In a comment thread, I offered this definition of 'accident':
D1. A is an accident of substance S =df (i) A is a particular; (ii) A is dependent for its existence and identity on S; (iii) A is predicable of S.
A particular, by definition, is an unrepeatable item. So a substance and one of its accidents are both particulars. To mark the difference between, say, Socrates and his pallor, we can say that the substance is a concrete particular while the accident is an abstract particular. A universal, by definition, is a repeatable item.
David Brightly responds:
Bill, I'm worried about condition (iii). I'm not sure what it means for a particular to be predicable of a substance. I understand what it means for a universal U to be predicable of a substance s, viz, s might instantiate U. But since particulars are unrepeatable no substance can instantiate a particular. For me the notions of universality and instantiation are bound together like opposite poles of a diameter (but perhaps I'm wrong on this). So 'predicable' applied to particulars must mean something else. Does 'p is predicable of s' simply mean that s 'has' p or that p is 'in' s? If this is right another question arises. What work does (iii) do that isn't already built into (i) and (ii) together? Can you give an example where (i) and (ii) hold for particular p and substance s yet p is not an accident of s because p is not predicable of s?
When I say 'My coffee cup is blue,' I am predicating a property of my cup. We predicate properties using predicates. The predicate is a linguistic item, 'blue.' If I were speaking German the predicate would be different, 'blau.' But the property predicated would be the same. When I predicate in overt English speech, I produce a token of the word-type 'blue.' The property, however, is an extralinguistic item. I don't produce it. I am just assuming (though I could easily argue for it) that we cannot get by with predicates alone: we need properties. Properties, or at least some properties, do not depend on the existence of English or any language, not do they depend on the existence of minds.
D2. F-ness is a property =df F-ness is a predicable entity.
D3. Property F-ness is predicable of individual a =df a is F.
D4. The predicate 'F' is true of a =df a is F.
D5. The indicative sentence 'Fa' is true =df a is F.
Given that there are properties, the question arises whether they are universals or particulars. Note that there is nothing in the notion of a property defined as a predicable entity to require that properties be universals. The definition leaves open whether they are universals or particulars.
If blueness is a universal, and not a constituent of the cup, then we can say that the cup instantiates blueness.
D6. U is a nonconstituent universal =df U is possibly instantiated.
If blueness is a particular, and not a constituent of the cup, and is therefore an accident of the cup, then we can say that blueness inheres in the cup.
D7. A is an accident of substance S =df A inheres in S.
Note: not 'possibly inheres,' but 'inheres.' Let us refer to instantiation and inherences as 'ties.' Obviously, they are very different ties.
I think these definitions answer Brightly's first question. If properties are accidents,then properties are predicable without being instantiable.
The second question concerns the work that (iii) does in (D1). Could a particular be dependent on a substance without being predicable of it? I think so. A bulge in a carpet satisfies the first two conditions but not the third.
Admittedly, the sentence, 'The carpet is bulged' predicates bulgedness of the carpet. Bulgedness is a property of the carpet. Bulgedness, however, is not the same as the bulge in the carpet. Suppose the carpet has two bulges in it. Then we have one accident *bulgedness* but two bulges. The accident is a property of the carpet; the bulges are not. If Socrates is freckled, then he has many freckles. But his *freckledness* is one accident.