Perhaps one family of properties is entirely determined by the existence of another family. For instance, psychological, moral or ethical properties might be entirely determined by broadly speaking physical ones by a relation such as supervenience , realisation or grounding. Furthermore, while some accounts of supervenience relate facts rather than properties, properties still play a crucial role as constituents in facts or states of affairs.
Mathematical properties might be thought to be determined by logical properties, but in that case the relation of determination is one of logical entailment rather than ontological priority. See Frege and Russell. The question of which families of properties exist mind-independently and which do not, and whether interesting relations exist between families of properties, can be clarified only by examining specific features of the different subject areas associated with them, a much larger task than can be accomplished here.
Furthermore, although it makes intuitive sense to divide properties into families such as the physical, the psychological and so on, further philosophical consideration reveals difficulties in clarifying such distinctions and making them philosophically rigorous while retaining an interesting account of the relationship between them.
There is, for instance, not much philosophical substance to a distinction between physical properties and mental ones if these families can be defined only in opposition to each other. Finally, one might be interested in whether some properties within a family are dependent upon others of the same family, making some individual properties more fundamental than others.
For example, one might think that all ethical properties are determined by one or two fundamental ones— being good or being just , for instance—or one might maintain that mathematical properties are entirely determined by the properties of natural numbers.
Again, it is the task of the different areas of philosophy concerned, such as Moral Philosophy or the Philosophy of Mathematics in these cases, to work out whether these dependencies are viable.
The question of whether some properties are more fundamental than others, in the sense of their determining the existence of other properties, is also of more general metaphysical interest when we overlook the boundaries between different families of properties, since it is related to the question of how many properties there are. Does every possible property exist? Does every predicate pick out a property? The answers to these questions lie somewhere on a continuum between minimalism on the one hand, which maintains that a very sparse population of properties exists, to maximalism on the other, which asserts the existence of every possible property and perhaps even some impossible ones.
This contrast between the minimalist and maximalist ends of the continuum is also captured by two conceptions of properties as being sparse and abundant Lewis a.
How we decide which point on this continuum is the most plausible depends in part upon the role we think that properties play in the world and also upon the identity conditions which we think properties have: that is, upon what makes one property the same as or different from another.
Furthermore, it may turn out that there are different conceptions of properties in play, intended to fulfil different metaphysical roles, which may be able to coexist alongside each other. Thus, a dualist account of properties is also a possibility, or else one might find some way in which the sparse properties and the abundant ones are connected.
The minimalist maintains that the properties which exist are sparse or few in number, a set of properties which may determine the behaviour of the rest.
From a physicalist standpoint, the properties of fundamental physics are the most promising candidates for being members of the minimal set of sparse properties: properties of quarks, such as charge and spin , as opposed to properties such as being made of angora , liking chocolate or being green. Some sparse properties may exist which we have yet to discover, and which we may never discover; their existence is in no way tied to our language use or what we have the ability to pick out.
Although there are few sparse properties, this is a comparative claim: there may still be infinitely many of them if we consider determinate properties such as specific masses—such as having mass of 1.
The maximalist, on the other hand, obeys a principle of plenitude with respect to which properties exist. Perhaps one of the most abundant population of properties is postulated by Lewis and quickly rejected for not being metaphysically useful , who regards qualitative similarity and difference to be determined by membership in sets of actual and possible individuals.
In the least discriminating understanding of this account of properties, any set of actual or possible individuals counts as a property, making the collection of properties into a super-abundant transfinite collection which far outruns our ability to name them.
Such entities might even range beyond the possible to include universals which can never be instantiated, or which could be instantiated only if the laws of logic were non-classical, such as universals corresponding to the properties of being a round square or being a true contradiction. A prima facie less abundant form of maximalism considers properties to be the semantic values of predicates, thus entities which either determine the meaning of any actual predicate in a human language or determine any meaning which there is or could be.
Whether this second maximal account of properties is only prima facie less abundant than the previous suggestion or is genuinely less abundant depends upon the relationship between possibility and range of meanings, a question which will not be considered here.
If the range of possible meanings turns out to be coextensive with the range of possibilities, there may be no difference between these options. Even if we restrict ourselves to actual languages, there are many predicates, and so if there are properties which correspond with each of them, we will have a very abundantly populated ontology.
How finely grained such a maximalist ontology is depends upon how we distinguish one property from another or, relatedly, one predicate from another.
In this view, there are uncontroversially properties for being red and being not red. But one might wonder whether there is a distinction between being red and not being not red which can be determined only when we have a principle for individuating properties or predicates.
One might attempt to hold an intermediate position between maximalism and minimalism. For example, one might argue that which properties exist are those which have explanatory utility, giving us a more abundant population of properties than the minimalist physicalist accepts and a more restricted one than that which maintains that there is a property to determine the meaning of every predicate.
But on reflection it is not clear how different this view will turn out to be from the maximalist accounts based upon the semantic values of predicates; after all, predicates exist because we use them in explanatory sentences. One might need a more restrictive account of legitimate explanations in order to whittle the range of properties down. One advantage of a liberal, maximalist account of properties is epistemic: if properties are based upon predicates of our language, or on the types which we employ in our explanations, then properties are easy to find.
However, this epistemic advantage over minimalism may not persist once we move away from the properties we encounter in the natural and human world and consider how we know about the myriad uninstantiated properties which most maximalists endorse, or once we consider the properties which are not instantiated by spatio-temporal objects but by abstract ones.
These cases are particularly problematic because, if a version of the causal theory of knowledge is true, it is not clear how we could know about the properties of abstract objects or about properties which are not instantiated in the actual world at all. At this point, maximalism loses the epistemic advantage, although it still promises a useful account of meaning based upon which properties exist.
Third, the maximalist can explain predicate meaning directly: the properties which exist determine what our predicates mean. But for the minimalist, these advantages do not mitigate what he regards as the vastly uneconomical, overpopulated ontology of properties which the maximalist endorses. The maximalist accepts properties such as being threatened by a dragon on a Sunday and being fourth placed in the Mushroom Cup on MarioKart in the guise of a gorilla.
The former is a property which has never been instantiated, while the latter is one which is only instantiated in a world of computer games, motor races and gorillas. Are we to say that these properties have always existed? If we are not, then they must have come into existence at some point in the history of the universe, in virtue of a more minimal set of properties which forms the basis for all the rest.
If we treat these original properties as fundamental, the minimalist argues, then parsimony will be restored. In addition to rejecting higher-level properties which appear to be superfluous to the causal workings of the universe, such as being within two miles of a burning barn or being fourth placed in the Mushroom Cup on MarioKart in the guise of a gorilla , some minimalists also adhere to a Principle of Instantiation and reject all alien properties which are never instantiated in the actual spatio-temporal world.
Alien properties, such as being a perfect circle or being threatened by a dragon on a Sunday , are rejected in favour of treating them as conceptual or ideal entities which are mind-dependent. Minimalists disagree about how minimal the set of sparse properties should be, with some physicalist minimalists accepting only the properties of fundamental physics whatever they turn out to be.
However, if we restrict properties to this extent, we are left with the question of what a great many things which we thought were properties actually are. If being water or being square , being green or being a mouse are not properties, then they must be something else, since they form such a central position in our worldview that eliminating them entirely from the ontology is out of the question.
It does not seem plausible to treat them in the same way that Armstrong does with alien properties and to maintain that they are mind-dependent or ideal.
At this point, it seems that a compromise is needed. Both minimalism and maximalism are viable in their own right, but as far as explanation goes, they lack precisely what the other can provide. Ideally, the property theorists would like the best of both worlds. There are two ways in which this compromise can be achieved: first, by a form of dualism about properties which treats sparse and abundant conceptions of properties as different categories of entities Bealer According to Lewis a, , there is a fundamental set of sparse, perfectly natural properties which determine the existence of all the other properties by set-theoretic, Boolean combinations.
All other properties lie along a continuum, placed according to how simply they are related to the perfectly natural ones. Those which are closely related count as natural properties, with naturalness being a matter of degree which is determined by closeness to perfectly natural properties. If we suppose that the sparse properties are physical ones, then properties such as being green or being a mouse are both natural to some degree or other, as is to a lesser extent being fourth placed in the Mushroom Cup on MarioKart in the guise of a gorilla , but eventually naturalness trails off.
The abundant properties exist in virtue of being determined by the sparse natural properties. The ontological distinction which Lewis marks can also be characterized in other ways. For instance, Armstrong maintains that some universals are genuine ones, with the existence of other universals being determined by them. Such a distinction between perfectly natural sparse properties and the rest is a primitive one, however, and is thus not open to further analysis.
If one considers parsimony to be an objective fact about the universe, then it is plausible to accept that some such minimal set of properties exists, but its existence has to be assumed rather than being argued for McGowan A particular is said to instantiate a property P, or to exemplify, bear, have or possess P.
In the case of Platonic forms, the particular participates in the form of P-ness which corresponds to or is identified with the property P. One might wonder whether instantiation can be analysed further in order to give us some insight into the relationship between a particular and the properties which it instantiates, but it turns out that this is very difficult to do. In fact, instantiation runs into two major problems: the instantiation regress and problems about whether self-instantiation is possible.
The first problem arises if instantiation is treated as a relation. Presuming that relations are analogous to properties, or are a species of property, then the instantiation relation will behave in a similar way to a property. Let us say that particular b is P. If a relation of instantiation connects b with P, then b instantiates P.
But then something must connect b, P and the instantiation relation let us call it I 1 , and so there must be another instantiation relation I 2 which does this job. However, now the question arises of what connects b, P and I 1 with I 2 , and the answer must be that there is another instantiation relation I 3 to do that; and then there must be another relation I 4 to connect b, P, I 1 and I 2 with I 3.
For each instance of instantiation , we require another relation to bind it to the entities which we already have and so there will never be enough instantiation relations to bind a property P to the particular which has it. It appears that treating instantiation as a relation leads to an infinite regress, and so the instantiation relation is not coherent after all.
The instantiation regress is often associated with a regress suggested by F. There are several ways in which the property theorist might try to avoid this regress.
First, she might appeal to the notion of an internal relation: that is, a relation which exists if the entities it relates exist. Examples of internal relations include x being taller than y or x resembling y. All that is needed for such relations to hold is the existence of the things which they relate, Mount Everest and the Eiger for the former, for instance, or two black kittens for the latter.
However, one cannot say that instantiation is itself an internal relation because the existence of a particular b and a property P is not sufficient to determine that b is P. For example, the existence of a particular cat, Fluffy, and of the property of being white do not on their own guarantee that Fluffy is white; something more is required, in this case that Fluffy instantiates the property of being white. Even if Fluffy is white, the problem here is that the relation between Fluffy and being white is a contingent one; Fluffy could exist and be black or tabby and so the mere existence of Fluffy and whiteness does not determine the existence of the instantiation relation.
Although see Broad , David Armstrong argues that, while we cannot do without the first-order instantiation relation between particular and property, we can then treat whatever is required to bind particular, property and instantiation as being an internal matter. In terms of the example of the regress above, the additional instantiation relations, I 2 , I 3 and so on, exist if particular b, property P and I 1 exist such that b instantiates 1 P.
Nothing more is required, and the supposed regress is a cheap logical trick, rather than implying ontological infinitude. Armstrong claims that instantiation is a fundamental universal-like tie which is not open to further analysis. Do they provide, as he claims, an ontological free lunch , 56; MacBride , —6?
In addition, one might also question whether his solution works for every account of the ontology of properties. If we are to treat instantiation as fundamental, then different accounts of the ontological nature of properties might require their own accounts of instantiation. Alternatively, the property theorist might challenge the claim that the instantiation regress is vicious Orilia Although this may not be what we intuitively expect of the relationship between particulars and the properties they have, one might argue that there is nothing ontologically wrong with such infinitude unless one has already presupposed that the world is finite.
After all, we are happy to accept that the real numbers are infinite, such that there are infinitely many numbers between any two real numbers, and so it is not clear why such infinitude cannot occur in the natural world.
If one allows that the world is infinitely complex, then the instantiation regress is not vicious, although its consequences for the way the world must be are quite counterintuitive Allen, , 29— It seems plausible to maintain that any property instantiates being a property , and furthermore if one thinks that properties are abstract objects such as transcendent universals that the property of being abstract instantiates the property of being abstract.
Moreover, the situation with the Instantiation Regress would be simplified if it were possible for instantiation to instantiate itself. That way, one might argue that the apparently infinite multitude of instantiation relations were in fact instances of the same relation, instantiated over and over again, with different numbers of relata each time on some versions of the regress.
However, there is a logical problem with self-instantiation which has led some philosophers to suggest that self-instantiation should not be allowed. Let us suppose that, for every property of being Q , there is also a negative property of being not Q. But such a property appears to be logically impossible once we consider whether it instantiates itself: if the property of not instantiating itself does not instantiate itself, then it does instantiate not instantiating itself and so it instantiates itself.
But if it does instantiate itself, then it is self-instantiating and so it does not instantiate itself. We have a paradox. One might mitigate this consequence by introducing a theory of types for properties in addition to banning self-instantiation. Thus, we would have first-order properties which are instantiated by particulars, second-order properties which are instantiated by first-order properties, third-order properties which are instantiated by second-order properties and so on; each nth-order of properties can only be instantiated by the entities of the n-1 th order.
Being a property would then be a shorthand for being a second-order property a property instantiated by first-order properties , or being a third-order property a property instantiated by properties of first-order properties and so on, and these properties do not self-instantiate.
However, this hierarchy is perhaps too strict for daily use and conflicts with our intuitive judgments. For example, if a table instantiates the property of being crimson, it also instantiates the property of being red and being a colour ; but the property of being crimson also intuitively instantiates being red and being a colour.
Alternatively, one might solve the problem of self-instantiation by limiting which entities count as genuine properties and accepting a more minimalist position. This response rejects the premise that corresponding to every property Q, there is a property of being not Q which is instantiated just when Q is not. Thus, everything which does not instantiate the property of being red is not thereby not red , and we need not think that the property of not self-instantiating accompanies the property of self-instantiating.
The paradox associated with there being a property of self-instantiation need not arise. While Plato regarded participation in a form as making something the kind of thing it is, Aristotle also treated such kinds as giving a particular the causal power to do something, the potential to have certain effects. This contrast between understanding properties as qualitative, categorising entities and as dispositional or causally powerful ones survives in contemporary philosophy as the distinction between categorical and dispositional properties.
We can conceive of a property such as mass in two contrasting ways: on the one hand, mass is a measure of how much matter a particular is made of; on the other, the mass of a particular determines how much force is required to move it, how much momentum it will have when moving and thus what will happen if it hits something else, and how much energy will be produced if the mass were to be destroyed. Some philosophers argue that all dispositional properties are dependent upon categorical ones Armstrong ; Lewis , ; Schaffer ; others argue that all properties are dispositional and have their causal power necessarily or essentially Cartwright ; Mumford , ; Bird ; Marmadoro a ; some accept that a mixture of categorical and dispositional properties exist Ellis , ; Molnar ; and still others contend that all properties have a dispositional and a categorical aspect Schroer or are both categorical and dispositional Heil , Dispositional properties, properties which have their causal roles essentially, are also known as dispositions, powers, causal powers and potentialities; however, it is important to note that these terms are not always used interchangeably.
There are three primary motivations for the view that all dispositional properties must depend somehow upon categorical ones: first, dispositional properties are regarded as epistemologically suspect, since we cannot experience a dispositional property as such. Second, dispositional properties are considered to be ontologically suspect.
Third, it is thought that we do not need to think of dispositions or dispositional properties as being an ontologically independent category of entities because statements about the dispositional properties an individual instantiates can be analysed as conditional statements about the categorical properties which that individual instantiates, or else we can give an ontological account of how dispositional properties depend upon categorical ones.
These issues are considered in turn. The first motivation is more common within the empiricist tradition, but not exclusive to it. To say that a particular has a disposition or a causal power to do something does not entail that the causal power is actually manifested or that the effect is produced, since the particular may not be in the appropriate conditions for the effect to occur.
For instance, although a particular sugar cube is soluble, such a disposition may never be manifested if the sugar cube is never near water; its being soluble ensures that it could dissolve, that it would were the circumstances to be right, and perhaps also that it must do so although dispositionalists disagree about whether a causal power manifests itself as a matter of necessity in the appropriate circumstances. Thus, accepting the existence of irreducible dispositional properties involves accepting the existence of irreducible modality in nature, perhaps amounting to natural necessity, which makes each property produce its respective effects.
As Hume pointed out, such natural necessity cannot be detected by experience, since we can only experience what is actually the case, and so strict empiricists have rejected irreducible dispositional properties on this basis. Some of those who think that at least some dispositional properties are irreducible to categorical ones accept this view about our experience and argue that we have other reasons to accept natural necessity, while others argue that we can experience irreducible modality in nature after all, perhaps through our own intentions being dispositional Mumford and Anjum, The second ontological objection to irreducible dispositional properties is raised by Armstrong , 79 who argues that accepting dispositional properties commits one to Meinongianism.
Imagine even that we had no interest in markers, generally, and that consequently, there is no generic word for markers. In that case, being brown would be an essential property of a brarker and thus, swapping its brown ink for black would constitute an identity-destroying change.
A brarker would have ceased to exist and a blarker would have come into existence. We can raise the same problem for essences, modally construed. As Quine observed, in Word and Object :.
Mathematicians may conceivably be said to be necessarily rational and not necessarily two-legged; and cyclists necessarily two-legged and not necessarily rational. But what of an individual who counts among his eccentricities both mathematics and cycling? Is this concrete individual necessarily rational and contingently two-legged or vice versa?
Just insofar as we are talking referentially of the object, with no special bias toward a background grouping of mathematicians as against cyclists or vice versa, there is no semblance of sense in rating some of his attributes as necessary and others as contingent. If our interest in Oscar is as a cyclist, then being two-legged is an essential property and being rational, an accidental one.
But if our interest in Oscar is as a mathematician, then being rational is an essential property and being two-legged an accidental one. You may be wondering what the problem is. Why does it matter if properties are essential or accidental, only under a particular description?
From the standpoint of understanding change, it may not matter much. Just as what counts as an essential or accidental property is relative to a description, what kind of change has occurred is relative in precisely the same way. There is no absolute or description-free conception of change and no absolute fact as to whether a change has been identity-preserving or identity-destroying.
It is, however, a serious problem from the epistemic standpoint. I suppose, as you imply, that part of the problem here is the timelessness of the definitions. Oscar was a mathematician-cyclist until he became demented and had a leg amputated — henceforth he lost an essential part of his identity. Hi Dan, like Thomas I appreciate this even if I might have little to add.
In this case I have to mull over how much I require the concept of essence to employ realism. For example, to believe that there is an object by which I write or draw using a liquid which dries on a surface… does that really hinge on essentialism?
It seems like so many of these issues in philosophy are related to the need or the desire to seek absolute foundations. Is this not a similar issue to your recent topic regarding the focus on rationality as well as on the True, and the Good. It seems like much of his thought was a reaction against these foundational trends. Of the western philosophers I have read his writings resonate most strongly for me. Is that right, and are there other reasons?
Analytic Philosophy programs to a great extent — or at least when I was in graduate school — largely ignore him, as they do Peirce. James is about the only American Pragmatist you are likely to get, if lucky. I consider it a substantial hole in my education and suspect it narrows my imagination.
I am therefore always happy to have someone bring him into a conversation, in order to expand it. The preservation of the text has been inadequate so certain terms are unclear. The Accidental Properties of Numbers and Properties. Identity Over Time. Andre Gallois - - Stanford Encyclopedia of Philosophy. Essence and Modality. Edward N. Zalta - - Mind Penelope Mackie - - Oxford University Press. Theological Compatibilism and Essential Properties.
Nicola Ciprotti - - Nordicum-Mediterraneum 3 1. Andrew Newman - unknown. Artifact and Essence. Brandon Warmke - - Philosophia 38 3 Essences and Natural Kinds. Defending Coincidence: An Explanation of a Sort. Mark Moyer - unknown. Understanding and Essence. In other words, from the fact that it is necessary that every individual that is a cat is an animal, it does not follow that every individual that is in fact a cat is such that necessarily it is an animal.
In still other words, this type of essentialism about natural kinds does not entail sortal essentialism. It is perhaps worth mentioning that similar remarks apply to the case of a necessary a priori connection between properties. It is a necessary a priori truth that all mathematicians are rational. Following our model, we can say that it is essential to the kind mathematician to be such that all of its instances are also instances of the kind rational thing. It does not follow that Andrew Wiles, who is in fact a mathematician, could not fail to be rational—in which case he would also fail to be a mathematician.
To give an even more perspicuous example, it is a necessary a priori truth that all bachelors are unmarried. It does not follow that Michael, who is in fact a bachelor, could not be married. Philosophers have thought not only about whether an object has this or that particular property essentially but also about whether an object has a special kind of essential property, an individual essence , a property that in addition to being essential to the object is also unique to it in the sense that it is not possible that something distinct from that object possesses that property.
The claim that there are substantive examples of individual essences has had few defenders. Leibniz was one, and he thought that such essences could be given by purely qualitative properties. Forbes is another, but he disagrees with Leibniz that an individual essence can be given by a purely qualitative property. The haecceity or thisness of an object, the property of being identical to that very object, provides a trivial example of an individual essence for each object.
Skeptics about essentialism have doubted the very intelligibility of such a question. Here is one prominent thought behind such anti-essentialism. The point is supposed to be that it makes no sense to say of the number nine, independently of any way of referring to it, that it is or is not essentially greater than seven.
Similarly, an anti-essentialist might say that when a person who is both a mathematician and a cyclist is thought of as a mathematician, being rational is essential to him, while being two-legged is not; but when the very same person is thought of as a cyclist, then although being two-legged is essential to him, being rational is not. Again, the point is supposed to be that it makes no sense to say of the very person who is the mathematical cyclist, independently of any way of thinking about him, that he is or is not essentially rational or two-legged.
According to the anti-essentialist, asking whether Andrew Wiles who we may suppose is a cycling mathematician could fail to be rational is like asking whether Andrew Wiles is taller than—both questions demand another relatum. Could he fail to be rational, relative to what way of referring to him?
Is he taller than whom? In response the essentialist will point out that the anti-essentialist's thought does not square very well with intuition. Could that very object have failed to be greater than seven? Intuitively the question seems intelligible, and the answer seems to be that it could not have failed to be greater than seven. Intuition also has it that the claim that the number of planets is greater than seven is not itself necessary.
The de re reading is this: the number of planets has the property of being necessarily greater than seven. The de dicto reading is this: the claim that the number of planets is greater than seven has the property of being necessary.
The essentialist is pointing out that the anti-essentialist's argument asserts that the latter intuition undermines the former, but does not say why. Assuming that we have knowledge of some essentialist claims, how might we account for that knowledge?
For the purposes of the present discussion, let us assume that we know that being such that there are infinitely many primes, being human, and originating from sperm s and egg e are essential properties of Socrates.
The first example is different from the last two in that it seems that we can know a priori that being such that there are infinitely many primes is essential to Socrates whereas it seems that we can know only a posteriori that being human and originating from s and e are also essential to him.
While it is a vexed philosophical issue just how to account for a priori knowledge of necessary truths such as logical truths, mathematical truths, and the homelier necessary truths like the truth that nothing can be red all over and green all over at the same time, accounting for our knowledge of the necessary truth that Socrates is such that there are infinitely many primes, does not seem to be problematic in some extra special way.
If we had a good account of our a priori knowledge of the necessary truth that there are infinitely many primes, then it would take little more to account for our knowledge of the necessary truth about Socrates that he is such that there are infinitely many primes.
For example, our knowledge that originating from s and e is essential to Socrates is based in part on our a priori knowledge that every organism has its origin essentially and in part on our empirical knowledge that Socrates is an organism that originated from s and e. Similarly our knowledge that Socrates is essentially human appears to be based in part on our a priori knowledge that everything has its kind essentially and in part on our empirical knowledge that Socrates is of the kind human.
Thus our knowledge of the claim that originating from s and e is essential to Socrates should be no more problematic epistemologically than our knowledge of the two claims on which it is based and our knowledge of the validity of the argument from those two claims.
As I have already mentioned, although there are difficult philosophical issues concerning our knowledge of logical truths, our knowledge of the validity of the argument in question does not seem to add any special problems of its own. Similarly, although there are philosophical issues concerning empirical knowledge, our knowledge that Socrates originated from s and e does not appear to add any special problems.
However our a priori knowledge that every organism has its origin essentially does seem to have special problems over and above the problems associated with accounting for our a priori knowledge of logic, mathematics, and the homelier necessary truths. The latter claims are generally supported by universally held intuitions or by arguments that are universally accepted whereas the former, like most philosophical claims, is supported by a less robust intuition and by a more controversial argument.
To see in some detail how philosophers have gone about defending origin essentialism, see the. Supplement on Arguments for Origin Essentialism. For more about arguments for sortal essentialism, see Wiggins and Mackie , chapters 7 and 8.
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