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This latter class may be exemplified by the questions as to the causes
respectively of echo； of reflection； and of the rainbow： the
connexions to be proved which these questions embody are identical
generically； because all three are forms of repercussion； but
specifically they are different。
Other connexions that require proof only differ in that the 'middle'
of the one is subordinate to the 'middle' of the other。 For example：
Why does the Nile rise towards the end of the month？ Because towards
its close the month is more stormy。 Why is the month more stormy
towards its close？ Because the moon is waning。 Here the one cause is
subordinate to the other。
16
The question might be raised with regard to cause and effect whether
when the effect is present the cause also is present； whether； for
instance； if a plant sheds its leaves or the moon is eclipsed； there
is present also the cause of the eclipse or of the fall of the
leaves…the possession of broad leaves； let us say； in the latter case；
in the former the earth's interposition。 For； one might argue； if this
cause is not present； these phenomena will have some other cause： if
it is present； its effect will be at once implied by it…the eclipse by
the earth's interposition； the fall of the leaves by the possession of
broad leaves； but if so； they will be logically coincident and each
capable of proof through the other。 Let me illustrate： Let A be
deciduous character； B the possession of broad leaves； C vine。 Now
if A inheres in B （for every broad…leaved plant is deciduous）； and B
in C （every vine possessing broad leaves）； then A inheres in C
（every vine is deciduous）； and the middle term B is the cause。 But
we can also demonstrate that the vine has broad leaves because it is
deciduous。 Thus； let D be broad…leaved； E deciduous； F vine。 Then E
inheres in F （since every vine is deciduous）； and D in E （for every
deciduous plant has broad leaves）： therefore every vine has broad
leaves； and the cause is its deciduous character。 If； however； they
cannot each be the cause of the other （for cause is prior to effect；
and the earth's interposition is the cause of the moon's eclipse and
not the eclipse of the interposition）…if； then； demonstration
through the cause is of the reasoned fact and demonstration not
through the cause is of the bare fact； one who knows it through the
eclipse knows the fact of the earth's interposition but not the
reasoned fact。 Moreover； that the eclipse is not the cause of the
interposition； but the interposition of the eclipse； is obvious
because the interposition is an element in the definition of
eclipse； which shows that the eclipse is known through the
interposition and not vice versa。
On the other hand； can a single effect have more than one cause？ One
might argue as follows： if the same attribute is predicable of more
than one thing as its primary subject； let B be a primary subject in
which A inheres； and C another primary subject of A； and D and E
primary subjects of B and C respectively。 A will then inhere in D
and E； and B will be the cause of A's inherence in D； C of A's
inherence in E。 The presence of the cause thus necessitates that of
the effect； but the presence of the effect necessitates the presence
not of all that may cause it but only of a cause which yet need not be
the whole cause。 We may； however； suggest that if the connexion to
be proved is always universal and commensurate； not only will the
cause be a whole but also the effect will be universal and
commensurate。 For instance； deciduous character will belong
exclusively to a subject which is a whole； and； if this whole has
species； universally and commensurately to those species…i。e。 either
to all species of plant or to a single species。 So in these
universal and commensurate connexions the 'middle' and its effect must
reciprocate； i。e。 be convertible。 Supposing； for example； that the
reason why trees are deciduous is the coagulation of sap； then if a
tree is deciduous； coagulation must be present； and if coagulation
is present…not in any subject but in a tree…then that tree must be
deciduous。
17
Can the cause of an identical effect be not identical in every
instance of the effect but different？ Or is that impossible？ Perhaps
it is impossible if the effect is demonstrated as essential and not as
inhering in virtue of a symptom or an accident…because the middle is
then the definition of the major term…though possible if the
demonstration is not essential。 Now it is possible to consider the
effect and its subject as an accidental conjunction； though such
conjunctions would not be regarded as connexions demanding
scientific proof。 But if they are accepted as such； the middle will
correspond to the extremes； and be equivocal if they are equivocal；
generically one if they are generically one。 Take the question why
proportionals alternate。 The cause when they are lines； and when
they are numbers； is both different and identical； different in so far
as lines are lines and not numbers； identical as involving a given
determinate increment。 In all proportionals this is so。 Again； the
cause of likeness between colour and colour is other than that between
figure and figure； for likeness here is equivocal； meaning perhaps
in the latter case equality of the ratios of the sides and equality of
the angles； in the case of colours identity of the act of perceiving
them； or something else of the sort。 Again； connexions requiring proof
which are identical by analogy middles also analogous。
The truth is that cause； effect； and subject are reciprocally
predicable in the following way。 If the species are taken severally；
the effect is wider than the subject （e。g。 the possession of
external angles equal to four right angles is an attribute wider
than triangle or are）； but it is coextensive with the species taken
collectively （in this instance with all figures whose external
angles are equal to four right angles）。 And the middle likewise
reciprocates； for the middle is a definition of the major； which is
incidentally the reason why all the sciences are built up through
definition。
We may illustrate as follows。 Deciduous is a universal attribute
of vine； and is at the same time of wider extent than vine； and of
fig； and is of wider extent than fig： but it is not wider than but
coextensive with the totality of the species。 Then if you take the
middle which is proximate； it is a definition of deciduous。 I say