory and to any realistic theory that holds the claim in the first paragraph above: give an account of artifacts without invoking mind-dependent elements. My claim is that these elements are universals, so they are abstract and multiply exemplifiable, but they depend upon us and they are neither immutable nor external.