against determinable universals

8/6/2019 Against Determinable Universals

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Against Determinable

UniversalsUniversity of Durham, November 24, 2009

Dr Markku KeinnenUniversity of Turku

[email protected]


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IntroductionIn this presentation, I argue against the existence of determinable universals.Properties and relations are assumed to be tropes.Both d eterminate and d eterminable properties (if considered as universals) are identified with sortalnotions applying to tropes that are in certain formalrelations to each other.I take up certain recent arguments for determinableuniversals (Armstrong 1997; Johansson 2000; Ellis

2001) and attempt to formulate a trope theorist answer tothem.


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G eneral motivation

[3]: Determinable universals are prima faciere d un d ant postulations : property tropes alreadysuffice to determine the determinablecharacteristics of objects. We need not introduceseparate determinable properties.

[4]: Property tropes seem to fall under a certain(highest) determinable because of their verynature and we need not introduce determinableuniversals to explain this.


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Examples of determinates of

determinablesMo nadic natural pr o pertiesQ ualities : shapes, coloursQ uantities : masses, lengths, charges

N atural relati o ns

Q uantitative relations : distances, durations, space-time

intervalsSince quantities are best a posteriori candidates for natural properties, I will concentrate on quantities.


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C onventions

Let us stipulate that two objects share ad eterminate feature falling under determinable D(e.g., a specific mass) iff they are exactly similar

in respect of D (mass).Moreover, we can say that object i hasdeterminable characteristics D if the attributionof determinable D to i is true of i.

In continuation, I will concentrate on the highestdeterminables (mass, charge) and on the lowestdeterminates (specific masses, charges).


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G eneral characteristics of the

determinate determinable relationDownwar d entailment : If object i possesses adeterminable characteristics D, i must possess some

determinate feature F falling under D. For instance, anobject having a mass must have some determinatemass.Upwar d entailment : If object i possesses somedeterminate feature F, i must possess thedeterminable under which F falls. For instance, acircular object must have a shape.


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R elations between determinates of

a determinableEx clusiveness : The determinate features falling under a common determinable D are exclusive of each other.For instance, a 1 kg object cannot have any other mass.Resemblance : The different objects possessing adeterminate feature falling under determinable Dresemble each other in respect of D. For instance,objects having specific masses resemble in respect of mass more or less closely.

Assume that the determinate features are determinedby the determinate properties of objects. Thecorresponding determinate properties falling under thedeterminable resemble more or less closely.


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Different categorizationsDeterminate properties are commonly considered asfirst-order properties (universals or tropes).By contrast, d eterminable universals (if postulated) canbe categorized in three alternative ways:

1) (Russellian) first-or d er universals , i.e., universalproperties of objects.2) (Russellian) secon d -or d er universals , i.e., properties of

determinate properties (Armstrong 1997; Johansson2000 (?)).

3) Neo-Aristotelian property kin d universals , i.e.,determinable kinds of tropes (Ellis 2001). According tothis approach, determinate universals are determinatekinds of tropes (or, modes).


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Different categorizationsIn what follows, I will take the thir d Neo-Aristotelianapproach as granted for three reasons:

1) It is suitable for a theorist who assumes that propertiesof objects are tropes.

2) G illett & R ives (2005) have already argued against thefirst approach fairly convincingly (redundancyargument).

3) We can construct all main arguments for determinableuniversals by assuming that determinable universalsare kinds of property and relation tropes. Including thearguments Johansson (2000) presents.


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The Neo-Aristotelian approach to

determinable universalsAn important recent representative: Brian Ellis (2001,2002).Properties of objects are particulars: tropes (or modes).

The distinct tropes (1 kg tropes) are exactly similar because of being instances of the same determinatekind universal (of being a 1 kg trope).The distinct tropes (mass tropes) belong to the samedeterminable kind because of being instances of adeterminable kind universal (of being a mass trope).The determinate kinds of tropes are sub-kinds of thedeterminable kinds.


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Arguments for determinable

universals[1]: T he Argument from Resemblance (Ellis 2001:sec.2.3; cf. also Johansson 2000: sec.3)The distinct tropes belonging to the same d eterminatekind (e.g., two 1 kg tropes) are exactly similar to each

other. Moreover, the tropes belonging to the samed eterminable kin d (two mass tropes) resemble eachother (are connected by quantitative distance), while thetropes falling under distinct determinables do notresemble (are not connected by quantitative distance).Property tropes resemble exactly because they areinstances of the same determinate kind universal.Similarly, the best explanation of why the tropesbelonging to a determinable kind resemble is that theyare instances of a d eterminable kin d universal .


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universals[3]: T he Argument from the Physical Magnitu d es (cf.Johansson 2000: sec.4)The physical quantities falling under the same

determinable and related by quantitative distance form a

physical d imension : we can add the determinatequantities in the same dimension and obtain newdeterminates falling under the same determinable.Secondly, many determinate quantities belonging tocertain d istinct d imensions can be multiplied by eachother and we obtain determinates falling under a newdeterminable.The best explanation of these facts is that (many)physical dimensions correspond to determinableuniversals, ontological d eterminables having thedeterminate quantities in question as their instances.


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universals[4]: T he Argument from the Laws 0n Determinables(Johansson 2000: sec. 7)The determinable kinds of tropes are subjected to lawsconstraining the inter-determinable (e.g., determinabledependences) or intra-determinable relationships (e.g.,determinate exclusions). These laws are made true bythe determinable kind universals determining theessential nature of each determinable kind.Determinable kind universals must not be replaced withnominalist constructions.


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Arguments for Determinable

Universals[5]: T he argument from spectral kin d s (Ellis 2001: 65-66,79).Some of the determinable kinds of tropes (e.g., mass,distance) are spectral kin d s . Spectral kinds allow for acontinuous (or, a dense) variation among the intrinsicvalues of their instances. Spectral kinds cannot beconstituted by their instantiated values: it is probable thatevery quantity which is a spectral kind has uninstantiatedvalues (i.e., gappy instances). Thus, the quantity tropesbelonging to a spectral kind do not suffice to constitute it.Hence, we need to introduce determinable quantityuniversals to act as spectral kinds having uninstantiatedvalues.


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Arguments for Determinable

universalsFor instance, it can be argued that masses form aspectral kind.

1) It is consistent with physics that masses get arbitrarilysmall values (or, that there are infinitely many massesbetween any two distinct masses).

2) It is conceivable that there are arbitrarily small masses.3) Arbitrarily small instantiated masses are possible.4) Hence, the quantity mass gets arbitrarily small values,

many of which are uninstantiated.5) C onsequently, the quantity mass cannot be construed

by means of property tropes in formal relations to eachother.


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universals[6]: T he Argument from Functional Laws (Armstrong1997)Functional laws (such as Newtons inverse square law of gravitation) establish necessary connections between

determinate quantities falling under some distinctdeterminables (e.g., masses, distances and gravitationalattractions by some force). In establishing the necessaryconnections, they are completely undiscriminativebetween determinates (they do not contain exceptions).Since (some of) these quantities have uninstantiatedvalues, we cannot build the truthmakers of functionallaws solely by of means of the instantiated determinatequantities. We must introduce determinable universals toact as the parts of the truthmakers of functional laws.


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The trope nominalist account of

determinablesTropes are particular properties. A trope is:

1) C ategorially simple, i.e., it is either simple or all of its

proper parts are further tropes (entities of the samecategory).

2) A concrete, i.e., spatio-temporal entity.3) C ountable and identifiable (has identity of its own

indepedent of the identity any other entity).4) Has a thin particular nature to determine a single

feature of the object possessing the trope (e.g., themass of 1 kg).


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The trope nominalist account of determinables

According to trope nominalism , two distinct tropes t 1 andt 2 (e.g., two distinct 1 kg tropes) are exactly similar simply because of being particular properties they are.

Thus, exact similarity is an ungroun d e d internal relation(strict internal relation) between tropes t 1 and t 2.C onsequently, we need not introduce any further entitiesto ground their exact similarity.We must not introduce such entities: since determinate1kg tropes t

1and t

2are exactly similar because of their

existence, any further entity (e.g., relational trope of similarity) that would ground their exact similarity wouldbe a re d un d ant postulation .


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The exactly similar tropes (e.g., all 1 kg tropes) are allcertain kinds of tropes (1 kg tropes). They belong to thesame determinate kind because they are exactly similar to each other.

The property tropes t 1 and t 2 are the truthmakers of theclaim of their belonging to a determinate kind:

[1]: t 1 and t 2 are 1 kg tropes.

The trope nominalist can identify the d eterminate kin d of tropes (the kind of 1 kg tropes) with a kind term applyingto a group of tropes exactly similar trope to each other.C onsequently, she can reject the existence of determinate property kind universals


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We obtain the trope nominalist account of determinablesas a generalisation of the trope nominalist account of determinates (tropes belonging to a determinate kind).

Prima facie , all quantity tropes belonging determinablekind D are connected by quantitative distance and(usually) ordered by greater than relation.However, we cannot express quantitative distancesbetween tropes without recourse to the determinablekind itself (the specifications of quantitative distancesuch as trope t is 1kg greater than trope u containreference to the determinable kind via the unit).


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The Trope Nominalist account of determinables

Some quantities (such as electric charge) take positiveand negative values and we must introduce both positiveand negative relations of proportion.If the relations of proportion between determinatequantities falling under D are given, we can determine

order between them and specify quantitative distancesbetween them (given some conventionally chosen unit of the quantity).

The formal relation relation of exact similarity is a specialcase of the proportion relations (1 : 1 proportion).


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Thus, tropes t 1 and t 2 are truthmakers of claim [5]:

[5]: t 1 and t 2 are mass tropes

The trope nominalist can identify each d eterminable kin d of tropes (the kind of mass tropes) with a kind termapplying to a group of tropes connected by the formal

relations of proportion and (possibly) combinatorialexclusion, i.e., with a formal kin d of tropes.C onsequently, the trope nominalist can reject theexistence of determinable kind universals.


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The trope nominalist answer [A1]: According to the trope nominalist , certain propertytropes are exactly similar to each other simply becauseof their existence. The introduction any further entity(e.g., a determinate kind universal) to account for theexact similarity of tropes leads to redundancy.Similarly, the quantity tropes falling under highestdeterminable D are connected by the relations of proportion because of their existence. Therefore, theyresemble each other (i.e., are connected by quantitativedistance). The tropes belonging to distinct determinable

kinds are not connected by the relations of proportion. Again, the introduction of any further entities (e.g.,determinable kind universals) to account for these factsleads to redundancy.


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The trope nominalist answer [A2]: The division of tropes into determinate anddeterminable kinds is objective and mind-independentbecause tropes are in the required formal relationsindependent of us and our classifications. Hence, we

need not introduce determinate or determinable kinduniversals to make true the attributions of natural kind totropes.Determinate kinds are sub-kinds of determinable kindsbecause the formal relation determining the membershipof trope in a determinate kind (i.e., exact similarity) is aspecial case of the formal relations that determine themembership of tropes in a determinable kind (i.e., therelations of proportion).


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The trope nominalist answer [A3]: The present approach does not directly explain the(alleged) truth of certain e x istence claims concerningdeterminates of determinables (Johansson (2000).Since certain monadic determinate quantities (such as

masses and charges) are additive, the determinatetropes falling under D possessed by two objects a and bdetermine the quantitative feature falling under Dpossessed by the object composed by a and b. (Thosewho like complex properties, can introduce a complextrope corresponding this feature.)

Second, we can either postulate tropes belonging to afurther determinable kind that form a physical dimensionof some derived physical quantity or try to explain thatdimension away as a determinable kind of tropes.


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The trope nominalist answer [A4]: Johanssons examples of laws concerningdeterminables fail to show that we need to postulatedeterminable universals.First, determinate tropes falling under a determinable are

in the relations of proportion to each other, we can givethem certain quantized values (given some chosen unit).These values can be added and (in some cases)subtracted.Secondly, the determinate tropes falling under adeterminable are exclusive of each other because theyare connected by formal relation of combinatorialexclusion.Thirdly, the tropes acting as properties of a certain kindof object can be generically dependent on the tropesbelonging to another determinable kind.


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The trope nominalist answer [A5]:S pectral kin d s cannot be constructed by means of the present approach. However, some proposedexamples can be explained away:

1) Masses: the argument that masses form a spectral kind

was rather weak based on the considerations of conceivability (understood as consistency with physics).C ounter-proposal: The fundamental values of quantity(rest) mass are given by the rest masses of thefundamental particles. Although the quantity mass doesnot come in natural units, it does not get arbitrarily small

values. All masses of objects are multiples of thefundamental masses.2) Distances (d urations an d space-time intervals ): if space

is infinitely divisible, distances have a stronger claim for a spectral kind.


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The Trope Nominalist answer

[A6]: Pace Armstrong, we need not identify instances of functional laws (i.e., determinate laws) with relationsbetween universals. According to dispositionalistapproach, the statements of determinate law are madetrue by the property tropes possessed by objects.However, many determinate laws seem to describe howthe objects possessing these property tropes wouldbehave in counterfactual situations.


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C onclusionThe Trope Nominalism identifies the determinable kindsof tropes with kind terms applying to groups of tropesconnected by the formal relations of 1) proportion , and(usually) 2) combinatorial e x clusion .

The existence of property kind universals is rejected.Tropes are in the formal relations of proportion becauseof being the tropes they are (as formal relationsproportions are not relational entities).Burden: spectral kin d s must be explained away.

Benefit: similarities between the determinates of adeterminable are given by means of the relations of proportion. This helps us to give a more unified list of formal relations.


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R eferencesArmstrong, D. M. (1978): A T heory of Universals, Vol. 2 of Universals an d S cientific Realism(C ambridge: C ambridge University Press).Armstrong, D. M. (1997): A Worl d of S tates of Affairs , (C ambridge: C ambridge University Press).Bigelow, J. & Pargetter, R . (1990): S cience an d Necessity , (C ambridge: C ambridge UniversityPress).C ampbell, K. K. (1990): Abstract Particulars. (Oxford: Basil Blackwell).Fales, E. (1990): Causation an d Universals. (London & New York: R outledge).

G illett, C . & R ives, B. (2005): The Non-existence of Determinables: Or, a world of AbsoluteDeterminates as a Default Hypothesis, Nous 39:3, 483-504.Ellis, B. (2001): S cientific E ssentialism , (C ambridge: C ambridge University Press).Ellis, B. (2002): Philosophy of Nature , ( C hesham: Acumen).Johansson, I. (2000): Determinables as Universals, T he Monist 1, 101-121.Maurin, A-S. (2002): If T ropes , (Dordrecht: R eidel).

R ussell, B. (1912): T he Problems of Philosophy, (Oxford: Oxford University Press).Sanford, D. (2006): Determinates and Determinables , Standford Encyclopedia of Philosophy

Shoemaker, S. (1980): C ausality and Properties, in van Inwagen (ed.): T ime an d Cause ,(Dordrecht: R eidel).Simons, P. (2003): Tropes, R elational, Conceptus .


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against determinable universals

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