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Resemblance Nominalism: A Solution to the Problem of Universals
Gonzalo Rodriguez-Pereyra offers a fresh philosophical account of properties. How is it that two different things (such as two red roses) can share the same property (redness)? According to resemblance nominalism, things have their properties in virtue of resembling other things. This unfashionable view is championed with clarity and rigor.
- GenresPhilosophy
252 pages, Hardcover
First published July 4, 2002
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October 7, 2012
Until recently, Nominalism has fallen out of fashion. Many challenges have been seen as decisive against Nominalism in any form. I here emphasize until recently, for Rodriguez-Pereyra's book,
Resemblance Nominalism: A Solution to the Problem of Universals
remedies this. It answers all of the objections and provides novel solutions. In it, he defends a brand of Nominalism where some particular is said to have some property in virtue of which it resembles all other particulars of that property. The success of this account, however, is not a simple matter. Though I take Rodriguez-Pereyra's Resemblance Nominalism to be coherent, intelligible, and a viable alternative to Universalism and Trope theory, certain considerations bar me from ever accepting it.
To see why this is, it is necessary to provide some background of the issues themselves and Rodriguez-Pereyra's views in particular. The problem of Universals generally has three approaches to a solution. The first, Universalism, posits Universals which are co-located and instantiated by particulars. The second, Trope theory, claims that there are only particulars, but these particulars come in two varieties: tropes (property particulars) and the particulars which have those tropes. The final, Nominalism, contends that there are only particulars and the properties of those particulars are not distinct entities.
Typically the problem centers around properties. That is, how can multiple particulars have the same property? The various solutions offer differing accounts of properties that some object has. So for a Universalist, a is F just if some particular a has some Universal F. For a Tropist, a is F just if a particular a has some particular F. The problem has generally been seen that Nominalism cannot account for this since it denies a separate entity as a property. Although there are forms of Nominalism which deny properties all together, the form defended here does not. What it denies is that properties are entities. So for some a to be F is just for there to be some a which resembles some b which is also F in its being F.
The problem of Universals usually invokes the conflation of two questions: how is it possible for a to be F and how is it possible for a and b to be F? Given the ontological nature of these questions, the real problem is taken to be a matter of truthmakers. What is it that makes a F and what is it that makes it the case that a is F and b is F?
"The idea of a truthmaker is...the idea of that which makes something true, or that in virtue of which a certain truth is true." (31) Thus, given the truthmaker, the truth is thereby determined. The insight of truthmakers is that being and truth are asymmetrically related to grounding. Being grounds truth.
Truthmkaers are characterized by Rodriguez-Pereyra as:
(T*) An entity E is a truthmaker for a sentence 'S' iff E is an entity in virtue of which 'S' is true.
To solve the problem of Universals, one needs to explain sentences like 'a is F' and 'a has the property of being F' since the truthmakers of these will also be the basis for the truthmakers of existential generalizations, disjunctions, and joint conjunctions. since a truthmaker for an existential generalization is any entity which fulfills the property, the truthmaker of a disjunct is any one of the disjuncts fulfilling the property and for a joint conjuction, the joint conjuncts fulfill the property.
Since the problem of Universals has to do with the truthmakers (or conjuncts) which account for the properties of particulars, the One-Over-Many is reformed into the Many-Over-One. The question is no longer, 'how is a F and b F?', since we analyze this sentence by the truthmakers which themselves are the joint conjuncts taken individually.
The question now is about the truthmakers of sentences attributing determinates or determinable properties?
The distinction between determinate and determinable properties is relative, but they can be divided into the lowest determinate (properties that are determinate, but not determinable with respect to other properties) and the highest determinable (properties that are determinable, but are not determinate with respect to other properties).
The determinates can be thought of as the disjuncts of the determinable. If all of this is sound, the problem of Universals may be rephrased as having to do with the lowest determinate properties of a particular.
The type of properties which fit the bill for lowest determinate properties are sparse properties. These are the least common properties to each particular. An example is being exactly 245.3*F. So it is in sparse properties that we are trying to find the truthmakers for sentences of the type 'a is F' or 'a has the property of being F', where F, G, H, etc. stand in for sparse lowest determinate properties.
Resemblance Nominalism answers the Many-Over-One question by saying what makes a have the property F is that a resembles all F objects, but this says nothing about what properties are.
"[Resemblance Nominalism] just says that what makes it true that a particular has a property is that it resembles other particulars and what makes it true that certain particulars stand in a certain relation is that certain ordered n-tuples resemble each other."
The resemblance of Resemblance Nominalism is posited as objective, ontological, primitive, reflexive, symmetrical, non-transitive, trans-temporal, 'relation' that comes in degrees and can obtain between no more than two entities.
Resemblance Nominalism is supposed to derive its formal properties from a list of axioms:
(1) If x resembles y then resembling y, along with other particulars, makes x have some property Xi.
(2) Resembling the X-particulars is what makes a particular Xi.
(3) The particulars whose resemblance to which makes a particular Xi are the same as the particulars whose resemblance to which makes any other particular Xi.
(4) If Xi and Xj are different properties then the particulars whose resemblance to which makes a particular Xi are not the same as the particulars whose resemblance to which makes a particular Xj.
(5) If x resembles y to degree n then resembling y, along with other particulars, makes x have properties Xi&...&Xn, where 1 < n.
(6) There is no x which any particular y resembles to degree n and degree m where n!=m.
From axioms 1 and 2 we derive the notion of symmetry. For if a resembles b, then a has some property F. Since a is F in virtue of resembling b, b is also F. Since b is F and a is F, it follows from 2 that b resembles a.
It can also be shown that if a resembles b to degree n then b resembles a to degree n. This is so since by 5 it follows that a has certain properties Fi&...&Fn in virtue of resembling b then b is Fi&...&Fn in virtue of resembling all Fi&...&Fn particulars. The degrees to which a resembles b, then, could not differ.
These axioms also guarantee reflexivity. For if a is F in virtue of its resembling b, then by 2 a is one of the F particulars to which a resembles. a can also be the only F in that it resembles itself.
Non-transitivity is derived from the axioms as well. If a and b resemble each other and b and c resemble each other, it does not follow that a and c resemble each other since it may be the case that b and c are G in virtue of resembling each other where a and b are F in virtue of resembling each other. This is secured by 4 which claims that if a is F in virtue of resembling b and b is G in virtue of resembling c, if a and c are not G in virtue of resembling each other then F and G are distinct properties.
Similarly, non-tranitivity can be derived for degrees of resemblance. That is, if a, b and c resemble, a and b may resemble to degree n while a and c may not.
Exact resemblance is defined as:
(ER) x and y exactly resemble each other iff there is some particular w that x resembles and for any particular z, x and z resemble each other to degree n iff y and z resemble each other to degree n.
This says that if we have a particular a with two properties and a particular b, they exactly resemble each other if and only if there is some other object z (say with three properties) and a resembles any z to a degree of 2 if and only if b resembles z to a degree of 2. The biconditional guarantees that the properties a shares with z are the same as the properties that b shares with z. Thus, since these properties are shared, it establishes that a and b resemble each other to a degree of 2. This is because for any particular which a resembles to degree n if and only if b resembles z to degree n. That means that if a is a red circle and z is a red-green circle, b must also be a red circle. z could be any combination of properties including being only a red circle. So say a is a red circle, z is a red-green circle and b is a green circle, this may at first appear to be a counter-example since both a and b resemble z to a degree of 2 and a and z share the same two properties. But z could just as easily have been just a red circle. If this were the case, a would resemble z to a degree of 2, but b would only resemble z to a degree of 1. Thus this formula guarantees exact resemblance.
The above definition also establishes the transitivity of exact resemblance. If a exactly resembles b and b exactly resembles c, then a exactly resembles c. If some object a, some object b and some object c and any object z resemble each other to a degree of n if and only if b and z resemble each other to a degree n and b and z resemble each other to degree n if and only if c and z resemble each other to degree n, then a and c resemble each other exactly since a and c resemble any z to degree n.
Similarly symmetry and reflexivity can be derived.
Resemblance according to Rodriguez-Pereyra only links two particulars. This is because if a, b and c resemble each other, this can best be expressed by a's resembling b, b's resembling c and a's resembling c. A collectivist account about resemblance cannot account for why if more than two particulars resemble, any two of them do. Being a collectivist about the resemblance of a, b and c does not entail a resembling b, b resembling c or a resembling c.
This is not all there is to Resemblance Nominalism, however. For it is also committed to other philosophical views, and it is in these cases that I have the most difficulty.
Resemblance is transtemporal. According to Rodriguez-Pereyra, a Resemblance Nominalist is committed to a Non-Presentist view. This is because present particulars can resemble past particulars as past particulars resemble present ones. Why this is necessary is because we can imagine a seventeenth century apple which is the exact shade of red as an apple in my hand. Now, it has been established that the same objects that make one particular F also make another particular F. Thus, since the seventeenth century apple is red in virtue of resembling other seventeenth century apples and the shade of red is the same as a contemporary apple, the apple in my hand is part of the particulars to which the seventeenth century apple resembles. The same goes for the apple in my hand. So the particulars to which an F thing is F in virtue of resembling these other F particulars are particulars across time. Particulars may only resemble so long as they exist, so since a Presentist denies the existence of past apples, a Resemblance Nominalist cannot be a Presentist.
At last Rodriguez-Pereyradiscusses the issues of coextension facing Resemblance Nominalism. Although he illustrates that most examples of coextensive properties are not technically coextensive, the issue nevertheless remains. There is always a possibility of coextention and Resemblance Nominalism must face this. It appears, unfortunately, that the only way a Resemblance Nominalist can account for coextensive properties is to be a realist about possible worlds.
Naturally, Resemblance Nominalism must also accept Counterpart Theory. This allows one to account for the accidental properties of some particular. So if a is F at w and a' is G at w', even if in each world w and w' a is the only F particular in w and a' is the only G particular in w', the properties F and G can be distinguished.
One cannot also relativize resemblance to worlds. For if a is F at w and a' is F at w', it would be absurd to say that what makes a F at w is distinct from what makes a' F at w'.
Though realism about possible worlds and counterpart theory do help to solve those difficulties regarding coextensive, accidental, and lone properties, it is an enormous ontological commitment. It doesn't seem likely that there is any other way out, however. Even if one tries to account for possibilia via essences, one will still fall into difficulty. Fortunately, the Resemblance Nominalists commitment to realism about possible worlds gets something intuitively right about properties. That is, properties are the same across worlds, even if particulars are distinct. In a way, this makes counterpart theory more intuitive than is typically presented.
From here, Rodriguez-Pereyra discusses Russell's difficulty as well as the Imperfect Community and Companionship difficulties. My aim in this review is to provide a summarize a positive account of Resemblance Nominalism, and it is my conviction that so long as one accepts the premises previously laid out, the solutions to these difficulties are successful.
Rodriguez-Pereyra presents the argument that Resemblance Nominalism is the preferred theory given six considerations:
1. Coherence
2. Preserrvation of intuitions and received opinions
3. Ideological economy
4. Quantitative ontological economy
5. Qualitative ontological economy
6. Avoidance of ad hoc ontology
From this, he gives priority to the 6th. There are no entities within Resemblance Nominalism which are postulated simply for the sake of solving the problem of Universals. Taking possibilia and stages as part of its ontology does not count according to Rodriguez-Pereyra because these are entities which have bee postulated eleswhere for philosophical purposes and Resemblance Nominalism merely borrows them. Universalism and Trope theory on the other hand do postulate entities for the sole purpose of solving the problem of Universals.
Now, though I agree that Resemblance Nominalism does not inherently postulate ad hoc entities, I still think it does extraneously. Resemblance Nominalism requires dubious or contentious entities for it to work, and though these entities are not created for the purpose of Resemblance Nominalism, they are nevertheless used by and for it. Perhaps this makes Resemblance Nominalism in some way posit second-order ad hoc entities (if realism about possible worlds wasn't a concept developed for other purposes, it would have to be invented and posited by Resemblance Nominalism and would thus be a first-order ad hoc entity). This of course is still in some way better than Universalism and Trope theory.
Though I count myself as a perdurantist, I do not consider myself a realist about possible worlds. Nor do I expect to be persuaded of this in the near future. Accepting Resemblance Nominalism is not, for me, a good enough reason to eschew my actualist intuitions. For this reason, I cannot accept Resemblance Nominalism. The wonderful thing about Universalism and Trope theory is that they can be accepted whether or not one is a realist about possible worlds or an eternalist, though I will admit if one already were both, one has no reason not to accept Resemblance Nominalism.
With that said, this book is a wonderful exercise in Metaphysics. Though I cannot myself accept the conclusion, that does not mean that others can not. This is a work which sets a standard for Philosophy, and even if one is not concerned with the problem of Universals, it should still be appreciated for its rigor, clarity and explanatory force. Highly recommended!
To see why this is, it is necessary to provide some background of the issues themselves and Rodriguez-Pereyra's views in particular. The problem of Universals generally has three approaches to a solution. The first, Universalism, posits Universals which are co-located and instantiated by particulars. The second, Trope theory, claims that there are only particulars, but these particulars come in two varieties: tropes (property particulars) and the particulars which have those tropes. The final, Nominalism, contends that there are only particulars and the properties of those particulars are not distinct entities.
Typically the problem centers around properties. That is, how can multiple particulars have the same property? The various solutions offer differing accounts of properties that some object has. So for a Universalist, a is F just if some particular a has some Universal F. For a Tropist, a is F just if a particular a has some particular F. The problem has generally been seen that Nominalism cannot account for this since it denies a separate entity as a property. Although there are forms of Nominalism which deny properties all together, the form defended here does not. What it denies is that properties are entities. So for some a to be F is just for there to be some a which resembles some b which is also F in its being F.
The problem of Universals usually invokes the conflation of two questions: how is it possible for a to be F and how is it possible for a and b to be F? Given the ontological nature of these questions, the real problem is taken to be a matter of truthmakers. What is it that makes a F and what is it that makes it the case that a is F and b is F?
"The idea of a truthmaker is...the idea of that which makes something true, or that in virtue of which a certain truth is true." (31) Thus, given the truthmaker, the truth is thereby determined. The insight of truthmakers is that being and truth are asymmetrically related to grounding. Being grounds truth.
Truthmkaers are characterized by Rodriguez-Pereyra as:
(T*) An entity E is a truthmaker for a sentence 'S' iff E is an entity in virtue of which 'S' is true.
To solve the problem of Universals, one needs to explain sentences like 'a is F' and 'a has the property of being F' since the truthmakers of these will also be the basis for the truthmakers of existential generalizations, disjunctions, and joint conjunctions. since a truthmaker for an existential generalization is any entity which fulfills the property, the truthmaker of a disjunct is any one of the disjuncts fulfilling the property and for a joint conjuction, the joint conjuncts fulfill the property.
Since the problem of Universals has to do with the truthmakers (or conjuncts) which account for the properties of particulars, the One-Over-Many is reformed into the Many-Over-One. The question is no longer, 'how is a F and b F?', since we analyze this sentence by the truthmakers which themselves are the joint conjuncts taken individually.
The question now is about the truthmakers of sentences attributing determinates or determinable properties?
The distinction between determinate and determinable properties is relative, but they can be divided into the lowest determinate (properties that are determinate, but not determinable with respect to other properties) and the highest determinable (properties that are determinable, but are not determinate with respect to other properties).
The determinates can be thought of as the disjuncts of the determinable. If all of this is sound, the problem of Universals may be rephrased as having to do with the lowest determinate properties of a particular.
The type of properties which fit the bill for lowest determinate properties are sparse properties. These are the least common properties to each particular. An example is being exactly 245.3*F. So it is in sparse properties that we are trying to find the truthmakers for sentences of the type 'a is F' or 'a has the property of being F', where F, G, H, etc. stand in for sparse lowest determinate properties.
Resemblance Nominalism answers the Many-Over-One question by saying what makes a have the property F is that a resembles all F objects, but this says nothing about what properties are.
"[Resemblance Nominalism] just says that what makes it true that a particular has a property is that it resembles other particulars and what makes it true that certain particulars stand in a certain relation is that certain ordered n-tuples resemble each other."
The resemblance of Resemblance Nominalism is posited as objective, ontological, primitive, reflexive, symmetrical, non-transitive, trans-temporal, 'relation' that comes in degrees and can obtain between no more than two entities.
Resemblance Nominalism is supposed to derive its formal properties from a list of axioms:
(1) If x resembles y then resembling y, along with other particulars, makes x have some property Xi.
(2) Resembling the X-particulars is what makes a particular Xi.
(3) The particulars whose resemblance to which makes a particular Xi are the same as the particulars whose resemblance to which makes any other particular Xi.
(4) If Xi and Xj are different properties then the particulars whose resemblance to which makes a particular Xi are not the same as the particulars whose resemblance to which makes a particular Xj.
(5) If x resembles y to degree n then resembling y, along with other particulars, makes x have properties Xi&...&Xn, where 1 < n.
(6) There is no x which any particular y resembles to degree n and degree m where n!=m.
From axioms 1 and 2 we derive the notion of symmetry. For if a resembles b, then a has some property F. Since a is F in virtue of resembling b, b is also F. Since b is F and a is F, it follows from 2 that b resembles a.
It can also be shown that if a resembles b to degree n then b resembles a to degree n. This is so since by 5 it follows that a has certain properties Fi&...&Fn in virtue of resembling b then b is Fi&...&Fn in virtue of resembling all Fi&...&Fn particulars. The degrees to which a resembles b, then, could not differ.
These axioms also guarantee reflexivity. For if a is F in virtue of its resembling b, then by 2 a is one of the F particulars to which a resembles. a can also be the only F in that it resembles itself.
Non-transitivity is derived from the axioms as well. If a and b resemble each other and b and c resemble each other, it does not follow that a and c resemble each other since it may be the case that b and c are G in virtue of resembling each other where a and b are F in virtue of resembling each other. This is secured by 4 which claims that if a is F in virtue of resembling b and b is G in virtue of resembling c, if a and c are not G in virtue of resembling each other then F and G are distinct properties.
Similarly, non-tranitivity can be derived for degrees of resemblance. That is, if a, b and c resemble, a and b may resemble to degree n while a and c may not.
Exact resemblance is defined as:
(ER) x and y exactly resemble each other iff there is some particular w that x resembles and for any particular z, x and z resemble each other to degree n iff y and z resemble each other to degree n.
This says that if we have a particular a with two properties and a particular b, they exactly resemble each other if and only if there is some other object z (say with three properties) and a resembles any z to a degree of 2 if and only if b resembles z to a degree of 2. The biconditional guarantees that the properties a shares with z are the same as the properties that b shares with z. Thus, since these properties are shared, it establishes that a and b resemble each other to a degree of 2. This is because for any particular which a resembles to degree n if and only if b resembles z to degree n. That means that if a is a red circle and z is a red-green circle, b must also be a red circle. z could be any combination of properties including being only a red circle. So say a is a red circle, z is a red-green circle and b is a green circle, this may at first appear to be a counter-example since both a and b resemble z to a degree of 2 and a and z share the same two properties. But z could just as easily have been just a red circle. If this were the case, a would resemble z to a degree of 2, but b would only resemble z to a degree of 1. Thus this formula guarantees exact resemblance.
The above definition also establishes the transitivity of exact resemblance. If a exactly resembles b and b exactly resembles c, then a exactly resembles c. If some object a, some object b and some object c and any object z resemble each other to a degree of n if and only if b and z resemble each other to a degree n and b and z resemble each other to degree n if and only if c and z resemble each other to degree n, then a and c resemble each other exactly since a and c resemble any z to degree n.
Similarly symmetry and reflexivity can be derived.
Resemblance according to Rodriguez-Pereyra only links two particulars. This is because if a, b and c resemble each other, this can best be expressed by a's resembling b, b's resembling c and a's resembling c. A collectivist account about resemblance cannot account for why if more than two particulars resemble, any two of them do. Being a collectivist about the resemblance of a, b and c does not entail a resembling b, b resembling c or a resembling c.
This is not all there is to Resemblance Nominalism, however. For it is also committed to other philosophical views, and it is in these cases that I have the most difficulty.
Resemblance is transtemporal. According to Rodriguez-Pereyra, a Resemblance Nominalist is committed to a Non-Presentist view. This is because present particulars can resemble past particulars as past particulars resemble present ones. Why this is necessary is because we can imagine a seventeenth century apple which is the exact shade of red as an apple in my hand. Now, it has been established that the same objects that make one particular F also make another particular F. Thus, since the seventeenth century apple is red in virtue of resembling other seventeenth century apples and the shade of red is the same as a contemporary apple, the apple in my hand is part of the particulars to which the seventeenth century apple resembles. The same goes for the apple in my hand. So the particulars to which an F thing is F in virtue of resembling these other F particulars are particulars across time. Particulars may only resemble so long as they exist, so since a Presentist denies the existence of past apples, a Resemblance Nominalist cannot be a Presentist.
At last Rodriguez-Pereyradiscusses the issues of coextension facing Resemblance Nominalism. Although he illustrates that most examples of coextensive properties are not technically coextensive, the issue nevertheless remains. There is always a possibility of coextention and Resemblance Nominalism must face this. It appears, unfortunately, that the only way a Resemblance Nominalist can account for coextensive properties is to be a realist about possible worlds.
Naturally, Resemblance Nominalism must also accept Counterpart Theory. This allows one to account for the accidental properties of some particular. So if a is F at w and a' is G at w', even if in each world w and w' a is the only F particular in w and a' is the only G particular in w', the properties F and G can be distinguished.
One cannot also relativize resemblance to worlds. For if a is F at w and a' is F at w', it would be absurd to say that what makes a F at w is distinct from what makes a' F at w'.
Though realism about possible worlds and counterpart theory do help to solve those difficulties regarding coextensive, accidental, and lone properties, it is an enormous ontological commitment. It doesn't seem likely that there is any other way out, however. Even if one tries to account for possibilia via essences, one will still fall into difficulty. Fortunately, the Resemblance Nominalists commitment to realism about possible worlds gets something intuitively right about properties. That is, properties are the same across worlds, even if particulars are distinct. In a way, this makes counterpart theory more intuitive than is typically presented.
From here, Rodriguez-Pereyra discusses Russell's difficulty as well as the Imperfect Community and Companionship difficulties. My aim in this review is to provide a summarize a positive account of Resemblance Nominalism, and it is my conviction that so long as one accepts the premises previously laid out, the solutions to these difficulties are successful.
Rodriguez-Pereyra presents the argument that Resemblance Nominalism is the preferred theory given six considerations:
1. Coherence
2. Preserrvation of intuitions and received opinions
3. Ideological economy
4. Quantitative ontological economy
5. Qualitative ontological economy
6. Avoidance of ad hoc ontology
From this, he gives priority to the 6th. There are no entities within Resemblance Nominalism which are postulated simply for the sake of solving the problem of Universals. Taking possibilia and stages as part of its ontology does not count according to Rodriguez-Pereyra because these are entities which have bee postulated eleswhere for philosophical purposes and Resemblance Nominalism merely borrows them. Universalism and Trope theory on the other hand do postulate entities for the sole purpose of solving the problem of Universals.
Now, though I agree that Resemblance Nominalism does not inherently postulate ad hoc entities, I still think it does extraneously. Resemblance Nominalism requires dubious or contentious entities for it to work, and though these entities are not created for the purpose of Resemblance Nominalism, they are nevertheless used by and for it. Perhaps this makes Resemblance Nominalism in some way posit second-order ad hoc entities (if realism about possible worlds wasn't a concept developed for other purposes, it would have to be invented and posited by Resemblance Nominalism and would thus be a first-order ad hoc entity). This of course is still in some way better than Universalism and Trope theory.
Though I count myself as a perdurantist, I do not consider myself a realist about possible worlds. Nor do I expect to be persuaded of this in the near future. Accepting Resemblance Nominalism is not, for me, a good enough reason to eschew my actualist intuitions. For this reason, I cannot accept Resemblance Nominalism. The wonderful thing about Universalism and Trope theory is that they can be accepted whether or not one is a realist about possible worlds or an eternalist, though I will admit if one already were both, one has no reason not to accept Resemblance Nominalism.
With that said, this book is a wonderful exercise in Metaphysics. Though I cannot myself accept the conclusion, that does not mean that others can not. This is a work which sets a standard for Philosophy, and even if one is not concerned with the problem of Universals, it should still be appreciated for its rigor, clarity and explanatory force. Highly recommended!
October 25, 2014
This is basically a highly technical work of pure analytic philosophy. It is focused upon the very ancient and old philosophical question of how is it that so many different particular things can share a common property? There are red sunrises, red roses and red houses, what makes all of them red?
The solution proposed in this work is basically an extremely minimalist one. Whereas the universalist would have said that all of them, in some sense, possessed a universal called "redness", the resemblance nominalist simply says that what makes different red things red is that they resemble all other red things, and that there is no additional entities called "redness" or universals or whatever. There just are red particular things, and they resemble, that is all.
Of course Rodriguez's theory is much more complicated and precise than that. However, in order to spare you the frightening use of complex set theoretic concepts, I shall simply do a convenient hand waving as well as a massive oversimplification, and say that his theory explains what makes something red, as opposed to green, consists simply in it resembling all other particular red things and not green things. Thus his theory has one basic primitive fact which cannot be further reduced, that some particular things resembles other particular things, and from this network of resemblances, a particular being red simply is it resembling all other particular red things. What makes something green would simply be it resembling a distinct set of particulars, all the particular green things, etc.
Rodriguez's main focus in this book is to explicate this theory in precise formulas as well as to refine this theory to solve various technical problems which his theory faces which we need not really concern ourselves, unless you want to wade through pages and pages of set theoretic notations. Thus his focus is mainly upon the narrow metaphysical question of accounting for our application of properties to particulars by simply using resembling particulars alone.
My focus however would be upon the more "macro" implications or applications which his theory leads to which I think would be more interesting than the precise details of his theory, especially in relation to analytic theology.
There was a work on analytic theology I read a very long time ago, Robert Adam's "Finite and Infinite Goods", which is, ironically perhaps, an exposition of the idea of God as a sort of platonic form of the Good. However, what makes his theory of particular interest in this present discussion about resemblance nominalism is how he defines "finite goods":
"…there is something to be said for the hypothesis that being excellent in the way that a finite thing can be consists in resembling God in a way that could serve God as a reason for loving the thing."
Thus, like the Platonists, he postulate an ultimate Form of the Good which makes all particular good things good, and this Form of the Good he simply identifies with God. However, in an odd nominalistic twist, he argues that the relationship between the particular goods with the Infinite Good is that of "resemblance", that partially what makes particular finite things good good is that they resemble the Infinite Good or God.
But this resemblance relationship is but half the story. Adams introduces a "voluntaristic" twist in that the finite goods are good partially by objectively resembling God, yet this resemblance, by itself, is not a sufficient to make it good, it must resemble in a way which would give God a reason to love it. Thus, the definition of "good" runs through God's subjectivity as well. What makes a finite good good is that it resembles God in such a way which God accepts as a reason to love it.
Turning ourselves back to resemblance nominalism, Rodriguez in his discussion on various versions of resemblance nominalism postulated two versions. The first is called the Aristocratic version, whereby in order for a red thing to be red, it is sufficient to resemble the "paradigm" cases of red things. As long as a particular thing resembles such particular paradigm cases, that is enough for it to be red. Then there is another version, the "egalitarian" version, whereby there is no specially privilege particular red things and that something is red because it resembles all the red things without exception.
Let us use this insight for discussing Adams' conception of finite goods. In a sense, Adams' theory is inclined towards the "Aristocratic" version, whereby particular good things are good by resembling the paradigm case, in this context, God.
But suppose you have a slightly more apophatic conception of God. Then you would think that God is not a particular good thing on the same plane as all other good things. He is "beyond Good and Evil" and is therefore not a particular good thing, no matter how exalted and ideal, among other good things.
So what we will be left with is a set of particular resembling good things, the egalitarian version, and what makes all these good things good is that they all resemble all other good things. However, we can have the voluntaristic half of the equation to employ. Let us, following Milton, accept that all being or creation was not sprung out, ex nihilo, or out of nothing, but flows out of the substance of God's infinite life and being. Then following the scholastic, we can simply identify being with goodness, and all material things are, in some sense, good, by virtue of having flowed out of God's life.
However, what makes something good, in the eyes of God, is him imposing his will upon all these plurality and masses of many finite goods, all resembling each other in various ways, and charting a destiny, a course, a path, drawing, reconciling and drawing all these finite goods together and organising all of them into an ever growing whole. Thus, "goodness" here would be defined in terms of those resembling good thing which God hath will for us to love. Thus, we have a sort of account here of evil, which is finite goods which fall out of God's will, and will simply wither and be exhausted, while only those finite goods caught up God's will will never perish and be integrated and drawn in together with all other finite goods unto everlasting life.
In this conception, there everlasting life doesn't really consist of a "beatific vision" of directly beholding God. Remember, ex hypothesi, God is not a particular good thing among other good things, but 'beyond good and evil", he merely supplies and creates the finite good things, but he is not among them. Thus, everlasting life consists of experiencing more and more of these finite good things ever flowing out of God's infinite life and riches.
However, we may not actually need to abandon aristocratic nominalism just yet. We could give our theory an "Arian" twist, and postulate that among the set of all particular good things, there is a "paradigm" good, not God the Father himself, but the Word, the Wisdom of God, which contains within himself the fullness of the meaning of all other particular finite good things. And then we can postulate that all finite good things are good because they both resemble this divine Word, or the "first born of all creation", and in such as way which conforms to God's will for them in the Word. Thus, the Word is the focus of God's reconciling work of drawing and integrating all finite good things unto himself through Christ, herein all finite good things find their meaning and fulfilment in him by resembling him and fulfilling God's will in him.
I think this is enough theological speculation for now. But apart from the intrinsic metaphysical merits of resmeblance nominalism itself, as well as the impressive rigorous set theoretic devices and formulas for this theory, it also provides the theoretical tools whereby one can explicate a specifically "Scotist" theological vision. Wherein salvation doesn't consists of an immediate vision of the Infinite good to the oblideration of all other particular finite goods, but salvation is a perpetual journey of experiencing and loving all the particular finite creaturely goods which God sends to us, reconciling, drawing and integrating them into an organic growing whole as the elect continues their everlasting journey into the infinite riches of God's life. Resemblance nominalism does full justice to the particularities of our creaturely and finite goods which we enjoy here, while we intuitively sense a "resembling" connection between all of them, because they all come from God, but it is the will of God, in the divine Word, which draws the plurality and flux of resembling networks between the finite goods into a organised whole, and invites us into this growing everlasting growing good.
The solution proposed in this work is basically an extremely minimalist one. Whereas the universalist would have said that all of them, in some sense, possessed a universal called "redness", the resemblance nominalist simply says that what makes different red things red is that they resemble all other red things, and that there is no additional entities called "redness" or universals or whatever. There just are red particular things, and they resemble, that is all.
Of course Rodriguez's theory is much more complicated and precise than that. However, in order to spare you the frightening use of complex set theoretic concepts, I shall simply do a convenient hand waving as well as a massive oversimplification, and say that his theory explains what makes something red, as opposed to green, consists simply in it resembling all other particular red things and not green things. Thus his theory has one basic primitive fact which cannot be further reduced, that some particular things resembles other particular things, and from this network of resemblances, a particular being red simply is it resembling all other particular red things. What makes something green would simply be it resembling a distinct set of particulars, all the particular green things, etc.
Rodriguez's main focus in this book is to explicate this theory in precise formulas as well as to refine this theory to solve various technical problems which his theory faces which we need not really concern ourselves, unless you want to wade through pages and pages of set theoretic notations. Thus his focus is mainly upon the narrow metaphysical question of accounting for our application of properties to particulars by simply using resembling particulars alone.
My focus however would be upon the more "macro" implications or applications which his theory leads to which I think would be more interesting than the precise details of his theory, especially in relation to analytic theology.
There was a work on analytic theology I read a very long time ago, Robert Adam's "Finite and Infinite Goods", which is, ironically perhaps, an exposition of the idea of God as a sort of platonic form of the Good. However, what makes his theory of particular interest in this present discussion about resemblance nominalism is how he defines "finite goods":
"…there is something to be said for the hypothesis that being excellent in the way that a finite thing can be consists in resembling God in a way that could serve God as a reason for loving the thing."
Thus, like the Platonists, he postulate an ultimate Form of the Good which makes all particular good things good, and this Form of the Good he simply identifies with God. However, in an odd nominalistic twist, he argues that the relationship between the particular goods with the Infinite Good is that of "resemblance", that partially what makes particular finite things good good is that they resemble the Infinite Good or God.
But this resemblance relationship is but half the story. Adams introduces a "voluntaristic" twist in that the finite goods are good partially by objectively resembling God, yet this resemblance, by itself, is not a sufficient to make it good, it must resemble in a way which would give God a reason to love it. Thus, the definition of "good" runs through God's subjectivity as well. What makes a finite good good is that it resembles God in such a way which God accepts as a reason to love it.
Turning ourselves back to resemblance nominalism, Rodriguez in his discussion on various versions of resemblance nominalism postulated two versions. The first is called the Aristocratic version, whereby in order for a red thing to be red, it is sufficient to resemble the "paradigm" cases of red things. As long as a particular thing resembles such particular paradigm cases, that is enough for it to be red. Then there is another version, the "egalitarian" version, whereby there is no specially privilege particular red things and that something is red because it resembles all the red things without exception.
Let us use this insight for discussing Adams' conception of finite goods. In a sense, Adams' theory is inclined towards the "Aristocratic" version, whereby particular good things are good by resembling the paradigm case, in this context, God.
But suppose you have a slightly more apophatic conception of God. Then you would think that God is not a particular good thing on the same plane as all other good things. He is "beyond Good and Evil" and is therefore not a particular good thing, no matter how exalted and ideal, among other good things.
So what we will be left with is a set of particular resembling good things, the egalitarian version, and what makes all these good things good is that they all resemble all other good things. However, we can have the voluntaristic half of the equation to employ. Let us, following Milton, accept that all being or creation was not sprung out, ex nihilo, or out of nothing, but flows out of the substance of God's infinite life and being. Then following the scholastic, we can simply identify being with goodness, and all material things are, in some sense, good, by virtue of having flowed out of God's life.
However, what makes something good, in the eyes of God, is him imposing his will upon all these plurality and masses of many finite goods, all resembling each other in various ways, and charting a destiny, a course, a path, drawing, reconciling and drawing all these finite goods together and organising all of them into an ever growing whole. Thus, "goodness" here would be defined in terms of those resembling good thing which God hath will for us to love. Thus, we have a sort of account here of evil, which is finite goods which fall out of God's will, and will simply wither and be exhausted, while only those finite goods caught up God's will will never perish and be integrated and drawn in together with all other finite goods unto everlasting life.
In this conception, there everlasting life doesn't really consist of a "beatific vision" of directly beholding God. Remember, ex hypothesi, God is not a particular good thing among other good things, but 'beyond good and evil", he merely supplies and creates the finite good things, but he is not among them. Thus, everlasting life consists of experiencing more and more of these finite good things ever flowing out of God's infinite life and riches.
However, we may not actually need to abandon aristocratic nominalism just yet. We could give our theory an "Arian" twist, and postulate that among the set of all particular good things, there is a "paradigm" good, not God the Father himself, but the Word, the Wisdom of God, which contains within himself the fullness of the meaning of all other particular finite good things. And then we can postulate that all finite good things are good because they both resemble this divine Word, or the "first born of all creation", and in such as way which conforms to God's will for them in the Word. Thus, the Word is the focus of God's reconciling work of drawing and integrating all finite good things unto himself through Christ, herein all finite good things find their meaning and fulfilment in him by resembling him and fulfilling God's will in him.
I think this is enough theological speculation for now. But apart from the intrinsic metaphysical merits of resmeblance nominalism itself, as well as the impressive rigorous set theoretic devices and formulas for this theory, it also provides the theoretical tools whereby one can explicate a specifically "Scotist" theological vision. Wherein salvation doesn't consists of an immediate vision of the Infinite good to the oblideration of all other particular finite goods, but salvation is a perpetual journey of experiencing and loving all the particular finite creaturely goods which God sends to us, reconciling, drawing and integrating them into an organic growing whole as the elect continues their everlasting journey into the infinite riches of God's life. Resemblance nominalism does full justice to the particularities of our creaturely and finite goods which we enjoy here, while we intuitively sense a "resembling" connection between all of them, because they all come from God, but it is the will of God, in the divine Word, which draws the plurality and flux of resembling networks between the finite goods into a organised whole, and invites us into this growing everlasting growing good.
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