The four principles of adaptation

The four principles of adaptation

Edward M. Hulburt *

Woods Hole Oceanographic Institution, 520 Woods Hole Road, Woods Hole, MA 02543, USA

Received 24 July 2001; received in revised form 6 March 2002; accepted 16 April 2002

Abstract

There are four principles of adaptation. The first is that if two quite different entities occur under the same condition,

then one is adapted and the other is not adapted to this condition. Thus the warm-blooded vertebrate is adapted to

year-round temperature in temperate regions because it is behaviorally active year-round, whereas the cold-blooded

vertebrate is not adapted to year-round temperature because it is not active year-round. The second principle is that if

one entity occurs under two quite different conditions, then it is adapted to one condition but is not adapted to the

other condition. Thus the North American forest is adapted to moist conditions in the east and west, but is not adapted

to the non-moist, semi-desert regions of the southwest. The third principle is that if one entity is adapted to a second,

then the second is adapted to the first. Thus the white spruce was adapted to an expanding locale between 12 000 and

9000 years ago in the mid-west of North America, and this locale was adapted to the spruce. The fourth principle is that

two quite different entities occur under two quite different conditions, and one is adapted to its condition and the other

is adapted to its condition. Thus, there is a tendency (an entity) toward many boned toes in the paddle limbs of aquatic

vertebrates and this is an adaptation to swimming, and there is a tendency toward two or one toes in land vertebrates

and this is an adaptation to running. The four principles have a logically valid structure. An example is: if an animal is

behaviorally active under year-round temperate temperature, P , then the animal is adapted to year-round temperate

temperature, Q ; equivalent to: if the animal is not year-round adapted, �/Q , then the animal is not year-round active,

�/P :(P ‡/Q )�/(Q ‡/�/P ). Generation of this formula from the axioms of Logic for Mathematicians (Rosser, 1953)

takes a number of proofs. When it is said that an entity is behaviorally active, it is meant that the entity has the property

of being behaviorally active. When it is said that an entity is adapted (to year-round temperature), it is meant that the

entity has the property of being adapted, the property of adaptedness (to year-round temperature). This is the

philosophical realist view. So by empirical justification and logical and philosophical ramification, an integrated model

of the principles of adaptation is sought. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Logically valid model; Adapted; Not adapted; Warm-bloodedness; Cold-bloodedness; Terminal evolution; Repeating

evolution; Axiomatic proof; Property; Universal

1. Introduction

Mathematical models are the models par ex-

cellence. But logical models can be achieved* Tel.: �/1-5085483074

Ecological Modelling 156 (2002) 61�/84

www.elsevier.com/locate/ecolmodel

0304-3800/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 3 8 0 0 ( 0 2 ) 0 0 1 2 4 - 2

(Hulburt, 1992, 1996, 1998, 2001). How can a

mathematical model be transformed into a logical

model? Next will be provided an attempt at such a

transformation.Mathematical models in ecology can be exem-

plified by predator-prey models. Here is one

(Caughley and Lawton, 1981, p. 106). ‘‘If the

rate of renewal of the food of the herbivores, g , is

independent of the standing crop of plants, v , food

availability changes as dv /dt�/g ,’’ or dv�/gdt .

There is an arresting feature about this equation. It

is logically valid. To see this, think that if a larger

value of t is matched by a larger value of v , then a

not larger value of v is matched by a not larger

value of t . My thought is that this is a legitimate

appraisal of the equation and brings out its

logically valid structure. This appraisal underlies

the first and second principles that will be pre-

sented later.

Equally well the equation could be appraised in

this way: if t is a certain value then v has its value

and if v has its value then t is a certain value*/

which is to say that t is a certain value just in case

v has its value too. Though redundant, this is valid

and is the basis of the third principle to be

presented.

Then too, the equation could be appraised in

this way: if t is a certain value then v has its value,

t is in fact a certain value, so v does have its value

(modus ponens). Yet in the paper cited above, in

addition to v , the amount of food (for the

herbivore), there is H , the amount of the herbi-

vore, so that dH�/[rH (1�/dH/g )]dt . Thus if t is a

certain value then H has its value, t is in fact a

certain value, so H does have its value*/modus

ponens again. So there are two cases of modus

ponens, a valid structure, available from the food�/

herbivore model. In the coming pages this two-

modus ponens structure will be the foundation of

the fourth principle.

In the second equation being analyzed, v is the

amount of plant food, g is the rate of renewal of

plant food, H is the amount of herbivore, r is ‘‘the

herbivore’s intrinsic rate of increase,’’ and b is ‘‘therate of intake sufficient to maintain a herbivore

and allow its replacement in the next generation.’’

Both the amounts of food and of herbivore are

properties of the system. The three rates are

properties of each plant and each animal in the

system. Each plant and each animal is composed

of properties. The rate properties are transmitted

to the system, where the system is conceived of asan entity, like a plant or animal. So the system is a

system of properties. Properties are the constitu-

ents of the system and thus are the structure of the

system as a model.

Thus the plan of this adaptation enterprise is to

use logically valid expressions gotten from simple

and basic equations and to use a system of

properties, for the parameters of the equationsreally are properties.

2. The plan of the adaptation enterprise

The intent of this enterprise is to justify adapta-

tion in three ways. The first way is that there

should be a factual basis, an observational basis

for the inference to adaptation, for the justification

of adaptation. The second way is that there shouldbe a proof method to derive this inference, to

generate this justification. The third way is that

there should be a philosophical framework to

insure the reality of the justification of adaptation.

The first way means that basing adaptation on

natural selection is to be excluded. Natural selec-

tion is a supposition; it is the grand surmise of

evolution (Dennett, 1995; Dawkins, 1996). But it israrely factual, observational. A case of natural

selection was observed in the Galapagos finches

(Boag and Grant, 1981). But this is rare. So when

Stern (1970) says ‘‘whatever has been produced by

selection is to be designated as better adapted,’’

this approach will be excluded because we cannot

know usually that natural selection really did

happen. Likewise when Gould and Vrba (1982)

Fig. 1. Upper figure: percentage of time shells of mussels remain open during 24-h periods at different temperatures ranging from 1.0

to 24.9 8C (from Loosanoff, 1942). Lower figure: mean rate of water pumping by oysters at five homogeneous temperature levels

(from Loosanoff, 1958).

E.M. Hulburt / Ecological Modelling 156 (2002) 61�/8462

Fig. 1 (Continued)

E.M. Hulburt / Ecological Modelling 156 (2002) 61�/84 63

Table 1

Growth of pure cultures of unicellular algae

Growth rates of isolates of several diatom species in div./day at various temperatures

Temperature (8C)

1 4.5 7 9 11.5 14.2 17 20.3 22 25.7 27.5

Asterionella glacialis Cape Cod 0.45 0.79 1.28 1.51 1.28 0.47 1.84 1.23 1.38 1.23 0

Thalassionema nitzschioides Cape Cod 0.74 0.67 0.80 1.11 1.14 1.14 1.58 1.84 1.38 0.52 0

Temperature (8C)

2.8 4 7 10 13 16 19 22.2 24�/25 27�/28 30

Skeletonema costatum Long Island Sound 0.38 0.50 0.75 0.92 1.04 1.33 1.66 1.58 2.21 1.80 0

Growth rate of Nannochloris atomus in div./day at various temperatures

Temperature (8C)

5 10 15 20 25 30

New York 0.00 0.14 0.65 0.80 0.71 0.32

Cape Cod, Long Island Sound, and New York are on the eastern coast of the USA, and are where the species were isolated.

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say that the wing is an adaptation for flight since itwas produced by natural selection, this approach

will be excluded because we cannot know for sure

that natural selection really did produce the wing

as an adaptation for flight. Thus the justification

for adaptation will not have this suppositional

basis. Instead, the justification for adaptation will

be expressed in four formulae, four compound

descriptive statements based on fact, on observa-tion.

The second way means that the formulae, the

logically valid expressions, for adaptation will be

generated from axioms in a manner well estab-

lished in symbolic logic, in mathematical logic.

The third way means that there are not merely

adapted entities but there is the property of

adaptation, adaptedness, which the adapted enti-ties have. The property adaptedness bridges the

gap between the adapted entities and produces the

connectedness of the enterprise as an overall

model.

Thus the inference to adaptedness will be based

on fact, will be derivable, and will be model

oriented. This will result in an integrated model.

A crucial flaw in the inference from naturalselection to adaptation is that the inference cannot

yield any but adapted entities. An example from

Kricher and Morrison (1988), pp. 141�/143, says

that in the eastern woodchuck of the USA, ‘‘the

ability to hibernate. . . is an adaptation.’’ The grey

squirrel lacks this adaptation, they point out. For

the woodchuck, they want us to believe without a

shred of evidence that ‘‘In the past, probablymillions of years ago, woodchuck ancestors pos-

sessing the ability. . . to sleep deeply for at least

part of the winter, were the ones that survived the

best. . . and left most offspring in the overall

woodchuck population.’’ They speculate about

the origin of an adaptation and in the process

leave unmentioned the obvious contrast between

the woodchuck that is adapted because it hiber-nates and the squirrel that is not adapted because

it does not hibernate.

In the next part, the adaptational enterprise to

be presented will differentiate between cases

wherein adaptation and its denial pertain and

cases wherein only the affirmation of adaptation

pertains. This differentiation will be accomplished

by the four principles of adaptation. But the fourprinciples will be concerned with a deeper feature,

the composition of adaptation itself.

In order to prepare for the next section the

following technical details are presented: P , Q , R ,

S are short statements abbreviated; ‡/ goes

between a statement beginning with if and one

beginning with then ; �/, �/, �/, �/ are abbrevia-

tions for and , or , not, equivalent to ; �/ is therefore ;Fx , Gx are x is F , x is G.

3. The first two principles of adaptation

What is the purpose of the first two principles ofadaptation? The purpose is to show what adapta-

tion is, what the composition of adaptation is.

Once natural selection is excluded as an explana-

tory basis of adaptation, an ecological explanatory

basis of its composition can be taken up as follows

next.

The first and second principles of adaptation are

these:First*/if two quite different entities occur under

the same condition, then one is adapted to the

condition and the other is not adapted to the

condition.

Second*/if one entity occurs under two quite

different conditions, then it is adapted to one

condition but not adapted to the other condition.

4. The justification of the first principle of

adaptation

The first principle applies with two quite differ-

ent entities occurring under the same condition.The two quite different entities may be:

Case 1, reproductively different,

Case 2, responsively different,

Case 3, physiologically different,

Case 4, behaviorally different.

Under case 1, as justification for the inference of

being adapted, is the empiricality that comes from

pure culture growth of four species of marine

plankton algae at various temperatures (Hulburt,


1982, 1992; Ryther, 1954) (Table 1). Three of thespecies have growth rates, reproductive rates, of

0.38�/0.74 div./day at temperatures of 1�/2.8 8C.

They have rates of 1.04�/1.28 div./day at 11.5�/

13 8C, and rates of 0.52�/1.80 div./day at 25.7�/

27 8C, with no growth at 30 8C. Together these

three species compose a single though scattered

entity with an approximately single reproductive

range of wide span. This array of cells in threespecies occurs under a water temperature range of

1�/22 8C, which is the annual range off southern

New England of USA (New York to Cape Cod),

where this single, scattered array is prevalent

throughout the year. A fourth species, a scattered

entity, has a smaller reproductive span, its growth

rate bring 0.0 at 5 8C, being very small, 0.14 div./

day, at 10 8C and being moderate from 15 to30 8C. But this species is endemic near New York,

growing to great abundance in summer and fall

(Ryther, 1954; Hulburt, 1981, 1982). So there are

two quite different entities, one with a wide

reproductive range, and one not with a wide

reproductive range; and they occur under the

same external temperature condition. So there

are two entities, one adapted to this condition,the other not adapted to this condition. Redun-

dantly, one entity’s reproductive attribute and its

attribute of being adapted are had by it. The other

entity’s reproductive attribute and its attribute of

not being adapted are had by it, too.

Under case 2, as justification for being adapted

and for being not adapted, come empirical, factual

observations, just as in case 1. The observationsare on the responses, two quite different responses,

of two quite different scattered arrays of organ-

isms, the oyster (Crassostrea virginica ) and the

mussel (Mytilus edulis ).

Both scattered arrays (Quine, 1960, pp. 97�/99),

both species, pump large quantities of water

through slightly opened shells by the cilia of their

gills. At 16 8C to about 28 8C 9.0 l/h is pumpedthrough the oyster; at 10�/0.0 8C less than 1.0 l/h

is pumped through (Loosanoff, 1958). (Fig. 1).

Stoppage of ciliary motion occurs at 5�/2.0 8C(Galtshoff, 1928) and the time open is much less at

5 8C than at 13�/22 8C. Together these observa-

tions show that the oyster has the attribute, the

property, of not responding to the full, year-round

temperature range of southern New England. Sothe oyster has the attribute, the property, of not

being adapted to the full, year-round range of

southern New England. But the mussel has ciliary

movement down to �/1.0 8C and no change in

time open, 78�/99%, between 24.9 and �/0.5 8C(Loosanoff, 1942*/see Fig. 1). So the mussel does

have the attribute, the property, of responding to

southern New England’s temperature range and sothe mussel has the attribute, the property, of being

adapted to this range. Thus, in case 2 two entities,

two quite differently responding entities, occur

under the same condition and one has the attribute

of being adapted and the other has the attribute of

not being adapted to this condition. To put the

foregoing matter in more detail, each individual

oyster has the non-year-round response attribute,a physicalistic attribute, from which the inter-

preted attribute, not being adapted year-round, is

inferred, and these attributes are transmitted to the

conglomerate entity of all southern New England

oysters. Same for each mussel, except being

responsive and adapted are the attributes.

Case 3, like cases 1 and 2, justifies the inference

of being adapted from two purely empiricalsituations, warm-blooded animals and cold-

blooded animals. What it is that keeps a warm-

blooded animal warm is sought on two fronts, one

the heat of metabolism which is six times higher in

endotherms (birds and mammals) than in ec-

totherms (amphibia and reptiles) (McFarland et

al., 1979, p. 267) and the other the nervous system

control of heat regulation (Ransom et al., 1937;Mills and Heath, 1972; Hagan and Heath, 1980;

Hammel, 1968; Heinrich, 1977; Gordon and

Ferguson, 1980; Nelson et al., 1984; Satinoff,

1964, 1978; Lepkovsky et al., 1968). In temperate

regions the two quite different entities, the warm-

blooded array and the cold-blooded array, occur

under wide annual temperature ranges. So the

warm-blooded array is adapted, has the propertyof physiological adaptedness, to wide annual

ranges, and the cold-blooded array is not adapted,

does not have the property of physiological

adaptedness, to wide annual ranges. The two quite

different entities differ physiologically.

But in case 4 the different entities differ beha-

viorally. The entities only differ from case 3


entities in that hibernators are put in with the cold-

blooded ectotherms. Thus, the behaviorally active

conglomerate entity under year-round temperature

is adapted to year-round temperature and the not

behaviorally active conglomerate entity under

year-round temperature is not adapted to year-

round temperature. Thinking of two individual

animals we might have the logically valid:If x is in a year-round active animal (P ), then x

is in an adapted animal (Q ), one that has

adaptedness to year-round temperature*/equiva-

lent to: if x is not in an adapted animal (�/Q ), one

which does not have any adaptedness to year-

round temperature, then x is not in a year-round

active animal (�/P ):

(P ‡ Q) � (�Q ‡� P) (1)

This model splits all temperate land vertebratesinto two groups, birds and mammals minus

hibernators as one group and amphibia and

reptiles plus hibernators as the other group. But

there are half as many x ’s as animals because in

expression (1) it is the same x that goes from being

in one active, adapted animal year-round to being

Fig. 2. The islands and banks colonized by A. segrei from its source island Cuba, upper left. Perch height distributions for adult male

(solid line, adult female (dotted line), and subadult male (broken line) sagrei populations on Jamaica, Exuma, Abaco, and Swan

Island, lower left. Average hourly body temperatures of sagrei , grahami , and lineatopus occurring in habitats with differing shade

conditions near Discovery Bay, Jamaica, compared with sagrei populations on Exuma and Abaco (from Lister, 1976).


in one not-adapted, not active animal year-round.

One group is held together by two attributes, by

two inhering properties, being year-round active

and being adapted, which define two identical sets1

(thus one group). The other group is likewise held

together by two inhering attributes, or properties,

being not adapted and being not year-round

active, which determine two identical sets (thus

the other group) 1. And the two groups are held

together by the single x that links two animals, one

from each group. It is true that x does not appear

in (P ‡/Q )�/(�/Q ‡/�/P) of expression (1); but

an alternative notation, (Fx ‡/Gx )�/(�/Gx ‡/�/

Fx ), does have x .

5. The justification of the second principle of

adaptation

Cases 1, 2, 3 next justify the second principle of

adaptation: if one entity occurs under two quite

different conditions, then it is adapted to one

condition but not adapted to the other condition.

Cases 1, 2, and 3 next do not infer being adapted

from physicalistic structure, from fact, they as-

sume outright being adapted and the denial of

being adapted as inhering attributes or traits of

physical structure.

Case 1 gives observations on the lizard Anolis

sagrei under competition and lack of competition

(Lister, 1976, one of many studies on Anolis in the

Caribbean), Fig. 2. A. sagrei adult males have a

perch height reaching 6 ft. on small trees in open,

sunny areas in Jamaica with four competitor

species. It has a perch height distribution reaching

8 ft. on Exuma with three competitor species and

has a perch height distribution reaching 10 and 13

Table 2

Latitudinal gradients in the incidence of some predator-related traits of low intertidal rocky-shore snails

Percentage of species with*/

Number of spe-

cies

Toothed aper-

tures

Elongate aper-

tures

Inflexible opercu-

lum

Strong external sculp-

ture

Temperate

Vancouver Is., British Co-

lumbia

17 5.9 0 0 5.9

Boothbay Harbor, Maine 5 0 0 0 0

Plymouth, England 12 8.3 8.3 0 0

Isla San Lorenzo, Peru 11 9.1 0 9.1 0

Montemar, Chile 20 5 0 10 10

Average�/3.58

Tropical

Playa de Panama, Costa Rica 15 40 47 20 20

Panama City, Panama 20 15 30 25 30

Fort Point, Jamaica 15 13 20 20 33

Playa Chikitu, Curacao 10 20 10 30 0

Dakar, Senegal 13 15 23 7.7 7.7

Takorada, Ghana 7 0 0 14 14

Average�/18.9

Taken from Vermeij (1978), p. 60.

1 Identical sets have the same members. Also, there is limited

complementation, for just two groups result, just two

complementary groups.


Fig. 3. The aereal distributions of several forest species. Left, the California redwood (Sequoia sempervirens ). Upper right, species and

races of Juniperus in the southern United States. Lower right, two species of pinon pine. (From Ornduff, 1998, left; Grant, 1963, upper

right; Lanner and Lanner, 1981, lower left.)

Fig. 4. The aereal distribution of the white spruce, Pices glauca 12 000 years ago, lower figure, and 9000 years ago, upper figure (from

Ritchie and MacDonald, 1986) and the proposed (David, 1981) and hypothesized wind circulation. The wind wants to blow from high

pressure over the ice to low pressure off the ice, the Coriolis force makes it blow 908 to the right, so that it blows clockwise around the

high over the ice.


Fig. 4 (Continued)


ft. in sunny to shady areas with large trees

on Abaco and Swan Is. with no competitor

Anolis species. This expansion in structural

niche is matched by expansion in its thermal

niche.

On Jamaica A. sagrei ’s body temperature is

between 31 and 33 8C because it has only a low

perch height on small trees of sunny places. By

contrast on Abaco when it is in the sun it has a 32�/

34 8C range but when it is in the shade of large

trees, where it can invade without competition, it

has a body temperature of 25�/28 8C. Thus it

occurs under two quite different conditions, one

with competitors and one without. It has two quite

different structural and thermal niche distributions

as a result. So it is adapted to the unrestricted,

competitor-absent condition and it is not adapted

to the restricted, competitor-present condition.

The attribution of being adapted and the attribu-

tion of not being adapted are made outright as

inhering traits or characteristics of the physical

entity A. sagrei and the physical conditions

justifying the attributions.

Whereas in case 1, the single entity, A. sagrei , is

adapted in part of its range, in another part of its

range, this single entity is not adapted. And this

simple distinction will be seen to pertain in cases 2

and 3.

Case 2 provides data justifying outright the

attribution of adaptation, and its denial, for

predation on low intertidal rocky shore snails

(Vermeij, 1978, pp. 57�/60). The incidence and

degree of shell characters that discourage shell

crushing by predators increase toward the tropics.

The percentage of species with toothed apertures,

elongated apertures, inflexible operculum, and

strong external sculpture is 3.58% from four

temperate places and is 18.9% from four tropical

places, Table 2. Additionally, the frequency of

repaired shell injuries from predation is 0.07 for

three snail species of the British Columbia coast

but is 0.30 for three different species of the Costa

Rican coast. So all these snails compose a single,

scattered array and this entity is exposed to quite

different predation conditions. So the snail array is

better adapted to temperate predation and is not

better adapted to tropical predation*/is better

adapted in part of its range and worse adapted in

another part of its range.

In case 3, the North American forest is com-

posed of many woody plants, of many woody

species, of many woody associations of species.

And so, no matter whether one considers in the

east the mixed mesophytic forest of Appalachia, or

the beach-maple association northward, or the

oak-hickory association to the south and east and

west, or the northern boreal forest with white

spruce dominating and spreading from Newfound-

land and New England across Canada to the

Rocky Mountains, or the high Engelmann

spruce-subalpine association and the Douglas fir

association below and below this the ponderosa

pine association of the Rocky Mountains, or the

Sitka spruce dominated association extending

from Alaska south to the Olympic Peninsula

where it is joined by western hemlock, arborvitae,

and grand fir, or the broad-leaved evergreen oaks

in the coastal ranges of southern California

(Oosting, 1948, pp. 234�/299), no matter which

factual association is considered, the following

properties may be attributed as inhering in it:

a) All associations have the trait of tallness only

in moist environments,

b) All associations have the characteristic of

dense packedness only in moist environments,c) All associations have the property of competi-

tiveness only in moist environments,

d) All associations have the attribute of high

growth capacity only in moist environments,

for all these associations occur where rainfall is

greater than 30 in. per year. And where rainfall is

less than 30 in. per year in the desert or semi-desert

regions of the Southwest (the Great Basin and

Mohave Desert), pinon pines, sagebrush, and

creosote bush form several associations of small,

spaced-apart, uncompetitive, low growth woody

plants. The contrast of large luxuriant trees in

moist regions with small, spaced-apart, depauper-

ite trees and woody bushes of the arid Southwest is

striking, and we might say, thinking however of

the singleness of the North American forest: the

North American forest is adapted only to moist

regions, if and only if it is not adapted to any non-


Fig. 5. Uppermost figure. The plesiosaur Hydrothecrosaurus , Jurassic, 12 m long. Next to the top figure. The ichthyosaur Shonisaurus ,

Upper Triassic, 15 m long. Middle figure. The mosasaur Plotosaurus , Upper Cretaceous, 10 m long. Bottom figure. Left pair, the

artiodactyls Proebrotherium and Protoceras, Oligocene. Right pair, the periossodactyls Hyracotherium (left) and Tetraclaenodon

(right), Lower Eocene (from Carroll, 1988, pp. 248, 256, 234, 515 and 529).


moist regions.2 More simply this could be thelogically valid:

If the North American forest is adapted (P ) then

it is in a moist region (Q )*/equivalent to: if it is

not in a moist region (�/Q ), then it is not adapted

(�/P ):

(P ‡ Q) � (�Q ‡�P): (2)

This model stresses the continuity and singleness

of the North American forest, which occurs under

two quite different conditions. It is well adapted in

the part of its range where it is luxuriant, but in

another part of its range where it is depauperite it

seems to be just barely getting along and is not

adapted in the luxuriant sense. Thus the second

principle of adaptation is upheld: one entity (theNorth American forest) occurs under two quite

different conditions, adapted under one and not

adapted under the other.

6. The third principle of adaptation

What is the purpose of the third principle of

adaptation? As with the first and second princi-

ples, the purpose is to show what adaptation is,

what the composition of adaptation is. An ecolo-

gical explanatory basis is given. The suppositional

character of natural selection must be excluded

from the factual basis of the composition of

adaptation.The third principle of adaptation is this: one

entity is adapted to a second, and the second is

adapted to the first (and conversely): so they are

adapted to each other. There is only affirmation of

adaptation in this third principle. An obvious

example of the third principle is symbionts. If

symbiont x is adapted to symbiont y , then y is

adapted to x (and conversely), so they are adaptedto each other. But such reciprocal adaptation need

not be between two organisms. It can be between

an organism and some facet of the environment.

Cases of this are described in Hulburt (1996). One

of these cases will be extended in the followingelaboration in justifying the outright attribution of

adaptation as an inhering attribute of a species (or

variety) and as an attribute of their locales.

In order to stress the empiricality of the basis for

adaptational interpretation, Fig. 3 presents the

distributions of two species and one species com-

plex and Fig. 4 presents the distributions of one

species at two different times. In Fig. 3, theredwood has its present day small distribution

(Ornduff, 1998). Before the Pleistocene the red-

wood was widespread in the West (Axelrod, 1976),

but after the glacier melted it did not regain its

wide distribution. Nevertheless, it is secure and

dominant in its present coastal locale. More wide-

spread are two species of pinon pine, occurring

presently throughout several southwest states(Lanner and Lanner, 1981). Thence the distribu-

tion of overlapping varieties of juniper cover a

portion of the southern USA (Grant, 1963, p.

461). And finally the small locale of white spruce

at the height of glaciation 12 000 years ago

contrasts with its large locale 9000 years ago as it

spread north with the melting of the ice (Ritchie

and MacDonald, 1986).The question is: what do these distributions

show? What do they show? They show, it would

seem, that the locales of these species are adapted

to these species. Necessarily, these locales are

adapted to these species; otherwise the species

would not be there. Thus the third principle is

substantiated; if one species is adapted to its locale

or region then its locale or region must be adaptedto it (and conversely); so the two are adapted to

each other. More fully we might use the logically

valid model:

(a) If one species is adapted to its locale (P ),

then its locale is adapted to it (Q ), and (b) if its

locale is adapted to it (Q ) then the species is

adapted to its locale (P )*/equivalent to: (c) the

species is adapted to its locale if and only if itslocale is adapted to it.

[(P ‡ Q) � (Q ‡ P)] � (P � Q): (3)

Thus the property of being adapted, a universal,

is had by the species and is had by the locale too,

two cases of the same property.

2 Again limited complementation is meant. Non-moist does

not mean ‘everything in the world except moist’; non-moist

means dry.


7. The fourth principle of adaptation

What is the purpose, again, of the fourth

principle of adaptation? As with the first three,

the purpose is to show what adaptation is, what

the composition of adaptation is. The evolutionary

cases presented next must contribute to this end

purely by their content, unencumbered by the

assumption of natural selection.The fourth principle of adaptation is this: two

quite different entities occur under two quite

different conditions, and each entity is adapted

to its condition. There is only affirmation of

adaptation in the fourth principle. The fourth

principle is ideally suited to portray a terminal

phase and a chronic, repeating phase of evolution.

Two cases will be presented (more cases are givenin a very different way in Hulburt, 1998).

In case 1, in temperate regions, a great variety of

insects are active in summer. Their eggs are laid in

a variety of ways; these develop into larvae in a

great many ways; the worm-like aquatic larvae

mature as pupae and metamorphose into winged

insects (Howard, 1937). If this process goes

through without cessation at any point, it is non-diapause and it is caused ancillarily by the long

day-length of summer (Saunders, 1976, pp. 87�/

118). But in autumn, short days cause arrested

development, diapause, either at the reproductive

stage or at the larval and nymphal stages or at the

pupae stage (Beck, 1980, pp. 156�/180). After

winter diapause is broken by long day-length and

morphogenesis occurs because of concomitanthigh temperature. So there are two quite different

entities, two quite different processes*/for process

is a single entity. Thus, these two processes, non-

diapause or diapause, occur under very different

day-length conditions, the long-day of spring�/

summer or the short-day of autumn�/winter. So

summer adaptation ensues or winter adaptation

ensues. And these two physical processes and theirattributed inhering adaptations exemplify par

excellence a terminal aspect in evolution.

In case 2, the simple feature of paddle-like limbs in

non-fish vertebrates that return to the water

contrasts with the feature of normal four or two

limbs of land vertebrates (except legless forms)

(Carroll, 1988, pp. 156�/415). Slightly paddle-like

limbs but without extra toe bones occur earliest in

reptiles, in the mesosaurs of the Permian (late

Paleozoic). These reptiles had no opening behind the

eye opening and are called anapsids. Another group

had a single opening, high up, behind the eye

opening, are called euryapsids, and had two large

marine assemblages, the plesiosaurs and pliosaurs;

in these many-boned toes of their paddle limbs

occurred (Jurassic and Cretaceous [Mesozoic]).3 A

third assemblage, tuna-like in form, are the

icthyosaurs, in which occurred many-boned toes

of paddle limbs (Jurassic and Cretaceous). Then in

the diapsid group, with two openings behind the eye,

the large spectacular mosasaurs from the Cretac-

eous had, in some at least, many-boned toes (Fig. 5).

Returning to anapsids, the turtle lineage has aquatic

representation from Cretaceous to now with well

developed limbs but not apparently with extra toe

bones. Thence, moving to the mammal group

whales have paddle forelimbs from Eocene on, as

do dugongs (manatees); and walruses, sea lions, and

seals have all four limbs paddle-like. In some of

these, many-boned toes occur (whales). In summary

it is to be pointed out that there is a tendency toward

many-boned toes in the paddle limbs of aquatic

vertebrates. It will be asserted later that tendency,

like process, is an entity.

But in land vertebrates (continuing case 2) the

tendency is toe reduction: four toes in the bipedal

dinosaur Ornithomimus , four toes often in Cretac-

eous and Cenozoic birds, and two toes in ostriches

(Eocene to present). In ungulates (mammals) toe

reduction is repeated as four toes reduce to three in

early perissodactyls (Fig. 5). There were four toes

on front legs and three on back in titanotheres

(Oligocene) and tapirs (pre-Pleistocene-present)

and Eocene rhinoceroses, which then reduced to

three for the rest of the Cenozoic. There were three

then one from earlier to later Cenozoic horses. Toe

reduction was repeated from four to two in

artiodactyls (Fig. 5) (four in pigs, two in camels

and deer) (from Romer, 1959, pp. 256�/278). So it

is clear that a prominent aspect of land evolution is

3 Mesozoic: Triassic, Jurassic, Cretaceous. Cenozoic:

Paleocene, Eocene, Oligocene, Miocene, Pliocene, Pleistocene,

Recent.


a tendency toward two or one toes, instead of thenormal five, and this tendency is more marked

later, in the Cenozoic.

And so the fourth principle of adaptation is

upheld: two quite different arrays occur, an aquatic

array with a tendency toward many-boned paddle

limbs and a terrestrial array with a tendency toward

toe reduction, and one is adapted to swimming and

the other to running. We might rephrase this simpledistinction in the logically valid model:

There is a tendency toward limbs with many toe

bones (P ), or there is a tendency toward reduced-

toe limbs (R ); if there is the first tendency (P ), then

aquatic adaptedness ensues (Q ), and if there is the

second tendency (R ), then terrestrial adaptedness

ensues (S ); therefore aquatic adaptedness ensues

or terrestrial adaptedness ensues

(Q�S) : (P�R); [(P ‡ Q) � (R ‡ S)]; � (Q�S):

(4)

Whereas case 1 is the termination of an evolution-

ary process, case 2 is a chronic, repeating evolution-

ary process. Whereas case 1 is physiological�/

morphological, case 2 is just morphological.

8. Justification by the axiomatic method

The four principles of adaptation, as expressed

in the logically valid expressions (1)�/(4), can be

generated by application of the axiomatic method

of symbolic logic. It would seem naıve to acceptthese principles purely on the basis of their

mirroring the empirical detail that is said to justify

them. Do the principles themselves have a source

from which they can be generated? The answer is

that they do have such a source. Does this source

generate by small, interconnecting steps expres-

sions (1)�/(4)? The answer is that there are many

interconnecting steps that generate the outcomeseen in expressions (1)�/(4). The source is the

axioms of the axiomatic method, or propositional

calculus, of symbolic logic.

First, one must be prepared to accept the feature

of structure. One must see what is same-structure

in �/(�/QP ) and �/(�/PP ). But one must see in

this sequence change in structure, too. What hashappened, of course, is the substitution of P for Q

in the sequence from �/(�/QP ) to �/(�/PP ).

Substitution is a prime method of effecting the

small, interconnecting steps that get from axioms

to further expressions. A second method is the use

of one, just one, argument form, modus ponens,

which is: if this then that, given this; therefore

that*/P ‡/Q , P �/Q .It is the plan to have P and Q (and other letters)

arranged and rearranged in an interconnecting,

integrating manner. The letters are empty for this

procedure. But in the end the letters will be filled

as in expressions (1)�/(4), and thus an integrated

model will be gotten.

Among texts on mathematical logic such as

Church (1956), Mendelson (1979), Kleene (1964),and Hamilton (1988) different axioms are given

and a few proofs deriving further formulas are

given. But Rosser (1953) gives 29 proofs and

Hilbert and Ackerman (1950) gives 40 proofs.

Copi (1979) reworks the Rosser system and the

Hilbert and Ackerman system and presents for the

Rosser system 22 fully portrayed proofs and 32

more theorems are indicated (proofs left to thereader). Nidditch (1962) has 11 axioms, the rest

mostly 3 or 4. Nidditch presents 57 proofs, fully

portrayed and completely annotated. But here the

Rosser�/Copi system will be followed, because its

three axioms require a close fitting sequence of

proofs to gain the formulas of expressions (1)�/(4).

In what follows 18 proofs will be given, totaling

112 steps, and thus an exhaustive delineation ofinterconnection is a clear intent.

Two kinds of proofs will be given. One is where

axioms or previously proved formulas only are

used to gain a further proved formula. The other is

where assumed formulas are included to gain a

further formula. The first is ‘proof of. . .’ and the

second is ‘proof that. . .yields. . .’. Substitution of a

letter remains constant throughout a single proof.By substitution and premise assumption the three

axioms (next) generate and weave a remarkable

wealth of interconnection, wherein each proof is

necessary to the next. Part of the whole procedure

is given next, the rest (the larger part) is in

Appendix A.

A list of formulations is the following:


P ‡/Q , P ; Q modus ponens, rule 1 or R.1., where ‘‡/’ means ‘implies’, ‘if�/then’ (if P then Q )

�/ means ‘not’

V means ‘or’

�/ means ‘and’

P ‡/Q defined, df., as �/(P �/Q ), for P ‡/Q means getting Q if you get P and so not to get Q

must be denied or barred initially in �/(P �/Q )

P �/ Q defined, df., as �/(�/P �/Q ), for barring not getting both P and Q amounts to getting

one or the other or both

Df. definition

Pr. premiss

The axioms are:

Axiom 1 P ‡/PP

Axiom 2 PQ ‡/P

Axiom 3 (P ‡/Q )‡/[�/(QR )‡/�/(RP )]

Does it matter that the letters are in a certain order or that they are close together, in conjunction with each other? It does matter.

Every rearrangement must be fought for by substitution and the use of modus ponens (R.1).

Proof that P ‡/Q , Q ‡/R yield �/(�/RP )

1. (P ‡/Q )‡/[�/(Q �/R )‡/�/(�/RP )] Ax. 3, with �/R replacing

2. P ‡/R for R.1 from 1 and 2

3. �/(Q �/R )‡/�/(�/RP )

4. (Q ‡/R )‡/�/(�/RP ) df. of �/(Q �/R ) as Q ‡/R

5. Q ‡/R pr.

6. �/(�/RP ) R.1 from 4 and 5

Proof that P ‡/Q , Q ‡/P yield �/(�/PP )

7. �/(�/PP ) from 1 to 6, replacing R with P

Proof of �/�/P ‡/P

8. �/(�/�/P �/P ) from 7, replacing P with �/P

9. �/�/P ‡/P df.

Proof of (Q ‡/P )‡/(�/P ‡/�/Q )

10. (�/�/Q ‡/Q )‡/[�/(Q �/P )‡/�/(�/

P �/�/Q )]

Ax. 3, �/�/Q put for P , �/P for R

11. �/�/Q ‡/Q from 9, Q replaces P

12. �/(Q �/P )‡/�/(�/P �/�/Q ) R.1, from 10 and 11

13. (Q ‡/P )‡/(�/P ‡/�/Q ) df.

Proof that �/P ‡/�/Q yields Q ‡/P

14. (�/P ‡/�/Q )‡/[�/(�/QQ )‡/�/(Q �/

P )]

Ax. 3, �/P put for P , �/Q for Q , Q for R

15. �/P ‡/�/Q pr.

16. �/(�/QQ )‡/�/(Q �/P ) R.1, from 14 and 15

17. �/(�/QQ ) from 7, Q instead of P

18. �/(Q �/P ) R.1, from 16 and 17

19. Q ‡/P df.

Each one of the last four proofs depends on what was proved in a previous proof, 7 depending on 1�/6, 8�/9 depending on 7, 10�/13

depending on 9 at step 11, 14�/19 depending on 7 at step 17 The next proof starts with P ‡/(Q ‡/PQ ) gotten by steps 50�/112 in

Appendix A. But P , Q yielding PQ can be P yielding Q ‡/PQ , which can be P ‡/(Q ‡/PQ ). Reversing conclusion to premisses via

implications is the deduction theorem, D.T. (see Nidditch, 1962, pp. 30�/40 for many examples).

Proof that P , Q yield PQ )

20. P ‡/(Q ‡/PQ ) from 50�/112 in Appendix A

21. P pr.

22. Q ‡/PQ R.1, from 20 and 21

23. Q pr.

24. PQ R.1, from 22 and 23

Proof of (Q ‡/P )�/(�/P ‡/�/Q ))

25. (�/P ‡/�/Q )‡/(Q ‡/P ) from 15 and 19 and D.T. (above)


Steps leading to 27 generate the structure of

expressions (1) and (2). Steps leading to 35

generate the structure of expression (3). Steps

leading to 49 generate the structure of expression

(4). Step 27 is (Q ‡/P )�/(�/P ‡/�/Q ). But put-

ting P for Q and Q for P this becomes (P ‡/Q )�/

(�/Q ‡/�/P ). Changing expression (1) somewhat

we get a non-empty, filled 27 in order to be as close

to reality as possible: if x is in a year-round

reproductive�/responsive�/active organism (P )

then x is in an organism having adaptedness to

year-round temperature (Q )*/equivalent to: if x is

not in an organism having adaptedness to year-

round temperature (�/Q ), then x is not in a year-

round reproductive*/responsive*/active organ-

ism (�/P ). The x can be symbolized; thus 27 can

be: (Fx ‡/Gx )�/(�/Gx ‡/�/Fx ).

This filling of 27 with content includes also: if x

is in an adapted part of A. sagrei , or the temperate-

tropical snail conglomerate, or the North Amer-

ican forest, then x is in a favorable ecological

context*/equivalent to: if x is not in a favorable

context, then x is not in an adapted part of those

entities. Thus again: (Fx ‡/Gx )�/(�/Gx ‡/�/Fx ).

More succinctly and more fully we have: x is

adapted only to favorable contexts if and only if x

is not adapted to any unfavorable contexts.

This filling of 27 with content includes splitting

algal species’ x across those cells which are year-

round reproductive and adapted and those cells

which are not adapted and not year-round repro-

ductive; splitting mussel-oysters’ x across those

individuals which are year-round responsive and

adapted and those individuals which are not

26. [(Q ‡/P )‡/(�/P ‡/�/Q )] �/[(�/P ‡/�/

Q )‡/(Q ‡/P )]

from 13 and 25 by 24, where bracketed parts replace P and Q in 24.

27. (Q ‡/P )�/(�/P ‡/�/Q ) 27 is defined by 26, where the left parenthesized part implies the right parenthesized

part in the first bracket and the right part implies the left part in the second bracket.

‘�/’ means ‘equivalent to’. The tacit conjunction in PQ is changed from schematic to

reality by and , of step 26.)

Proof of [(P ‡/Q ) �/(Q ‡/P )]�/(P �/Q ))

28. P ‡/Q pr.

29. Q ‡/P pr.

30. (P ‡/Q ) �/(Q ‡/P ) from 28 and 29 by 24

31. P �/Q df. as in 2

32. [(P ‡/Q ) �/(Q ‡/P )]‡/(P �/Q ) pr.

33. (P �/Q )‡/[(P ‡/Q ) �/(Q ‡/P )] pr.

34. {[(P ‡/Q ) �/(Q ‡/P )]‡/(P �/Q )} �/{(P �/

Q )‡/[(P ‡/Q ) �/(Q ‡/P )]}

32, 33 by 24

35. [(P ‡/Q ) �/(Q ‡/P )]�/(P �/Q ) df. as in 26 and 27

Proof that P �/ R , (P ‡/Q ) �/(R ‡/S ) yield Q �/ S

36. P �/ R pr.

37. P ‡/Q assumption

38. R ‡/S assumption

39. �/Q ‡/�/P from 37 and 13 by R.1, P for Q , Q for P

40. �/S ‡/�/R from 38 and 13 by R.1, R for Q , S for P

41. (�/Q �/S )‡/(�/R �/Q ) from 40 and 53 in Appendix A

42. (�/R �/Q )‡/(�/P �/R ) from 39 and 53 in Appendix A

43. (�/Q �/S )‡/(�/P �/R ) from 41, 42, and 61�/70 of Appendix A

44. [(�/Q �/S )‡/(�/P �/R )]‡/[�/(�/P �/

R )‡/�/(�/Q �/S )]

from 43 and 13

45. �/(�/P �/R )‡/�/(�/Q �/S ) R.1 from 44 and 43

46. (P �/ R )‡/(Q �/ S ) df.

47. Q �/ S R.1 from 46 and 36

48. (P ‡/Q ) �/(R ‡/S ) from 37 and 38 by 24

49. P �/ R , (P ‡/Q ) �/(R ‡/S )�/Q �/ S from 36, 48, and 47, �/ meaning ‘therefore’ and replacing ‘yield’.


adapted and not year-round responsive. The x is

split across warm bloodeders (minus hibernators)

and cold bloodeders (plus hibernators); x is split

across these two groups. Each group is composed

of two identical sets (classes)4 because each group

has two attributes, being year-round active and

being adapted in one group, being not adapted

and being not year-round active in the other

group.

Step 35 is [(P ‡/Q ) �/(Q ‡/P )]�/(P �/Q ): if one

species has adaptedness to its locale (P ), then its

locale has adaptedness to it (Q ), and if its locale

has adaptedness to it (Q ) then the species has

adaptedness to its locale (P )*/which is equivalent

to (�/): the species has adaptedness to its locale if

and only if its locale has adaptedness to it (P �/Q ).

Thus the species may be the redwood, or may be

one of the pinon pines, or may be one of the

junipers, or may be the white spruce.

Step 49 is P �/R , (P ‡/Q ) �/(R ‡/S )�/Q �/S :

there is the process of diapause or there is the

process of non-diapause (P �/ R ), if there is the

diapause process then there is winter adaptedness

(P ‡/Q ) and if there is the non-diapause process

then there is summer adaptedness (R ‡/S ), there-

fore there is winter adaptedness or there is summer

adaptedness (Q �/S ). Likewise, there is a tendency

toward limbs with many toe bones or there is a

tendency toward reduced-toe limbs (P �/R ), if

there is the first tendency then aquatic adaptedness

ensues (P ‡/Q ) and if there is the second tendency

then terrestrial adaptedness ensues (R ‡/S ), there-

fore aquatic adaptedness ensues or terrestrial

adaptedness ensues (Q �/S ).

Once the schematic formulas 27, 35, and 49 are

filled in with descriptive words, part of the reality

that is aimed for in this enterprise has been gotten.

A vital point is this: our words describing what is

are as close to what is as we can get. Here no

widening of the gap between description and what

is being described will be indulged in. The linguis-

tic ‘x is a mussel and x is adapted’ will be

excluded. The ‘x ’ of the linguistic ‘x is a mussel’

will be avoided. The spurious two entities of ‘x ’

and ‘a mussel’ will be replaced by x as a part of the

single mussel. Were one to mention the NorthAmerican forest as x being adapted only to moist

environments, this would be explained as x is part

of each twig, each plant, each association of the

conglomerate entity the North American forest,

this x integrating this single, broad, scattered

thing. For x is real. As is the connective and ,

that was fought for by interconnecting proofs, a

woven integrated reality. And especially to beincluded are the other connectives, if�/then , or ,

which are vital to the integrated reality which the

sequence of proofs is.

The view here is that the connectives if�/then ,

and , or are elements as real as the elements they

connect. Same for not . The deduction theorem was

just mentioned, saying that P , Q yielding PQ can

be reversed to P ‡/(Q ‡/PQ ), that �/P ‡/�/Q

yielding Q ‡/P can be reversed to (�/P ‡/�/Q )‡/

(Q ‡/P )*/though only after the proof has been

accomplished. But proof and reversal show the

remarkable degree of connectedness, of integra-

tion, intended for adaptation.

9. A philosophical model: a glimpse beyond

An integrated model was sought in the first

section by justifying the four principles of adapta-

tion with empirical detail. An integrated model

was sought in the second section by espousing the

point of view that the computational elaboration

of proof is a semblance of a model that once filled

in with descriptive words is a complete model.

There remains to be considered the philosophicalapproach, an integrated approach. The philoso-

phical approach is, aptly, the approach of the

realist in the nominalist�/realist controversy of the

20th century, wherein the nominalist, the extreme

nominalist, admits only particulars and the realist

admits particulars and properties.

Already the realist approach has been taken,

saying in one breath that the particular, the algalarray, is adapted to, has the property adaptedness

to, year-round temperature, that the particular,

the warm-blooded single animal, is adapted to, has

the property adaptedness to year-round

temperature*/whereas the complementary array

and the cold-blooded single animal is not adapted4 The sets are identical because they have the same members.


to, does not have adaptedness to, year-roundtemperature. These statements introduce the rea-

list approach, presented in four books (Bergmann,

1967; Wolterstorff, 1970a; Armstrong, 1978a,b,

1989). According to Wolterstorff ‘‘Necessarily, for

anything at all, if it is courageous, then it

exemplifies courage; and, if there is something

which exemplifies courage then there is such a

thing as courage’’ entails ‘‘Necessarily, if some-thing is courageous, then there is such a thing as

courage’’. Adapted could of course be put for

courageous; adaptedness could be put for courage,

courageousness. The argument is one of many

variations presented by Wolterstorff in chapter 5.

But Wolterstorff admits that properties, attributes,

cannot be irreducibly established, cannot be im-

mune to reduction to particulars, to something iscourageous, to something is adapted. This was in

1970.

But Jackson (1977) (in a three paged paper)

provided an ‘‘apparently decisive’’ objection to the

reduction of properties, attributes, to particulars,

to the nominalist view. ‘‘Everything red is both

shaped and extended, but red is neither a shape

nor an extension.’’ ‘‘This is not to deny that ‘Red isa color’ entails that necessarily everything red is

colored. But the former says more than the latter.

If red’s being a color were nothing more than a

matter of every red thing necessarily being colored,

then red’s being a shape and an extension would be

nothing more than the fact that necessarily every

red thing is shaped and extended. And red is not a

shape and not an extension. It seems that ‘Red is acolor’ says, as the realist maintains, something

about red not reducible to something about red

things.’’ These are Jackson’s important words.

Previously the reduction of properties to particu-

lars was argued to be difficult by Pap (1959) and

Quine (1960), pp. 118�/124). Wolterstorff (chapter

9) contends the reducibility of properties is easy,

but he is wrong since he says that ‘rednesses arecolors’ reduces to ‘red things are colored’*/but

rednesses are indistinguishable and so not numer-

able.

When properties (attributes) are viewed as

confined to particulars, properties are called tropes

(Armstrong, 1989, pp. 113�/133, Williams, 1953;

Campbell, 1981; Stout, 1921�/1923, 1923, 1936).

One particular is a bundle of tropes. ‘‘Particular

being’s distinguishing mark is that it is exhausted

in the one embodiment, or occasion, or example’’

(Campbell, 1981). It occurs new once. It is, once

only. Likewise for the compresent tropes it is made

of. For Stout (1923) the tropes of a particular

when all assembled make the particular. One is to

see that one living oyster has the attribute, the

property, the trope of a calcium carbonate shell

compresent locationally with another trope, a

pumping rate of 9.0 l/h from 16 to 28 8C. These

and other tropes are either glued together by

multicellularity or more loosely hung together,

like pumping rate, to make a concrete living being,

a one-time only embodiment. But these and other

tropes are integrated by if�/then and and in P ‡/

(Q ‡/PQ ), which if filled with descriptive content

is: if there is shell separately, then if there is

pumping rate separately, then there are both shell

and pumping rate together. But though a loca-

tionally tight chunk, like an oyster, is construct-

able by tropes and the reality integrating feature,

P ‡/(Q ‡/PQ ), each chunk is isolated from every-

thing else. Each chunk5 is alone, all alone.

But consider properties, or universals, them-

selves. ‘‘It seems to follow that universals are, or

may be, multiply located; for are they not to be

found wherever the particulars that instantiate

them are found? If two different electrons have

charge e , then e , one thing, a universal, is to be

found in two different places, the places where the

two electrons are. . .’’ (Armstrong, 1989, p. 98).

The universal e is repeated in two electrons. And

the same is true of the oyster’s pumping rate, 9.0 l/

h at 16�/28 8C. This rate, one thing, a universal, is

to be found in two different oysters. If we were

dealing in tropes there would be two charges e ,

two pumping rates; but now we are dealing in

universals and there is one charge e and one

pumping rate instantiated, exemplified in two

electrons, in two oysters. Tropes are instantiations.

Universals are extraordinarily more integrative

than tropes. A single e unites all the electrons in

the universe. A single pumping rate unites each

lonely oyster with all the other oysters.

5 Chunk is from Williams (1931).


Particulars can, of course, range in size fromthat of the electron to that of the whole universe.

In the middle range are the chunky oyster and the

broad, flat American forest. Each tree in the

American forest has the properties, the universals,

tallness, dense packedness (with others), competi-

tiveness, high growth capacity, and adaptedness in

moist environments. Each tree transmits these

universals to the whole moist part of the forest,and so these five single things, among many

others, integrate the moist forest.

Universals are repeatedly instantiated, exempli-

fied, embodied in particulars. To be is to be a

particular, and to be a particular is to have a

universal. We can go up from particulars to

particulars exemplifying universals to universals,

as in Wolterstorff’s argument. And we can godown in the same way. But can we go sideways?

Again, if we were dealing in tropes, we would have

a separate roundness in each round thing, a

separate adaptedness in each mussel. We would

want these roundnesses to be members in a

similarity set as Williams (1953), p. 11 suggests,

for they resemble each other perfectly*/same for

the adaptednesses. But what is the commonproperty that would define, here, a similarity set?

There is none. A billiard ball is round, so it is a

member of the set of round things because it has

the common property with others of roundness.

But there is no common property of roundnesses

(as Campbell, 1981, p. 485, points out). So each

roundness cannot be a member in a set. This

impasse is the outcome of the initial mistake ofthinking that roundnesses are distinguishable, are

numerable. But if we are dealing in universals this

impasse does not come up.

Universals go sideways, in the simplest manner,

from particular to particular, grouping them,

integrating them into sets, classes. For there is

nothing more integrative than the classifications

that universals, common properties, achieve.Classifications into sets, or classes, are rigid.

Sets, classes, are. They are not gettings to be. They

are not developments, trends, processes, tenden-

cies. But these are as crucial, as integrative as sets

(classes). The development of expansion of the

white spruce from 12 000 to 9000 years ago is a

development in the spruce’s adaptedness to its

locale and the locale’s adaptedness to the spruce.These are two cases that the universal adaptedness

has (Wolterstorff, 1970b), for particulars have

universals while universals have cases, two expres-

sions of reality. Then there are the processes of

diapause and non-diapause, and the tendencies

toward increased bones in the toes of aquatic

paddle limbs and reduced toes in land limbs, four

further cases that the universal adaptedness has.

10. Universals and the principles of adaptation

Universals characterize the things which em-

body them. Characteristics, which are universals,

likewise characterize the things, the particulars,

which embody them. Though particulars embody,

exemplify universals or characteristics, particularsnever characterize. Only characteristics character-

ize (Bayliss, 1953, pp. 57�/58). Characteristics are

properties, are traits, are qualities, are features, are

parameters. Characteristics inhere in things, imbue

things, penetrate things, permeate things. So do

properties, which are the same as characteristics*/

and both are universals. Properties are collected

together to embody, to make, to compose, toconstitute something, some individual, some par-

ticular, whether the particular is tight or scattered

(one oyster versus the forest, the ecological sys-

tem), whether the particular is small or large (algal

cell or Cretaceous mosasaur). Properties and

particulars have almost an asymmetric relation.

For properties are embodied in, are exemplified in

particulars, while particulars embody, exemplifyproperties. But both have each other. For a

universal to exist it must have a particular; for a

particular to exist it must have a universal.

Because particular and universal cannot be inde-

pendent: they must depend on each other (Allaire,

1960). And in this way they constitute all existence.

There is, of course, a great deal more to

universals than the small bit just presented. Oneissue is: what holds several properties together to

make, to form a particular? It was pointed out that

a multicellular glue holds the physical portion of a

biological entity together; but in general for several

properties to be held together in a metaphysical

sense a nexus is required. Thus Bergmann (1967)


stresses that in a spot that it is red and round there

are really three constituents, red, round, and thenexus. If and is taken as a constituent of reality it

is a quasinexus (Bergmann, 1967, p. 93). This

looks back to P ‡/(Q ‡/PQ ) and looks forward to

the conjunction of properties next.

The four principles of adaptation are character-

istics. They characterize the biological entities of

the world. The four principles are universals par

excellence. But they are complex universals, com-

plex properties, because they are and -connected,

conjunctions of properties (Armstrong, 1978b, vol.

2, chap. 15). What this amounts to is as follows.

For the first principle, for example, we have the

property of being active and adapted year-round,

the property of being not-adapted and not-active

year-round. For the second principle, for example,

we have the property of being dense-packed andmoisture adapted, the property of being non-

dense-packed and not-moisture-adapted. For the

third principle, for example, we have the property

of being adapted to locale by the white spruce and

adapted to the white spruce by the locale. For the

fourth principle, for example, we have the prop-

erty of being diapause and winter-adapted, the

property of being non-diapause and summer-

adapted. And this is the brief resume of the four

principles of adaptation.

Acknowledgements

The author is indebted to Betty Shaughnessy for

typing this article.

Appendix A

The proof 20�/24, which joins two compound

statements by and in 26, starts with P ‡/(Q ‡/PQ ),

gotten by steps 50�/112. These steps are based on

Copi (1979), pp. 227�/250, except steps 82�/99,

which are based on Rosser (1953), pp. 64�/65.In the following sequence of proofs there are

several salient features. Thus from the repeated use

of steps 53 and 60 (Rule of Thumb 1) and from the

reasoning of steps 62, 63�/70 (Rule of Thumb 2)

and by the laborious derivation of associativity in

82�/99 and the dazzling substitution in 100, the

final result of the simple and crucial 112 is

achieved.

References

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Philo. Rev. 69, 485�/496.

Proof that P ‡/Q yields RP ‡/QR

50. P ‡/Q pr.

51. (P ‡/Q )‡/[�/(QR )‡/�/(RP )] Ax. 3

52. �/(QR )‡/�/(RP ) R.1 from 50 and 51

53. RP ‡/QR from 15 and 19, �/(QR ) of 52 replacing �/P and �/(RP ) of 52

replacing �/Q in 15

Proof that �/P ‡/�/Q yields P ‡/P

54. �/P ‡/�/Q pr.

55. (�/P ‡/�/Q )‡/[�/(�/QP )‡/�/(P �/P )] Ax. 3, P replacing R , and �/P and �/Q put for P and Q

56. �/(�/QP )‡/�/(P �/P ) R.1, from 55 and 54

57. �/(�/QP ) from 6, with �/Q for �/R

58. �/(P �/P ) R.1 from 56 and 57

59. P ‡/P df.

Proof of RP ‡/PR

60. RP ‡/PR from 59 and 53. Rule of thumb 1; surround P ‡/P with R

Proof that P ‡/Q , Q ‡/R yield P ‡/R

61. P ‡/P from 59

62. P ‡/Q pr.

63. Q ‡/R pr.

Appendix A


64. (P ‡/P )‡/[�/(P �/Q )‡/�/(�/QP )] Ax. 3, putting P for P and Q , �/Q for R

65. �/(�/QP ) R.1 done twice, as in 2�/6

66. �/R ‡/�/Q from 63 and 13 by R.1, R for P

67. (�/R ‡/�/Q )‡/[�/(�/QP )‡/�/(P �/R )] Ax. 3, �/R , �/Q , and P for P , Q , and R

68. �/(�/QP )‡/�/(P �/R ) R.1, from 67 and 66

69. �/(P �/R ) R.1, from 68 and 65

70. P ‡/R df. Rule of thumb 2: Q ’s cancel in P ‡/Q , Q ‡/R ; P ‡/R

Proof that P ‡/Q , P ‡/R yield P ‡/QR

71. P ‡/Q pr.

72.P ‡/R pr.

73. PP ‡/RP from 72 and 53, P for R , R for Q

74. RP ‡/QR from 71 and 53

75. PP ‡/QR from 73 and 74 by reasoning of 62, 63�/70

76. P ‡/PP Ax. 1

77. P ‡/QR from 76 and 75 by reasoning of 62, 63�/70

Proof that R ‡/S yields PR ‡/PS

78. R ‡/S pr.

79. PR ‡/SP from 78 and 53, with R and S for P and Q , with P for R

80. SP ‡/PS from 60, with S put for R

81. PR ‡/PS from 79 and 80 with reasoning as in 62, 63 to 70

Associativity proofs, 82�/99

Proof of (PQ ) R ‡/P

82. (PQ )R ‡/PQ Ax. 2, with PQ put for P , R put for Q

83. PQ ‡/P Ax. 2

84. (PQ )R ‡/P from 82 and 83 by reasoning of 62, 63 to 70

Proof of (PQ )R ‡/Q

85. (PQ )R ‡/PQ Ax. 2, with PQ put for P

86. PQ ‡/QP from 60, with P for R and Q for P

87. (PQ ) R ‡/QP from 85 and 86, reasoning as in 62, 63�/70

88. QP ‡/Q Ax. 2

89. (PQ )R ‡/Q from 87 and 88, as in 62, 63�/70

Proof of (PQ ) R ‡/R

90. (PQ )R ‡/R (PQ ) from 60, putting PQ for R and R for P

91. R (PQ )‡/R Ax. 2, putting R for P and (PQ ) for Q

92. (PQ )R ‡/R from 90, 91, as in 62, 63�/70

Proof of (PQ ) R ‡/P (QR )

93. (PQ )R ‡/QR from 89 and 92 by reasoning as in 71, 72, to 77

94. (PQ )R ‡/P (QR ) from 84 and 93 by reasoning as in 71, 72, to 77

Proof of P (QR )‡/(PQ ) R

95. P (QR )‡/(QR )P from 60, (QR ) put for P , P put for R

96. (QR )P ‡/Q (RP ) from 95, like 94, outer parentheses like 94’s outers

97. Q (RP )‡/(RP )Q from 96, like 60, (RP ) for P and Q for R

98. (RP )Q ‡/R (PQ ) from 97, like 94, outer parentheses like 94’s outers

99. R (PQ )‡/(PQ ) R from 98, like 60, PQ for P

Proof of [(PQ )‡/R ]‡/[P ‡/(Q ‡/R )]

100. P �/�/(Q �/R )‡/P (Q �/R ) from 81, �/�/(Q �/R ) for R , Q �/R for S

101. P (Q �/R )‡/(PQ )�/R from 95�/99, �/R for R

102. P �/�/(Q �/R )‡/(PQ )�/R from 100 and 101, as in 62, 63�/70

103. {[P �/�/(Q �/R )]‡/[(PQ )�/R ]}

‡/{�/[(PQ )�/R ]‡/�/[P �/�/(Q �/R )]}

from 102, bracketed parts replacing Q and P in 13

104. �/[(PQ )�/R ]‡/�/[P �/�/(Q �/R )] from 103 and 102 by R.1

105. [(PQ )‡/R ]‡/[P ‡/(Q ‡/R )] from 104, df.

Proof of P ‡/(Q ‡/PQ )

106. P ‡/P from 59

107. Q ‡/Q from 59, Q put for P

108. PQ ‡/QP from 107 and 60, P for R , Q for P

109. QP ‡/PQ from 106 and 60, Q put R


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The four principles of adaptation