The Resemblance-Relation as it Appears When Analysed in the Context of Universals, Classes, Concepts and Counterparts

 

… this Aristotelian notion of classification, that is to say, of ‘division’ as he called it… Aristotle, in his life’s work, seized upon the general notion of classification… He also applied this theoretical doctrine to the immense material to be collected by direct observation in the fields of zoology, physics, sociology. ..  Plato [also] notes that the determinations of compatibilities and incompatibilities are the key to coherent though and to the understanding of the world… (A.N. Whitehead, in his Adventures of Ideas, 1933)

 

Introduction

 

We can find this somewhat strange relation, or process, or entity, or… thing (?), resemblance, everywhere we look. Scientific - indeed all - classifications rely on and/or assume the existence of the resemblance-relation; if not the existence of the actual universal, resemblance. Resemblance is also the bread and butter of all our categorisations. For example, from those categorisations or conceptualisations of the Kantian transcendental variety to the mundane ones we think up on the toilet but which we still require in order to make sense of the world (if only our world) and its constituent objects, beings, properties or relations (taken as resemblance’s various and many values or extensions, as it were). We also have many and varied non-technical or non-philosophical predicates that refer to and/or require resemblance. For example, ‘… is the common nature of…’; ‘… have features in common’; ‘… are twins or doppelgangers’; ‘… is the spiting image of…’; ‘… is a mental image of…’; ‘.. is a representation of…’; ‘… is a picture of…’; ‘… is a copy of…’; ‘… is a reflection of…’; ‘there is a similarity between… and …’; ‘… and … are like peas in a pod’; ‘… and … look alike’; ‘… is an imitation of…’; ‘that action was sheer pretence’; ‘… is a simulacrum of…’; ‘… is a repeat of…’; ‘… is a reoccurrence of…’; ‘… is a memory of…’; ‘… is a recurrent feature of…’. And so on.

 

In terms of this paper. The first section paper concerns itself with universals; particularly the universal resemblance, which Russell took specific note of in his [1912]. I put both the realist/Platonist and the nominalist case for the universals or properties/relations featured in my examples. Both ontological polar standpoints seem to be problematic when set within the admittedly cursory analysis that follows

 

The second section of this paper takes on board classes or sets. This is of interest because of the very important place classes hold within not only philosophy but everyday life or everyday experience. We see that problems arise for the resemblance-relation when we deal with the null class or classes with only one member. Not only that, we will also see how classes can proliferate ceaselessly and how we often subsequently come up with all sort of bizarre classes if Occam’s razor is not used or ready-to- hand. The resemblance-relation between particular class-members will go alongside an analysis of the resemblance-relation as it occurs between classes qua classes.

 

After the section on classes we will cover concepts. As is clear, concepts and classes are very closely related. For example, in Frege’s scheme we move from a linguistic predicate, say F, to the abstract and non-linguistic concept (or sense/intension) of that predicate [see Frege, 19]. And from there we move to the concept’s extension: the class of all Fs. Some philosophers have argued that concepts and classes amount to the same thing. In any case, as we will see with classes, we have the resemblance-relation between those entities that ‘fall under a concept’, as Frege puts it, and the resemblance-relation between concepts qua concepts or concepts and other concepts. As again in Frege:

 

Do the objects that ‘fall under the concept’ F resemble one another in the same manner as the members of an extension-class resemble each other?

 

In terms of moral concepts, as with all others, we can often see that certain moral concepts, or at least their linguistic predicates, are so closely related to one another that it is impossible to deal with one without bringing in the other. However, does this result mean that the similar or closely related concepts resemble each other in any way; or is resemblance beside the point in these cases?

 

Finally we deal with David Lewis’s notion of possible world counterparts and attempt to manoeuvre this discussion into the parallel question, at least in this paper, of the identity or non-identity of in/discernibles. It will become clear that we cannot have a perfect and complete resemblance between an object in our world and its counterparts at other worlds. If there were such an absolute resemblance, then the Lewisian notion of counterparts would simply break down; or at least it would leave counterpart theorists with nothing much left to do with such counterparts. The resemblance-relation in counterpart theory helps the counterpart theorist determine an object’s essential properties (i.e., those properties which every possible counterpart of x, at our world, must both have and share with our object) and contingent properties (i.e., when counterparts of x at our world either drop or gain properties). In terms of Max Black’s well-known two-membered world [1956], the resemblance-relation is shown to have little or no use. And if we place Black’s own objects, a and b, in our own world, we will still find that perfect and complete resemblance is inherently problematic - if not impossible.

 

The Resemblance-Relation and Universals

 

Russell did well to argue that even the most hard-core nominalist must accept at least one universal – viz., resemblance (Russell, 1912) This in itself makes such an entity and/or relation of interest to all philosophers, whether nominalist or realist. Indeed it should (excuse the normative modal term) be of interest to philosophical whatever-ists of all kinds. But instead of going on Russell’s journey straight to the abstract universal resemblance (that is, to contemplate the importance of such an entity or relation or whatever has in a direct sense) we will show instead that the resemblance-relation is already of both great importance and relevance to all cognitive thought and all experience. The resemblance-relation, or resemblance simpliciter, permeates every thought and experience a human rational agent has or could have. Indeed resemblance can be deemed a legitimate Kantian ‘condition of every possible experience’[Kant, 1787], as it were, or a Fregean/Wittgensteinian condition of all describability and thus of all natural languages [Wittgenstein, 1921, Frege, 1956]. Without this possible-objects-of-predications-of-being, as can be extracted inferentially from Kant’s position, there would be a truly unmanageable ‘manifold’ of sensation, but not one of experience (in the strict Kantian sense). At the least, we would never have any thoughts of the more cognitive kind without resemblance or the resemblance-relation.

 

In the aforementioned work by Russell, he also says that universals can be found not only in nearly every sentence we utter or write (even when in ellipsis, as with verbal ejaculations), but also in the sense that nearly all universal-words are in the majority class when it comes to different types of word (in natural language dictionaries). Again, we can say roughly the same about resemblance-words, either those that refer directly to a resemblance of some kind, or those that must necessarily rely on a prior acceptance of the resemblance-relation; or, instead, those resemblance-words which imply or entail the universal resemblance.

 

To begin. We can account for universals primarily in terms of resemblance-relations. Particular1 resembles particular2 because realists take both to be instantiations of universal1. In this case P1 must be taken to resemble U1 before it can be taken as an instantiation of it – either taken qua kind or qua individual. Once the particular-universal resemblance-relation has been set up, then we can look for resemblance-relations between P1 and other particulars. However, if we don’t take P1 as being an instantiation of U1, we may as well compare, so the realist would argue, a star with a tree. The resemblance-relation between particular and particulars as well as that between particular/s and universals can be schematised this way:

 

U1

Ö Ó  Õ

P¹ n P² n Pn

 

This ostensible reliance on a universal is a little like the traditional observations-then-generalisation account of scientific method or procedure. Broadly speaking, the scientist was taken to go out into the world and simply make numerous, presumably rather arbitrary at first, observations of all the things he found under the sun. Eventually he would hope to have enough – relevant - observational data to go ahead and make the required and necessary scientific connections between the various contents of his myriad observations. He would then pronounce his final generalisation. This Grande finale of connectivity was taken to be the end-result of all the scientist’s – otherwise free! - observations up to that point.

 

Now we know that this does not - and could not - possibly happen, at least not in the simplified way I have just described. If the scientist didn’t have a prior theory, hypothesis or simple hunch about what to observe, where to observe, and why he should observe, he wouldn’t have known where or when to start in his observations. The manifold would overcome him, as Kant might have called it.

 

In the hypothetico-deductive model or method, instead, a prior hypothesis and/or scientific theory works like the earlier universal, U1. In strictly non-scientific terms, we cannot simply go out into the world and try to note as many resemblances between numerous different particulars or different kinds as we can and see where this leads us. Instead we must allow a universal or universals to guide us in our endeavours. Universals will also give us the exemplary or prototypical particular with which we can also compare other particulars or kinds to see if they actually either resemble it or the aforementioned universal U1.

 

If P1 requires U1 in order to set up the resemblance-relation P1 n P2, then wouldn’t we require a further universal in order to set up the prior foundational resemblance-relation between P1 and U1?

 

We began with:

 

U1

Ö Ø

 P1 n P²

 

Now we have:

U2

Û

;U1:

P¹nP2

 

That is, P1 requires a higher-order universal, U2, in order to set up its prior resemblance-relation with the lower-order U1, which itself was thought to ground P1’s resemblance-relations with P2. This is a rendition or version of  ‘the third man argument’ in which it was argued, by Aristotle, that a universal is just as much a particular as any concrete particular. If we require U1 in order to set up a resemblance-relation between P1 and P2, then the resemblance-relation between P1 and U1 must itself require a resemblance-relation to be set up between U1 and the higher-order U2.  How would we know, otherwise, that P1 resembled U1 without that resemblance-relation itself being founded on a prior and equally necessary resemblance-relation between U1 and the higher-order U2? But if we don’t require the higher-order universal U2, then perhaps we don’t require the first-order universal U1 or any universal for that matter. That is, if we don’t require U2, then why do we need U1 for the resemblance-relation P1n P2?

 

This situation is similar to an argument from Wittgenstein [Wittgenstein, 1956, as simplified in D. M. Taylor, 1970] that if Joan needs a mental image or representation of a red rose in order to be able to pick out and then collect a red rose (after being asked to do so), then that mental image or representation itself will require another mental image to substantiate itself, as it were, as an acceptable and genuine mental image of a red rose:

 

 

 

 

 

 

 

 

… (ad infinitum)

↑

a higher-order mental image of the prior mental image of a  red rose

↑

a mental image of a red rose

↑

red rose (the concrete particular)

 

Instead Wittgenstein suggests that our Joan can easily manage to pick out and then collect a red rose without relying on any mental image of a red rose. And, of course, this supposed mental image of a red rose is an analogue of our prior universal, U1 [see also a Brentano version of this in note (1)].

 

So the requirement for - or the postulation of - a specific universal, on this picture, entails an infinite regress of yet higher-order universals and must therefore, one assumes, be dispensed with from the beginning.

 

Nominalists, of course, also deny both the existence of and need for universals. The resemblance-relation is set up exclusively between P1 and P2.    We do not require or need U1 or any other universal. The nominalist will assume that P1 and P2 share the properties of which they are constituted. But properties can themselves be taken as universals!

 

If the nominalist sets up a resemblance-relation between, say, cat1 and cat2 because he takes them to share the properties being furry, being whiskered, being a mammal, etc., then all these examples can easily be seen as - or actually be - the universals furriness, whiskeredness, mammalianhood. (Or, alternatively, the less oblique and clumsy universals whiskers, mammal, etc.) Like our earlier naïve scientific empiricist (who required an hypothesis and/or theory to set his scientific ball rolling), our nominalist is required to accept, prior to setting up his resemblance-relations between particulars, the being of various universals. If he does not do so, then he may as well see if cat1 resembles a frog or a can of Coke. In addition, he must have already assumed that the cat he observed as a cat, was a cat. And if it is indeed a cat, then it must also be a member of the kind cat. But natural kinds can be taken as being a type of universal!

 

The nominalist can reply to this statement by saying:

 

My cat, cat1, has its status as a cat due to my prior acceptance - and knowledge of - non-realist or purely nominalistic identity-conditions or criteria of individuation. Such things had already established that my cat is indeed a cat without my countenancing - or relying upon - any universals whatsoever.

 

The realist can say that this reply is a cop-out. He can say that these prior individuations and identity-claims can only have been set up by the nominalist’s prior acknowledgement - and use - of universals; even if in some tacit or underhand manner, as it were. Not only that, these purportedly non-realist individuations and identity-claims would have become, for our nominalist, universals in their own right. That is, various properties, types and natural kinds, set up by the nominalist’s previous, say, trope-individuations and trope-identities, would themselves have become - or have been – effectively universals for our nominalist; even if they were only quasi-universals or disguised universals. If he hadn’t accepted prior property-universals and kind-universals, he might as well have compared the wart on the leg of cat1 with the wart, or lack thereof, on the leg of cat2. This also means that he must have already established – in terms of his cat’s physical constitution - which property-universals were essential to the individuations of his cat - or of cats generally - and also by the prior identification of his cat as a member of the universal-kind he calls ‘cat’.

 

Even our nominalist would presumably not have seen cat-warts as an essential or important property of all cats. But this acknowledgement would not just have been an acceptance of kind essentialism, but also a parallel prior acceptance, however tacit, that universals of some kind provide the basis or foundation for his individuations and identifications of the essential or important properties of his cat as well as the acceptance that his cat is a member of the natural kind cat. These universals must have provided our nominalist with the resemblance-relations he later set up - or cognised - between his cat, cat1, and another cat, cat2; or between cat1 and any other cat when such cats are taken, explicitly by the realist but not by the nominalist, as the instantiation of a natural kind or universal-kind.    

 

 

Classes and the Resemblance-Relation

 

Every member of a particular class is such precisely because it resembles other members of the same class.  It must also resemble the archetypal member of the class (if there is one), which in turn must resemble a universal and thereby determine its class-membership in the first place. Each member of a particular class must resemble every other member of that class in at least one or more, but not all, respects.

 

Magpies resemble each other because we have the resemblance-relation black-stripes-to-black-stripes and white-stripes-to-white-stripes. A magpie is also a member of the kind magpie; which in turn can be taken to do the work of the universal. However, there is a difference. The scientist, in his dealings with magpies, will probably completely ignore the black and white stripes and deem other properties to be essential: e.g., beak structure, type or design of wing, or even genetic code. We can now say that the beak structure of one magpie resembles that of another and indeed of all magpies. Magpie1 and magpie2 are both instantiations of beak structure1 (as universal), wing-type1, and/or genetic code1. So we are still in the world of universals! However, if black and white feathers are indeed contingent properties of the kind magpie, then our everyday classifications of magpies will not have natural-kind correlates or analogues, at least not in our simple example. That is, the class whose members are birds with black and white feathers will be a genuine and bona fide class that is not equivalent to the scientific natural kind magpie as now recognised. Not only that, the class of black and white birds will include birds that are not magpies. For examples, pied wagtails are members of this extensive class. Here again we see that the class of black and white birds includes the universals, or at least it members do, bird, black, white and so on. Classes, then, are more abundant or profligate than scientific natural kinds. For example, the class of all living things does not have an equivalent, correlate or more precise natural kind correlate such as, say, mammal (but not animal).

 

On the Cantor/Frege theory of numbers, we identify two or more classes as belonging to the same super-class or class of classes that itself functions as a number. For example, the number 2 is the class of all two-membered classes. It has sometimes been said that a member of one two-membered class, in our case, is matched up with a member of another two-membered class. Certain logicians and philosophers have said that there must be some kind of resemblance-relation between member1 of two-membered class1 and member1 of two-membered class2. But surely this is more of a correspondence-relation than a resemblance-relation. At least Cantor and others have used the word ‘correspondence’ in this way.

 

Here again resemblance-as-a-universal shows its face. Correspondence-relations are parasitic on previous resemblance-relations and thus on the universal resemblance. That is, particular1 corresponds with particular2 because it resembles it. We can say that a statue of Tony Blair ‘corresponds’ with the particular or individual, Tony Blair. However, perhaps a resemblance-relation is not required for the establishment of a correspondence-relation. This is certainly true of a linguistic statement, say, ‘Puddy is on the mat’. This sentence does not resemble Puddy or Puddy’s being on the mat. In the tradition, it is the statement or proposition itself that was said to correspond with, but not resemble, the concrete fact Puddy’s being on the mat. But even here we can still argue that the compositional structure of the words and predicates in ‘Puddy is on the mat’ resembles the compositional structure or arrangement of the fact or truth-condition – that is, Puddy’s being on the mat.

 

Take Wittgenstein’s ‘picture theory’ of atomic propositions and atomic facts [Wittgenstein, 1921]. An atomic proposition was said to ‘picture’ the (or its) atomic fact. However, in Wittgenstein’s case only the form, structure or arrangement of the atomic proposition is said to picture, isomorphically, the atomic fact. The propositional picture or ‘sign’ left out the content (or the empirical content) of the atomic fact. The arrangement, form or structure of the predicates, variables and logical connectives in an atomic proposition were seen to picture the atomic or ‘simple’ object-referents and predicate-extensions of the atomic fact. So did Wittgensteinian picturing require a resemblance-relation between atomic fact and atomic proposition? Why not. A structures can resemble other types of structure; a form can resemble other types form; and an arrangement or configuration can resemble another kind of arrangement or configuration.

 

And if resemblance is brought into this scenario, then universals will also be brought in. That is, structure1 resembles structure2 because structure1 resembles U1, as does structure2. However, we have already seen that this need for a universal-as-foundation or as a basis for all resemblance-relations between particulars; or of abstract particular and abstract universal in the structure1 case. Structure1’s own universal, U1, will require its own meta-universal to substantiate itself - and thus our initial abstract particular, structure1.

 

We have already established that all the members of a specific class must resemble one another in at least one or in more - but not all - respects. A member of one class can resemble a member of a another class even though they both belong to different classes (i.e., they don’t belong to each other’s class). Our previous class of black and white birds, which includes the class of magpies, will have one or more members which resembles a member of, say, the class of black and white chessboards or the class of black and white frogs (if there such things). Clearly, a black and white bird resembles a black and white chessboard or frog because the universal black-and-white-things, as well as the non-hyphenated universal black and the universal white, instantiated by a magpie resembles the property-universals of black and white chessboard or frogs. Both bird and chessboard (or frog) are also members of the class of all black and white animals; or, more broadly, members of the class of black and white entities.

 

Can a class, qua class, resemble another class, taken qua class? If Russell was right to argue that classes are nothing ‘over and above’ their members, as he once did, then clearly one class can resemble another class precisely because of the resemblance-relations of member1 of class1 with member1 of class2 and all the other member-to-member resemblance-relations. The null class, of course, has no members so, on this reading, it cannot resemble another class. On the other hand, a class with just one member will resemble another class with just one member not because of member-to-member relations, or member1 of class1, resembling member1 of class2, but because class1 resembles class2 in its structural property of having only one member. The one-membered structure of class1 resembles the one-membered nature or structure of class2 - and that is all. But is that a genuine resemblance-relation? It can be because this resemblance between class1 and class2 itself relies on one or more universals: e.g., unity (or oneness) and/or one-memberedness. Even the complex universal classes whose member-classes have only one member will also exhibit such structural relations that in turn become resemblance-relations. Thus class1 can resembles class2 in virtue of the fact that class1 resembles the universal unity or one-memberedness, etc., which in turn enables us to set up a resemblance-relation between class1 and class2 by means of the aforementioned universals:

 

the universal unity (or oneness)

Ö                                     Õ

class with one member1 ↔  class with one member2

 

 

As with Wittgenstein’s propositional pictures again, class1 resembles class2 in terms of its one-membered structure or form, not in terms of their members or of class-content.    

   

 

Concepts and the Resemblance-Relation

 

Even though concepts have been interpreted in a wide number of ways in Western philosophy, and, indeed, often enough in more recent years, all such concepts or concept-applications must rely on and assume resemblance either between a singular concept and its many and varied instantiations; but also when it comes to applying the concept, say F, to thing x. Thing x resembles other things that are also F. And sometimes things that are not even of x’s domain or extension-class. Other things may fall under predicate-concept F, which in turn will resemble other concepts that have similar or the same set of necessary conditions of application and identity/individuation but which do not have the same complete set of properties or conditions which could be used to make an exact match between its conditions and the necessary and sufficient conditions for predicate F (i.e., that would make it the concept F).

 

Moral concepts also require resemblance. If act x is deemed to be good. And act y resembles act x in enough ways, then act y must also be a good. Moral concepts require the resemblance-relation.

In addition, if moral concept F resembles moral concept G suitably enough, then there may be an argument for saying that we should incorporate moral concept G into all our accounts of moral concept F and also be cognisant of their agential and extensional exemplifications in the world by moral agents or persons. For example, the moral concept [goodness] resembled that of [justice] in that the good was often seen, or only seen, in circumstances that are just; in that good citizens often or only became good in just environments, whether political or private [Aristotle,]. Just environments were deemed to create or produce good persons or citizens. More linguistically, such a resemblance between the concept [goodness] and the concept [justice] may be even stronger if one argues that

 

The just is a form or expression of the good

 

or

 

The good is a form or expression of the just (or an expression of justice).

 

However, connections can also be made between moral concepts that are not based on resemblance in any obvious way. Kant’s connection, for example, between the concept [duty] and the concept [freedom] - or [moral freedom] - was very strong and a conceptual necessity or requirement for his entire moral system [Kant, 1787 ] Clearly, however, neither these concepts nor their agential or societal expressions resemble one another in any way.

 

If moral concepts do resemble each other to a high degree, if not perfectly and completely, then we can apply Occam’s razor to one or the other of the concepts concerned; or, alternatively, to their synonymous predicate-expressions. Schopenhauer, for example, argued that the concept [God] and the concept [world] - or [nature] - are either very alike or identical in Spinoza’s system. So why, he argued, call nature ‘God’ or God ‘nature’ if they almost perfectly  and completely resemble each other or are even identical (Schopenhauer, 1821)? Schopenhauer suggests that the Spinozian should either erase the predicate ‘God’ or the predicate ‘nature’ from this philosophical vocabulary and thereby stop playing games with the ambiguities their parallel usages engender.

 

The same can be said, in the moral sphere, about the Platonic concepts or Ideas/Forms [the Good] and [the True] which become virtual synonyms if not in Plato’s own work then in the work of many later Platonists and neo-Platonists. Clearly, however, it can be seen that on no known non-Platonic reading can the concepts [the good] and [the true], or the predicates ‘good’ and ‘true’, be true synonyms, identities or resemblances. It is still the case, however, that in the Greek tradition these concepts, though non-resembling, are strongly connected in other – sometimes - inferential ways. Even centuries later pragmatists like William James and Dewey, if not Peirce, made their own connection between the concept [the good] and the concept  [the true]. Indeed in James’s case we nearly have a complete and perfect resemblance, if not an actual identity, when, for example, James wrote that ‘the true is what is good in the way of belief and action’ (James, 1926). Thus the innocuous use of the verb ‘is’ (in that quotation) suggests a literal identity between [the good] and [the true] rather than a strong resemblance of some kind. That is, if the true ‘is the good’ then

 

 

[the true] = [the good]; or, [the good] = [the true]

 

However, if we treat concepts intensionally, as they often are or must be taken, then despite this identity we still have two concepts with two different intensions; or, alternatively one concept with two intensions, despite their identical extensions: viz., the class of all things true and the class of all things good (or the set of true things and the set of good things). This kind of situation is elaborated in an example from Quine (Quine, 1970). That is the class of cordates (creatures with a heart) is part of the class of renates (creatures with a kidney), or vice versa. Therefore we will find a strong resemblance between a particular cordate and a particular renate; but not an exact identity. Even if renates and cordates were identical, it can be the case that we still use the predicates ‘renate’ and ‘cordate’ because the mode of presentation in the use of the predicate ‘renate’ takes us directly to the animal’s liver, whereas the predicate ‘cordate’ takes us directly to its heart. Thus despite their identity, or, as it were, their near perfect and complete resemblance, a kind of quasi-resemblance can be set up between these animals picked out by the aforementioned predicates. A renate therefore resembles a cordate because an animal whose kidney is stressed or deemed important resembles an animal, a cordate, whose heart is stressed or deemed important. Thus a biologist could tell a heart specialist that the cordate whose heart he has just dissected is the same animal as that named a ‘renate’; that if of interested, in this exaggerated tail, to the kidney surgeon or specialist. We have, therefore, made a specific animal resemble itself but if both a cordate and a renate. Of course, other cases of either a renate or cordate may not resemble other renates or cordates if an animal with a heart but no kidney were to be compared to an animal with both a kidney and a heart. So such operations are possible if only by means of our modes of presentation or our intensional concepts.

 

The Resemblance-Relation and Lewisian Counterparts

 

Even arcana like David Lewis’s counterparts ride on the back of resemblance. Every possible world counterpart of object x at our world must resemble other counterparts of x at every possible world at which the counterparts-of-x actually have some kind of being. Perfectly and completely resembling counterparts would not be Lewisian counterparts; or at least they would not play the role of distinguishing the essential from the contingent properties of objects, which they do in possible world/counterpart theory.

 

Just as it makes no sense to have a one-membered sortal - or, in turn, a sortal with an infinite amount of things which fall under it - because of its logical invalidity and instrumental uselessness, so a perfectly- resembling counterpart would either be logically impossible, qua the indiscernibility of indiscernibles argument and others (see later), or instrumentally useless because such a counterpart would not enable us to distinguish what is essential in those counterparts because they would have exactly the same essential and contingent properties as x has in our world. They would not, therefore, retain, in certain cases, x-@-OW’s essential properties and thus show us - or help us show others - that because each of these counterparts retain a set of properties at all worlds and cases, and loose certain properties in others, those which are retained across worlds are deemed essential to x-@-OW and thus also essential also to x-@-OW’s counterparts at all the other worlds at which they have some kind of being.  A counterpart, or all counterparts, of x-@-OW must not or cannot perfectly and completely resemble x-@-OW by sharing all its properties; whether essential or contingent. Indeed we could not justify the essential/contingent distinction at all. We would need to come to the Leibnizean conclusion that because every counterpart of x-@-OW shares every property with it the latter, and thus perfectly and completely resembles it, then we must conclude that all x-@-OW’s properties are either essential or that all contingent (Leibniz, 1953). However, if this were the case, the contingent/essential distinction would break down if only essential or contingent properties existed. The Lewisian counterpart theorist, but not the Leibnizean essentialist, could not distinguish x-@-OW’s essential properties from its contingent ones. Such counterparts would not actually be counterparts at all but, perhaps, transworld individuals or simply duplicates or replicates [Lewis, 1986]. Even if perfect and complete world-to-world resemblance were possible, the predicate ‘counterpart’ would still be inapposite, at least in Lewis’s scheme. The technical term ‘counterpart’ implies that counterparts of x-@-OW must resemble it but not in every particular. There must be cases of property non-resemblance between x-@-OW and its counterparts at other worlds. Lewis and others would see these cases of property non-resemblance as contingent. All the properties of resemblance, or indeed of perfect resemblance, would, likewise, be deemed essential.

 

Because possible worlds are themselves big counterparts of our world, then all counterpart-worlds or possible worlds will have features, conditions and properties at variance with those in OW. If a counterpart of x-@-OW is an inhabitant of such a counterpart-world, then it must be an inhabitant of a world that is, at  least one particular, at variance with OW. If that is the case, then due to the prior counterpart-world’s non-resembling properties of x-@-OW, this will entail object-nonresemblance at that and other counterpart-worlds. That is, on Max Black’s argument (Black, 1956), possible world non-resemblance would generate at least one case of non-resemblance between the counterpart of x-@-OW and x itself, just as if extra objects were injected into Black’s otherwise two-membered world would make it the case that both of his globes would no longer be indiscernible (if they ever were), as they might have been, but not after the immigration of new objects. For example, Lewis often talks about possible worlds, or counterpart-worlds in our case, that share our logical and mathematical truths and laws. Indeed they must do. However, possible worlds may have different physics or even a Euclidean or Kantian geometry, not, say, a Riemannian or Einsteinian one. Such possible worlds will still resemble OW in that they too have their own objects and in causal commerce with one another and thus the constituents of events. Counterpart-worlds will even share certain types of objects, events and kinds with us at OW. However, the different physics or geometries would in and of themselves generate or cause differences between counterpart objects and events and objects and events in OW. We will have cases of non-resemblance. The logical and mathematical truths and laws of every counterpart-worlds (plus non-counterpart worlds) will perfectly resemble those at OW and thus also be essential or necessary resemblances because necessary or essential truths and laws. Again, this must be the case with every counterpart-world whatsoever.

 

Thus we do not have any perfect and complete resemblance between OW and any other counterpart-world even if all worlds share the same logic and mathematics. Everything must resemble everything at OW for complete and perfect OW-counterpart-world resemblance, not just the logic and mathematics of OW and all other worlds. However, we will also have cases of resemblance not only between logic and logic, but also between property and property - if not between object and object. For example, disregarding the problems and differences possible physics will cause, a counterpart-world will have the property blueness or even the non-natural property goodness despite no perfect object-to-object or event-to-event resemblances. An animal at a counterpart-world will be blue even though the animal itself is not a counterpart of any animal we know at OW [see Armstrong theory of combinatory juxtapositions of our world properties in his 1986]. There will still be causal processes or events, such as x causing y, or a meteorite exploding on the surface of a planet at a particular possible world, even if all the constituents of the causal process, the objects, events and properties, do not resemble our objects and events but only share certain properties with them.

 

To recap. If the resemblance of x-@-OW to one of its counterparts were perfect and complete it would be an identity and therefore not a Lewisian counterpart at all. We can now ask:

 

i) Can the resemblance between x-@-OW and, say, counterpart1 ever be perfect and complete? ii) Would such a resemblance it be a case of any kind of resemblance at all?

 

As is well known, if x-@-OW and counterpart1-@-W1 exemplified a genuinely perfect and complete resemblance, then, according to Leibniz’s law, they would be, or they must be, one and the same object. In

 

x = y

 

a numerical identity is stated between x and y. We cannot say that

 

  x-@-OW = c1-@-W1

 

even if based on complete and perfect resemblance. For a start, c1 is evidently stationed at another possible world, not at our world. We cannot, therefore, be talking about numerical identity. Perhaps we cannot talk of any kind of identity between c1-@-W1 and x-@-OW.

 

Can one thing resemble itself? Some, or all, essentialists say that

 

x instantiates the essential property self-identity in that it is identical to itself.

 

Surely not! Many philosophers believe in that strange property, self-identity, as well as the negative correlate, self-diversity. So if that essential property is acceptable, then perhaps the property or resemblace-relation, resemblance-between-a-@-OW and c1-@-W1 can be a resemblance between a thing and itself, in the guise of c1-@-W1.

 

If we give the earlier variables x and y names and a status as individual constants. And if ‘a’ stands for ‘Tony Blair’ and ‘b’ stands for ‘the British Prime Minister’, then we can ask:

 

Does Tony Blair resemble the British Prime Minister?

 

Surely that statement doesn’t make sense. But it would make a little more sense if we treated ‘the British Prime Minister’ as a definite description and not as a name or Kripkean rigid designator, as is usually the case [Kripke, 1971]. At least we can now say that

 

Tony Blair, qua Tony Blair, resembles the British PM, qua the British PM.

 

This wouldn’t be a resemblance-relation between a person, Tony Blair, and himself, but one between an individual under, say, definite description1 and then under definite description2. Or, alternatively, between a particular falling under, as it were, the proper name ‘Tony Blair’ and that particular then falling under the definite description ‘the British PM’. This would be an intensional resemblance of some kind - not between descriptions or concepts and other descriptions or concepts of the same thing, say D1 and D2, but a de re or extensional resemblance between a thing and itself; or, more specifically and hopefully less counter-intuitively, a resemblance-relation between Tony Blair qua Tony Blair and the British PM qua the British PM. [See also Russell's 1918 in the proceeding contexts.]

 

The Resemblance-Relation and Identity and Indiscernibility

 

Let us now go back to our previously non-specified a and b. If the law of the identity of indiscernibles is false and therefore that two things, a and b, can be exact duplicates of one another and yet be numerically distinct in terms of, say, spatial location if nothing else (as in Max Black’s well-known [1956]), then perhaps a and b in Max Black’s own strange and empty world could or do resemble one another even though that resemblance is complete and perfect and thus correspondingly making the use of the predicate ‘resembles’ both strange and problematic in this context. Again:

 

Can we have a resemblance between a and b that is perfect and complete?

 

It can now be argued that:

 

The predicate ‘resembles’, or ‘resemblance’, is a use-word, as it were, in that enables us to connect one thing with another and yet it still enables and allows us to differentiate between a and b.

 

Complete and perfect resemblance may well help us connect a with b but also be able to differentiate them. In Black’s world the only means of differentiation between a and b are the spatial locations of the two entities concerned. But even here Black himself, and many others, have called into question the argument for spatial disconnectedness as a creator of truly discernible properties, relational or intrinsic, by which we can discover or have a position of discernibility between a and b. He does so with his ingenuous argument that if we take the case of his two ostensibly - or possibly - perfectly symmetrical and perfectly resembling globes, a and b, we can imagine a situation in which both objects rotate around each other in the figure of 8. This scenario would thus deny us the efficacy of spatial discernibility or disconnectedness in determining two otherwise identical objects. In that case we could differentiate Black’s a from Black’s b, or even connect them together in any meaningful way. If that is the case (if we stick with Black’s strange world), if ‘resemblance’ is a use-word that enables us to connect one thing with another thing and yet still allows or enables us to differentiate between them, then the idea of connecting object a with object b in a world otherwise empty of all other objects makes little sense. And in any case, if there are no other objects in this world, then we wouldn’t seem to need to differentiate a from b in the first place when they are the only objects on the scene!

 

Sortals also rely on resemblances between one or more particulars or members that fall under them. Sortals, on our terms, must have at least one or more members or objects to sort in the first place. One must thereby rule out an - or the - infinitely-membered sortal as well as a one-membered sortal. How could one sort a single thing into a sort? In the case of these bogus sortals, differentiations, connectivity and indeed resemblance make little sense in these respects. Sortals must sort something. The predicate ‘resembles’, as a use-word, must help or enable us to connect particulars to particulars, and also to differentiate particulars from particulars, if we are to make sense and use of them qua sortals.

 

In Max Black’s world we will find no room at all for resemblance; or at the least no use for the word ‘resembles’. Even if our a and b miraculously escaped from Black’s world and became immigrant members of our world, and thus begin to live amongst an indefinite number of other objects and properties, and if the resemblance between them were complete and perfect, as before, then even here resemblance would make little sense and have little value. (Of course, Black’s own a and b, ostensibly and initially indiscernible yet not numerically identical, couldn’t have exactly the same properties, whether relational or intrinsic, in our world as they formerly did in Black’s, as Black himself might have argued and many others have argued.)

 

 

Conclusion

 

In the opening discussion of the resemblance-relation and its connection with and to universals, both the nominalist and realist’s divergent accounts of universals were seen to be problematic. However, in terms of proportionality, the realist/Platonist position came out marginally better, I think, than its nominalist alternative (which is not to under-stress its evident problems). It is primarily the problem of the infinite regress of higher and yet higher-order universals that offered us a seemingly decisive blow against realism with respect to universals. However, in retrospect, and in a moment of ignorance of all the arguments discussed in this paper, universals just seem to make intuitive sense, in spite of the – possibly - counter-intuitive parallel belief in an abstract realm of abstract objects. A partly intuitive defence of universals is given by Russell in his [1912], which was referred to in the first section of this paper.

 

Classes also proved to be capable of generating their own similar infinite regress problems, as well as the noticeable and sometimes bizarre promiscuity of classes engendered by an over reliance on the resemblance-relation. However, it is evident that the resemblance-relation must be of vital, if not of necessary, importance when it comes to class-members, class-inclusion and class-exclusion. It is also evident that there are many vital and indeed necessary relations and connections to be made between classes and concepts (well expressed in Frege’s scheme). With concepts we have the resemblance-relation between classes as well as the reference-relations between the objects which fall under concepts. We also sometimes have an identity, rather than just a similarity, between concepts. In addition, concepts qua intensional entities are of  use when treating similar or even identical objects in terms of the intensions rather than extensions of their predicate-expressions and which also enable us to make the required resemblance-relations I concentrated upon in the paper.

 

I then discussed Lewisian counterpart theory and the way in which resemblance-relations play an important role both in making connections or noting resemblances between counterparts and their objects at our world, as well as between counterpart-worlds and our world. I took perfect and complete resemblance to be both logically impossible and instrumentally inefficacious in counterpart theory (indeed, in any context). Similar considerations were restated when we discussed Max Black’s two-membered world and the resemblance-relations, or lack thereof, between object a and object b. In addition, if these ostensibly  indiscernible objects were transported to our world, this  would automatically create similar problems and indeed problems of even greater intensity.

 

In conclusion. The resemblance-relation, or resemblance simpliciter, turns out to be of vital importance and indeed necessary constituent of so many, if not all, of our cognitions and experiences, just as Russell argued in 1912 and Kant argued, if only in a sense and indirectly, in the 1780s.

 

Note:

 

 (1) Similarly in Brentano’s theory of mind [see his 1911]. Brentano thinks here primarily in terms of mental act and the mental object of that act. The mental act takes a mental object as its subject; or,  we can say, as its intentional object. But can the mental act itself also become the object of a higher-order mental act? Thus:

 

… (ad infinitum)

ä

mental act and mental object

ä

mental act (as object)

ä

mental object of the initial mental act

 

However, this schema cannot be mentally exemplified for psychological and logical reasons. If the higher-order mental act has another mental act as its object, then the subject or mind of these acts would require the possibility of two mental acts occurring simultaneously, each with its own independent mental object. The lower-order act’s object would be a simple mental object. The higher-order act’s mental object would be another mental act seen as mental-act-object (of a mental act). A mental act which has its own mental object cannot itself be the mental object of another mental act. At least not if mental-act2 were simultaneous with mental-act1. We can have a higher-order mental act of a lower-order mental act in the sense that we can scrutinise the lower-order mental act in retrospect but not in action or in transitu, as it were. I can think the thought: ‘I thought a good thought about Mary this morning.’ But when I was thinking, ‘Mary is really fit’, this morning, that mental act, thinking that Mary is fit, couldn’t itself have been a mental object of an higher-order mental act to which it would be its mental object. The mental act cannot be the mental object of another mental act, just as our P1 earlier did not require U1 in order to resemble P2. Again, if one universal is allowed, then an infinite number must also be entailed by its acceptance and utilisation, just as if we allow mental acts themselves to become higher-order mental acts-as-objects, which themselves have lower-order mental-objects, could itself become the act-object of yet another  higher-order mental act. And so on.

 

References:

 

Aristotle  (1985) in his Nicomachean Ethics, tr. T. Irwin

Armstrong, D.M. (1986) ‘The Nature of Possibility’, in the Canadian Journal of Philosophy, pp. 575-94

Black, M. (1954) ‘The Identity of Indiscernibles’, in his Problems of Analysis

Brentano, F. (1911) On the Classification of Psychical Phenomena

James, W.  (1929) ‘The Will to Believe’ and ‘Humanism and Truth’, in his Selected Papers on Philosophy

Kant, I. (1787) the Critique of Pure Reason (various editions)

Kripke, S. (1971) ‘Identity and Necessity’, in Identity and Individuation, ed., M.K. Munitz

Frege, G. (1879/1972) Begriffsschrift, translated as Conceptual Notation, trans. by J.L. Austin

                (1956) ‘The Thought: A Logical Inquiry’, taken from Mind, vol. 65, pp. 289-311

Leibniz, G. (1943/1973) Philosophical Writings, ed. G.H.R. Parkinson and trans. by Parkinson and M. Morris

Lewis, D. (1986) ‘Counterparts or Double Lives’, in his On the Plurality of Worlds

                 (1968) ‘Counterpart Theory and Quantified Modal Logic’, in The Journal of Philosophy, 65, 5

                 (1986) ‘Counterparts or Double Lives?’, in his On the Plurality of Worlds

Quine, W.V.O. (1970) ‘Meaning and Truth’, in his Philosophy of Logic

Russell, B. (1912) ‘The World of Universals’, in his The Problems of Philosophy

Taylor, D.M. (1970) ‘Understanding and Knowing the Meaning of Words’, in his Explanation and Meaning

Wittgenstein, L. (1921) Tractatus Logico-Philosophicus

                           (1953) Philosophical Investigations (Blackwell)

 

Suggested Further Reading:

 

Allaire, E.B. (1963) ‘Bare Particulars’, in Philosophical Studies, 14

Lewis, D. (1983) ‘New Work for a Theory of Universals’, in the Australasian Journal of Philosophy, pp. 343-77

Price, H.H. (1953) ‘Universals and Resemblances’, in his Thinking and Experience

Russell, B. (1918) ‘Existence and Description’, in The Monist (1918)

Simons, P. (1994) ‘Particulars in Particular Clothing’, in Philosophy and Phenomenological Research, 54.3