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Wednesday, February 06, 2013


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Peter possesses his colouredness essentially. Hence colouredness is an ontological part (OP) of Peter. If Peter is an OP of the property exemplification (PE) entity Peter's whiteness, and as seems reasonable, ontological parthood is transitive, then colouredness is an OP of Peter's whiteness. The latter thus has two universals as constituent, whiteness and colouredness. How to choose between them? If we treat them symmetrically then the PE entity Peter's whiteness looks to be identical to the PE entity Peter's colouredness. But this makes Peter's colouredness an accident. Contradiction?

Thanks, David. I appreciate your challenging comments.

>>Peter possesses his colouredness essentially. Hence colouredness is an ontological part (OP) of Peter.<<

Can't one reasonably resist this inference? Necessarily, Peter is some color or other. But it doesn't follow that being colored is an OP of Peter. It could be maintained that being blue is or being red is, but not the determinable of which these are determinates. The consituent ontologist is not required to say that every property of a concrete object is an ontological constituent of it.

Is ordinary parthood transitive? If it isn't, then ontological parthood probably isn't either.

The pages of a book are proper parts of a book, and books are proper parts of libraries. But pages are not proper parts of libraries.

A platoon is part of a company and a company is part of a battalion, but a platoon is not part of a battalion.

Poindexter's beard is part of Poindexter, and Pondexter is part of the philosophy department, but Pondexter's beard is not part of the philosophy depratment.

Thank you Bill. I agree that these interpretations are debatable. A colour scientist might say that there is a real distinction between (of visible light) uniformly strongly transmitting (transparent), uniformly strongly absorbing (black), uniformly strongly reflecting (white), and varyingly (with wavelength) strongly reflecting (coloured). Distinct colours correspond to distinct variations. He might also say that the determinable/determinate distinction was not absolute. Navy is a determinate of the determinable blue, blue is a determinate of the determinable coloured.

I accept that the consituent ontologist is not required to say that every property of a concrete object is an ontological constituent of it. He says that accidental properties are indeed otherwise. My understanding is that ontological constituency is his device for explaining necessary properties. If he accepts that colouredness (understood to include black, white, and transparency) is a necessary property, is he not then obliged to use his device to account for it, on pain of admitting modes of necessity?

In 'x is part of y' the sense of 'part' seems modulated by the substance/collective character of the terms 'x' and 'y'. In the book and Poindexter examples 'part' is not univocal, I think. In the military example we can understand 'a platoon' as denoting the concept 'platoon', etc, and 'part' meaning 'primary subdivision of', a relation between concepts. 'Primary' rules out transitivity. But understanding these terms extensionally as denoting sets of men, and parthood as the subset relation, then surely if Lieutenant L's platoon is part of Major M's company, and Major M's company is part of Colonel C's battalion, then Lieutenant L's platoon is part of Colonel C's battalion? So there is opportunity for debate here too. But is it not reasonable simply to demand of the constituent ontologist whether his ontological parthood relation is transitive?

Dear Bill,

of course I agree that

(T) there is no accident of Peter's color over and above Peter's whiteness.

But it seems to me that this is inconsistent with your theory. Assume T and your theory, and various antinomies will follow. In order to avoid being distracted by the special problem whether and how "colouredness" is essential to Peter, let me choose another pair of subordinate properties: "courage" and "virtue". It is contingent not just that Peter is courageous, but also that Peter is virtuous; but if Peter has courage, he has a virtue.

Now see: if Peter is virtuous, then Peter exemplifies virtue, therefore there is the (temporally indexed) nexus of exemplification [NE] between Peter and virtue. Or could you be forced to take the position that Peter can exemplify virtue without there being a NE between him and virtue? If not, then there is the complex [Peter+virtue+NE+TI]. If the complex [Peter+courage+NE+TI] is called "Peter's courage", then the former must be called "Peter's virtue", by parity of reason. But then Peter's courage is not Peter's virtue, whereas in reality Peter's courage is Peter's virtue (perhaps the only Peter's virtue). Besides, on the principle that any instance of a genus is an instance of some of its species it holds that any instance of virtue must be an instance either of courage, or of temperance, or of prudence, etc. But Peter's virtue construed as above is an instance of virtue without being an instance of any of the species of virtue. This is a contradiction.

Perhaps you will say that Peter exemplifies virtue by the very same NE by which he exemplifies courage. But this does not help, for there still is the complex [Peter+virtue+NE+TI], only it shares its NE with Peter's courage, and it still demands to be called "Peter's virtue". In order to escape the conclusion, you would have to deny that there is any NE between Peter and virtue at all - but then it seems plain contradiction to say that Peter still exemplifies virtue.

Where have I gone wrong?

Hi Lukas,

I apologize for being such a quibbler, but if Peter is courageous, it doesn't follow that Peter is virtuous, although it does follow that he has a virtue. For Peter might be a terrorist.

So let's talk about the property of having a virtue. I grant the following. (i) If Peter is courageous, then he has a virtue. (ii) If Peter has a virtue, it does not follow that he is courageous. (iii) It is not essential to any person that he have a virtue, or any particular virtue such as courage.

We are assuming that being courageous is an accident of Peter as substance. In your excellent article you speak of Aristotleian accidents, accidental forms, tropes, and modes.

My question concerns the exact nature of accidents. Do they have any inernal structure or not? My main point is that the cannot be simple. I won't repeat the arguments I gave. But I am not committed to any particular theory of their complexity.

As for your objection, why can't I say what I said earlier? In reality, there is, corresponding to the true sentence 'Peter is courageous,' the accident *courageousness.* But there is no accident in reality corresponding to the predicate in the true sentence 'Peter has a virtue.'


my objection is aimed at the particular theory you proposed earlier. It seems to me that you cannot say, consistently with that theory, that there is no accident in reality corresponding to the predicate "(has) viertue" because if "Peter has a virtue" is true, then there is Peter, virtue, and the (temporally indexed) NE between them - which jointly amounts to an accidetn Peter's virtue, in your theory.

Bill, I'm rather confused about the distinction between accidents of a substance and what we might call its inessential properties. Consider a knife. A knife has bladedness in that part of it is in the shape of a blade and this bladedness, which resides in the shape of the knife, would appear to be dependent on the knife and thus accidental. Ontologically the knife's bladedness is a PE entity with the knife and the universal bladedness as constituents. On the other hand, bladedness would appear to be an essential property of a knife. Ontologically the knife is then a particular with the universal bladedness as a constituent. These two views are in some tension. Can it be relaxed?


One issue is whether a property can exist without being had by anything. Consider first-level properties, properties of individuals, to keep it simple. View 1: Necessarily, first-level properties exist only if had by individuals. It is impossible that there be such a property had by no individual. View 2: Possibly, some properties exist that are not had by any individuals.

If to have a property is to exemplify a property, then the difference is between saying that unexemplified properties are impossible and that unexemplified properties are possible.

But this difference is not the same as the difference between essential and accidental properties. An essential property of x is a property x cannot exist without, while an accidental property of x is one x can exist without.

Now the bladedness of a knife is essential to it. This is logically consistent with the bladedness existing only if the knife exists. Suppose there is only one knife K and that properties cannot exist unless exemplified. Then the following are consistent:
1. K is essentially bladed
2. Had K not existed, bladedness would not have existed.

So you may be confusing the two issues I distinguished. If a property P is dependent for its existence on an individual x, it does not follow that P is an accidental property of x.


We must also distinguish between an accidental property and an accident. Every accident is an accidental property of the substance of which it is the accident, but an accidental property of a thing needn't be an accident of it. Accidents are particulars, but properties could be construed as universals.

Thanks, Bill. Having the definitions close together helps. But I must be missing something as I'm continuing to find apparent anomalies.

>> An essential property of x is a property x cannot exist without, while an accidental property of x is one x can exist without.

1. So the properties of the knife K are partitioned into two exclusive sets, its essential properties and its accidental properties.

>> Now the bladedness of a knife is essential to it.

2. So bladedness is an essential property of K.

But (my hypothesis) the bladedness of K cannot exist independently of K.

3. So the bladedness of K is an accident of K.

>> Every accident is an accidental property of the substance of which it is the accident.

4. So the bladedness of K is an accidental property of K.

But (2) and (4) are in tension. If we identify bladedness with the bladedness of K we are in direct contradiction with (1). Conversely, if we do not make this identification, perhaps we say bladedness is universal and the bladedness of K is particular, then we have entities from distinct metaphysical realms vying to be properties of K. This suggests that 'property' is not univocal.


I'm not sure you got the point of the distinction I made.

Your (1) is correct, and (2) follows from it. But (3) does not follow.

Suppose bladedness is a universal. Then it cannot be an accident since every accident is a particular. This is so even if universals cannot exist without being exemplified. What you seem not to appreciate is that the exemplification of a universal does not make of that universal a particular or an accident.

There is also an important difference in the nature of the connection between a universal and a particular and an accident and a substance. Even if universals cannot exist unexemplified, there is no necessity that U be exemplified by k; the necessity is merely that U be exemplified by some concrete particular or other. An accident A, however, is necessarily such that it inheres in the very substance of which it is an accident.

Thank you for your patience, Bill. I am having trouble finding solid ground under this. One last question perhaps. We have a necessary condition for a particular to be an accident of a substance: it must be incapable of existing independently of the substance. Is there a sufficient condition?

Well, let me see if I can define 'accident' in terms of 'particular.' A definition specifies necessary and sufficent conditions.

A is an accident of a substance S =df (i) A is a particular; (ii) A is an item whose identity and existence are dependent on the identity and existence of S; (iii) A is predicable of S.

I think that does the trick. The RHS specifies three necessary conditions which are jointly sufficient for an item to be an accident.

Or can you spot a counterexample?

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