shorter logic-第50章
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and its proposer may be met with the question what he means by Identity； whereupon we should
soon see that he attaches no idea to it at all； and that Identity is for him an empty name。 As we
have seen； besides； Identity is undoubtedly a negative … not however an abstract empty Nought；
but the negation of Being and its characteristics。 Being so； Identity is at the same time self…relation；
and； what is more； negative self…relation； in other words； it draws a distinction between it and
itself。
Diversity
§ 117
Difference is first of all （1） immediate difference； i。e。 Diversity or Variety。 In
Diversity the different things are each individually what they are； and unaffected
by the relation in which they stand to each other。 This relation is therefore
external to them。 In consequence of the various things being thus indifferent to
the difference between them； it falls outside them into a third thing； the agent of
Comparison。 This external difference； as an identity of the objects related； is
Likeness； as a non…identity of them； is Unlikeness。
The gap which understanding allows to divide these characteristics is so great that
although comparison has one and the same substratum for likeness and
unlikeness； which are explained to be different aspects and points of view in it；
still likeness by itself is the first of the elements alone； viz。； identity； and
unlikeness by itself is difference。
Diversity has； like Identity； been transformed into a maxim： 'Everything is various
or different'： or 'There are no two things completely like each other'。 Here
Everything is put under a predicate； which is the reverse of the identity attributed
to it in the first maxim： and therefore under a law contradicting the first。
However； there is an explanation。 As the diversity is supposed due only to
external circumstances； anything taken per se is expected and understood always
to be identical with itself； so that the second law need not interfere with the first。
But； in that case； variety does not belong to the something or everything in
question： it constitutes no intrinsic characteristic of the subject： and the second
maxim on this showing does not admit of being stated at all。 If； on the other hand；
the something itself is； as the maxim says； diverse； it must be in virtue of its own
proper character： but in this case the specific difference； and not variety as such；
is what is intended。 And this is the meaning of the maxim of Leibnitz。
§ 117n
When understanding sets itself to study Identity； it has already passed beyond it； and is looking at
Difference in the shape of bare Variety。 If we follow the so…called law of Identity； and say； The
sea is the sea； The air is the air； The moon is the moon； these objects pass for having no bearing
on one another。 What we have before us therefore is not Identity； but Difference。 We do not stop
at this point； however； or regard things merely as different。 We compare them one with another；
and then discover the features of likeness and unlikeness。 The work of the finite sciences lies to a
great extent in the application of these categories； and the phrase 'scientific treatment' generally
means no more than the method which has for its aim comparison of the objects under
examination。 This method has undoubtedly led to some important results； we may particularly
mention the great advance of modern times in the provinces of comparative anatomy and
comparative linguistics。 But it is going too far to suppose that the comparative method can be
employed with equal success in all branches of knowledge。 Not … and this must be emphasised …
can mere comparison ever ultimately satisfy the requirements of science。 Its results are indeed
indispensable； but they are still labours only preliminary to truly intelligent cognition。
If it be the office of comparison to reduce existing differences to Identity； the science which most
perfectly fulfils that end is mathematics。 The reason of that is that quantitative difference is only the
difference which is quite external。 Thus； in geometry； a triangle and a quadrangle； figures
qualitatively different； have this qualitative difference discounted by abstraction； and are equalised
to one another in magnitude。 It follows from what has been said formerly about mere Identity of
understanding that； as has also been pointed out （s。 99）； neither philosophy nor the empirical
sciences need envy this superiority of Mathematics。
The story is told that when Leibnitz propounded the maxim of Variety； the cavaliers and ladies of
the court； as they walked round the garden； made efforts to discover two leaves indistinguishable
from each other； in order to confute the law stated by the philosopher。 Their device was
unquestionably a convenient method of dealing with metaphysics … one which has not ceased to be
fashionable。 All the same； as regards the principle of Leibnitz； difference must be understood to
mean not an external and indifferent diversity merely； but difference essential。 Hence the very
nature of things implies that they must be different。
Likeness and Unlikeness
§ 118
Likeness is an identity only of those things which are not the same； not identical
with each other： and Unlikeness is a relation of things alike。 The two therefore do
not fall on different aspects or points of view in the thing； without any mutual
affinity； but one throws light into the other。 Variety thus comes to be reflexive
difference or difference （distinction） implicit and essential； determinate or
specific difference。
Difference and identity in natural science
§ 118n
While things merely various show themselves unaffected by each other； likeness and unlikeness on
the contrary are a pair of characteristics which are in completely reciprocal relation。 This advance
from simple variety to opposition appears in our common acts of thought when we allow that
comparison has a meaning only upon the hypothesis of an existing difference； and that on the other
hand we can distinguish only on the hypothesis of existing similarity。 Hence； if the problem be the
discovery of a difference； we attribute no great cleverness to the man who only distinguishes those
objects； of which the difference is palpable； e。g。 a pen and a camel： and similarly it implies no very
advanced faculty of comparison when the objects compared； e。g。 a beech and an oak； a temple
and a church； are near akin。 In the case of difference； in short； we like to see identity； and in the
case of identity； we like to see difference。 Within the range of empirical sciences； however； the one
of these two categories is often allowed to put the other out of sight and mind。
Thus the scientific problem at one time is to reduce existing differences to identity； on another
occasion； with equal one…sidedness； to discover new differences。 We see this especially in
physical science。 There the problem consists； in the first place； in the continual search for new
'elements'； new forces； new genera and species。 Or； in another direction； it seeks to show that all
bodies hitherto thought to be simple are compound： and modern physicists and chemists smile at
the ancients； who were satisfied with four elements； and these not simple。 Secondly； and on the
other hand； mere identity is made the chief question。 Thus electricity and chemical affinity are
regarded as the same； and even the organic processes of digestion and assimilation are looked
upon as a mere chemical operation。 Modern philosophy has often been nicknamed the Philosophy
of Identity。 But； as was already remarked （s。 103； note） it is precisely philosophy； and in particular
speculative logic； which lays bare the nothingness of the abstract； undifferentiated identity； known
to understanding： though it also undoubtedly urges its disciples not to rest at mere diversity； but to
ascertain the inner of all existence。
§ 119
Difference implicit is essential difference；
