Metaphysics 9/8/09 Notes
Resemblance Nominalism: F-ness = a resemblance class
• ‘a’ is ‘F’ iff ‘a’ resembles all the F-things, not because it has some sort of universal
Two versions of this view (both say F-ness is identical to a certain class that has certain resemblances, but the question is how those resemblances work):
• Aristocratic Version
o The resemblance class is picked out by certain exemplars, paradigm cases of the property in question
o Ex. Redness is the class of things that resemble a certain number of exemplars, for example a red brick, a red bird, and a red mailbox, as much as those three resemble each other
o Then take a blue brick – it resembles the red brick, but not the bird or the mailbox, so the blue brick is not red
• Democratic Version
o No need for exemplars, just general resemblances
o The class is such that between any two things in the class there is a resemblance relation
o Redness is the maximal class of mutually-resembling red things
• If there’s anything outside the class that resembles all the other members of the class, it has to be included in that class
Overall resemblance is primitive, unlike the class nominalists that take classes to be primitive
• For class nominalists things resemble each other because they are members of a natural class, while resemblance nominalists say that things are parts of a natural class because they resemble each other
Resemblance is primitive, and also comes in degrees (just like natural classes that come in degrees in class nominalists)
• Inexact resemblance is a symmetrical relation (A resembles B and B resembles A), but it’s not transitive (A resembles B and B resembles C to some degree, but A does not necessarily resemble C to the same degree)
• Exact resemblance is symmetrical and transitive

Objections to Resemblance Nominalism:
Resemblance Nominalism has to deny that resemblance is an internal relation, but intuitively it is
• Internal relation is 4g is smaller than 2g, while external is something is a mile apart
• Internal = their existence/nature dictates this relation, always
• External = even if the objects have the same nature they could fail to stand in a certain relation
• Armstrong: resemblance is an internal relation – two shoes will always resemble each other if their existence/nature doesn’t change
o But resemblance nominalists can’t say that because they say the resemblance relation comes before their properties/natures, resemblance is the basis for something having properties according to this theory
Imperfect community objection
• You can have a class that satisfies the conditions for being a property class without having any one property that unites them
• Take three particulars a, b, c
• Suppose that a has properties A&B, b has B&C, c has C&A
• These form a property class according to resemblance nominalism
o They don’t all have one property in common, so being a member of this class doesn’t give you any property F
• The condition of a maximal mutually-resembling-entities class is not enough for all the things in that class to have a property in common
• One way to get out of this is to add further conditions (dude in Oxford)
o You can have resembling pairs, not just single objects, so you can add the condition that there have to be resemblances between pairs: the a/b pair has to resemble the b/c pair, etc etc
Coextensive properties objection
• All F things are G’s, and all G things are F’s – all the white things are square and all the square things are white
o If it’s true that all these things form a resemblance class, then it should turn out that whiteness and squareness is the same as squareness
o That is, to be white is to resemble all the white things and to be square is to resemble all the square things, but if they’re coextensive then they have to be the same thing
• Again can get rid of this problem by being a modal realist (see 9/3 notes)
Once instance objection
• Suppose there was only one white thing in the world
o Being white is supposed to be a matter of resemblance, but if it’s the only instance what does it resemble?
• One move is to say that it at least resembles itself, it’s white in virtue of it resembling itself
o Suppose, though, the white thing is also square, and uniquely so
o You can say it resembles itself, but then whiteness is the same as squareness
• Again, solve this problem by being a modal realist (see 9/3 notes)
Resemblance regress objection – Bertrand Russell
• Take two objects a and b that resemble each other, and c and d that resemble each other
• Either resemblance is a universal, or it’s not
o If it is, you’ve already admitted one universal so you might as well go all the way and you don’t need resemblance nominalism
o If it’s not a universal, you’re going to have infinite regress:
• The resemblance relation b/w a&b and c&d are not identical, because resemblance is not a universal
o What makes each of them a resemblance relation? What makes them fall under the same type, the resemblance type?
o Must be because the resemblances resemble each other… but how do they resemble? By another order of resemblance… and on and on and on.
• This isn’t quite a vicious regress, in that it could happen, but it’s not economical and it’s really messy
o It’s cleaner to say that all resemblance relations are the same in that they have a universal
Objection to all forms of nominalism (see 9/3 as well)
• “Red is a color” – what makes this true?
o Universalists say that “red” refers to a universal
o Nominalists have to get this to be true by not appealing to universals
• Nominalists translate this to “necessarily, all red things are colors”
• Want to say “Fness is a G” = “necessarily all F things are a G”
• But what if F=red and G=extended
o But if we go back in the other direction, we get “red is an extension”, which is false
• The translation fails, therefore there’s something wrong with it