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existing between these earths； and supposes that nature is richer in
substances than our senses would indicate。 The faculty of the
understanding belongs to us just as much under the presupposition of
differences in the objects of nature； as under the condition that
these objects are homogeneous； because we could not possess
conceptions； nor make any use of our understanding； were not the
phenomena included under these conceptions in some respects
dissimilar； as well as similar； in their character。
Reason thus prepares the sphere of the understanding for the
operations of this faculty： 1。 By the principle of the homogeneity
of the diverse in higher genera； 2。 By the principle of the variety of
the homogeneous in lower species； and； to complete the systematic
unity； it adds； 3。 A law of the affinity of all conceptions which
prescribes a continuous transition from one species to every other
by the gradual increase of diversity。 We may term these the principles
of the homogeneity； the specification； and the continuity of forms。
The latter results from the union of the two former； inasmuch as we
regard the systematic connection as complete in thought； in the ascent
to higher genera； as well as in the descent to lower species。 For
all diversities must be related to each other； as they all spring from
one highest genus； descending through the different gradations of a
more and more extended determination。
We may illustrate the systematic unity produced by the three logical
principles in the following manner。 Every conception may be regarded
as a point； which； as the standpoint of a spectator； has a certain
horizon； which may be said to enclose a number of things that may be
viewed； so to speak； from that centre。 Within this horizon there
must be an infinite number of other points； each of which has its
own horizon； smaller and more circumscribed； in other words； every
species contains sub…species； according to the principle of
specification； and the logical horizon consists of smaller horizons
（subspecies）； but not of points （individuals）； which possess no
extent。 But different horizons or genera； which include under them
so many conceptions； may have one common horizon； from which； as
from a mid…point； they may be surveyed； and we may proceed thus；
till we arrive at the highest genus； or universal and true horizon；
which is determined by the highest conception； and which contains
under itself all differences and varieties； as genera； species； and
subspecies。
To this highest standpoint I am conducted by the law of homogeneity；
as to all lower and more variously…determined conceptions by the law
of specification。 Now as in this way there exists no void in the whole
extent of all possible conceptions； and as out of the sphere of
these the mind can discover nothing； there arises from the
presupposition of the universal horizon above mentioned； and its
complete division； the principle： Non datur vacuum formarum。 This
principle asserts that there are not different primitive and highest
genera； which stand isolated； so to speak； from each other； but all
the various genera are mere divisions and limitations of one highest
and universal genus； and hence follows immediately the principle：
Datur continuum formarum。 This principle indicates that all
differences of species limit each other； and do not admit of
transition from one to another by a saltus； but only through smaller
degrees of the difference between the one species and the other。 In
one word； there are no species or sub…species which （in the view of
reason） are the nearest possible to each other； intermediate species
or sub…species being always possible； the difference of which from
each of the former is always smaller than the difference existing
between these。
The first law； therefore； directs us to avoid the notion that
there exist different primal genera； and enounces the fact of
perfect homogeneity； the second imposes a check upon this tendency
to unity and prescribes the distinction of sub…species； before
proceeding to apply our general conceptions to individuals。 The
third unites both the former； by enouncing the fact of homogeneity
as existing even in the most various diversity； by means of the
gradual transition from one species to another。 Thus it indicates a
relationship between the different branches or species； in so far as
they all spring from the same stem。
But this logical law of the continuum specierum （formarum logicarum）
presupposes a transcendental principle （lex continui in natura）；
without which the understanding might be led into error； by
following the guidance of the former； and thus perhaps pursuing a path
contrary to that prescribed by nature。 This law must； consequently； be
based upon pure transcendental； and not upon empirical；
considerations。 For； in the latter case； it would come later than
the system； whereas it is really itself the parent of all that is
systematic in our cognition of nature。 These principles are not mere
hypotheses employed for the purpose of experimenting upon nature；
although when any such connection is discovered； it forms a solid
ground for regarding the hypothetical unity as valid in the sphere
of nature… and thus they are in this respect not without their use。
But we go farther； and maintain that it is manifest that these
principles of parsimony in fundamental causes； variety in effects； and
affinity in phenomena； are in accordance both with reason and
nature； and that they are not mere methods or plans devised for the
purpose of assisting us in our observation of the external world。
But it is plain that this continuity of forms is a mere idea； to
which no adequate object can be discovered in experience。 And this for
two reasons。 First； because the species in nature are really
divided； and hence form quanta discreta； and； if the gradual
progression through their affinity were continuous； the intermediate
members lying between two given species must be infinite in number；
which is impossible。 Secondly； because we cannot make any
determinate empirical use of this law； inasmuch as it does not present
us with any criterion of affinity which could aid us in determining
how far we ought to pursue the graduation of differences： it merely
contains a general indication that it is our duty to seek for and；
if possible； to discover them。
When we arrange these principles of systematic unity in the order
conformable to their employment in experience； they will stand thus：
Variety； Affinity； Unity； each of them； as ideas； being taken in the
highest degree of their completeness。 Reason presupposes the existence
of cognitions of the understanding； which have a direct relation to
experience； and aims at the ideal unity of these cognitions… a unity
which far transcends all experience or empirical notions。 The affinity
of the diverse； notwithstanding the differences existing between its
parts； has a relation to things； but a still closer one to the mere
properties and powers of things。 For example； imperfect experience may
represent the orbits of the planets as circular。 But we discover
variations from this course； and we proceed to suppose that the
planets revolve in a path which； if not a circle； is of a character
very similar to it。 That is to say； the movements of those planets
which do not form a circle will approximate more or less to the
properties of a circle； and probably form an ellipse。 The paths of
comets exhibit still greater variations； for； so far as our
observation extends； they do not return upon their own course in a
circle or ellipse。 But we proceed to the conjecture that comets
describe a parabola； a figure which is closely allied to the
ellipse。 In fact； a parabola is merely an ellipse； with its longer
axis produced to an indefinite extent。 Thus these principles conduct
us to a unity in the genera of the forms of these orbits； and；
proceeding farther； to a unity as regards the cause of the motions
of the heavenly bodies… that is； gravitation。 But we go on extending
our conquests over nature； and endeavour to explain all seeming
deviations from these rules； and even make additions to our system
which no experience can ever substantiate… for example； the theory； in
affinity with that of ellipses； of hyperbolic paths of comets；
pursuing which； these bodies leave our solar system and； passing
from sun to sun； unite the most distant parts of the infinite
universe； which is held together by the same moving power。
The most remarkable circumstance connected with these principles
is that they seem to be transcendental； and； although only
containing ideas for the guidance of the empirical exercise of reason；
and although this empirical employment stands to these ideas in an
asymptotic relation alone （to use a mathematical term）； that is；
continually approximate； without ever being able to attain to them；
they possess； notwithst