Concerning tropes, Peter van Inwagen says, "I don't understand what people can be talking about when they talk about those alleged items." (*Existence: Essays in Ontology*, Cambridge UP, 2014, p. 211.) He continues on the same page:

Consider two tennis balls that are perfect duplicates of each other. Among their other features, each is 6.7 centimeters in diameter, and the color of each is a certain rather distressing greenish yellow called "optical yellow." Apparently, some people understand what it means to say that each of the balls has its own color -- albeit the color of one is a perfect duplicate of the color of the other. I wonder whether anyone would understand me if I said that each ball had its own diameter -- albeit the diameter of one was a perfect duplicate of the diameter of the other. I doubt it. But one statement makes about as much sense to me as the other -- for just as the diameter of one of the balls

isthe diameter of the other (6.7 centimeters), the color of one of the ballsisthe color of the other (optical yellow).

Although van Inwagen couches the argument in terms of what does and does not make sense *to him*, the argument is of little interest if he is offering a merely autobiographical comment about the limits of his ability to understand. And it does seem that he intends more when he says that he doubts whether* anyone* would understand the claim that each ball has its own diameter. So I'll take the argument to be an argument for the *objective* meaninglessness of trope talk, not just the PvI-meaninglessness of such talk:

1. It is meaningful to state that each ball has its own color if and only if it is meaningful to state that each ball has its own diameter.

2. It is not meaningful to state that each ball has its own diameter.

Therefore

3. It is not meaningful to state that each ball has its own color.

Therefore

4. Talk of tropes is meaningless.

The argument is valid, and (1) is true. But I don't see why we should accept (2). So I say the argument is unsound.

I am not defending the truth of trope theory, only its meaningfulness. I am maintaining that trope theory is a meaningful ontological proposal and that van Inwagen is wrong to think otherwise.

It is given that the two tennis balls have the same diameter. But all that means is that the diameter of ball A and the diameter of ball B have the same measurement, 6.7 cm. This fact is consistent with there being two numerically distinct particular diameters, the diameter of A and the diameter of B.

What's more, the diameters have to be numerically distinct. If I didn't know that the two balls were of the same diameter, I could measure them to find out. Now what would I be measuring? Not each ball, but each ball's diameter. And indeed each ball's *own* diameter, not some common diameter. I would measure the diameter of A, and then the diameter of B. If each turns out to be 6.7 cm in length, then we could say that they have the 'same diameter' where this phrase means that A's diameter has the same length as B's diameter. But again, this is consistent with the diameters' being numerically distinct.

There are two diameters of the same length just as there are two colored expanses of the same color: two yellownesses of the same shade of yellow. So I suggest we run van Inwagen's argument in reverse. Just as it is meaningful to maintain that the yellowness of A is numerically distinct from the yellowness of B, it is meaningful to maintain that the diameter of A is numerically distinct from the diameter of B. Looking at the two balls we see two yellownesses, one here, the other there. Similarly, measuring the balls' diameter, we measure two diameters, one here, the other there.

Again, this does not show that trope theory is true, but only that it makes sense. It makes as much sense as van Inwagen's proposal according to which optical yellow is an abstract property exemplified by the two balls.

I agree with you, Bill. Trope theory is a meaningful ontological proposal. I have great appreciation for PvI's work, but his alleged inability to understand certain claims seems a bit over the top sometimes. This seems like one of those times. I find it hard to imagine that he hasn't thought of things that you say in response to him, so I wonder why he still is so skeptical of trope theory's meaningfulness.

I'll add the following. Judging from the excerpt that you have included, PvI thinks it is self-evident, or nearly so, that the two tennis balls do not have their own diameter. And, as evidence for this alleged fact, he asserts, "...for just as the diameter of one of the balls IS the diameter of the other (6.7 centimeters), the color of the one ball IS the color of the other." If this is supposed to be an argument for the conclusion that tennis balls do not have their OWN diameters, it is bad. Trope theorists accept that the diameter of the ball IS the diameter of the other, but they would quibble with PvI on the use of 'is' in his statement. PvI is using the 'is' of identity, while trope theorists would use the 'is' of predication.

Notice that, once we identify the fact that PvI is using the 'is' of identity, it becomes clear that his statement is no argument. It's just a bald assertion that trope theory is wrong. He's simply asserting that the diameter of the first ball is numerically identical the the diameter of the second.

Posted by: Shields | Friday, July 18, 2014 at 08:54 PM

Thanks for the comment. I'm glad we agree. PvI has a habit of 'petering out' to use an expression that I heard recently. It is something like feigning incomprehension: "I don't know what that even MEANS." It is a bad habit of some analytic philosophers. Of course, it may be that PvI really has no idea what trope theorists are talking about. But note that he understands it well enough to reject it. I uspect he knows what it means; he just finds it murky and dubious. But the same could be said of his alternative.

I don't think he is asserting that the diameter of ball A is numerically identical to the diameter of ball B. I take him to be denying that there is any such particular as A's diameter in A and B's diameter in B. PvI rejects constituent ontology. (That is the theme of the essay in question.) So he is not saying that these two particular diameters are numerically identical. What he is saying is that there is an abstract property, the property of having a diameter of 6.7 cm, and that this abstract property is not a constituent of either ball, but is exemplified by both balls.

And the same goes for the property of being optically yellow. It is common to the two balls, but in no sense 'in' them. It is an abstract object that they exemplify. It follows, of course, that this property is invisible! Here is the makings of a powerful objection to PvI's view. But I wouldn't say his theory is meaningless.

Posted by: BV | Saturday, July 19, 2014 at 04:54 AM

I have trouble understanding trope-ontologies; but I fear in my case this fact says more about my limitations rather than about the credibility of trope-ontologies. However, in the case of PvI, I suspect things are somewhat different. While Bill is right that PvI appears to prefix his "argument" quoted by Bill as "almost" an autobiographical statement, it does not appear to me to be "merely" an autobiographical statement. At least not upon reading the whole article.

If tropes are particulars, then what are the conditions of their individuation? i.e., When are tropes the same and when different? How do we individuate tropes?

Consider a green ball on which red light is projected. Under the red light, the ball looks red; when removed from the red light it looks green. Which trope is a constituent of the ball; green or red? Why?

Bill says: "It is given that the two tennis balls have the same diameter. But all that means is that the diameter of ball A and the diameter of ball B have the same measurement, 6.7 cm. This fact is consistent with there being two numerically distinct particular diameters, the diameter of A and the diameter of B."

I must confess that I also have trouble understanding this argument. What else could a diameter be other than a given measurement (in whatever metric)? And as PvI contends, these measurements can be subject to various mathematical operations.

Consider this. A given ball is painted green. According to tropism, if I get this, green-trope is a constituent of the ball: i.e., this ball would not have been *this* ball unless green-trope is one of its constituents. Call this ball 'John'. Clearly it makes sense to say: "I would have owned John even if it would have been red." But according to tropism, if I understand it at all, this makes no sense to say, since the counterfactual "John could have been painted red" is necessarily false, since a red painted ball cannot be the same as John.

Posted by: Peter Lupu | Saturday, July 19, 2014 at 06:59 AM

In the neighborhood of the passage quoted by Bill, PvI says the following against tropism: "You can perform *arithmetic operations* on this object, for goodness' sake." (p. 209; his emphasis). What object? Well, the mass, in this case, or the diameter of a ball. What is the argument here?

Well, I suppose it is this. Suppose ball A has diameter x and ball B has diameter y (where y = 2x). Tropism tells us that x and 2x are different *particular* tropes, each of which is a constituent of balls A and of ball B, respectively. Now we can say: If ball A would have been twice as large, then its diameter would have equaled the diameter of ball B. But if A's diameter (i.e., x) and B's diameter (i.e., y = 2x) are genuine particulars, then it seems to me (and I think to PvI) that it is *really* strange that mathematical operations such as (x2) on a genuine particular should land us on another genuine particular. Given the nature of tropes (that is, if I understand tropism), this should occasion a major shocker.

Posted by: Peter Lupu | Saturday, July 19, 2014 at 07:26 AM

I hope I am not "petering out" on PvI's position, but I'm not sure I understand his abstract property talk. It sounds to me like these abstract properties are universals. The balls both exemplify the abstract property. It is one and the same property in each ball, but multiply located. This is why I said that he's asserting that the diameter of the first ball is numerically identical to the diameter of the second. He can say this and still reject constituent ontology. He can say that the abstract property (which I think is a universal) is not a constituent of either ball, but is exemplified by both balls.

Am I misunderstanding something? I haven't read this essay of PvI's, so I very well might be.

Posted by: Shields | Saturday, July 19, 2014 at 08:33 AM

Shields,

Here is the paper that provides the context, although the pagination is different from the 2014 collection that I cited:

http://andrewmbailey.com/pvi/Relational.pdf

Yes, his abstract properties are universals, but they are not in the things that have them. Hence these universals are not multiply located. They are not located at all. The multiple-location view is a constituent-ontological view, Armstrong being an example, and PvI rejects constituent ontology.

Read the whole essay and see if you don't agree with me.

Posted by: BV | Saturday, July 19, 2014 at 10:34 AM

>>Bill says: "It is given that the two tennis balls have the same diameter. But all that means is that the diameter of ball A and the diameter of ball B have the same measurement, 6.7 cm. This fact is consistent with there being two numerically distinct particular diameters, the diameter of A and the diameter of B."

I must confess that I also have trouble understanding this argument. What else could a diameter be other than a given measurement (in whatever metric)? And as PvI contends, these measurements can be subject to various mathematical operations.<<

Isn't it obvious, though, that a diameter of a physical thing such as a ball or a circular disc is distinct from the measurement of that diameter? Presumably there were balls and discs long before there were measurers or systems of measurement.

And what about the argument I gave? You have two balls and you want to know whether they have the same diameter, where 'same diameter' means 'same length of the diameter.' You must measure them. What are you measuring? A number? No. Something abstract? No. A ball? No. The diameter of a ball. A diameter in general? No, the particular diameter of this particular tennis ball. Which is distinct from the particular diameter of the other ball.

Posted by: BV | Saturday, July 19, 2014 at 11:07 AM

Peter sez:

>>According to tropism, if I get this, green-trope is a constituent of the ball: i.e., this ball would not have been *this* ball unless green-trope is one of its constituents.<<

No trope theorist I am aware of maintains this.

Posted by: BV | Saturday, July 19, 2014 at 11:15 AM

Peter again: >>Well, I suppose it is this. Suppose ball A has diameter x and ball B has diameter y (where y = 2x). Tropism tells us that x and 2x are different *particular* tropes, each of which is a constituent of balls A and of ball B, respectively.<<

You are confusing a physical reality with a number. If y = 2x, then x, y are numbers. But the diameter of a ball is not a number.

Posted by: BV | Saturday, July 19, 2014 at 11:20 AM

Bill,

"You are confusing a physical reality with a number. If y = 2x, then x, y are numbers. But the diameter of a ball is not a number."

Perhaps. But, then again, perhaps not.

What are the phrases 'the diameter of ball A' and 'the diameter of ball B' refer to. If they refer to a trope, then the following is necessarily false when the diameters of the two balls is the same:

(1) the diameter of ball A = the diameter of ball B.

because, ex hypothesis, the two phrases flanking the identity sign must refer to numerically distinct tropes. But, surely, (1) is true when the diameter of balls A and B are the same.

And now as for my confusion. What physical reality? The diameters? The numbers just are the diameter. What else could the diameter of a ball be but, well, its diameter.

Are tropes, according to tropism, constituents of an abject? And aren't colors of objects tropes? And isn't it the case that if something is a constituent of an object, that object cannot be the same unless it is made (in part) of that constituent. If so, then I cannot see how could it not be the case according to tropism that had this green ball been painted red, it would not have been this very ball.

Finally: what are the identity conditions of tropes?

Posted by: Peter Lupu | Saturday, July 19, 2014 at 06:43 PM

Bill says >>You are confusing a physical reality with a number. If y = 2x, then x, y are numbers. But the diameter of a ball is not a number.<<

What is a diameter then? A distance perhaps? But can we not add and scale distances?

Posted by: David Brightly | Sunday, July 20, 2014 at 12:49 AM

Peter,

Here is a prereq for this discussion: http://plato.stanford.edu/entries/tropes/

Posted by: BV | Sunday, July 20, 2014 at 05:08 AM

Bill,

Read it!!!

Also the previous version by John Bacon. Hence my comments.

Posted by: Peter Lupu | Sunday, July 20, 2014 at 05:56 AM

David,

If we go back to our plane geometry, the diameter of a circle is the length of the line that passes through the center and connects two points on its edge. Or you could say that the diameter is the length of the chord that passes through the center.

But note that 'diameter' is ambiguous as between 'LENGTH of the line that passes through the center and connects two points on its edge' and 'LINE that passes through the center, etc.'

The length is given by specifying so many units of measurement, say, 12 inches, or any positive real number, say 5.367 cm.

Obviously, we can perform math operations on these numbers. For example, if we divide the length of the diameter we get the length of the radius, and if we take the square of the radius and multiply by pi we get the area, and so on.

Now suppose we have two physically real discs and they have the same diameter in the sense that the lengths of their diameters is given by the same number, say 5 cm. That is consistent with each disc having its OWN diameter in the sense that a line drawn on disc A through its ceneter and connecting points on the edge is a numerically different line than a line drawn on disc B.

Now tell me if you follow and agree to all of this. If yes, then we take the next step.

I hope you are well.

Posted by: BV | Sunday, July 20, 2014 at 10:39 AM

Thank you Bill, I am well.

I certainly agree that 'diameter' is ambiguous between a length and a line segment. I have two caveats. (1) In the line segment sense a disc does not have a unique diameter, so phrases like 'THE diameter of the disc' or 'the disc's OWN diameter' are not well-defined. (2) In this sense a diameter is more a mereological part than a property.

Posted by: David Brightly | Sunday, July 20, 2014 at 05:07 PM

I suppose you mean that a disc has infinitely many (indeed continuum-many) diameters in that infinitely many line segments pass through the center and connect to the circumference. Is that what you mean?

But then you are conceding that that there are particular diameters, diameters as particular as the things whose diameters they are. Right?

And you seem to be conceding that these particular diameters are parts of the disc. Their being parts does not rule out their being properties unless you beg the question against the trope theorist.

Posted by: BV | Sunday, July 20, 2014 at 05:44 PM

Hello Bill, Yes, that's right. One can think of the disc as made of chords of arbitrarily small thickness, parallel to any given direction. One of these might contain the disc's centre and hence count as a diameter. But these will be concrete parts of the disc. My understanding is that tropes are

abstractparticulars. I confess that I find the SEP article rather impenetrable.Posted by: David Brightly | Monday, July 21, 2014 at 05:08 AM

Yes, tropes are abstract particulars. But this is the old use of 'abstract' not the new use introduced mainly by Quine in influential papers in the '50s. What is abstract in the old sense can be something visible (sense-perceivable more generally) and spatiotemporal. For example, the yellowness you see is a particular, located bit of yellow. What makes it abstract is that it is considered in abstraction from all else: it is just a bit of yellow.

Now consider one of the chords that passes through the center of the disc. The point is that that chord is not merely a chord in the sense of plane geometry but a physical reality, and, as such, a physical part of the physical disc.

PvI claimed that it makes no sense to think of two balls or two discs of the same size as having each their own diameter. My point it that that makes sense (despite giving raise to some difficult questions). The following dyad is consistent:

1. The physically real diameter of A is numerically distinct from the physically real diameter of B.

2. The length of A's diameter and the length of B's diameter are given by the same real number, say, 6.7 cm. In this sense, A and B have the same diameter.

One has to be careful not to equivocate on 'same diameter.'

Posted by: BV | Monday, July 21, 2014 at 11:50 AM

Hi Bill,

I finally got a chance to look at the PvI article, and I totally agree with your reading of it. I guess I don't have anything important to add to that.

On a related note, I recently wrote a paper concerning trope individuation that I would really like to publish at some point. I would welcome your comments, if you are interested in taking a look.

Posted by: Shields | Friday, July 25, 2014 at 08:55 PM

Glad we agree. Send me your paper and I'll see if I have any useful comments to make.

Posted by: BV | Saturday, July 26, 2014 at 04:29 AM