Symposium: On Determinables and Resemblance
Author(s): S. Körner and J. Searle
Source: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 33 (1959), pp.
125-158
Published by: Blackwell Publishing on behalf of The Aristotelian Society
Stable URL: http://www.jstor.org/stable/4106622
Accessed: 29/04/2009 10:38
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=black.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the
scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that
promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].
The Aristotelian Society and Blackwell Publishing are collaborating with JSTOR to digitize, preserve and
extend access to Proceedings of the Aristotelian Society, Supplementary Volumes.
http://www.jstor.org
ON DETERMINABLES AND RESEMBLANCE
PROF. S. KtiRNER AND MR. J. SEARLE
I-By
S. KiSRNER
INEXACTconcepts, i.e., concepts having border-line cases, are
involved in various propositions and theories the analysis of
which is either plainly unsatisfactory or at the least, highly
controversial. It seems both plausible and heuristically sound to
anticipate that by giving proper attention to the logic of inexact
concepts some light may be thrown on the structure of those
propositions and on the theories in which they play a part.
I have argued elsewhere that the logic of inexact concepts
provides us with useful equipment for clarifying the logical status
both of empirical laws of nature (which relate inexact empirical
characteristics) and of the theories of applied mathematics (which
relate inexact empirical to exact mathematical characteristics).1
In this paper I use the logic of inexact concepts in an effort to
clarify the notion of resemblance which is applied, e.g., when we
assert of a green and blue thing that they resemble each other in
respect of-the determinable-colour, or that two objects
resemble each other in any more general way.
As regards the definition (given in Section 1 below) of the
logical relations which may hold between inexact concepts, I am
faced with the awkwardchoice of eitherrepeatingformer statements
with hardly any change or assuming that I need not do so-the
reader of this paper being already well acquainted with what I
have had to say in the matter. The former alternative appears
to me to be much the more reasonable and I proceed upon it.
1. On the logical relations between concepts. I call a rule,
say r, for the assignment or refusal of a sign, say U, an inexact
See ' On the Nature of Pure and Applied Mathematics' in Ratio No. 3
and ChapterXI of ConceptualThinkingCambridge1955,Dover (New York),
1959.
1
126
S. KiRNER
rule, and U an inexact concept, if the followingtwo conditions
are fulfilled. Thefirst concernsthe possibleresultsof applying
U to objects. These are: (a) that the assignmentof U to some
object would conformto r whereasthe refusalwould violate it;
in which case the object, we may say, is a positive candidate
for U and, for the person making the assignment,a positive
instance of U; (b) that the refusalof U to some object would
conformto r whereasthe assignmentwould violateit; in which
case the objectis a negativecandidatefor U and, for the person
makingthe refusal,a negativeinstanceof U; (c) that both the
assignmentand the refusalof U to some objectwould conform
to r; in whichcase the objectis a neutralcandidatefor U. For
the person who assigns U to the object it will be a positive
instance of U; for the person who refuses U to the object, a
negative instance of U. The second condition concerns the
natureof the neutralcandidatesfor an inexactconcept U. If we
definea concept,say V, by requiringthat the neutralcandidates
for U be the positive candidatesof V, then V will again have
positive,negativeand neutralcandidates. (Example: Let U be
the inexact concept 'green' and V the concept 'having the
neutral candidatesfor 'green' as its positive candidates'. V
is inexact.)
The inexactnessof a concept,i.e., the possibilityof its having
neutral candidates,depends on the rules which govern its use,
and not on the actual inventoryof the world. 'Green' would
e.g., remaininexactif there were no colours. An exact concept
on the other hand cannot have neutralcandidates. For such a
concept,the distinctionbetweencandidatesand instanceshas no
point; clause (c) of the firstconditionabove, likewisethe entire
secondcondition,haveno application. The concepts(attributes,
predicates, statement-functionsetc.) of standard logic and
mathematicsare all exactor at least are requiredand assumedto
be so-for exampleby Frege.2
The following definitions of the logical relations between
conceptsapply to both exact conceptsand inexact. Let U and
2
Frege, Grundgesetzeder ArithmetikJena 1903, esp. Vol. II ? 56.
ON DETERMINABLESAND RESEMBLANCE
127
V be two concepts governed respectively by r (U) and r (V); and
let S, be a finite set of objects. Apply r (U) and r (V) to the
membersof S, collecting the positive instances of U into the
" associated set " [U],
and similarly the positive instances of
V into [V]1. Between the two associated sets the following
relationsmay obtain:
(1) [U], < [V], (proper inclusion)-also, of course
[U]1> [V], and [U],
I[V], (bilateral inclusion);
(2) [U]I/[V], (exclusion); and
(3) [U] O0[ V], (proper overlap, where each of the two
finite sets has at least one member not common to both).
Next, amplify S, by one or more objects into S2 and apply
r (U) and r (V) to all members of S2thus getting the "amplified
associated sets " [U]2 and [V]2. The relations between these
again may be: [U]2 < [V]2, [U],/[V]2, [U]2 0 [V]2. If the
relation, between the original and the amplified sets be the same,
I shall say that the relation is preserved in the amplification or
briefly that it is preserved.
The possible logical relations between concepts, including
inexact ones, may now be defined in terms of the preservabilityof
the relations between their associated sets-preservability, like
exactness or inexactness of a concept, being independent of the
inventory of the world:
(1) U < V by " Inclusion is the only preservable relation
between any two associated sets of U and V." The relation
is the familiar inclusion.
(2) U/V by " Exclusion is the only preservable relation
between any two associated sets of U and V." The relation
is the familiar exclusion.
(3) U O V by " Overlap is the only preservable relation
between any two associated sets of Uand V." The relation
is the familiar overlap.
(4) U @ V by " Inclusion and overlap are both preservable
between any two associated sets of U and V." The relation
will be called " inclusion-overlap ".
128
s.
KOiRNER
(5) U O Vby "Exclusionandoverlaparebothpreservable
relations between any two associated sets of U and V."
The relationwill be called " exclusion-overlap."
Betweenexactconceptsonly the firstthreerelationscan hold
and it is on this fact that e.g., the Eulerdiagramsare based. An
example of (5) would be any two concepts U and V (say
U = ' green' and V = ' blue ') such that althougheverypositive
candidatefor U is a negativecandidatefor V and everypositive
candidatefor Va negativecandidatefor U, U and Vhavecommon
neutral candidates. If no such object is elected as a positive
instance of U and of V, [U]/[V] will be preserved; otherwise
[U] O [V]. Similarexamplescan be providedfor (4).
Clearly U ( V must be distinguishedfrom ((U < V) or
(U O V)) since the formerstatementassertsthe preservabilityof
inclusion and overlapbetweenthe associatedsets, whereasthe
latter assertsthe preservabilityof one or the other. Similarly
(4) is not an alternationof (2) and (3).-From a purelycombinatorial standpointthe following further possibilitiescan arise:
(6) No relation preservable,(7) inclusion and exclusion preservable,(8) inclusion,exclusionand overlappreservable. But a
sign used in accordancewith rules allowingany of these is-on
any view of conceptualthinking-not used as a concept.
Our definitionsof the five logical relationsare based on the
assumptionthat we are free to " elect" a neutral candidate,
say xo, of a concept, say U, as a positive or negative instance
of U independentlyof previous elections of x0 or any other object
as a positive or negativecandidateof U or any other concept.
This freedom,which may be restrictedby furtherconventions,
implies that the relation of an inexact concept U to itself is
U @ U and not U < U. It will-after the definitionof the
absolute complementU of U-equally become clear that the
relationbetweenU and U is U 0 U and not U/U.
2. Sums, products and complements. Just as the number of
possible logical relations between concepts is increased by
admittinginexact concepts in addition to exact ones, so is the
numberincreasedof ways of formingnew conceptsfrom already
ON DETERMINABLESAND RESEMBLANCE
129
availableones by meansof logicalconnectives. In definingthem
we have considerable freedom. A guiding principle for
redefining" complement", " sum" and " product" of two or
more conceptshas been the requirementthat for exact concepts
they should reduce to the usual ones. This is the principle
observedalso, for example,when operationswhich have been
defined for one class of numbers are redefinedfor a wider
class.
The sum of two-exact or inexact-concepts, say U and V, is
determinedby the followingstipulation: An objectis a positive
candidateof (U + V)-in words, U or V-if, and only if, it is
a positivecandidateeitherof U or of V or of both; it is a negative
candidateof (U + V) if and only if it is a negativecandidateof
both; it is a neutralcandidateof (U + V) in all other cases.
The definition,though needed here only for pairs of concepts,
can easily be extended to any finite sum. Since the sum is
definedin termsof candidatesfor its members-and not in terms
of candidatesand instances-the stipulationcan be represented
afterthe fashionof the truth-tables. If U and
diagrammatically
V have no neutralcandidates(U + V) is the sum of two exact
concepts.
We now turn to the notion of the product(U.V) of two
concepts. An objectis a positivecandidateof (U.V) if, and only
if, it is a positive candidateof both; it is a negativecandidate
of (U.V) if, and only if, it is a negativecandidateof one or both
of them; it is a neutral candidateof (U.V) in all other cases.
For exactconceptsthis reducesto the usual definition.
The general definition of the complementis this: Two
of each otherif, and
concepts U and U are absolutecomplements
only if, a positivecandidateof U is a negativecandidateof U; a
negative candidateof U is a positive candidateof U; and a
neutralcandidateof U is a neutralcandidateof U. For exact
conceptsthis again gives the usual definition. (I am using the
term " absolutecomplement" becauselater in this essay I shall
be introducing,under the name of " determinatecomplement"
a notion whichhas no parallelin the logic of exact concepts.)
The generalizeddefinitionsof sum, productand complement
I
130
S. K6RNER
are consistent. Theirapplicationyields theoremswhich are for
the most part obviousgeneralizationsof theoremsof exactlogic.
For example,we have U + V = U. V in the sense that by our
definitionsan objectis a positive,negativeor neutralcandidate
of U + V if, and only if, it is respectivelya positive,negativeor
neutralcandidateof U. V.
On the whole the definitions of 'sum', 'product' and
'absolute complement' correspondto common uses of 'or',
' and ' and ' not'. If we call the conceptfor whicheveryobject
is a positivecandidatethe universalconceptand the conceptfor
which every objectis a negativecandidatethe null-conceptthen
it is not true that for everyconcept U-(U + U) representsthe
universalconceptand (U. U) the null-concept. This is so only
if U is exact.3
3. Linkedconceptsanddeterminables.If an objecta resembles
another object b with respectto the propertyU and also with
respectto the propertyV, and if in addition U is a speciesof V
in the sense that either U
V or U ? V, then U will here be
called, in conformitywith an establishedphilosophicalusage, a
" determinateunder V ". If, in the conceptualsystem under
consideration,V itself is not a determinateunder some other
property,then V will be called a " determinable" of the system.
(Example: 'green' is a determinateunder the determinable
'coloured '.) Before these notions can be used in clarifying
varioustypes of resemblance,they themselvesmust be clarified.
This will be done by definingthem in terms of relationswhich
hold betweeninexact concepts only, in particularof exclusionoverlap. (WheneverpossibleI shall use 'P ', 'Q ', 'R ', 'C1'
' C,' for signs of inexactconcepts.)
Let us say that a conceptP is linkedwithanotherconceptQif,
and onlyif, either(i) P O Qor (ii) in the conceptualsystemunder
considerationthere are availableconcepts C1,C2,... . Cn such
that P O C1,C, O C2. . . C, 0 Q.* Whetheror not a concept
*
In framingsome of the definitionsof this and the following sections I
have profitedfrom discussionwith Dr. P. Feyerabendand Dr. C. Lejewski.
* Added after readingMr. Searle's paper : If any link in this exclusionoverlap chain is (or is equivalentto) a conjunctionof concepts, then it must
notbepossible
to dropanyof themwithout
thechain.
breaking
ON DETERMINABLESAND RESEMBLANCE
131
is availablein a systemdependson the rules-prescriptive,
the formationof its
proscriptiveor permissive-governing
concepts. Most of the following examples are chosen from a
conceptual system of a type which is widely adopted and is
implicitin customaryways of speaking. (It is a system of the
second of the types discussed in section 4.)
If, as we shall assume throughout,with every concept its
absolute complement is also available, the first condition above
is redundant: If P O Q then P and P have not only the same
neutral candidates but share some of them with Q. We have
P 0 P, P O Q. If the first condition is fulfilled the second is
eo ipso also fulfilled. (Example: Since 'green' is linked with
' blue', ' green' is linked with ' not-green' and ' not-green'
with 'blue '.)
The relation of linkage between two inexact concepts is
symmetrical. If P is linked with Q then Q is linked with P.
It is transitive. If P is linked with Q, and Q with R, then P is
linked with R. And it is reflexive. In view of P o P, any
inexact concept is linked with itself via its absolute complement
I.e., P 0 P and P 0 P. Linkage is thus exemplified by any
system which contains at least one inexact concept and its
complement.
Conceptual systems are conceivable in which every concept
would be linked with every other. But this is not in general so.
(Example: Consider the concept 'green' and its absolute
complement 'not-green'. Although 'green' is linked with
' not-green ', it is not linked with all its speciesbeing a species
? P. Thus we• shall assume that
of P if either T < P or @
' green' is not linked with ' romantic ', ' angry', etc. and not of
course with any exact concept such as 'being a prime number'.
Unless we postulate "links" between any two inexact
concepts we can easily provide examples of unlinked inexact
concepts.)
In order to define the notion of a determinable we must first,
mainly in terms of linkage, define a stronger relation. Let us say
that a concept P is fully linked with a concept Q if and only if,
every species n of P is linked with every species K of Q. Since
12
132
s. KiRNER
P is a speciesof P, and Q a species of Q, full linkageimplies
linkage; while the converseis not true. (Example: ' green' is
fully linkedwith ' yellow or red ' but not with ' yellow or angry',
since' angry'-a speciesof ' yellow or angry'-is not linkedwith
' green'.) It follows from the definitionof full linkagethat the
relationis symmetricaland transitive. Thus,if a conceptis fully
linkedwith another,it is also-via this concept-fully linkedwith
with itself. (Examples: ' green' if fully linked with ' red' and
viceversa; ' green' is fullylinkedwith' blue', ' blue ' with' red '
and therefore ' green' with ' red '; ' green' is fully linked
with ' red ', ' red' with ' green' and, therefore,' green' with
'green'.)
The notion of a determinablecan now be defined. A concept
is
Q a determinableof a conceptP if, and only if, (i) P is a species
of Q, but not also Q a species of P. (ii) Q is the sum of all
concepts which are fully linked with P. It follows that every
concept can have at most one determinable. (Example:
'Coloured' is the determinableof 'green'.) But not every
concepthas a determinable. (Examples: No exact concepthas
a determinablesince, having no neutral candidates,it is not
linked with any concept. Again 'green or angry' has no
determinable:For assumethat D is the determinable. Then in
view of condition (i) D must have a species 8 which is not a
species of 'green or angry', but fully linked with it. This
implies that 8 if fully linked with 'green' and with 'angry'.
Fromthe full linkagebetween' green' and 8 on the one handand
8 and ' angry' on the otherit followsthat ' green' is fully linked
with 'angry'. But-according to the example of the last
paragraphbut one-the two conceptsare not even linked.)
Whenwe say that an objectis not greenwe sometimesmean
that it is not even coloured. At other times we mean that it is
not greenbut coloured. In the firstcase the objectis a positive
or neutralcandidateof the absolutecomplementof ' green', in
the secondcase it is a positiveor neutralcandidateof what may
be called the determinatecomplementof 'green'. A concept
Q is the determinatecomplementof a conceptP if, and only if,
Qhas the samespeciesas the determinableof P, withthe exception
of P and its species. WritingDet (P) for the determinableof P
ON DETERMINABLESAND RESEMBLANCE
133
is briefly:Q = Det(P) - P. (Example:' green'
thedefinition
of
and'not green,butcoloured'are determinate
complements
eachother.)
It follows that a concept,if it has a determinatecomplement
at all, can have at most only one; and that a concept has a
determinatecomplementonly if it has a determinable. We shall
writeP' for the determinatecomplementof P. If a conceptP
has a determinatecomplementP' then the determinatecomple-
ment of P' is P, i.e., (P ')' = P.
(See last example.) If P has
no determinatecomplementwe may identifyP' with the nullconcept, i.e., P '= O.
In generalwe shall haveP ' P althoughin some conceptual
systems the absolute and the determinatecomplementmay be
identicali.e., P' = P. (Example: Considera conceptualsystem
containingonly colour-concepts. In such a system'not-green'
and 'coloured, but not green' are identical.) If P and Q are
any two species of the same determinable,say D, then by the
definitions of 'determinable' and 'determinate complement'
(P + P ') = (Q + Q ') = Det (P) = Det (P ') = Det (Q) =
Det (Q ') = D. That is to say all these expressionsrepresent
the same concept, or are differentlabels which are assignedor
refusedto objectsin accordancewith the samerules. (Example:
"(blue + blue')" = "(green + green')" = Det (green)
-
. .
. = 'coloured '.) Two determinables, say P and Q, are
identicalif every speciesz of the one is fully linked with every
speciesK of the other. Theyare differentif some species7rof one
is not fully linked with some speciesK of the other. (Example:
' coloured' and 'having shape' are different determinables
although, in various senses of the term "imply ", they imply
each other.)
I am preparedto admit that the definitionsof linkage, full
linkage, determinableand determinatecomplement could be
improvedand,perhaps,standin need of improvement. ButI do
not at presentdoubtthat the procedureof definingthemin terms
of exclusion-overlapand thus withinthe frameworkof the logic
of inexactconceptsis on the rightlines.
4. Exact and inexact determinables. The determinates a
134
s. Ki0RNER
underthe determinableD (8 < D or a @ D, but not vice versa)
are necessarilyinexact, since their inexactnessis a necessary
condition of linkage between them. The determinableitself,
however,may be exact or inexact. It is obvious (i) that D is
inexactif, and only if, D 0 D and (ii) that D is exactif, and only
if, DID. For (i) if D is inexactthe rulesgoverningits assignment
or refusaladmit of neutralcandidates. D has by definitionof
the absolute complementthe same neutral candidatesas D;
moreoverthepositiveandnegativecandidatesof D arerespectively
the negativeand positivecandidatesof D. This implies D o D.
On the other hand D 0 D implies the inexactness of D.
Statement(ii) is shownto be true in the sameway.
A statisticalenquiryamongEnglish-speaking
peoplemight,for
all I know, show that most of them use, say, the determinable
" coloured" as an exact concept. On the other hand,to use it
as an inexactconceptby no meanscommitsone to any great or
unreasonablemodification.Imagine,for example,a bluewindowpane becominggraduallymore and moretransparentin the sense
of affectingless and less the colours of the objects behind it,
untilin the end it becomesinvisible,though,of course,remaining
tangible. Should we, at every stage of the process,say of the
window-panethat it is a positiveor that it is a negativecandidate
of 'coloured', and never that it is a neutralcandidateof this
determinable? Few people can have ponderedthis question;
even fewercan have decidedit.
Those who are not awareof havingmadea previousdecision
can decidethe questioneitherway. They may so arrangetheir
languagethat at one stage of the process of becominginvisible
the window-paneis a neutral candidate of 'coloured' and
therefore,of ' not-coloured'. In this case ' coloured' 0 'not
coloured' and the determinableis inexact. On the other hand
they could decide that a fully transparentwindow-panehas by
definitionthe colour of the objectsbehind it and make further
arrangementsto ensure the exactnessof 'coloured'. Similar
examplescouldbe givenshowingthat determinables
may be both
exact or inexact.
The conceptualsystemsembodiedin most naturallanguages
ON DETERMINABLESAND RESEMBLANCE
135
include, as far as one can judge from one's limited knowledge,
exact and inexactconceptsand exact and inexactdeterminables.
It is neverthelessinstructiveto considersome " pure" types of
conceptualsystem,namely,(1) systemsin which all conceptsare
exact; (2) systemswhichcontainonly exact determinables,their
speciesandthe sums,pruductsand absolutecomplementsof these
species; (3) systemswhich contain only inexact determinables,
theirspeciesand the sums,productsand absolutecomplementsof
their species.
The firsttype of systemis exemplifiedby everytheoryof pure
mathematicsso farconstructed. Everyconcept,here,is exactand
has only exact species. To distinguish this thorough-going
exactness of mathematicalconcepts from the exactness of a
determinable,whosespeciesareinexact,one mightcall the former
"purely exact". An inquiry into the relations, and lack of
relations,betweeninexact and purelyexact conceptsis, I think,
importantto the philosophyof mathematics. (See referencesin
footnote 1.)
It is sometimes assumed that all empirical concepts are
organizedin systems of the second type-those which contain
only exact determinables. In such a system every empirical
concept is an exact determinableor a conjunction of such
determinables,a determinateunder an exact determinable,or a
sumor productof suchdeterminates.A good casemightbe made
in supportof the viewthat Locke'ssystemof empiricalknowledge
and the systems of his empiricistsuccessorsare of this type.
Part of what Wittgensteinshows by the constructionof various
" languagegames" is that languagesor conceptualsystemsof the
second type are by no means the only possible or "proper"
ones.
Systemsof the thirdtype mightpossiblythrow some light on
certainprominentfeaturesof Hegeliandialecticand of dialectic
in general. Theseare: No categoryis sharplyseparatedfrom any
other. On the contrary,all categoriesare connectedwith each
other. Hegelian negation leads allegedlyin a unique manner
from one category,the thesis,to anothercategory,the antithesis,
which is not the absolutecomplementof the thesis. The thesis
and the antithesiscombine into a third categorythe synthesis
136
S. KiRNER
which includesthem both. (Hegel, as is well known,is fond of
using the Germanword "aufheben" in describingdialectical
reasoning, because in its various senses it suggests negation,
preservation,and lifting to a higher level.) The process-or
rather the non-temporalstructureexhibitedby the process-is
completewhen the last synthesisis reached. This is the Idea or
Absolute which includeswithin itself all the precedingtheses,
anitheses and syntheses. Although Hegel begins the process
with the category of Being-in his view the most reasonable
starting point-this category being the emptiest-he holds, as
did Fichtebeforehim-that it could startwith any category.
Evena puresystemof the secondtypeconformsto someof the
foregoingprinciples,as can be seen by re-namingthe termsused
" categories
in the definitionsof section3: We call determinables
level
"
of
first
their
";
(or syntheses)
properspecies categoriesof
level zero "; the determinatecomplementof a category its
"antithesis"-so that the antithesis of an antithesis is the
originalthesis. Now clearlyeverythesis (of a categoryof level
zero)uniquelydeterminesits antithesis;andtheirsum,a synthesis
of firstlevel, includesboth thesisand antithesis. If all syntheses
or categoriesof firstlevel(alldeterminables)
areexact," dialectical
"
reasoning from thesisto antithesisto synthesismust stop at the
firstlevel.
If the categoriesof first level are inexact,exclusion-overlaps
and linkages between them become possible. We can then
define second-levelsynthesesbetween theses and antithesesof
first level. This is done, if in the definitionsof section 3, we
replace " determinable" by "category (or synthesis)of second
level ", and replace "proper species of a determinable"by
"proper species whichare categoriesof first level". We can
then "reason dialectically"from first-levelthesis to first-level
antithesisand second-levelsynthesisand so on, until aftera finite
or infinite numberof steps we reach a synthesiswhich has no
antithesis-the Absolute. Everysynthesisincludesthe preceding
synthesisand morespeciesof zero level thanits predecessor;the
last synthesisincludes(undercertainspecifiableconditions)all of
them. Thus all the above-mentionedprinciplescan be satisfied
by a pure system of the third type.-This analogy could be
ON DETERMINABLESAND RESEMBLANCE
137
elaboratedin more detailand with greaterprecision. But I fear
that in merelydrawingattentionto it I may alreadyhave angered
both Hegelianand anti-Hegelianphilosophers.
To exhibitthe structureof varioustypesof conceptualsystems,
howeverpedestrianor fanciful,is not to raisethe questionof their
adequacy. To say that "reality" is best describedby one of
these types, and that one should thereforebe preferredto all
the others is to defenda metaphysicalview or, as I understand
it, a general programmefor the construction of conceptual
systems.
5. Resemblance. Determinablesare respectsin whichobjects
resembleeach other. Oncethe notion of a determinableis clear
the notion of resemblancecan be definedwithout difficulty. If
D is exact then an objecta and an objectb resembleeach other
with respect to D if a and b are positive candidates of D.
If D
is inexactthen a and b resembleeach other also if one or both
are neutralcandidatesof D. (See the exampleof the windowpane at the beginningof the precedingsection.) This relationis
transitive,reflexiveand symmetrical:for clearly'D(a) and D(b)'
and' D(b) and D(c)' imply' D(a) and D(c)'; 'D(a) and D(a)'
implies 'D (a) and D(a)'; ' D(a) and D(b)' implies ' D(b) and
D(a) '.-An object a resemblesan object b, if a and b resemble
each otherwith respectto one of a numberof D's. This relation
is obviously intransitive,reflexiveand symmetrical. There is
nothingnew in these statementsexceptthat the term " respectof
resemblance" is no longerundefined.
Thereare, however,weakernotions of resemblancewhichdo
not fit these definitions. These are now often called "family
resemblances", a notion which is central to Wittgenstein's
philosophy and is applied by him in particularto "language
games ".
In a customarysenseof " familyresemblance"-for instance,
when speaking,say, of the resemblancebetweenthe membersof
the Habsburgfamily-one uses the termto indicatethat any two
membersof the familyare positivecandidatesfor one at least of
a limitednumberof determinables. But this Wittgensteinrejects
as mereverbiageand as tantamountto sayingthat " something"
138
S. KiRNER
runs " througha threadwhich we have twistedfibreupon fibre,
namelythe continuousoverlappingof thesefibres".4
But if Wittgenstein'sfamily resemblanceis not resemblance
with respectto determinables,what is it ? From his remarks,
and in particularhis referencesto Frege's rejectionof inexact
concepts,two thingsseemto emerge:first,thatfamilyresemblance
between objects cannot be definedin terms of exact concepts,
second,that the conceptsin termsof whichit can be definedmust
admitof commonneutralcandidates. Familyresemblancescan,
it would thus appear,be stated only in a language-conceptual
system-some of whose concepts are linked with each other
throughexclusion-overlaps.
Sometimes,and not only in poeticalmoods or whenspeaking
in metaphors,we do assertof two objectswhichdo not fall under
thattheyresembleeachother. (Examples:
the samedeterminable
In calling the colour of some red objects " warm" we imply a
connexion between 'red' and 'warm' without implying that
these two conceptsare determinatesundera commondeterminable. Again, one mightstill say that red objectswouldresemble
blue ones in coloureven if therewerea " discontinuity" in one's
colour-conceptssuch that ' blue' and ' red' werenot eitherfully
linkedor even linked.)
The questionariseswhen do we, or are we to, say of objects
underconceptswhich are not fully linked-i.e. of objectsunder'
concepts which are not determinatesunder a common determinable-that they resembleeach other ? No clear-cutanswer,
can be given. All that can be said is that the modification
necessaryto introducefull linkagebetweenthe concepts,i.e., to
replacethe conceptsby suitabledeterminatesunder a common
determinable,must not be too great.
I am not very confident that this definition of "family
resemblance" in termsof a set of inexactconceptspartlylinked
and more or less easilymodifiableinto a set
by exclusion-overlap
linked
of fully
concepts, fairly representsWittgenstein'smetaphoricallyexpressedposition. But the notion does justice to
'
Wittgenstein,PhilosophicalInvestigationsOxford 1953, esp. ??67-71.
ON DETERMINABLESAND RESEMBLANCE
139
many weak senses of resemblanceby defining them, at least
partly, in terms of clear notions. And this, in any case, is
desirable.
6. Analyticpropositionsinvolvinginexact concepts. I wish now
to indicateverybrieflyin conclusionhowin termsof the preceding
discussionthe structureof analyticpropositionsinvolvinginexact
conceptscan be understood. I believeit can be understoodin
the same mannerand to the same extent as the structureof the
more familiaranalyticpropositionsbelongingto exact systems.
Thismay be seenfromtwo simpleexamples,by use of somewellknown terms from semantics as developed in particular by
Tarski.5
The analyticcharacterof e.g. the statement' The class of even
numbersis includedin the class of evennumbers' is explainedby
the meta-statement:If a is a class-variablethen the statementform 'a C a' is satisfied by every model derived from it
through replacingthe variableby the name of a class. It is in
particularsatisfiedby our example.
The analytic characterof e.g., the statement'(The concept
'green' is included in the concept 'coloured')' is similarly
explained by the meta-statement: If P is an inexact-conceptvariable then the statement-formP < (P + P ') is satisfiedby
every model derivedfrom the statementthrough replacingthe
variableby the name of an inexactconcept.
It is in particularsatisfiedby our example if the constant
'green' has a determinatecomplement,since 'coloured' and
" (green + green') " are then names of the same concept. If
on the otherhandin the systemunderconsiderationthe constant
inexact concept substitutedfor the variablehas no determinate
complement, the substitution-instancefor P' represents the
null-conceptand the resultingmodelagainsatisfiesthe statementform. Indeedthe meta-statementremainstrue if it is generalized
by permittingP to be any concept-variableand permitting
6
Tarski, Logic, Semantics,Metamathematics,Oxford 1956,e.g., Chapter
XVI.
140
S. K6RNER
substitutionsof it by the name of any concept,exact or inexact.
A moresystematictreatmentof so-called"analyticbutnotL-true"
statements,by findingthem their properhome in an explicitly
formulatedlogic of inexactconceptsdoes not seemto presentany
very greatdifficulty. But it lies beyondthe limits of this paper.
II.-By
JOHNR. SEARLE
THEnotion of determinablesand the relation of determinate
to determinablewas first introducedinto modern philosophy
by Johnson in the following words: "I propose to call such
termsas colour and shapedeterminablein relationto such terms
as red and circular which will be called determinates ..."
Professor K6rner's paper is mainly concerned with defining
this distinction-or at any rate a related distinction-in terms
of the notion of an inexactconcept. I wish to state at the outset
that it does not seem to me that the problemof elucidatingthe
distinction between determinatesand determinableshas any
special connexion with the problem of inexact concepts, nor
is it clear to me why Professor Kbrner thinks it has. The
is the samewhether
relationof determinatesto theirdeterminables
or not the determinatesare exact or inexact. Since the notion
of inexact concepts seems to me irrelevantI shall attack this
problemin a way quite differentfrom Korner.
First a word about terminology. In what follows I shall
speak not only of determinateand determinablewords but also
of classes,concepts,andproperties:I shallemploythe expression
" term" to cover all of these indifferently. I shall employ the
expression" the determinablerelation" to mean the relationin
which any determinateand its determinablestand to each
other.
I. The Distinction between the Determinable Relation and the
Genus-Species Relation
In elucidatingthe relation of determinatesto determinables
the first considerationwhich springsto mind is that the determinateterm is more specificthan the determinable. But clearly
not any two termswhich stand in the relationof greaterto less
specificityeo ipso stand in the relation of determinateto determinable: " yellow" is in some sensemore specificthan " yellow
or angry" but it is not a determinateof " yellow or angry" in
the sensein whichit is a determinateof " colour". Furthermore
" human" is specificrelativeto " animal" but " human" and
142
JOHN R. SEARLE
" animal" stand in the relation of species to genus not
determinate and determinable. This last point might seem
more doubtful and I shall begin by elucidatingthe distinction
between the determinable relation and the genus-species
relation.
What are these two relations and how do they differ? A
species is markedoff within a genus by means of differentia.
Thuse.g., the classof humans(species)is includedwithinthe class
of animals(genus)but markedoff from otherclasseswithinthat
class in that each humanpossessesother properties-forty-eight
chromosomes,a certain shape, etc. (Philosophersalways say
that the differentiais rationality. It is not of course but for
shorthandlet us supposeit is)-which constitutethe differentia.
And it is the possessionof these differentialpropertiesas well
as membershipof the genus which entails of each human that
it is human. No analogous specification of a species via
to determinables.1
differentiaexistsfor the relationof determinates
Both species and determinatesare included within genus and
determinablerespectively-all humans are animals and all red
things are coloured-but whereaswe can say " all humansare
animalswhich are rational", how could we fill the gap left for
a differentiain " all red things are coloured things which
are . .. ." ? The onlywordwhichpresentsitselfas a candidate
is " red " itself ! Perhapsour failureto find a differentiais due
to the fact that colour termsdo not admit of verbaldefinitions,
so let us invent a verbaldefinitionfor red. Let us say that all
red things are coloured things which are "rouge ". But is
"rouge " a differentia of "coloured" in the way that
" rational" is a differentiaof " animal" determiningthe species
human? Some determinatesdo admit of verbal expansions,
so let us consider one of these e.g., anythingsphericalhas a
shapeandhaseachpointon its surfaceequidistantfroma common
centre. Butin both of thesecasesthe candidatefor the differentia
seems to mean the same as the candidatefor the species and
1 Cf. A. N. Prior, "Determinables, Determinates,and Determinants",
Mind, 1949.
DETERMINABLESAND THE NOTION OF RESEMBLANCE
143
hence falls necessarily under the genus. For what can " rouge "
mean if not " red ", and we know that " has each point equidistant . . ." just means " spherical ". But this is quite unlike
our standard species-genus examples, for "rational" is not
synonymous with " human" nor does it entail " animal ".
What these examples show can be stated in two ways: first, in
order for some property to be a genuine differentia of a species
within a genus, it must be logically possible that entities outside
the genus could have that property, i.e., the differentia must be
logically independent of the genus. For example, even if humans
are in fact the only rational things it is at least logically possible
that calculating machines, spirits, etc., could show signs of
rationality. But it is not logically possible that things without
shape could have all points on their surface equidistant from a
common centre.
Secondly: where two properties stand as determinate to
determinable nothing can fulfil the function of a differentia, for
anything which in conjunction with the determinable entailed
the determinate would (with exceptions to be discussed later) have
to entail the determinable.
In short, a species is a conjunction of two logically independent
properties-the genus and the differentia. But a determinate is
not a conjunction of its determinable and some other property
independent of the determinable. A determinate is, so to speak,
an area marked off within a determinable without outside help.
These two relations can be illustrated graphically:
species
determinable
determinate
genus
differentia
The species is determinedby the intersectionof two logically
independentterms,but anythingwhichmarkedoff the determinate
could not be independentof the determinable.
144
JOHNR. SEARLE
II. The First Criterion: Specificity
Using the materialsfrom this discussionwe can now lay
down a criterionfor decidingof any two termswhetheror not
they stand in the determinablerelation. In constructingour
criterionwe shallemployonly the notionsof termand entailment
between terms. Let us first review the conditions any such
criterion(or definition)must satisfy: what characteristicsof the
relationmustit elucidate?
1. It must show that any determinableis a more specific
form of its determinable. This is a basicfeatureof the criterion
and most of its otherfeatureswill be designedto eliminatepairs
of termswhichstandin this relationbut whichhaveotherfeatures
renderingthemunlikepairsof termsstandingin the determinable
relation.
2. It must enableus to distinguishthe determinablerelation
from the genus-speciesrelation.
3. It must enableus to distinguishthe determinablerelation
from the relationof a determinableto a conjunctionof one of its
determinateswith some independentterms-e.g., we need to
distinguishthe way " red " standsto " colour" (or "red thing"
to "coloured thing") from the way "red rose" stands to
"colour " (or " colouredthing").
4. It must enableus to distinguishthe determinablerelation
from the relationof some arbitrarydisjunction(sum)of termsto
one of its members-e.g., we must be able to distinguishthe
relationof " colour" to " yellow" from the relationof " yellow
or angry " to " yellow ".
5. It would help also if we could distinguishthe way " red"
is a determinateof " colour" from the way " scarlet" is a determinate of " red ". In some sense one wants to say that both
these pairs standin the determinablerelation,yet the relationof
either" red " or " scarlet" to " colour" seemsmorefundamental
than the relation of " scarlet" to "red ". Furthermoreone
DETERMINABLES AND
THE NOTION OF RESEMBLANCE
145
would like some way of showing that e.g., " red " and " yellow "
are on the same level as determinates of " colour " whereas
" scarlet " is on a different and lower level.
1. Let us say of any two terms A and B: A is a specifier of
B if and only if A entails B, but B does not entail A. In applying
this criterion we shall tacitly assume that the necessary syntactical
adjustments are made throughout; e.g., strictly speaking " is
spherical" entails " has a shape " but we shall say for short
"
" spherical entails " shape ".2
This criterion is of course very weak as it stands. In the
context of another problem Aycr has tried to strengthen it by
adding the qualification that A must not be a component of B.3
But this qualification is worthless since the notion of a component is unexplicated: presumably A is a component of B if
the word expressing A is also used to express B. (What else
could it mean ?) But then we can always eliminate componency
by using a different word. Thus e.g., " yellow " is a component
of " yellow or angry " only until we introduce a different word,
say " yengry " to mean " yellow or angry ". Let us therefore
abandon this terminology of componency and simply say: A is
a specifier of B if and only if A entails B, and B does not entail A.
(In symbols, letting "S " mean " is a specifier of " and " -"
B.
mean " entails ": ASB -- df. A
(B -, A).) A necessary
condition of A's being a determinate of B is that A is a specifier
of B.
2. If A is a specifier of B then A and B will not stand in the
relation of species to genus if there is no term C such that the
conjunction of B and C entails A, but not C by itself entails B,
that is, there must not be any differentia which taken with the
genus entails the species but which does not by itself entail
2
Laterwe shall see that it is more accurateto say " spherical" presupposes
rather than entails "'shape " and we shall have to make a slight revision
in our criterionaccordingly.
3 A. J. Ayer, " Negation ', Philosophical Essays.
K
146
JOHN R. SEARLE
the genus. Any specifier which satisfies this condition I shall
call an " undifferentiated specifier ". For example " negro " is
a specifier of "man" but not an undifferentiated one since
" black " and " man " entail " negro ", but " black " does not
by itself entail " man ". But " spherical " is an undifferentiated
specifier of " shape ": though " has all points equidistant from
a common centre " taken together with " has a shape " entails
" spherical ", "has all points equidistant from a common
centre " entails " has a shape ". It is a necessary condition of
A's being a determinate of B that A is an undifferentiatedspecifier
of B.
This criterion still suffers from a serious defect for it does not
so far allow us to say that " scarlet " is a determinate under
"red ". This can be shown as follows: suppose that beside
scarlet there are three other shades which along with " scarlet "
exhaust the term " red ". Then" scarlet " is not an undifferentiated specifier of " red " because " neither one nor two nor three
but red " entails " scarlet ". And " neither one nor two nor
three " does not entail " red ". However, as " neither one nor
two nor three " is clearly logically related in some way to " red "
since its negation entails " red ", we can remedy the criterion
by amending it to read, rather long-windedly, A is an
undifferentiated specifier of B if and only if A is a specifier of
B and there is no term C such that though C and B entail A,
neither C nor its negation entails B. This admits " scarlet " as
an undifferentiated specifier of "red ", "eighteen years old "
as an undifferentiatedspecifier of " under thirty years old ", etc.,
but excludes genus-species terms. (In symbols, letting "U "
mean " undifferentiated", then:
AUSB = df. ASB.3. (I C) [(C. B-->A).e
(C ->-B v
C-
B)].)
3. Satisfying our third condition is a bit awkward but
absolutely essential. After all, so far we are not even in a
position to show how the relation of " red'" to " colour"
differs from that of " red rose " to " colour ", since " red rose "
is an undil'iere-ntiatedspecifier of " colour ". However, one
would like to exclude " red rose ", because it is a conjunction of
DETERMINABLESAND THE NOTION OF1RESEMBLANCE
147
a determinate of " colour " with a term not a determinate of
" colour ". How do we do this without circularity, i.e., without
using the notion of determinate which we are trying to define?
We can exploit the logical consequences of the fact that " red
rose " is a conjunction of terms one of which is a determinate of
" colour " and one of which is not. The one which is not,
" rose ", though it may entail " colour ", is neither a determinate
of " colour" nor synonymous with "colour" and therefore
must be equivalent to a conjunction of terms some of which are
logically independent of "colour" e.g., " has a smell ". Thus,
our original term " red rose " is equivalent to a set of terms some
of which do not entail " colour " and we build our definition
on this feature. We eliminate this class of cases by requiring
that if A is a specifier of B then A must not be equivalent to a
set of terms such that one (or more) of them entails B while
the others do not. Let us say of any A and B satisfying this
relation that A is a non-conjunctive specifier of B. Recalling
our problem with " red " and " scarlet ", we must amend the
criterion to read: A is a non-conjunctive specifier of B if and
only if A is a specifier of B, and A is not equivalent (entails and
is entailed by) to any set of terms C, D, E, etc., such that one or
more of them C entails B but of some others of them D, neither
D nor its negation entails B. Being non-conjunctive entails
being undifferentiated,so this criterion satisfies both requirements
2 and 3 in one fell swoop. It is a necessary condition of A's
being a determinate of B that A is a non-conjunctive specifier of
B. (In symbols letting "N " mean "non-conjunctive ", and
mean "equivalent " : ANSB - df . ASB . N(~ C, D)
" -"
Bv
D -->-B)].)
[(A = C. D). (C ->-B) .r (D
4. It might seem that we could satisfy the fourth requirement
by insisting that " yellow " was not a determinate of " yengry "
since non-conjunctive specifiers of " yengry " are not separated
by a single fundamentun divisionis the way non-conjunctive
specifiers of " colour " are. The instinct here is sound but the
difficulty lies in formulating the point as a criterion in a way that
will not render it too circular or question-begging to be useful.
It will not do to say simply that there must be a single
fundamnenitun•
K2
148
JOHN R. SEARLE
divisionis, for how do we decide if there is one ? Nor will it do
to say that all determinates under a given determinable have
something in common, for what is it that e.g., all colours have
in common that makes them colours? Any answer must be
circular.4
We can however formulate a non-circular criterion by
reminding ourselves of certain features of determinates alluded
to earlier. Genuine determinates under a determinable compete
with each other for position within the same area, they are, as
it were, in the same line of business, and for this reason they
will stand in certain logical relations to each other. Johnson
supposed that all determinates under a determinable were
mutually exclusive; but this is not quite accurate, " green "
excludes " red ", but " scarlet " does not exclude " red ", it is
a specifier of it, yet all three are determinates of " colour ".
Let us say of any two terms that they are logically related if
either entails the other or either entails the negation of the
other. (In symbols, letting "R" mean "is logically related ",
ARB = df. (A ->-B) v (B -+ A) v (A ->- B).) It is a necessary
condition of any two terms A and B being determinates of a
third term C that A and B are logically related. (We can of
course expand this definition to include pairs of inexact concepts,
i.e., concepts with a common vague boundary.)
Ignoring for a moment the fifth condition, we can now state
a criterion for the determinable relation: For any two terms
A and B, A is a determinate of B if and only if A is a non-conjunctive specifier of B, and A is logically related to all other
non-conjunctive specifiers of B. (In symbols, letting "dt."
mean "is a determinate of ",
A dt. B = df. ANSB. (C) (CNSB D ARC).)
Let us pause for a moment to consider the nature of this
criterion. Our essential condition for the determinable relation
4
Cf. D. F. Pears, " Universals", in Flew, Logic and Language,Second
Series.
DETERMINABLES AND THE NOTION OF RESEMBLANCE
149
is specificity, but we need to exclude pairs of terms which stand
in the relation of specificity but which do not stand in the determinable relation. These fall into four classes: where the specifier
is a conjunction of the specified with some other term (this is
the genus-species situation), where the specifier is a conjunction
of a determinate of the specified with some other term, where
the specified is a disjunction of the specifier and some other term,
and where the specified is a disjunction of a determinable of the
specifier and some other term. (In symbols, letting " A " stand
for a determinable and " a " for one of its determinates and
"b" for some independent term, the cases of specificity we
wish to eliminate are: a. bSa, a. bSA, aSavb, aSAvb.) The
first two cases are climinated by conditions two and three, the
last two by condition four. K6rner, incidentally, makes no
provision for eliminating the first two. and his criterion suffers
thereby as we shall see.
5. Once we have a basic criterion for the determinable
relation the fifth condition is easily satisfied. Two terms A and B
are same level determinates of C if and only if they are both
determinates of C and neither is a specifier of the other. Thus
" yellow " and " red " are same level determinates of " colour ",
as are also " red " and " not red ", but " red " and " scarlet "
are not same level determinates.
The more fundamental position which " colour" occupies
vis a vis both " red " and " scarlet " is shown by the fact that
the predication of " red " " not red ", " scarlet" or " not
scarlet" of any object presupposes that "coloured" is true
of the object. A term A presupposes a term B if and only
if it is a necessary condition of A's being either true or false
of an object x, that B must be true of x. For example, as we
ordinarily use these words, in order for it to be either true or
false of something that it is red, it must be coloured. Both
" red" and " scarlet " then presuppose their common determinable "coloured ". But "scarlet" does not presuppose its
determinable "red", and we may generalise this point as a
criterion: B is an absolute determinableof A if and only if A is a
determinte of B, and A presupposes B. Thus "coloured " is an
150
JOHN R. SEARLE
absolute determinable of " red "'. but " red " is not an absolute
determinable of scarlet.
Presupposition is not a kind of entailment, e.g., it does not
follow the same rule for contraposition which entailment follows,
so having introduced the notion of presupposition we shall have
to revise our previous definitions to include both entailment and
presupposition. Where before we had e.g., "A entails B ", we
must read "A entails or presupposes B " throughout.5
The notion of an absolute determinable is relevant to the
traditional problem of categories: every predicate carries with it
the notion of a kind or category of entities of which it can be
sensibly affirmed or denied. For example, " red" is sensibly
affirmed or denied only of objects which are coloured-this is
part of what is meant by saying that "red" presupposes
"coloured ". Absolute determinables then provide us with a
set of category terms.
With the addition of criteria for " same level determinate "
and " absolute determinable ", our criterion now satisfies the five
conditions we set for it. It is worth emphasising that the aim
of the five conditions and the resulting criterion is not simply to
pick out terms standing in the determinable relation-for the
paradigms at least we know what pairs to look for before we
even begin our investigation-but to cast light on the nature
of the relation. The philosophical tradition bequeathes us pairs
of terms that look similarly related: " colour " and " red",
" number " and " seventeen "," temperature " and " 30 degrees",
etc. But exactly how are these pairs similar and how do they
differ from other pairs of terms? The criterion is an attempt to
answer these questions and it seems to me a merit of this
criterion as against Professor Kirner's that it provides us
with the beginnings of a philosophical elucidation of the
relation.
The weakness of this approach on the other hand lies in the
inappropriateness of attacking certain areas of ordinary language
5 This was pointed out to me by Mr. P. F. Strawson, who also made
othervaluablecriticismsof thispaper.
DETERMINABLES AND THE NOTION OF RESEMBLANCE
151
with such crude weapons as entailment, necessary and sufficient
conditions, etc., and. the consequent air of unreality surrounding
any such approach. Part of Wittgenstein's point in his discussion of family resemblance is simply to cast doubt on any
general philosophical method of this sort, for not all terms admit
of clear cut analyses of the required kind. We cannot, e.g., say
exactly what terms entail and are entailed by " game ". The
criterion then must be taken as an ideal model and not a description of the way language actually works.
III. The Second Criterion: Resemtblancewith Respect to.
If a criterion like the foregoing is of any serious philosophic
importance, if it really marks a division that is important in
our conceptual scheme, then it is likely that ordinary language
has some way of its own for making the same distinction. It
seems to me that ordinary speech does mark off tle de
ei•ninable
relation-though in a rather rough and ready way-through
certain variations on the notion of resemblance.
The most important and the most frequent observation made
about " resemblance " (and its brother notions, " likeness " and
" similarity ") is that they are in some sense incomplete predicates. One has not been given any information, or at any
rate only very minimal information, about two entities if one is
merely told that they resemble each other. For to be told that
two objects resemble each other is to be told that they have
some property in common, but it is not so far to be told what
property they have in common, and since any two entities will
have some property in common, it is not so far to be told
anything. The statement A resembles B thus invites the question
"how ?"-it invites completion.
What has been less frequently noticed is that it admits of at
least two distinct kinds of completion. These two kinds are
marked grammatically by such locutions as " resembles in that "
and "resembles with respect to ". Two red objects resemble
each other in that they are are both red, but that they are both
red entails that they resemble each other (are alike, are exactly
alike) with respect to (in respect of) colour. And these latter
locutions seem to me to provide us with another criterion for
152
JOHN R. SEARLE
the determinable relation. If to say of any two objects x and y
that they have the property A entails that they resemble each
other (are alike, are exactly alike) with respect to (in respect of)
B, then-with qualifications to emerge later-A is a determinate
of B.
In the light of this criterion consider the following list of pairs
of determinably related terms; the paradigms are near the top,
less paradigmatic cases near the bottom:
A
spherical
108 degrees F.
blue
3 ft. wide
18 years old
worth ?1 10s. Od.
pint
false
scarlet
male
decrepit
drunk
shatters easily
B
shape
temperature
colour
width
age
value
volume
truth value
redness
sex
physical condition
degree of sobriety
degree of brittleness.
Each of these pairs satisfies both criteria for the determinable
relation. Yet we need to make some qualifications to the
application of the second criterion: whenever two entities satisfy
the same A term precisely, we are more inclined to say that they
are of the same (have the same) B, reserving the locution
" resembles with respect to " for cases where the two objects do
not resemble each other exactly. That is, we move from "are
exactly alike with respect to colour, shape ", etc., to " have the
same colour, shape ", etc. I state my criterion in terms of the
former rather than the latter, for though the latter is the more
natural form, the former is not incorrect, and it has greater sortal
powers, in particular it excludes certain genus-species terms (e.g.,
" silver " and " metal ") the latter would include.
The most important class of counter-examples which the
DETERMINABLESAND THF NOTION OF RESEMBLANCE
153
secondcriterionallows are cases wherethe A term is a conjunction of a determinateof the B term with one or more unrelated
terms. (These counter-examplesare those discussed under
condition3 of the firstcriterion.) For example,if two dogs are
both cocker spaniels, then they resemble each other with
respectto shap-,: but " cocker spaniel" is not a determinateof
" shape".
With these qualificationsand exceptionsthe second criterion
gives an interestingif not very precisetest for the determinable
relation drawn from ordinarylanguage. One of its merits is
that it excludesgenus-speciesexamples: we do not, e.g., say of
two humans that they " resembleeach other with respect to
animality".
Upon scrutinyof the lists A and B in termsof the two criteria,
severalquestionspresent themselves. On the second criterion,
A terms (determinates)are characteristicallyadjectives and
adjective-likeexpressions,B terms (determinables)are characteristicallyabstractnouns. Why? Is this connected with the
fact that species terms are characteristicallynouns, and the
secondcriterionexcludespairsof species-genusterms? Why do
the two criteriagive similarresultsat all'?
Perhapsthe followingconsiderationwill give us the beginnings
of answersto such questions. First let us introducetwo new
expressions: by the expression " individuatingterm" I shall
mean a term which provides a principle of individuation,a
principleof counting,e.g., " man" is an individuatingterm, as
it allows " one man", " three men", etc. By the expression
" characterisingterm" I shall mean a descriptiveterm which
does not provide by itself a principleof counting, e.g., " red "
is a characterisingterm. Individuatingterms are characteristicadjectivesand
ally nouns, characterisingtermscharacteristically
verbs.6 Paradigmspeciesterms are conjunctionsof separately
specifiableterms, some of which are called the genus, other the
differentia. Paradigmindividuatingtermsareusedto individuate
the paradigmindividuals,materialobjects. But any material
6
For a similardistinction see P. F. Strawson, Individuals.
154
JOHN R. SEARLE
object will admit of description by several terms, not all of them
individuating terms. The concept formation of any individuating term, then, is likely to involve a conjunction of several terms
not all of them individuating terms (cf. Locke on nominal
essence) e.g., we learn to discriminate horses from the rest of
our environment and to form the concept horse, but since any
horse is describable by several terms, not all of which are
individuating, the concept horse will be analysable into other
terms not all of which are individuating. We thus develop at
least two distinct kinds of terms, individuating terms, which
divide the world and which are in some sense conjunctions,
i.e., they admit of some sort of " definition ", and characterising
terms which describe the world in ways which cut across the
divisions set up by the individuating terms and which are not
characteristically conjunctions of other terms.
These two kinds of terms proliferate two different conceptual
hierarchies: because the relation of species to genus just is the
relation of a conjunction to one of its components, the individuating terms, being conjunctions, proliferate a genus-species
hierarchy. But characterising terms, " brown ", " rough ", etc.,
do not admit of any such analysis and hence do not admit of a
genus-species hierarchy. We invent a term (e.g., "colour ",
" texture ", " shape ") to cover a whole range of characterising
terms which are all in the same line of business. But this higher
order term (determinable) is not part of an analysis of the lower
order terms, it is just a name for the line of business they are
all in.
Thus we see the start of a growth of a connexion between the
determinable relation and characterization on the one hand, and
the genus-species relation and individuation on the other.
Roughly speaking individuating terms are characteristically conjunctions of determinates and hence admit of genus-differentia
analysis, but paradigm characterising terms are not such conjunctions.
Perhaps this point will be clearer if we consider a prominent
class of counter-examples. Names of shapes often serve as both
characterising and individuating terms e.g., " is spherical" and
"is a sphere ". This is because shapes provide a convenient
DETERMINABLESAND TIHENOTION OF RESEMBLANCE
155
principle of individuation without the help of any other term.
But they are unlike most individuating terms in this respect;
the term " horse " for instance includes not only the notion of a
certain shape, but several other characteristics as well.
Note also that the determinable expression often provides,
or has cognates which provide, a (rather weak) principle of
individuation, not of objects, but of its determinate terms. Thus,
e.g., besides the characterising expression " is coloured" we
have the individuating expression " is a colour ". These abstract
noun forms of the determinable term neatly fit the syntactical
requirementsfor list B of the second criterion. Near the bottom
of list B we seem to run out of abstract nouns. Why? Wherever
we have only two or three expressions competing in the same
area, language is less likely to provide us with an abstract noun
to cover the whole area than if we have several. Thus we do not
have an abstract noun collecting " drunk " and " sober" as
" temperature " collects our elaborate terminology for degrees
of heat. In such cases we have to fabricate " degree of sobriety "
or some such expression. If we had an elaborate terminology
for degrees of sobriety we should most likely have a word corresponding to "temperature ". " Male" and " female " we
do collect under " sex ", but we do not have a word collecting
" dead ' and " alive ".
The foregoing suggests an explanation why the two criteria
give similar results: the first relies on the fact that determinates
compete for position without outside help within an area covered
by the determinable. The second relies on the fact that language
provides us with abstract nouns, or the possibility of forming
abstract nouns, to cover the range of such characterising universals, and it ties certain possible completions of the incomplete
predicate " resembles " to such abstract nouns.
IV. Professor K5rner'sApproach.
My attack on this problem has been rather different from
Professor K6rner's. Indeed I am not quite sure I have understood exactly what his aims are. Perhaps I can best emphasize
our difference of approach and expose any misunderstanding I
156
JOHN R. SEARLE
may have of his paper by stating in a crude form the objections
I have to it.
1. His definition excludes any exact concept as a possible candidate for a determinate. Thus no numerical concept can be
a determinate and any concept we care to define exactly ceases
to be a determinate. He accepts these consequences with more
equanimity than seems to me justified. For surely it must
restrict the philosophical interest of any definition enormously
if it excludes vast areas of what are usually taken as paradigmatic
terms standing in the determinable relation, with no justification
or explanation offered. Indeed any such definition must be
positively misleading if-as I have suggested-the exact concepts
share the essential features of the determinable relation along
with the inexact.
2. Leaving aside the question of exact concepts, whatever
relation Kbrner defines, it is not the determinable relation as
ordinarily understood, not even the determinable relation
between inexact concepts. Now of course, it is open to anyone
to define his terms as he likes, but Professor K6rner insists that
his definition is " in accordance with established philosophical
usage ". That it is not is shown conclusively by the fact that
his definition provides no way of distinguishing the determinable
relation from the genus-species relation. But part of Johnson's
point in introducing the notion, and he after all established the
"philosophical usage" in question, was to distinguish the
determinable relation from the genus-species relation.
3. Even if we ignore both problems raised in my first two
objections the criterion breaks down. Professor K6rner only
offers us one example, " colour ", of how it is supposed to work,
but it does not seem to me to work even for that one example.
He inadvertently offers us a proof of this in his discussion of
the example of the blue window pane: imagine a blue window
pane growing progressively more transparent until it reaches one
hundred per cent transparency, i.e., invisibility. At some point
"the window pane is a neutral candidate of coloured and therefore
DETERMINABLES AND
THE NOTION OF RESEMBLANCE
157
of not coloured" i.e., invisible. But precisely at that point,
I should like to add, it is also a neutral candidate of " blue "
and " invisible ". Thus " blue " and " invisible " are fully
linked. But the definition of the determinable relation stipulates
that the determinable must be the sum of all concepts fully linked
with any determinate. Hence, by the definition, if " blue " is
a determinate of " colour " so is " invisible ", which is absurd.
Other empirical concepts can be made to run off the rails in the
same way. " Shape " for instance will go via the extensionless
point. "Human" and "animal" will not qualify since
" human " is linked to plant concepts; " human " and " organism " will have no hope since the organic and the inorganic are
similarly linked.
Furthermore the criterion provides no way of excluding
arbitrary conjunctions (products) of terms only one of which is
a genuine determinate. Thus " blue monkey ", " red horse ",
and " yellow cow " would all count as determinates of" colour ".
On the criterion as stated I do not see how these difficulties can
be avoided.
4. 1 cannot think he means exactly what he says in his definition
of " resemblance ". He says as part of his definition that two
objects resemble each other with respect to a determinable D
if they are both positive candidates of D. Thus on the definition,
a brown object and a blue object must be said to resemble each
other with respect to colour since they both are coloured (both
are positive candidates of " coloured "); a midget and a giant
would resemble each other with respect to size since they both
have a size. This is clearly not what is ordinarily meant by
" resembles with respect to ".
5. I am puzzled by the definition of inexactness. One
ordinarily thinks of inexact concepts as those which have borderline cases (though I should prefer some other term such as
" vague " to " inexact "). But on the proposed definition this
is not sufficient for inexactness. It is also necessary that the
borderline cases should have borderline cases, the borderline
cases of' the borderline cases should have borderline cases, and
158
JOHN R. SEARLE
so on ad infinitum--and all this independent of any inventory
of the world. I do not see how the definition of inexactness can
have any application, for to establish that any concept is inexact
we must establish that an infinity of progressively narrower
concepts have borderline cases. Since human powers of discrimination are finite this can have no meaning in empirical
terms.
I might summarize my objections to Professor K6irner'spaper
by saying that it does not seem to me that the criterion works
and even if it could be made to work I do not see how it casts
light on the determinable relation.