Determinates vs. Determinables (Stanford Encyclopedia of Philosophy) Cite this entry Search the SEP • Advanced Search • Tools • RSS FeedTable of Contents• What's New• Archives• Projected ContentsEditorial Information• About the SEP• Editorial Board• How to Cite the SEP• Special CharactersSupport the SEPContact the SEP ©Metaphysics Research Lab,CSLI,Stanford University  Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia FreeDeterminates vs. DeterminablesFirst published Fri Apr 26, 2002; substantive revision Fri Oct 27, 2006Everything red is colored, and all squares are polygons. A square isdistinguished from other polygons by being four-sided, equilateral, andequiangular. What distinguishes red things from other colored things?This has been understood as a conceptual rather than scientificquestion. Theories of wavelengths and reflectance and sensoryprocessing are not considered. Given just our ordinary understanding ofcolor, it seems that what differentiates red from other colors is onlyredness itself. The Cambridge logician W. E. Johnson introduced theterms determinate and determinable to apply to examples such as red andcolored. Chapter XI, of Johnson's Logic, Part I (1921), “TheDeterminate and the Determinable,” is the main text fordiscussion of this distinction.This entry consists of the following sections. Section 1 attendsclosely to Chapter XI, of W. E. Johnson's Logic, Part I. Section 2briefly discusses Johnson's use of the determinate-determinablerelation elsewhere than Chapter XI of Logic, Part I, and connects thiswith A. N. Prior, “Determinables, Determinates, andDeterminants” (1949). Section 3 describes a 1959 symposiumbetween Stephan Körner and John Searle entitled “OnDeterminables and Resemblance” and examines both contributionscritically. Section 4 describes the Munsell Color Solid so that colorexamples can be more exact. Section 5 describes and criticizes attemptsto define the determinate-determinable relation by means of predicateentailment in the style of Searle. Section 6 pays more attention tothis distinction and directs attention to a certain understanding of“disjunctive predicate.” Contrived disjunctive andconjunctive predicates are the typical cause of difficulties inattempts to define the determinate-determinable relation. Section 7distinguishes independent predicates from non-independent predicates,and thus distinguishes disjunctive and conjunctive predicates fromnon-disjunctive and non-conjunctive predicates, in a way that assumesno prior classifications of determinates under a determinable. Section8 explores a view advanced by Johnson and endorsed by many others thatthe things in the world, as distinguished from ourdescriptions and conceptions of them, are absolutely determinate. Thissection entertains the contrary view that nothing is absolutelydeterminate.1. W.E. Johnson's Chapter on the Determinable2. W. E. Johnson and A. N. Prior3. The Körner-Searle Symposium4. The Munsell Color Solid5. After Searle6. Predicates and Properties7. Boundaries and Borderlines8. Absolute DeterminacyBibliographyOther Internet ResourcesRelated Entries1. W. E. Johnson's Chapter on The Determinable1.1 Substantive and AdjectiveJohnson invents phrases and also attaches new meanings to familiarwords. His terms determinate, determinable, occurrent, continuant andostensive definition have entered the philosophical lexicon. Some ofhis innovations are largely forgotten. Throughout Logic and especiallythroughout Part I, Chapter XI, Johnson uses a distinction betweensubstantive and adjective. Although he draws and observes manydistinctions meticulously, the distinction between the mention of alinguistic expression and its use is not among them. Adjective andsubstantive sometimes appear in his writings to be linguistic items.More often they are definitely non-linguistic. They are logicalcategories, “the ultimate comprising classes” (1922, p.60). “My distinction between substantive and adjective is roughlyequivalent to the more popular philosophical antithesis betweenparticular and universal; the notions, however, do not exactlycoincide” (1922, p. xiii). The term ‘adjective’remains in all forthcoming quotations from Johnson. In discussion ofJohnson, the term ‘property’ often replaces‘adjective’ although it is not an exact equivalent.Johnson is interested in the logical differences between ‘Redis a colour’ and ‘Plato is a man’. He says that thesecond sentence involves adjectival predication. ‘Human’ isan adjective (property) predicated of Plato. ‘Colour,’ onthe other hand, is not an adjective (property) predicated of red (1921,p. 176).1.2 Similarity and DifferenceColor is one of Johnson's central examples. Red and blue aredeterminate with respect to the determinable color, and Carolina Blueand Duke Blue are determinate with respect to blue. The relation of a determinate to its determinable resemblesthat of an individual to a class, but differs in some importantrespects. For instance, taking any given determinate, there is only onedeterminable to which it can belong. Moreover, any one determinable isa literal summum genus not subsumable under any higher genus; and theabsolute determinate is a literal infima species under which no otherdeterminate is subsumable. (Part I, Introduction, 1921, p.xxxv)What makes red and blue and Carolina Blue all colors? Johnson deniesthat there is some property [some “secondary” adjective]that red and blue share that makes them both colors. The view thatcolor is itself a property that red and blue share requires anexplanation of what distinguishes the color red from the color blue.Explanations such as “Red is the color of fire trucks” and“Blue is the color of my true love's eyes” miss the point.They refer to mere contingent facts. An appropriate explanation shouldprovide a necessary truth such as ‘Triangles are three-sidedpolygons.’Rather than resemblance, the sharing of some property, that make redand blue colors, says Johnson, it is differences between colors.In fact, the several colours are put into the same groupand given the same name colour, not on the ground of any partialagreement, but on the ground of the special kind of difference whichdistinguishes one colour from another; whereas no such differenceexists between a colour and a shape. (1921, p. 176)The absence of a difference or exclusion of this kind explains whyred and square is not a determinate of a single determinable.“Taking any given determinate, there is only one determinable towhich it can belong” (1921, p. xxxv). The nature of the exclusionalso explains why no two determinates of the same determinable canqualify exactly the same entire spatio-temporal part of any object(1921, p. 181).Arguments about the incompatibility of colors in the 1950s and 1960swere concerned with theories of necessity, analyticity, the apriori, and meaning. (Edwards and Pap, 1973, has a bibliography ofsuch works, pp. 745-746.) These discussions rarely address specificallythe relation between determinables and determinates. Nor do assumptionsabout the incompatibility of determinates often connect with theproblem of understanding incompatibility in general. When the problemof incompatibility reopens there may be less emphasis on philosophy oflanguage and logic and more emphasis on the branch of metaphysics thatstudies the nature of properties and the recently formed hybrid ofmetaphysics and science that studies the nature of color and othersensory qualities.1.3 Determinables and GeneraTreatments of the determinate-determinable relation often contrastit with the species-genus relation. Features such as three-sideddifferentiate the species triangle under the genus polygon, while theonly feature that distinguishes the determinate red under thedeterminable color is the very determinate itself. A genus-speciesrelation obtains when a proper definition of the form X =YZ is possible. When no such definition is possible andcertain other formal requirements are satisfied, thedeterminable-determinate relation obtains. For this neat, sharpcontrast, Johnson provides at best only equivocal support. His remarksare sometimes incompatible with this contrast.Consider Johnson's examples. The introduction of the term‘determinable’ in Chapter XI reads: “I propose tocall such terms as colour and shape determinables in relation to suchterms as red and circular which will be called determinates”(1921, p. 174). So circular is a determinate of the determinable shapedespite the existence of a proper definition that distinguishes circlesfrom other shapes. Different shapes are incompatible and are thereforeunder the same determinable. Being related by incompatibility (in theright way) appears to be necessary and sufficient for items to bedeterminates under a single determinable. Some determinates such as redcannot be differentiated by a traditional, conjunctive genus-speciesdefinition. Others such as square and circular can be sodifferentiated. Johnson's example of shape shows that adeterminable-determinate relation does not require the impossibility ofa conjunctive definition.Rather than insist on a sharp contrast, Johnson attempts to subsumetraditional species-genus relations under determinate-determinablerelations:We have now to point out that the increased determination ofadjectival predication which leads to a narrowing of extension mayconsist—not in a process of conjunction of separateadjectives—but in the process of passing from a comparativelyindeterminate adjective to a comparatively more determinate adjectiveunder the same determinable. Thus there is a genuine difference betweenthat process of increased determination which conjunctivally introducesforeign adjectives, and that other process by which without increasing,so to speak, the number of adjectives, we define them moredeterminately.In fact, the foreign adjective which appears to be added on in theconjunctive process, is really not introduced from the outside, but isitself a determinate under another determinable, present from thestart, though suppressed in the explicit connotation of the genus.(Johnson, 1921, pp. 178-9)Johnson goes on to provide a symbolic representation of botanicalclassification in which there are five determinables. One of thesedeterminables is number of cotyledons under which fall the determinatesacotyledon, monocotyledon, and dicotyledon. The other determinablesconcern stamens, the corolla, forms of attachment, and divisibility.The determinables in this botanical example represent “the summumgenus ‘plants’ as describable under these five heads”(1921, p. 180). A determinable can have several dimensions.Johnson's discussion of color variations illustrates suchdimensions. Colors vary according to hue, saturation and brightness,and these variations are independent of one another. If hue,saturation, and brightness are determinables, they are not separate,since they depend on each other. There cannot be saturation withouthue, for example, even though no determination of saturation requiresany particular determination of hue. Johnson says that the determinablecolor is “single, though complex, in the sense that the severalconstituent characters upon whose variations its variability dependsare inseparable” (1921, p. 183).There is a difficulty here because the dependence patterns betweenthe three variables are not entirely uniform. Hue and saturation cannotexist without each other, or without brightness, but degrees ofbrightness do not require either hue or saturation. Black and whitemovies and photographs and many other achromatic examples come to mind.Dimensions of quality space can vary in their dependence relations oneach other.1.4 Quality OrderThere are differences between determinates under the same determinable.Johnson says these differences are comparable. The difference betweenred and yellow, for example, is greater than that between red andorange. In this case the several determinates are to be conceivedas necessarily assuming a certain serial order, which develops from theidea of what may be called ‘adjectival betweenness.’ Theterm ‘between’ is used here in a familiar metaphoricalsense imagined most naturally in spatial form. (1921, pp.181-182)The three-place relation (Dabc) the difference betweena and c is greater than that between a and b, however, does not byitself provide an adequate definition of ‘between.’ Adiagram helps to illustrate this point. Assume for the purpose ofdiagramming that the difference between a and c specifies acertain distance in quality space. A circle with center a andradius ac represents points in the space at distanceac from point a. Any distance between pointa and any point b within this circle is less than thedistance between a and c. A point b withinthis circle represents Dabc. As Figure 1 illustrates,Dabc is consistent with the distance between b andc being greater than the distance between a andc. Figure 1In this situation, b is not between a andc in any sense. For example, the difference (or distance)between red and yellow is greater than the distance between red andpurplish red, but purplish red is not between red and yellow.There is a similar difficulty with Mohan Matthen's suggestion aboutdistance measure. A feature A that is a lot redder thananother one B is more dissimilar to B than Cwhich is only a little redder than B; this comparison can becaptured by a distance measure: A is further away fromB than from C (Matthen, 2005, pp. 107-8).Consider the following instances:C: pale yellow A: pale orange B: very slightly redder than dark olive brownCompared to B, A is much redder than C.Although A and C are more dissimilar in respect ofhue, overall they resemble each other more than either resemblesB because they are both pale, quite close to white, not dark,quite close to black, and also because they do not differ maximallywith respect to hue (yellow and orange are contiguous rather thanopposed hues on the color wheel).The word ‘betwixt’, which appears in the next paragraph,comes from Goodman (1951), pp. 244-253, but only the word, notGoodman's definition or intended sense. This is an occasion to remarkthat Goodman and Carnap (1928) develop constructions of quality ordermuch more elaborate than Johnson's. They do not use a primitiveequivalent to Dabc in their constructions. Johnson returns toquestions of quality order in Part II of Logic, Chapter VII, “TheDifferent Kinds of Magnitude.”The following conjunctive definition, which overcomes thisparticular difficulty, is not a revision of a formulation by Johnson.It is the beginning, rather, of a brief attempt to define betweennessby means of Johnson's primitive Dabc: Let us say thatb is betwixt a and c if and only ifDabc and Dcba. Orange, but not reddish purple, isbetwixt red and yellow. Figure 2 adds to the circle in figure 1 anothercircle with the same radius with point c in the middle. Apoint b betwixt a and c is within theintersection of these two circles. Figure 2Betwixtness is too wide a notion to explicate betweenness. Supposethat the points in Figure 3, a specification of Figure 2, stand for thefollowing colors:R:a fully saturated, bright sample of redY:a fully saturated, bright sample of yellowO1:a fully saturated, bright sample of orangeO2:a less saturated, less bright sample of orange Figure 3O1 and O2 are both betwixt R and Y. But it isnatural to represent O1 as ‘right between’ R andY. O2 is somewhat off to the side. A better definition of‘between’ will count O1 but not O2 asbetween R and Y.Relying again on the notion of distance, one candistinguish two senses of between. (1) B issomewhere between A and C if and only if thedistance between A and B plus the distance betweenB and C is equal to the distance between Aand C. That is, B is located somewhere on thestraight line (in Euclidean space) between A and B.(2) B is exactly or halfway betweenA and B if and only if B is somewherebetween A and C and also the distance betweenA and B is equal to the distance between Band C. The following definition, built on Johnson's primitive,attempts to define somewhere between in sense (1):b is somewhere between a and cif and only if b is betwixt a and c, andnothing is both betwixt a and b and betwixtb and c.When two circles with no interior points in common are tangent, thepoint in common is on the straight line segment between the twocenters. Any point on a straight line segment between points xand y is the point in common between two circles with centersx and y that have no interior points in common. AsFigure 4 illustrates, b is on a straight line segmentbetween a and c if and only if the circle abis tangent to the circle cb. This is the case if and only ifnothing is betwixt a and b and also betwixtb and c; for any such thing has to be both aninterior point of circle ab and an interior point of circlecb, and these circles have no interior points in common. Figure 4Figure 5, illustrates a point b that is betwixt aand c but is not situated like point b in Figure 4.In this case, point b is on the intersection of two circlethat have interior points in common. Figure 5 shows this region as ashaded area. Anything within this shaded area is both betwixta and b and betwixt b and c. Figure 5Although a distance between points in these diagrams can be equal,or double, or half, another distance between points, that is due to theconventions of drawing these diagrams. There has been no explication ofthese distance notions by means of the primitive Dabc. Adefinition of right between would provide a sufficientcondition for the equality of the distance between a andb and the distance between b and c, butthere is no attempt here to provide such a definition using only theprimitive Dabc.Johnson uses his notion of betweenness to draw two independentdistinctions between quality order, interminable series in contrastwith cyclic, and continuous series in contrast with discrete (1921, pp.182-183). His use of the three-place relation the differencebetween a and c is greater than that between aand b undermines a point he insists on earlier thatresemblance between determinates does not group them under adeterminable. Johnson's three-place relation can also be expressedthe similarity between a and b is greater than that between a andc. Comparisons between differences are also comparisons betweenlikenesses or similarities. Perhaps his point can be expressed asfollows: no two-place relation of resemblance groups determinates undera determinable, although a three-place relation can be useful for thispurpose. Johnson's chapter ends with the pronouncement that "Thepractical impossibility of literally determinate characterization mustbe contrasted with the universally adopted postulate that thecharacters of things which we can only characterize more or lessindeterminately, are, in actual fact, absolutely determinate" (1921, p.185). Section 8 examines this claim.2. W. E. Johnson and A. N. PriorJohnson discuses determinates and determinables in Parts II and IIIof Logic (1922, 1924) and also elsewhere in Part I. In Part I, in achapter entitled “Laws of Thought,” Johnson formulates fourprinciples of adjectival determination that correspond to four morefamiliar principles of propositional determinations such as ‘Notboth P and not-P’ and ‘Either Por not-P.’In Part III, Johnson is concerned primarily with induction andcausation. Throughout Part III, he distinguishes the‘occurrent’ from the ‘continuant’ and oftendiscusses change, cause, and continuants with reference to determinatesof determinables.In Part II, Johnson refers to determinables in several differentcontexts. One discussion is especially important for understandingPrior's later treatment of the topic. Johnson introduces the notion ofa structural proposition which he compares to “what Kant meant by‘analytic’” (1922, pp. 14-15). In a structuralproposition, “it is impossible to realise the meaning of thesubject-term without implicitly conceiving it under thatcategory” (1922, p. 15).Arthur N. Prior takes up the question of structural propositionsthat relate determinates to determinables in the two-part article“Determinables, Determinates, and Determinants” (Prior,1949).Since a subject's being in a certain universe or category,i.e., its being determinable in certain ways, is presupposed in everygenuine characterization of it, an assertion that it is in thiscategory, and is thus determinable, would have for its predicatesomething which cannot really be separated from the subject in order tobe predicated of it. (Prior, 1949, p. 18)Prior's article reveals his very wide-ranging knowledge of the historyof logic. The article together with Prior (1955), reflects a detailedknowledge of Johnson's entire logical system, not only the three-partLogic (1921, 1922, 1924), but also Johnson (1892). Although some of thetopics in Prior (1949) have not prompted much subsequent discussion inconnection with determinates and determinables, Prior puts his fingeron one theme that is now central. The problem of fitting the relation between determinatesand determinables into a purely “conjunctional” logic mightbe summarily described as the problem of justifying the inference from“This is red” to “This is coloured” on theassumption that all formal inference consists in the passage from aconjunction to one of its conjuncts. (Prior, 1949, pp.191-192)As mentioned earlier, there seems to be no conjunction of the properkind of the form ‘x is F and x iscolored’ that is equivalent to ‘x is red.’Examples of improper conjunctions are: x is red and x is colored, x is either red or not colored, and x iscolored.3. The Körner-Searle SymposiumThe 1959 Joint Session of the Aristotelian Society and the MindAssociation included a symposium “On Determinables andResemblance” in which Stephan Körner spoke first and JohnSearle spoke second.Körner presents a logic of inexact concepts which reappears inhis 1966 book Experience and Theory. This logic recognizes, in additionto traditional set members and non-members, intermediate or neutral setmembers. Two overlapping sets are related by exclusion-overlap if, bystipulating of each neutral candidate that it is either positive ornegative, it is possible to end up with two overlapping sets and it ispossible to end up with two sets related by exclusion (Körner,1966, pp. 45-46. This clarifies or revises Körner, 1959, pp.127-128). He gives blue and green as examples to illustrate exclusionoverlap. Blue and green (strictly, the set of blue things and the setof green things) are not absolutely exact; they have neutralcandidates. Since nothing is a member of the green set and also amember of the blue set, these sets exclude each other. When eachneutral candidate is converted by stipulation either to a member or toa non-member, the two adjusted sets may still exclude each other,because no neutral candidate has been designated both green and blue,or if there is at least one formerly neutral candidate that is now bothgreen and blue, the adjusted sets overlap.Körner claims that determinates under the same determinable arelinked, directly or indirectly, by exclusion-overlap. Red and green arenot directly related by exclusion overlap, but they are presumablyrelated indirectly by direct links between red and orange, orange andyellow, yellow and yellowish green, yellowish green and green. Theconcepts of red and green are therefore linked. Concepts are linked ifand only if they are related by exclusion overlap or the ancestral ofexclusion overlap (1959. pp. 130-131). Concepts P andQ are fully linked if and only if every species of Pis linked with every species of Q (1959, p. 131). Full linkageis crucial to Körner's treatment of determinates anddeterminables.Körner attempts to explain the determinate-determinablerelation by means of full linkage. He asserts that full linkage is astronger relation than mere linkage. It is difficult, however, to beconvinced that this is true. If at least one species of P islinked to at least one species of Q, and all the species ofP are linked to each other, as are all the species ofQ, then every species of P is linked with everyspecies of Q, and P and Q are fully linked.Körner claims that ‘angry,’ a species of ‘yellowor angry,’ is not linked with ‘green.’ This would bean interesting and important result, if true. Körner hereidentifies a problem that occupies subsequent discussions. How are weto distinguish ordinary predicates such as ‘green’ fromdisjunctive predicates such as ‘yellow or angry’?It appears that on Körner's own definitions,‘green’ and ‘yellow’ are linked,‘yellow’ is linked to ‘yellow or angry,’ and‘yellow or angry’ is linked to ‘angry,’ so‘green’ is linked to ‘angry.’ Untilexplanations are forthcoming how one or more of these alleged linkagesviolate Körner's requirements, the main influence of hiscontribution is to direct attention to the problem of disjunctivepredicates.John Searle makes a fresh start. In his attempt to explicate thedeterminate-determinable relation, he uses the notion of predicateentailment. In the standard sense, entailment is a relation betweenitems, such as propositions, that have truth-values. Searle extendsthis notion to a relation between predicates. ‘Red’ entails‘colored’ because it is impossible for something to be redand not colored. This is a natural extension, and others have adoptedit. Indeed, talk of predicate entailment leads easily to talk ofproperty entailment: the property red entails the property colored.Searle and others who follow him draw a sharp distinction betweenthe determinate-determinable relation and the genus-species relation.(He repeats this distinction in Searle, 1967.) The definition of aspecies is by means of genus and differentia, which are logicallyindependent. (Predicates F and G are independent whennone of the following entailments hold: F entails G,G entails F, F entails not-G, andnot-F entails G.) A determinate of a determinablecannot be defined in this way, by a conjunction of independentpredicates. A traditional (although inadequate) definition ‘Manis a rational animal’ passes the genus/differentia test.‘Rational’ and ‘animal’ are independent terms.The attempted definition ‘Red is a color that is red’ doesnot pass because ‘red’ entails ‘colored.’There are both historical and logical difficulties with thisview.The genus-species relation is an ancient philosophical topic. Nocrisp, clear definition can be consistent with everything that has beensaid before. Searle's confident exposition, however, contradicts somestandard views. A logic text in wide use for many decades gives thefollowing as a rule of definition:The better the definition, the more completely will thedifferentia be something that can only be conceived as a modificationof the genus: and the less appropriately therefore will it be called amere attribute of the subject defined. (Joseph, 1916, p.112)Aristotle mentions differentia that entail the genus, as in‘Walking animal’ (Topics, IV. 6) and ‘Footedanimal’ (Metaphysics, Z. 12). In his Commentary on Z. 12, Bostocksays that the first differentia should entail the genus (Aristotle,1994, pp. 176-184). Other philosophers have adopted Searle's proposal,so it is evidently attractive. It does not represent a consensus ofearlier writers.The nature of conjunction poses a logical problem for Searle'saccount of species. If two conjunctions are logically equivalent, itdoes not follow that the conjuncts of one are logically equivalent tothe conjuncts of the other. The forthcoming example concernsconjunctive propositional functions about pure numbers. It is easy toconstruct parallel examples about mass, length, temperature, years ofservice, taxable income, and so on.Ax: x is greater than 4 but less than 7 Bx: x is greater than 4 but less than 6. Cx: x is greater than 5 but less than 7. Dx: x is less than 6. Ex: x is greater than 5. Fx: Bx & Cx. Gx: Dx & Ex. Hx: Bx & Ex. Ix: Cx & Dx.The last four predicates, Fx, Gx, Hx, andIx, are equivalent, so they entail the same predicates and areentailed by the same predicates. They all entail Ax, andAx entails none of them. Their conjuncts, by design, havevarious entailment relations. Both conjuncts of Fx entailAx. Neither conjunct of Gx entails Ax. Oneconjunct of Hx and of Ix entails Ax and theother conjunct in each case does not.Searle says that “a species is a conjunction of two logicallyindependent properties—the genus and the differentia”(1959, p. 143). Does he mean (a) that every conjunction equivalent tothe species satisfies this requirement or (b) that at least oneconjunction satisfies the requirement? Stipulation (a) is too difficultto satisfy, for any species is equivalent to the conjunction of itselfand the genus. Stipulation (b) is too easy to satisfy, as will be shownnext. The following predicates continue the numerical example:Jx: x is greater than 5 but less than 6. Kx: Jx or (x is greater than 2 but lessthan 3). Lx: Ax & Kx.Jx and Lx are equivalent to each other and also toFx, Gx, Hx, and Ix. If we considerAx to be the genus, then Lx is a conjunction of thegenus and a term Kx logically independent of the genus. Onecan perform a trick of the same kind with the standard example ofcolor. Consider the following contrived ‘genus anddifferentia’ definition of red as a species of the genuscolored:x is red =df (x iscolored) & (x is red or x is notcolored).Searle's distinction between genus-species anddeterminate-determinable requires some principled way of excludeddisjunctive predicates such as ‘Kx’ and‘x is red or x is not colored.’Explaining the determinate/determinable relation requires this anyway,whether or not accepts Searle's views about the relation of species togenus.Searle attempts to define the determinate-determinable relation andto eliminate hybrid, cross-type conjunctive and disjunctive predicatesby using only the relation of predicate entailment. When a predicate Aentails a predicate B, but B does not entailA, Searle says that A specifies B (1959, p.145). A is a non-conjunctive specifier of B if andonly if A specifies B and there is no pair of termsC and D such that A is equivalent to(entails and is entailed by) the conjunction of C andD, C specifies B, D does not entailB, and not-D does not entail B. Take theletters A, B, C, and D asabbreviations for some new predicates:A: red B: colored C: colored but not green D: red or (not colored and not prime)A specifies B. There are terms C andD such that A is equivalent to (C &D), C specifies B, D does notspecify B, and not-D does not specify B. Soaccording to this definition, red is not a non-conjunctive specifier ofcolored, a result that is opposite to what Searle intends. He says thata necessary condition of As being a determinate of Bis that A is a non-conjunctive specifier of B. Likeeveryone who addresses this topic, Searle takes the relation betweenred and colored to be a paradigm of the determinate-determinablerelation.Searle adds another condition with the intention of excludingdisjunctive predicates such as ‘yellow or angry.’ Adeterminate of a determinable must not only be a non-conjunctivespecifier of the determinable, it must be logically related to allother non-conjunctive specifiers of the determinable. Suppose that thedefinition of ‘non-conjunctive specifier’ can be emendedsomehow to allow red as a non-conjunctive specifier of colored. The newrequirement of logical independence wrecks the project once againbecause it eliminates colored as a determinable. Consider darkish redto darkish orange. Darkish red to darkish orange and red are notlogically related. Some things are both; some are neither; some are thefirst but not the second; some are the second but not the first. SoSearle's requirements again disqualify his paradigm. (A similarobjection occurs in Sanford, 1970, pp. 162-163.)4. The Munsell Color SolidIn order to construct more exact color examples, this entry willbegin to specify colors by reference to the Munsell Color Solid andwill use the color designations in the Inter-Society ColorCouncil-National Bureau of Standards (ISCC-NBS) system (see Kelly andJudd, 1976, and the entry “Color” in Webster's ThirdUnabridged Dictionary, or Munsell: The Universal Language of Color). These standard color designation names such asdeep yellow and dark grayish yelloware hereafter printed in boldface. There are 267 names in all, and anumber from 1 to 267 is associated with each name. Although the contextusually makes it clear when we are talking about (mentioning) a wordand when we are using the word to talk about what the word is about,the difference between bold face and the ordinary font will alsoobserve the customary use/mention distinction. The predicatedeep yellow refers to the color deep yellow. There are other recognized representations of color space. Projects in the physics of color, psychophysics, color science, and thephilosophy of color often use one or more of these rather than theMunsell system. The Munsell system functions as it was intendedto by providing a universal objective standard for very close colormatching. It is especially well suited to the purpose ofthis article because it provides a large number of quite determinate,but not completely determinate, color predicates. Practicalusefulness, rather than a philosophical need for examples, led to thedemarcation of these narrow extensions. Any pair of surface color that the human eye can distinguish withrespect to any color dimension, hue, brightness, or saturation(chroma), corresponds to a pair of points in The Munsell Color Solid.Estimates of the number of distiguishable colors range from two millionto five million. For all practical purposes, one can regard the MunsellColor Solid as a continuum of colors. Pictures of the Munsell ColorSolid, however, often depict the whole solid as contstructed out of 267blocks of uniform determinate color (as in the color plates inWebster's Third or The 267 Color Centroids).These standard color names are ambiguous between determinate anddeterminable. For each of the 267 regions in the color solid, there isa determinate representative color, the ‘center of gravity’or centroid color. These are the colors of the Centroid Color Chipsthat science and commerce use to standardize color descriptions ofminerals, paint, dye, ink, plastic, and so forth. Paleyellow is both the name of a determinate centroid color and adeterminable color. The scientists who construct the color solid regardthe determinable use as primary.There are many pairs of easily distinguishable colors whichreceive in this system the same designation, while there are also manypairs that can scarcely be distinguished which receive differentdesignations. This property is, of course, an unavoidable result ofdividing the color solid into an arbitary number of blocks, one foreach of the 267 designations. Analogous disadvantages result foridentifying the time of events according to date; two events occurringon the same date may be separated by many hours, but on the other handtwo scarcely separable midnight events may have to be assigneddifferent dates (Kelly and Judd, 1976. p. 4).In all the forthcoming uses of the Munsell color names, they shouldbe understood as names of determinables rather than determinates. Thereare distinguishable instances of pale yellow and some of these pairsare more easily distinguished than some pairs in which one color ispale yellow and the other is grayish yellow.The bold face of the standard names contrasts in this entry with theupper case italics of invented names defined by means of the standardnames. Some forthcoming definitions have the following pattern:WEAK YELLOW: pale yellow orgrayish yellow (89 or 90) ROBUST YELLOW: strong yellow ormoderate yellow or grayish yellow (84or 87 or 90).In the color solid, the regions corresponding to WEAKYELLOW and ROBUST YELLOW are as compact as any of thestandard regions. These color names are as comprehensible as thestandard names although, of course, they are more determinable. Weakyellow and robust yellow overlap because anything that is grayishyellow is both weak yellow and robust yellow. Neither entails theother.Kelly and Judd contains thirty-one color charts (not themselvesprinted in color) that represent cross sections of the Color Solid. Thevertical axis represents lightness (Munsell Value), and the horizontalaxis represents saturation (Munsell Chroma). All colors that are not onthe black-gray-white lightness axis have the same hue. Figure 6 is areproduction of a chart for yellow (Kelly and Judd, 1976, p. 22) thatrepresents the relation between pale yellow, grayish yellow, and othercolors. Figure 65. After SearleJohn Woods attempts to improve Searle's definitions in “OnSpecies and Determinates” (Woods, 1967). As Richmond Thomasondemonstrates with a remorseless barrage of difficulties, Woods'sefforts only make things worse, if this is possible (Thomason, 1969).Woods's requirements for determinables have, for example, the unwelcomeconsequence that if Gx is a determinable, Gx is atheorem of predicate logic (Thomason, 1969, pp. 95-96).Without offering a rigorous proof, Thomason offers the opinion thatthe overall project of defining species-genus anddeterminate-determinable in terms only of entailment and negation isdoomed. He proceeds “to search for an abstract, structuralcharacterization” (p. 97) and finds an appropriate structure inthe algebraic theory of semi-lattices. The resulting elegant theory isprobably useful to theorists who develop taxonomic schemes. It doesnot, however, appear to help with the problems that Körner andSearle confront. What disqualifies colored or rectangular as adeterminable of red? What disqualifies red and square as a determinateof colored?Besides proposing lattice-theoretic requirements for natural kinds.Thomason recommends a principle of disjointness (D) (p. 98) fortaxonomic systems that can be stated as follows:(D) If two natural kinds a and b of ataxonomic system share at least one member, then every member ofa is a member of b, or every member of b isa member of a.The two kinds red and darkish red or darkishorange fail to satisfy (D). They cannot both be natural kinds ofthe same taxonomic system. The algebraic theory of semi-lattices byitself provides no reason for favoring one or the other or neither as anatural kind. Many systems of classification appear not to accord with(D). In systems of biological, physical, and chemical taxonomy, itsenforcement appears arbitrary. These considerations also undermineJohnson's claim that “Taking any given determinate, there is onlyone determinable to which it can belong” (Johnson, 1921, p. xxxv,quoted above in Section 1.A).Although one may nevertheless attempt to respect principle (D), itis important to realize that not every system that respects (D) dividesthe color solid into natural kinds. Here is another definition in termsof Munsell classification:BELLOW: pale yellow ordeep blue (89 or 179).Something pale yellow can change to grayish yellow by continuouslybecoming a little bit darker and without changing at all in hue orsaturation and without occupying regions in the color solid other than89 or 90. Nothing pale yellow can change to deep blue in the same way.Either the change is discontinuous or the thing occupies many regionsother than 89 and 179. The predicate pale yellow or darkblue (BELLOW) is a disjunction of two determinatepredicates but does not itself correspond to a determinate.Pale yellow or grayish yellow (WEAK YELLOW)is determinable with respect to its disjuncts and is a suitabledeterminate of ‘colored.’ Disjunctive or conjunctivesyntactic forms by themselves are unreliable guides to naturalness orbeing a proper determinate or determinableDean Zimmerman has also suggested improvements to Searle's treatmentof determinables. He uses, in addition to the notion of predicate orproperty entailment, the notion of the Boolean part of a property.F is a determinate falling under determinableG =df (1) F implies G,but G does not imply F; (2) there is no propertyH such that: (a) G&H implies Fbut (b) neither H nor not-H implies G; (3)every Boolean part of F implies G; and (4) for everyproperty I such that I and G satisfy thepreceding three clauses, F and I stand in somelogical relation. (Zimmerman, 1997, p. 464)How does this definition fare for our paradigm, ‘F(red) is a determinate falling under determinable G(colored)’?Clause (3) requires that every Boolean part of the property redimplies the property of being colored. From Zimmerman's discussion(1997, pp. 462-463), it is not obvious whether red has a proper Booleanpart or whether its only Boolean part is red itself. Whatever theanswer, clause (3) seems to be satisfied for this example. Questionsremain, however, about parts of color properties. If the predicate‘robust yellow’ stands for a property, are strong yellow,moderate yellow, and grayish yellow its Boolean parts? Or is theproperty of being robust yellow somehow distinct from the properties ofbeing strong or moderate or grayish yellow? On the understanding of‘disjunctive predicate’ to be recommended below,‘robust yellow’ is disjunctive if and only if ‘strongor moderate or grayish yellow’ is also disjunctive. An account ofdisjunctive predicates, in this sense, could be useful in identifyingBoolean parts of properties. An appeal to the existence ornon-existence of such parts to explain disjunctiveness, on the otherhand, appears to assume what it purports to establish.Clause (1) of the definition above is satisfied and (2),unfortunately, is unsatisfied. Consider the following property:H: red or (not-colored andsquare)G&H implies F, that is,Colored and (red or (not-colored andsquare)) implies red. H does not implyG, that is, red or (not-colored and square)does not imply colored. Not-H does not implyG, that is, not-red and (colored ornot-square) does not imply colored. Zimmerman'sformulation does not repair a difficulty in Searle's, namely, that thered-colored paradigm fails to satisfy the definition of thedeterminate-determinable relation. Predicate H, to be sure, isa hideous monstrosity that stands for something stapled together fromBoolean parts of unrelated properties. A goal of the definitionalenterprise is to distinguish ordinary, healthy predicates from suchmonstrosities. So we cannot assume the distinction in order to draw thedistinction.Clause (4) had difficulties of its own. Assign a new meaning to theletter ‘F’:F: weak yellowF satisfies clause (1). Pretend F also satisfiessome revised and improved version of clause (2). Clause (3) does notstand in the way. But as one would expect, something is lurking in thewings:I: robust yellowI satisfies clauses (1), (2), and (3) as well asF. But I and F are logically unrelated. Allthe following are possible: not-F and not-I,F and not-I, I and not-F, andF and I. An example of the kind that thwarts Searlealso impedes Zimmerman.6. Predicates and PropertiesPhilosophical discussion often slides back and forth between talk ofpredicates and talk of properties. Some philosophers suggest that thereis an important logical difference between disjunctive predicates, onthe one hand, and disjunctive properties or universals, on theother.In a brisk Introduction to his early book Problems of Mind andMatter, in a section entitled “Generic and Specific,”John Wisdom says:The fact is red and hard and red or hardare not universals; for strictly there are no conjunctive ordisjunctive universals but only conjunctive and disjunctive facts.“This is red or hard” means “Either this is red orthis is hard.” (Wisdom, 1963, p. 31)D. M. Armstrong says something very similar about disjunctiveproperties (1978, p. 19-23). (Armstrong is willing to admit conjunctiveproperties.) A disjunction of property predicates such as‘red’ and ‘hard’ is not itself a disjunctiveproperty predicate. There is no property of being red or hard althoughthe disjuncts of the meaningful predicate ‘red or hard’ do(or might) correspond to the properties red and hard.At this point the following distinction is relevant:For some property predicates F and G, thecompound predicate F or G is not itself a propertypredicate.For all property predicates F and G (that do notnecessarily have the same extension), the compound predicateF or G is not itself a property predicate.A metaphysician of properties can accept (1) or not. Accepting (2) isnot an option. (2) is unacceptable. Armstrong writes: Disjunctive properties offend against the principle that agenuine property is identical in its different particulars. Supposea has a property P but lacks Q, whileb has Q but lacks P. It seems laughable toconclude from these premisses that a and b areidentical to some respect. Yet both have the “property”,P or Q. (1978, p. 20)Something that satisfies the first disjunct of the followingpredicate need not be identical to or resemble in any relevant respectsomething that satisfies the second disjunct: ‘More than tenmillion miles from Memphis or sings “All of Me” offkey.’ This example is intended to be a disjunction of laughablyunrelated components. Not every predicate of the form P or Qis good for a laugh in this way.Perhaps there is no current consensus about the accepted meanings tothe technical phrases ‘disjunctive predicate’ and‘conjunctive predicate.’ If that is so, then the followingprinciples are useful suggestions for fixing their meanings, ‘a’ standshere for ‘acceptable’ and ‘u’ stands for ‘unacceptable’:(Conj-a) If predicates F and G areequivalent (necessarily apply to the same things), then F isconjunctive if and only if G is also conjunctive. (Disj-a) If predicates F and G are equivalent,then F is disjunctive if and only if G is alsodisjunctive.On the other hand, it is useful to reject both the followingprinciples: (Conj-u) If F is equivalent to a predicate of theform K and L, then F is conjunctive. (Disj-u) If F is equivalent to a predicate of the formK or L then F is disjunctive.According to (Conj-u) and (Disj-u), all predicates are both conjunctiveand disjunctive. Even redundant predicates such as F and F andF or F demonstrate this result. Additional qualifications canof course eliminate these particular examples. Then there will be moreexamples with undesirable consequences, and more qualifications toeliminate them. So long as the qualifications must be expressed in theterms of standard logical dependence and independence, the projectrecapitulates the efforts of Searle and Woods. According to (Conj-a) and (Disj-a), Wisdom and Armstrong can agreethat disjunctive predicates do not stand for properties or universalsand they can disagree about whether conjunctive predicates stand forproperties or universals. Wisdom says they don't, Armstrong thinks thatthe arguments against disjunctive universals do not apply toconjunctive universals. Everyone should agree that if a predicateF is equivalent to a disjunction of two different propertypredicates, F may be disjunctive or may not. That depends onhow the disjuncts are related. Similar remarks apply to conjunctivepredicates.Some earlier examples of predicates, or similar predicates, appearin the following list:pale yellow or grayish yellow(WEAK YELLOW),pale yellow or deep blue(BELLOW),(greater than 5 and less than 7) or (greater than 4 and less than6),(greater than 5 and less than 7) and (greater than 4 and less than6),yellow or angry,yellow and angry.So far as one can discriminate just by means of predicate entailmentor the presence or absence of logical relations, (A) and (B) aresimilar. Each is a disjunction of predicates that exclude eachother.Pale yellow and grayish yellow do not differ with respect to hue orsaturation. They differ in brightness only to the extent necessary tohave distinct locations in the Munsell color solid. Pale yellow andgrayish yellow are determinate with respect the determinable weakyellow, and weak yellow in turn is determinate with respect toyellow.Bellow is not a determinate color with respect to the determinablecolor. One wants to deny that it is a color at all, even thoughBELLOW is equivalent to a disjunction of color predicates.Predicates (A)and (B) contrast sharply. Pale yellowand grayish yellow are as similar as they can be whilestill excluding each other. Pale yellow anddeep blue are about as dissimilar as two colors canbe. Direct ungrounded appeals to resemblance or being in the samedimension or having to do with one another will not solve our problem.A theoretically satisfactory treatment of the determinate-determinablerelation should explain these resemblances rather than be explained bythem. A new technical term disjoint marks the apparentdifference between (A) and (B). Pale yellow anddeep blue are disjoint predicate. Paleyellow and grayish yellow are not disjoint.The next section provides a definition of disjointness.So far as one can discriminate just by means of predicate entailmentor the presence or absence of logical relations, the components of (C)and (D) are logically unrelated. But (C) is not a conjunctivepredicate, and (D) is not a disjunctive predicate. Something thatsatisfies both disjuncts of (C), ‘greater than 5 and less than7’ and ‘greater than 4 or less than 6,’ can changecontinuously so as to satisfy the first but not the second, or canchange continuously in the other direction along the same dimension soas to satisfy the second but not the first. ‘Greater than 5 andless than 7’ and ‘greater than 4 and less than 6’obviously indicate overlapping intervals along the same dimension. (C)is a long-winded way of expressing ‘greater than 4 and less than7’ which has no appearance of being disjunctive. In the same way,(D) is a long-winded way of expressing greater than 5 and less than6’ which has no appearance of being conjunctive.So far as one can discriminate just by means of predicate entailmentor the presence or absence of logical relations, the components of (E)and (F), these components are related to each other in the same way asthose of (C) and (D). ‘Yellow’ and ‘angry’ arelogically independent. A puzzle that the Korner-Searle Symposium posesis still unsolved. (E) is a disjunctive predicate. ‘Yellow’is not a determinate of the determinable ‘yellow or angry’.(F) is a conjunctive predicate. ‘Yellow and angry’ is not adeterminate of the determinable ‘yellow.’Logically independent predicates can be determinates under the samedeterminable. ‘Yellow’ and ‘angry’ have anindependence of a kind, indicated here by the new technical termB-independence, that has conditions in addition to those forlogical independence. The next section specifies some conditions ofB-independence.Sections 3 to 7 of this article attend to the notion of disjunctiveand conjunctive predicates. Since this section is titled“Predicates and Properties”, it is appropriate here todiscuss some issues in which the distinction between predicates andproperties intersects the distinction between determinables anddeterminates in ways not explicitly connected with conjunctive anddisjunctive. Any general philosophic discussion of properties wouldextend vastly beyond the intended scope of this entry. Thephilosophic topic of universals has been at the center of firstphilosophy from Plato through medieval thought to the present. Anexample involving determinables can illustrate almost any view aboutproperties. The brief discussion here treats only some currentphilosophic positions about determinates and determinables whoseformulation requires positive or negative claims about properties.D. M. Armstrong begins Chapter 4, “Properties II,” ofArmstrong 1997 by saying:We come now to consider one of most difficult issues in thetheory of universals. Not only do particulars resemble, but so doproperties and relations. And just as particulars may resemble eachother more or less closely, so the same is true of properties andrelations (47).When A and B are neither identical nor distinct, some part of A isidentical to some part of B, and either (1) some part of A is notidentical to any part of B, or some part of B is not identical to anypart of A. This yields three possibilities: (1) but not (2): A includesB; (2) but not (1): B includes A; both (1) and (2): they overlapalthough neither includes the other. Armstrong regards these all aspartial identity (1997, p. 18). He extends the notion of partialidentity to cases of non-spatial inclusion and overlap.Armstrong develops the idea that ‘the resemblance ofdeterminate universals is constituted by partial identity, where thegreater the resemblance the greater degree of identity’ (p. 51).One example is duration. ‘The resemblances of all the determinatedurations under a single determinable is a matter of partialidentity’ (p. 55). For any two durations, there will be aduration that is part of each. This duration in common provides thepartial identity.What does this view imply about the number of duration properties? Ifthere is a fundamental duration d (a temporal atom) not partlyidentical with any shorter duration, such that every longer durationis exactly a whole number n times longer than d,then perhaps d is the only fundamental duration property. (Orperhaps there are incommensurable fundamental durations? If there aretwo kinds d and d′, for example, neither ispartly identical to the other, and every longer duration is the sum ofn times d plus the sum of m timesd′. Armstrong advocates an “a posteriorirealism” (p. 25). There are no uninstantiated properties oruniversals. Which ones exist depend on how the world happens to be.So which fundamental duration properties exist, if any? The necessaryexistence of infinitely many fundamental durations, and also thenecessary existence of any specific kinds of fundamental durations,seems to be contrary to the spirit of a posteriori realism. Theeternity of time in one or both directions appears to be irrelevant tothe question. If the theory of partial identity works at all, itshould work for long durations, for a long duration is partlyidentical to any shorter durations it contains. If there are no fundamental durations, then any duration of n secondsis partly identical to any shorter duration it contains. This viewentails that there are infinitely many non-equivalent ways of dividingan interval. Taking halves, halves of halves, halves of halves ofhalves, and so forth, for example, will not produce the same durationsas taking thirds, thirds of thirds, thirds of thirds of thirds, and soforth. There appears to be no principle for preferring one way ofregarding a duration as partly identical to its constituents toinfinitely many other ways.What might provide a partial identity analogous to duration in thecase of color? Nothing phenomenally apparent seems to play this role.Armstrong insists that very complex physical processes underliephenomenally simple color appearances. He speculates that thesephysical processes provide the partial identities that constitute theresemblances between color properties (pp. 58-9). A developed physicaltheory that specifies the respect in which a determinate red and adeterminate blue are partially identical might transform discussions ofthis topic.In many writings on universals Armstrong rejects the principles thatevery meaningful predicate corresponds to a property. Other authorsadvance views specifically about whether determinable or determinatepredicates correspond to properties.Lawrence Lombard uses a broad sense of determinable that he connectsboth with criteria of identity and with being a metaphysical category(Lombard 1986, p. 41). Cynthia Macdonald makes similar use ofa broad conception of determinable property in her general treatment ofcriteria of identity (Macdonald 2005, p. 60).Eric Funkhouser uses the notion of a ‘determinationdimension’. The notion of a determination dimension explains thelimited ways in which determinates specify the determinables they fallunder. Proper subsets arise only from a further specification alongdetermination dimensions, so our analysis does not let specificationslike red and square count as a determinate of red. Red and square doesnot have more precise values along the hue, brightness, or saturationdimension than does red (Funkhouser 2006).The question remains on what grounds we deny that having a shape anda color is a determination dimension. Agreeing with Funkhauser that wewant to deny it, because we want to preserve the results we hope toexplain, we can ask about the theoretical grounds for the denial inaddition to our desire to attain these results.A paper by Ingvar Johansson and one by Carl Gillett and BradleyRives both argue that there are absolutely determinate mind-independentproperties. (Section 8 of this entry examines the subject of absolutedeterminacy.) They disagree about the status of determinables.Johansson holds that the highest determinables such as color and volumeare objective properties. Intermediate concepts such as red and orangeon the other hand, those neither most nor least specific, ‘cannotrefer to ontological determinables.’ The limits of these conceptsare conventional (Johansson 2000).Gillett and Rives disagree with Johansson about the reality ofdeterminables. They argue that the recognition of genuine determinableproperties is unnecessary to causal explanation and a causal theory ofproperties. Determinates can do all the work. In particular,determinates contribute all the causal powers that determinable appearto explain.Even if statements about causal powers do not presuppose the existenceof determinables, Gillett and Rives should contend with others kind ofcausal statement. An experimental psychologist reports that thepresentation of the appropriate mask 50 to 100 milliseconds after thetarget disc is a necessary condition of a certain phenomenon. Thisstatement about a causally necessary condition does not entail thatsome more determinate time lag is a necessary condition. Regarding adeterminable such as between 50 and 100 milliseconds as equivalent toan infinite disjunction of determinates might allow uninstantiatedproperties into the ontology. The number of uninstantiateddeterminate disjuncts involved by many other determinables such asalloyed with more than one gram but less than a metric ton of gold iscertainly huge. The view that determinables are equivalent toinfinite disjunctions of determinates seems to be consistent, it alsoseems to run counter to the goal of Gillett and Rives to achieve asparse ontology.7. Boundaries and Borderlines‘B-independence’ stands for ‘boundaryindependence.’ The Munsell Color Solid is composed ofnon-overlapping regions that all share boundaries with other regions.The preliminary discussion in this section departs for a while fromcolors to consider a familiar, two-dimensional array of non-overlappingregions, the states in the United States. In case a map of the UnitedStates is not close at hand, the reader can look at Figure 7, a simplemap of the some of the states that figure in the followingexamples. Figure 7 Some spatial analogies about the boundaries of states and other regionscomposed of the states will motivate the forthcoming discussion ofdisjoint and B-independent predicates. Here are twodisjunctive definitions: x is in the Dakotas =dfx is in North Dakota or x is in South Dakota. x is in the North States =df xis in North Dakota or x is in North Carolina.In each case, the disjuncts exclude each other. North Dakota andSouth Dakota have no points in common. Neither do North Dakota andNorth Carolina. Predicate entailment fails to capture a topologicaldifference between the Dakotas and the North States. The Dakotas are acoherent, continuous region. The North States are a discontinuousregion. Something can be both on the boundary of North Dakota and onthe boundary of South Dakota. Nothing can be both on the boundary ofNorth Dakota and on the boundary of North Carolina, for theirboundaries are many miles apart. North Dakota and North Carolina aredisjoint. North Dakota and South Dakota are not disjoint.There is a close analogy here with some the color examples in thelast section. Weak yellow is a coherent, continuous region in thequality space of color. Bellow is a discontinuous region. Something canbe both on the boundary of pale yellow and on the boundary of grayishyellow. Nothing can be both on the boundary of pale yellow and deepblue. This is a topological difference that predicate entailment doesnot represent.Here are two more disjunctive geographical definitions. In the firstdefinition, the disjuncts exclude each other:x is in Dabraksa =dfx is in South Dakota or x is inNebraska.In the second definition, the disjuncts overlap; they are logicallyindependent; neither includes the other; they do not jointly exhaustthe total space: x is in Longkota =dfx is in the Dakotas or x is in Dabraska.Longkota is a coherent, continuous region. There is nothing inherentlydisjunctive about it. Boundary relations again indicate topologicalrelations between the Dakotas and Dabraska that logical entailment andnon-entailment do not capture. Consider something A on theboundary of South Dakota and Minnesota and Iowa. It is on the boundaryof the Dakotas and on the boundary of Debraska and on the boundary ofLongkota. But it is not on the boundary of the following two regions: x is in the Dakotas but x is not inDebraska (that is, x is in North Dakota) x is in Debraska but x is not in the Dakotas (thatis, x is in Nebraska).A is not close to any boundary of North Dakota orNebraska.One of our main puzzle predicates, ‘yellow or angry,’presents a topological contrast. Anything A on the boundary of‘yellow’ and on the boundary of ‘angry’ is alsoon the boundary of the following four predicates:‘yellow and angry’‘yellow but not angry’‘angry but not yellow’‘neither angry nor yellow’This reflects the fact that being yellow and being angry areconceptually independent besides being logically independent. Slightchanges in a that would move it from the boundary of‘yellow’ to being definitely yellow or definitely notyellow are independent of slight changes in a that would moveit from the boundary of ‘angry’ to being definitely angryor definitely not angry.It is possible to define a color predicate analogous to Longkota.This definition uses two earlier definitions that are repeatedhere:ROBUST YELLOW: strong yellow ormoderate yellow or grayish yellow. WEAK YELLOW: pale yellow orgrayish yellowSWELL YELLOW: WEAK YELLOW or ROBUSTYELLOW.The disjuncts of this last definition are logically independent.Nevertheless, SWELL YELLOW corresponds to a coherentcontinuous region in color space. Weak yellow and robust yellow have atopological relation that yellowness and anger do not have. There arelocations in the Munsell Color Solid (for example, on the borderline ofgrayish yellow and on the borderline of lightolive brown), where something x at this location ison the boundary of weak yellow and on the boundary of robust yellow andon the boundary of swell yellow but is not on the boundary of thefollowing two regions: Weak yellow but not robust yellow.Robust yellow but not weak yellow.Although the predicates WEAK YELLOW and ROBUSTYELLOW are logically independent, relations between the boundariesof their regions indicate a significant, objective connection.Although pale yellow is a highly determinate colorpredicate relative to ‘yellow’, it is far from beingmaximally determinate. A sentence from Kelly and Judd, quoted above inSection 4, is repeated here:There are many pairs of easily distinguishable colors whichreceive in this system the same designation, while there are also manypairs that can scarcely be distinguished which receive differentdesignations(Kelly and Judd, 1976. p. 4).Despite its relative specificity, pale yellowapplies to samples that are visibly different with respect to color.The same goes for grayish yellow. So something canchange gradually from pale yellow to grayish yellow. Is there somepoint along the way that is the precise boundary between these twocolor regions? This is a specific form of a question that dividesphilosophers who develop theories of vagueness. Without needing toadopt some view about the basic nature of borderline cases, one canadmit the possibility of borderline cases between pale yellow andgrayish yellow. It is possible that something can be on the borderlineof each region. Something is a borderline case of pale yellow if it isneither definitely pale yellow nor definitely not pale yellow.Körner also uses a logic of inexact concepts to treat‘yellow or angry.’ One of Searle's complaints aboutKörner is that "His definition excludes any exact concept as apossible candidate for a determinate" (Searle, 1959, p. 156). Does thisobjection apply to the suggestions in this section? The next sectionreturns to the question whether there are perfectly exact concepts.Borderline cases are used in this section to locate boundaries. Supposethat ‘more than five feet tall but less than six feet tall’is perfectly exact. Anything just slightly taller than five feet orjust slightly shorter than six feet is on the boundary. For thepurposes of exploring relations to other predicates, we can replace anexact predicate with one that it slightly inexact. For example, amendthe definition of the allegedly exact predicate by adding ‘so faras one can tell by using a wall, a pencil, a carpenter's level, and ayardstick.’ The definitions as amended definitely apply to somethings, definitely do not apply to others, and also have someborderline cases left over. (Following a harmless practice, thisarticle refers both to borderline cases of predicates and to borderlinecases of properties or regions.)This project treats borderlines and boundaries as interchangeable.The following is an attempt to generalize and formalize the suggestionsmade above:The ‘B’ operator is used totalk about boundaries and borderline cases.‘BFx’ means ‘x isa borderline case of F.’The definition of disjoint predicates promised at the end ofthe section follows: Fx and Gx are disjoint predicates if andonly if Fx and Gx are exclusive predicates and Forany x, if BFx, thennot-BGx.Disjoint predicates do not, or in a modal version, cannot, shareborderline cases. A predicate is exclusively disjunctive ifand only it is equivalent to a disjunction of disjoint predicates.A specification of a condition ofB-independence was also promised at the endof Section 5. Let us say that two predicates Fx andGx intersect if and only if there is something x suchthat:B(F & G)x& B(F & not-G)x& B(not-F & G)x& (not-F & not-G)x.The boundaries of B-independent predicatesnot only intersect; they intersect wherever they have a point incommon. Fx and Gx areB-independent only if: For any x, if BFx andBGx, then B(F &G)x & B(F ¬-G)x & B(not-F &G)) & B(not-F ¬-G)x.A predicate is inclusively disjunctive only if it isequivalent to a disjunction of B-independentpredicates. A predicate is conjunctive only if it isequivalent to a conjunction of B-independentpredicates. ‘Yellow or angry’ is inclusively disjunctive.WEAK YELLOW or ROBUST YELLOW is not inclusivelydisjunctive. ‘Yellow and angry’ is conjunctive.‘WEAK YELLOW and ROBUST YELLOW’ is notconjunctive.This approach appears to solve the puzzle that Körnerformulated and that Searle and others attempted to solve withoutsuccess. Conjunctive predicates do not correspond to determinates.Disjunctive predicates do not correspond to determinables.The discussion above provides only a necessary condition ofB-independence. Attempting to deal with Nelson Goodman's puzzle about‘grue’ and other perverse artificial predicates requiresreference to more complicated relations between boundary conditions.These further conditions which are represented as both necessary andsufficient for B-independence are not spelledout here. They appear, in successive versions, in three articles bySanford 1970, 1981 (in which the later parts are nearlyincomprehensible because of over-compression and lack of diagrams), and1994 (which has some diagrams). All three articles attempt to clarifythe determinate-determinable relation by explaining the nature ofdisjunctive and conjunctive predicates.8. Absolute Determinacy“The practical impossibility of literally determinatecharacterization must be contrasted with the universally adoptedpostulate that the characters of things which we can only characterisemore or less indeterminately, are, in actual fact, absolutelydeterminate.” This is the final sentence of W. E. Johnson'schapter “The Determinable.” Johnson is not the onlyphilosopher who holds that things are absolutely determinate. InSection 3 I mention several philosophers who maintain that there areabsolutely determinate properties. One of D. M. Armstrong's sixnumbered refutations of phenomenalism in Armstrong (1961) maintainsthat “physical objects, which are determinate, cannot beconstructions out of indeterminate sense-impressions” (p. 58). A physical object is determinate in all respects, it has aperfectly precise colour, temperature, size, etc. It makes no sense tosay that a physical object is light-blue in colour, but is no definiteshade of light blue. (p. 59)Understanding what it is for color, temperature, size, etc.,predicates to be perfectly precise helps in understanding what it isfor color, temperature, size, etc., properties to be perfectly precise.A precise predicate is not vague; it is exact rather than inexact; ithas no borderline cases. Precision contrasts with vagueness.Specificity, on the other hand, contrasts with generality.Light blue is more specific than ‘blue’which is more specific than ‘colored.’ The more specific apredicate, the narrower the range it covers. Is lightblue more specific than ‘smooth’? The absence ofan inclusion relation in either direction makes it difficult to answerthis question. Attempts actually to compare the numerical results aftercounting all the light blue things in the world and all the smooththings can lead only to frustration and failure. This entry does notaddress the problem of comparing degrees of specificity of determinatesunder different determinables.Specificity and exactness are independent in several ways. There canbe predicates F and G such that:F and G are not identical and are bothunspecific and inexact. For example: F: about the size of acat, G: about the size of a dog. F is more specific and more exact than G. Example:F: pale yellow and G: yellow (in theordinary rather inclusive sense).F is more specific than G, and G is moreexact than F. Example: F: about the size of a cat.G: has a volume not less than 50.3 cubic inches and not morethan 2000.8 cubic inches. Anything F is G and noteverything G is F, so F is more specificthan G. But G is more exact. It requires, at theboundaries, determination to the nearest tenth of a cubic inch.F and G are both specific and exact. Examples:F: pale yellow, G: deepblue. Neither of these color predicates is absolutely precise,but each is quite precise compared to ordinary color terms. The MunsellColor Solid is constructed with the intention that each of the 267regions has approximately the same degree of specificity.Although specificity and precision are independent in these ways,they are also significantly connected with respect to absolutedeterminacy. Any absolutely specific predicate is also absolutelyprecise. Suppose, for example, that ‘Armstrong blue’ is apredicate for an absolutely specific shade of blue. Two things that areArmstrong blue do not differ at all with respect to hue or brightnessor saturation. Given a predicate ‘F’ and twoobjects a and b such that a is a borderlinecase of ‘F’ and b is a definite positivecase of ‘F’, a and b differalong some relevant dimension. But anything that differs along anyrelevant dimension from something that is definitely F, when‘F’ is an absolutely specific predicate, is notF. Absolutely specific predicates cannot have borderlinecases.No predicate that can have borderline cases is absolutely specific.So if there are no absolutely precise or exact predicates, neither arethere absolutely specific predicates. Johnson presumably would notquestion this conclusion since he says that literally determinatecharacterization is practically impossible. He and Armstrong claimthings in the world are absolutely determinate, not the predicates wedo or could use to apply to things in the world.If things in the world are absolutely determinate, this presumablydoes not require that any absolute determination persists through thepassage of time or space. If a cumulus cloud changes continuously inshape and size, this does not by itself preclude its having, at any onetime, an absolutely determinate shape and size. The impression thatclouds do not have exact boundaries, however, is probably not basedentirely on their changeability.Objects with absolutely determinate sizes have absolutelydeterminate boundaries. If a thing has an absolutely determinate lengthalong some axis at a given time, then there is exactly one real numbern such that its length in (say) meters is n. Thingsthat we come across in ordinary life such as plants, animals,buildings, furniture, electronic equipment, clothing, and kitchenwaredo not have exact boundaries, nor do larger items such as mountains,lakes, continents, and stars.The view that things in the world are absolutely determinate isimplausible if it requires clouds, brains, and dinner plates to beabsolutely determinate. But this requirement can be put aside. If themicrostructure of the world is absolutely determinate, that is absolutedeterminacy enough. If all the atoms within you and in your vicinityhave absolutely determinate properties, then the indeterminate mass andshape and volume of you, your brain, and your teeth somehow superveneon the determinate microstructure. Here is a well-known passage fromDavid Lewis:The reason it's vague where the outback begins is not thatthere's this thing, the outback, with imprecise borders; rather thereare many things, with different borders, and nobody has been foolenough to try to enforce a choice of one of them as the officialreferent of the word ‘outback.’ (Lewis, 1986, p.212)The view that there are many things with precise borders does not byitself refute the view that there are things with imprecise borders.Here is a kind of parody of the passage just quoted. It ends with thesame point but begins with a contrary contention:The outback is a big thing, and it is vague where itbegins. The reason it has imprecise borders is that there are manythings, with different precise borders, and nobody has been fool enoughto enforce a choice of one of them as the official reference of theword ‘outback’.For the outback (a cloud, your brain), there are many more-or-lessprecise aggregates of particles such that each is about as good acandidate as there is to be identified with the outback (a cloud, yourbrain). This entry does not address the problem of the many, how tounderstand the relation between a single macro-object and manyoverlapping aggregates of micro-objects that more or less coincide withit.However one resolves the problem of the many, the question ofabsolute determinacy becomes the question of absolute determinacy ofthe physical basis, the microstructure. After quoting the passage fromLewis above, Roberto Casati and Achille Varzi write:There are plenty of objects out there—plenty ofslightly distinct and yet precisely determinate aggregates of landmolecules. And when we say ‘Mount Everest’ or ‘theoutback’, each one of a large variety of suchaggregates—each with its own perfectly crisp mereotopologicalstructure—has an equal claim to being a referent of that term.(Casati and Varzi, 1999, p. 95)And what evidence is there for this precisely determinate perfectcrispness? Logic and metaphysics cannot answer this question from itsown resources. Science textbooks represent particles and atoms asclouds. Textbook writers fifty years ago knew that the picture ofperfect little spheres, the electrons, in elliptical orbits around anucleus was misleading. Now the picture is simply obsolete.An attempt to measure the precise dimensions of a polished coppercube might begin using an ordinary school supply ruler, then using amachinist's steel rule, then using a micrometer, then, starting with alow power optical microscope, using a series of increasingly powerfulmicroscopes. At the microscopic level one can discriminate incrementsof length too small for a mechanical micrometer to detect. This doesnot produce a more precise determination of the length of the cube ifnothing at this level coincides with the boundary of the cube. So thesearch for the exact measurements of the cube is abandoned and replacedby a hope to find absolute determinacy somewhere at the foundations,the fundamental basis, or the limit. There is a (weak) kind ofnon-deductive argument here.Given a greatest degree of precision determined by the bestinstruments, sooner or later a more advanced technology producesinstruments that are still more precise. This process of makingmeasurement increasingly precise never ends; it asymptoticallyapproaches absolute precision at dimensionless points of matter orspacetime or something.This vision of absolute determinacy at the limit is apparentlyattractive. It appears to be internally consistent. It also appears,however, to be inconsistent with physics.Middle-sized objects do not have perfectly precise boundariesbecause there are microscopic objects that are neither definitelyincluded nor definitely excluded from the object. Some largermicroscopic objects lack perfectly precise boundaries for the samereason. There is no reason to believe that this process continuesinfinitely downward. Electron diameters are imprecise, but not becausethere are swarms of micro-electron-dust, each particle of which is alsoa swarm of something even smaller. Nor does the process stop with somebasic items that really are absolutely determinate.Instruments can measure the velocity of a tennis ball. They do not,of course, measure velocity with absolutely determinacy. They do notdiscriminate, say, 114.0 from 114.1 miles per hour. Given someunderstanding of margins of error, it is meaningful for one to say thata tennis ball was going 114 miles per hour at some temporal instantt. The notions of a limit and of convergence provide thismeaning. They provide no support for believing in the possibility of amomentary tennis ball that exists neither before instant t norafter instant t but does exist precisely at instant tand travels 114 miles per hour during its instantaneous existence. Ifit is possible for something to have a property for an instant, it doesnot follow that an instantaneous thing can have that property.The same goes for spatial points. If it is possible for something tohave a property at a point, it does not follow that it is possible thatsomething punctiform should have this property. When a region is paleyellow, we can say that any point in the region is pale yellow. But nopoint by itself can be pale yellow.Johnson said that it is a “universally adopted postulate thatthe characters of things which we can only characterise more or lessindeterminately, are, in actual fact, absolutely determinate.” Insaying it is a postulate, Johnson does not mean we merely assume it inorder to deduce its consequences. He means rather that it is bothobviously true and cannot be inferred from truths that are even moreobvious. But the so-called postulate seems not to be true.BibliographyAristotle (1994), Metaphysics, Books Z andH, translated with a commentary by David Bostock, Oxford:Oxford University Press.Armstrong, D. M. (1961), Perception and the PhysicalWorld, London: Routledge and Kegan Paul.------ (1978), A Theory of Universals (Volume II ofUniversals and Scientific Realism), Cambridge: CambridgeUniversity Press.------ (1997), A world of states of affairs, Cambridge: CambridgeUniversity Press.Carnap, Rudolf (1928), Der Logishche Aufbau der Welt,Berlin: Benary. Translated by Rolf A. George as The LogicalStructure of the World (1967), Berkeley and Los Angeles:University of California Press.Casati, Roberto and Varzi, Achille C. (1999), Parts andPlaces, Cambridge: MIT Press.Chisholm, Roderick M. (1987), “Brentano and One-SidedDetachability,” Conceptus, 53-54, pp. 153-159.Edwards, Paul, and Pap, Arthur (1973), A Modern Introduction toPhilosophy, Third Edition, New York: The Free Press.Fales, Evan (1990), Causation and Universals, London and New York:Routledge.Funkhouser, Eric (2006), “The Determinable-DeterminateRelation”, Nous 40, pp. 548-569.Gillett, Carl and Rives, Bradley (2005), “The Non-Existenceof Determinables: Or, a World of Absolute Determinates as DefaultHypothesis,” Nous, 39, pp. 483-504.Goodman, Nelson (1951), The Structure of Appearance,Cambridge: Harvard University Press.Johansson, Ingvar (2000), “Determinables areUniversals,” The Monist 83, pp. 101-121.Johnson, W. E. (1892), “The Logical Calculus”,Mind, I, New Series, Part I, pp. 3-30, Part II, pp. 235-250.Part III, pp. 340-347.------ (1921), Logic, Part I, Cambridge: Cambridge U.P.------ (1922), Logic, Part II, Cambridge: Cambridge U.P.------ (1924), Logic, Part III, Cambridge: Cambridge U.P.Joseph, H. W. B (1925), An Introduction to Logic. 2ndedition, Oxford: Oxford University Press. The first edition of thisbook was printed in 1906.Kelly, Kenneth L. and Judd, Deane B., (1976), Color: UniversalLanguage and Dictionary of Names, Washington: National Bureau ofStandards.Körner, Stephan (1959), “On Determinables andResemblance, I,” The Aristotelian Society SupplementaryVolume, XXXIII, London: Harrison and Sons, pp. 125-140.------ (1966), Experience and Theory, London: Routledgeand Kegan Paul.Lombard, Lawrence (1986), Events: A Metaphysical Study, London:Routledge & Kegan Paul.Macdonald, Cynthia (2005), Varieties of Things: Foundations ofContemporary Metaphysics, Oxford: Blackwell.Matthen, Mohan (2005), Seeing, Doing, and Knowing, Oxford: OxfordUniversity Press.Prior, Arthur N. (1949), ‘Determinables, Determinates, andDeterminants,’ Mind, LVIII, Part I, pp. 1-20, Part II,pp. 178-194.------ (1962), Formal Logic, Second Edition, Oxford:Oxford U. P. The first edition of this book was published in 1955.Sanford, David H. (1970), “Disjunctive Predicates,”American Philosophical Quarterly, 7, pp. 162-170.------ (1981), “Independent Predicates,” AmericanPhilosophical Quarterly, 18, pp. 171-174.------ (1994), “A Grue Thought in a Bleen Shade:‘Grue’ as a Disjunctive Predicate,” Grue! The NewRiddle of Induction, edited by Douglas Stalker, Chicago and LaSalle: Open Court, pp. 173-192.------ (1999), “Determinable,” The CambridgeDictionary of Philosophy, Second edition.Searle, John (1959), “On Determinables and Resemblance,II,” The Aristotelian Society Supplementary Volume,XXXIII, London: Harrison and Sons, pp. 141-158.------ (1967), Determinables and Determinates,“ TheEncyclopedia of Philosophy, edited by Paul Edwards, New York:Macmillan, Volume II, pp. 357-359. [This entry is reprinted inBorchert, Donald M. (ed.) (2006), The Encyclopedia of Philosophy,Second Edition, Detroit: Macmillan Reference. Vol. 3, pp. 1-3, with anAddendum by Troy Cross, pp. 3-4.]Thomason, Richmond (1969), “Species, Determinables andNatural Kinds, Noûs, III, pp. 95-101.Webster's Third New International Dictionary of the EnglishLanguage Unabridged (1961).Wisdom, John (1963), Problems of Mind and Matter,Cambridge: Cambridge University Press. This book was first printed in1934.Woods, John (1967), “Species and Determinables,”Noûs , I. pp. 243-254.Zimmerman, Dean W. (1997), “Immanent Causation,”Philosophical Perspectives, 11, Mind Causation, andWorld, 11, pp. 433-471.Other Internet ResourcesMunsell Color System, from WikipediaThe Munsell Color System, Adobe Technical GuideRelated Entries induction: new problem of | induction: problem of | Prior, Arthur | properties | vagueness Copyright © 2006 byDavid H. Sanford<dhs@duke.edu> |
|
