Accidental Sameness and its Logical Properties

I should thank Richard Hennessey for motivating me to address a topic I haven't until these last few days discussed in these pages, namely, that of accidental sameness.  Let us adopt for the time being a broadly Aristotelian ontology with its standard nomenclature of substance and accident, act and potency, form and matter, etc.  Within such a framework, how can we account for an accidental predication such as 'Socrates is seated'? 

In particular, what is expressed by 'is' in a sentence like this?  Hennessey seems to maintain that it expresses an identity which holds, if the sentence is true, between the referent of the subject term 'Socrates' and the referent of the predicate term  'seated.'  Here is what Hennessey says:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. Similarly, the referent of the subject term of “Plato is sitting” is the sitting Plato and that of its predicate term is one and the same sitting Plato. Here, once again, only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting. And, only if the referent of the “Plato” and that of the “sitting” of “Plato is sitting” are identical can it be true that Plato is actually the one sitting.

Hennessey is making two moves in this passage.  The first is the replacement of 'Socrates is seated' with 'Socrates is a seated being.' (I am using 'seated' instead of 'sitting' for idiosyncratic stylistic reasons;  the logic and ontology of the situation should not be affected.) I grant that the original sentence and its replacement are logically equivalent.  Hence I have no objection to the first move.

The second move is to construe the 'is' of the replacement sentence as expressing identity.  Together with this move goes Hennessey's  claim that ONLY in this way can the truth of the sentence be insured.  This claim is false for reasons given earlier, but this is not my present concern.  My concern at present is the second move by itself.  Can the 'is' of the replacement sentence be construed as expressing identity?

The answer to this is in the negative if by 'identity' is meant strict identity.  Strict identity, symbolized by '=,'  is an equivalence relation: it is reflexive, symmetrical, and transitive.  It is furthermore governed by the Indiscernibility of Identicals (If a = b, then everything true of a is true of b and vice versa) and the Necessity of Identity (If a = b, then necessarily a = b).  Now if the referent of 'Socrates' and the referent of 'seated' are strictly identical, then this is necessarily so, true in every possible world in which Socrates exists, in which case our sentence cannot be contingently true as it obviously is.  Socrates is seated only at some of the times at which he exists, not at all such times.  And at any time at which he is seated he is possibly such as not to be seated at that time.  (The modality in question is broadly logical.)

So if Hennessey wants to construe the 'is' as expressing a type of sameness, it cannot be that sameness which is strict identity.  An option which is clearly open to him as an Aristotelian is to construe the 'is' as expressing accidental sameness.  But what is that?

It is a dyadic relation that connects one substance and one accidental compound.  (Thus by definition it never connects two substances or two compounds.)  An accidental compound is a particular, not a universal.  It is a hylomorphic compound the matter of which is a substance and the form of which an accident inhering in that substance.  It is admittedly a somewhat 'kooky' object, to borrow an epithet from Gareth Mathews.  An example is seated-Socrates.  Socrates is a substance.  His seatedness is an accident inhering in him.  The two together form an accidental compound which can be denoted by 'seated-Socrates' or by 'Socrates + seatedness.'  Seated-Socrates is neither a substance nor an accident, but a transcategorial hybrid composed of one substance and one accident, but only if the accident inheres in the substance. (An accidental compund is therefore not a mereological sum of a substance and any old accident.)

The compound is not a substance because it cannot exist on its own, but it is parasitic upon its parent substance, in our example, Socrates. It is also not a substance because it is not subject to alterational change.  Change for an accidental compound is existential change, either coming into being or passing out of being.  When Socrates sits down, seated-Socrates comes into being, and when he stands up it passes out of being.  An accidental compound is not an accident because it is not related to its parent substance by inherence, but by accidental sameness.  A key difference is that inherence is an asymmetrical relation, while accidental sameness is symmetrical.

Hennessey can say the following: 'Socrates is seated' expresses the accidental sameness of Socrates with the accidental compound, seated-Socrates.  He needs to posit two objects, not one: a substance and an accidental compound.  If he holds that the referent of 'Socrates' and the referent of 'seated' are strictly identical, then the accidentality of the predication cannot be accommodated, and all predications become essential. That was my initial objection to Hennessey's view before I figured out a way to salvage it. 

What are the logical properties of the accidental sameness relation?  Like strict identity, it is symmetrical.  This should be obvious.  If Socrates is accidentally the same as seated-Socrates, then the latter is accidentally the same as the former.  The inherence relation, by contrast, is asymmetrical: if A inheres in S, then S does not inhere in A. This is one of the differences between the accidental sameness relation and the inherence relation. 

Accidental sameness is irreflexive.  This can be proven as follows:

1. No substance is an accidental compound.
2. If a is accidentally the same as b, then either a is a subtance and b a compound, or vice versa.
Therefore
3. No object, whether substance or compound, is accidentally the same as itself.

It can also be proven that accidental sameness is intransitive.  Thus, if a is accidentally the same as b, and b accidentally the same as c, it follows that a is not accidentally the same as c.  Suppose a is a substance.  Then b is a compound.  But if b is a compound, then c is a substance, with the result that a substance is accidentally the same as a substance, which violates the definition of accidental sameness.  On the other hand, if a is a compound, then b is a substance, which makes c a compound, with the result that a  compound is accidentally the same as a compound, which also violates the definition.  So accidental sameness is intransitive.

Clearly, there is accidental sameness only if there are accidental compounds.  But are there any of the latter?  Consider a fist.  A fist is not strictly identical to the hand whose fist it is. (They have different persistence conditions.) But a fist is not strictly different from the hand whose fist it is.  But surely there are fists, and surely what we have in a situation like this is not two individuals in the same place.  So it is reasonable to maintain that a fist is an accidental compound which is accidentally the same as the hand whose fist it is.

Still, there is something 'kooky' about accidental compounds.  So I'll end with a challenge to Hennessey, enemy of universals.  Why are accidental compounds less 'kooky' than universals, whether immanent or transcendent? 

Comments

[arash]

Bill,

what is the difference/correlation between the accidental sameness (e.g. between Socrates and seated-Socrates) and the material constitution (e.g. between the piece of marble and the statue) ?

[Bill Vallicella]

If one accepts that there is an accidental sameness relation, and therefore accepts that there are accidental compounds, then it is reasonable to maintain that material constitution is a type of accidental sameness.

Hunk of marble: parent substance
Being-formed to represent so-and-so, e.g., David: accident inhering in substance
Statue: accidental compound of hunk + being-formed to represent so-and-so

The statue is accidentally the same as the hunk of marble.

Thus we can avoid saying that hunk and statue are strictly identical -- which is clearly false given the difference in persistence conditions, that there is no statue which is van Inwagen's highly counterintutive nihilist view, and the counterintuitive view that, while the statue exists there are two distinct things in exactly the same place.