One difficult and commonly-raised problem for the Platonic realism as well as the substance theory is the problem of specifying what the so-called inherence relation is between a substance and its properties. For example, what is the relation between the apple, considered as a substance, and its redness, considered as a Platonic universal? The substance theorist might say a property inheres in a substance. That is the word often used: "inheres." A property's inherence in a substance is a bit, but only a bit, like being part of the substance. But it is definitely different from just being a part. When we say, for example, that the apple is red, we are saying that redness inheres in the apple. But then what is inherence? Can any good sense be made of it? It seems that all one can say is that it is what we mean when we say the apple is red--which is to suggest a circular explanation.
The substance theorist may just say that the name of the relation is "inherence," and that inherence is a primitive concept. It cannot be explained any further, but it also does not need to be explained any further. We know what it means to say that the apple has the property of redness, or the property of being juicy. It does not matter that we cannot explain what this talk of a substance "having" properties, or a property "inhering in" a substance, amounts to in any other terms. We have to start somewhere--we cannot define everything, or if we try we will run out of words.
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