## 1. Aristotle's *Posterior Analytics*




A demonstration in Aristotle is a syllogism that produces scientific
knowledge. Scientific knowledge is knowledge not simply that something
is the case, but *why* it is the case, what causes bring it
about. Perhaps we would do better to call it a scientific understanding
of the fact known. This means that one may have cognition that
something is true which is quite certain without having scientific
knowledge, and Aristotle's *Posterior Analytics* is not a
treatise on what we might nowadays call general epistemology. To
produce and transmit scientific understanding, Aristotle thought we had
to duplicate, in the deductive order of the science, the order of
causes found in reality. Just as the causes can be traced back to first
causes rooted in the nature of the thing known, so the science must
arise from first principles associated with the real definition of the
thing known expressing its nature.




It is notorious that Aristotle's syllogistic logic cannot capture the
logic of relations, and so is inadequate to the task of presenting the
deductive structure of mathematics. This difficulty was handled in
practice by placing the relational arguments outside the formal
structure of syllogistic which formed the framework of a science. The
principles of a demonstration, Aristotle thought, always had to be
universal, reporting, as they do, necessary connections. Now he was
accustomed to showing universal truths through one sort of
'setting forth' (*ekthesis*), working out the thing
informally in a particular case and then using universal
generalization to establish the universal truth. (*Posterior
Analytics* I 4, 73b33-74a4 clearly sets out the procedure.) The
'setting forth' stood outside the formal structure of the
syllogistic, and it allowed the establishment of universal premises
with complex terms, for instance, a premise to the effect that
"*every*
triangle-with-its-base-extended-so-as-to-form-an-external-angle *is
a*
triangle-with-its-external-angle-equal-to-the-sum-of-the-two-angles-opposite-it-in-the-triangle."
Aristotle here uses the term "universal" to mean not only
that the predicate belonged in every case to the subject, but also
that it could not be proved of the subject simply because of its
belonging to some wider universal to which that subject also
belonged. So it would not do to show by 'setting forth'
and assume as a first principle that an isosceles triangle has its
angles equal to two right angles, for this is because it is a
triangle, not because it is an isosceles triangle. A first principle
must be not just universally quantified, but *commensurately*
universal, so that the predicate belongs to the subject in every case,
and belongs to whatever else it belongs to *because* it belongs
to that subject, and because whatever else it belongs to, essentially
or accidentally, falls under that subject.




Aristotle does not lay down tight rules for discovering first
principles, though he points out that one needs a good deal of
experience of the subject, and that if we possess the first principles
they will explain why the subject has the attributes it does. His book
proceeds by explaining the logical form into which a science must be
put if it is to be transmitted to an ideal student. He takes the
mathematics of his time to be the paradigmatic science.




A demonstrative science then, requires for its being understood (1)
an understanding of the terms entering into it (later commentators
suggest that "nominal definitions" provide this), (2)
knowledge of certain axioms applicable to many sciences (for instance,
the law of the excluded middle), (3) knowledge of first principles,
that is,indemonstrable truths proper to the science under consideration
(*PA* I 1, 71a11-17; 2, 72a14-22; 10), (4) knowledge of real
definitions of the subject of the science, and its various species and
predicates (*PA* I 33, 89a18; II 3, 90b24; 13, 96b23; 17,
99b22). The principles of a demonstration must be true, indemonstrable,
and such as to provide the reason for the truth of the conclusion, but
they must also be necessary and per se (*PA* I 2). These last
two requirements were variously interpreted by medieval thinkers, but
we can note that Aristotle allows a statement can be per se in two
ways: (1) if its subject term somehow includes its predicate within its
definition, so that "A human being is rational" is per se,
and (2) if its predicate term includes its subject implicitly in its
definition as the proper subject for that sort of accident, so that
"A human being is able to laugh" is per se (*PA* I
4, 73a35-b24. (There are two other senses of "per se" given
here, and although it is reasonably supposed they have no bearing on
demonstration, some medieval commentators tried
to make something of them.) The middle term of a demonstration must
express the cause why the predicate of the conclusion belongs to its
subject. The predicate of the conclusion, the "attribute,"
will not be part of the essence of the subject, but will somehow follow
on its essence. It was disputed in the Middle Ages whether the middle
term in the highest sort of demonstration would be the real definition
of the subject, or the real definition of the attribute, or somehow include both, but it was
generally agreed that it would be a real definition, and that one of
the premisses of a demonstration would express a necessary truth not
derivable by a simple analysis of either the nominal or the real
definition of its subject. (The central text here, and that a very
difficult one suggesting a number of different possible lines of
analysis, is *PA* II 8-10.)




Various sorts of demonstration falling short of this ideal model,
because they do not give a full explanation of the cause why the fact
is true, were allowed in Aristotle's text (*PA* I 13), and the
medieval authors refer to these as demonstration that it is the case
(*quia*) as opposed to demonstration why it is the case
(*propter quid*). Most important here is the sort of
demonstration which argues from the cause to the effect rather than
effect to cause, for instance, the demonstration that stars, unlike the
planets, are far away because they twinkle, and whatever twinkles is
far away. Twinkling, of course, does not cause the stars to be far
away, but rather, the distance causes the twinkling. This sort of
demonstration plays a role in discussions of analysis and synthesis in
the fifteenth century. Demonstrations concerning particulars, and
demonstrations arguing from theorems in the science which are not
traced back to first principles, are also demonstrations that it is the
case.




Another important case is that in which principles are imported from
another science to complete a demonstration. So if one proves that
circular wounds heal more slowly because they have a large ratio of
area to circumference, and healing proceeds at the edge of a wound, one
has borrowed, in medicine, a principle from geometry. The physician
(qua physician) need not know this principle (that is, he need not know
the reason why it is so, so that he is able to prove it), but may rely
on the authority of the geometer (without being open to criticism as a
physician). In such a case the demonstration is said to be
"subalternate" to another science, and the nature of this
subalternation provided a subject for debate between more Augustinian
and more Aristotelian commentators on Aristotle.


## 2. The Medieval Reception of Aristotle before Robert Grosseteste




Although Boethius reports a translation of Themistius's paraphrase
of the *Posterior Analytics* into Latin, and may have done a
translation himself, neither of these works survived into the Middle
Ages. The Latins first became acquainted with the work through the
translation of James of Venice between 1125 and 1150. John of Salisbury
benefits from James in his *Metalogicon*, giving a list of
points from the work there (Book IV 6-8). The James translation became
the vulgate, and the translation done for Thomas Aquinas by William
Moerbeke never received much usage. Translations of Themistius's
paraphrase of the work, and a lost work by al-Farabi on demonstration
(or perhaps Averroes's critical remarks on that work), were used by
Albert the Great, and though they dropped out of circulation soon
thereafter, scholars sometimes cribbed from Albert's commentary. The
commentary of Alexander of Aphrodisias (or the commentary of
Philoponus, which is close to Alexander) was translated by James of
Venice. This translation also quickly dropped out of circulation, but
much of its content survived in marginal glosses. The Middle Commentary
of Averroes was translated by William of Luna around 1300, but was not
used before the latter half of the fifteenth century, though Albert the
Great seems to have some knowledge of Averroes, and so his doctrines
were not without influence.


## 3. Robert Grosseteste




The *Posterior Analytics* was little known in the twelfth
century, despite James of Venice's translation, then. Though earlier
discussions are to be noted, such as that of Richard Rufus (see Rega
Wood (1996)), the work first enters into the Western tradition in a
serious way in the commentary of Robert Grosseteste (1175-1253),
written around 1230. Grosseteste applies the theory in the
*Posterior Analytics* to itself, presenting it as a
demonstrative science of demonstration. Thus he suggests that Aristotle
first gives a definition of demonstration, a syllogism producing
scientific knowledge, and a definition of scientific knowledge, and
then, in a series of syllogisms, deduces the properties that a
demonstration must have, first considered in itself as a free-standing
syllogism, then considered in relation to other demonstrations, and
finally considered as it is part of a science. The second book of the
work, he claims, discusses the art of definition as the way to discover
demonstrations, and how it is that definition occurs as the middle term
and the cause of the truth of the conclusion, in a demonstration. He
finds thirty-two scientific conclusions in each of the two books, and
his list of conclusions forms the standard summary of the work for many
later writers. This analysis is most plausible in the beginning of Book
I, and the initially structured presentation degenerates to a mere list
of points made, often with little evident deductive structure, in the
discussion of the latter part of Book I and in Book II. Many portions
of the book are treated, plausibly enough, as ancillary to the
deductive science, concerned, for instance, with disproving common
errors.




Before Grosseteste, Aristotle's text was considered very difficult,
both in doctrine and in language, and it seems to have caused some
concern because of its apparent disagreement with the dominant
Augustinian theory of knowledge. Grosseteste not only explained the
book clearly, but also reconciled it with Augustine by treating
demonstration as the means by which a fallen humanity must come to
knowledge of the world. Augustine's Neoplatonic account of knowledge is
reserved for our restored or supernaturally assisted nature in its
contemplation of God, or of the natural world in God. No doubt,
Grosseteste's position as a well-known and conservative Bishop helped
to legitimize the science of demonstration for his more conservative
readers.




Grosseteste suggests that if the mind were healthy, and unaffected
by the Fall, it would be able to see in God the exemplary forms of all
the things he had created. But as it is, such knowledge of exemplary
forms is impossible, though the light of God illumines the forms of
particular things that we encounter in the world so that we can come to
know them. Such forms are in themselves universal and unchanging
(indeed, in themselves they are the same as, though not numerically
identical with, exemplary forms), and so they can ground necessary
truths. But the knowledge of a real definition of a substance, of a
simple form, does not impart knowledge of its causal powers. (Ockham,
it will be noted, shares this view.) For instance, the knowledge of the
causal power of scammony to purge red bile arises only after we observe
a number of cases where it does this, and so come to form an
*aestimatio* that it does in this or that particular case. (An
*aestimatio* is produced in the senses, and can be formed by
irrational animals. It is a kind of perception of a particular causal
conneciton, and is not necessarily correct. The idea seems to have come
from Augustine, *De Libero Arbitrio* II.) Then, spurred on by
this *aestimatio*, reason proposes an experiment, and introduces
scammony when every other cause for the purging of red bile is absent,
and if it often draws out red bile under these conditions, reason
concludes that it is a causal power of scammony to do this. The
intellect's ability to frame a universal concept after it becomes
familiar with particular individuals through the senses is paralleled
by its ability to form universal causal judgments after sensory
*aestimatio* informs it of particular causal events.
(Grosseteste (1981) I 14, lines 252-271.)




This knowledge of causal laws is knowledge of what a given agent is
suited to do, but it is knowledge of what it will actually do only
*for the most part*. This is not knowledge of what it will do
most of the time, or even frequently, but of what it will do of itself
as long as nothing is present to prevent it from doing it. It occurs
through knowledge of "material definitions" which depend on
prior, "formal definitions." The formal definition of a
thing specifies its function, and involves a final cause, while its
material definition specifies how it must be constructed so as to
perform that function, that is, to be an efficient cause of certain
effects. The formal definition tells us what the exemplary form is,
while the material definition specifies how that form and its causal
activity are actually realized in matter. (The distinction between
formal and material definition relies on an interpolation from
Alexander/Philoponus's commentary in the text of James's translation of
*Posterior Analytics* II 19. From Aquinas on people were aware
of this error in the translation.) Knowledge of mathematical truth
occurs without any efficient or final cause in the picture, and we can
see triangles, for instance, as they really are in themselves with a
direct mental view, rather than attempting to reconstruct them, as we
do in the case of thunder, for instance, where we know that some
physical arrangement is producing a noise (has that as its function, as
it were), but cannot view that physical arrangement directly. Thus
mathematical demonstrations are higher (*potior*) than natural
demonstrations, since what they show is *always* the case, and
they are more easily known. (Grosseteste (1981) I 18, lines
119-126.)




Knowledge of what is "for the most part" includes
knowledge concerning eclipses, and eclipses, of course, only rarely
occur. How can there be knowledge of, and necessary truths about, what,
most of the time, does not even exist? For one thing, eclipses are
always present in their "causal reasons," that is, in the
motions of the sun and moon, which guarantee that eclipses occur now
and again, and, moreover, we can say that it is always true that
*if* a certain situation occurs, in which no impediments are
present, an eclipse will occur necessarily due to the nature of the
Moon. (Grosseteste (1981) I 18, lines 189-214.)




One science can be subalternate to another, according to
Grosseteste, in several ways. In one, a science, say Music, the science
of audible proportion, falls under another, in this case the science of
proportion, but it is not a part of that science, since audibility is
an accident of proportion, not a difference which establishes some
species of it. Arithmetical and geometrical proportion, for instance,
are species of proportion, and so the science of arithmetical or
geometrical proportion would be a part of the science of proportion,
not subalternate to it. He says in this case that the one science falls
under the other univocally, since both *are* said to deal with
proportion. Now audible proportion may be no more than an accidental
unity, but it is still the case, Grosseteste holds, that proportion is
a necessary formal part of the real nature of harmony, just as its
audibility is. So the subject of music, harmony, is, as it were,
proportion realized in a certain matter, just as the actual material
constitution of a natural object is the realization of some higher
form, say that of an animal, the nature of whose functioning can be
understood quite independently of the realization of it in that
particular matter. Grosseteste sees subalternation as a phenomenon
revealing a deep metaphysical truth, the truth that a natural material
object is always the realization in matter of some higher form that is
what it is quite independently of that realization. So he does
*not* consider the case of the circular wound as subalternation,
for circularity in no way constitutes or realizes the function of a
wound. Medicine is not even in part subalternate to mathematics.
(Grosseteste (1981) I 12, lines 153-198.) In a second case of true
subalternation, Grosseteste holds, the science of the parts of a thing,
which realize its functioning, must be brought into play to understand
the thing. So the science of harmony is subalternate to the science of
numbers, Arithmetic, for numbers are the parts of proportions, and must
be known if proportions are to be known, even if proportions are not
numbers in the way that audible proportions are proportions. So the one
science falls under the other "almost univocally."
Similarly, medicine is subalternate to the science of the elements,
even though the elements are not strictly parts of the body (not
functional parts), since they still enter into its constitution and so
must be understood if the body is to be understood.




This account of subordination was intimately connected with
Grosseteste's metaphysics. He thought that the material world arose
from light, which propagates itself in a straight line through space,
so that matter can only be understood as arising from light in accord
with mathematical laws. Thus natural science will be subalternate to
mathematics, for even though mathematics is not the science of the
higher form, of light, considered in itself, it does govern the way in
which light realizes itself in space. The fact that the science of
nature depends on mathematics is a clue that the natural world
originates from a higher form in accord with mathematics. Similarly, a
living being comes about when a higher form lends functions of
digestion, reproduction, sensation and the like to matter, these
functions being accomplished by the causal operations of matter, so
that the biological sciences are subalternate to natural science.




Grosseteste identifies two types of demonstration of the highest
sort, natural and mathematical. His analysis of natural demonstrations
depends on a distinction between formal and material definition, which
was interpolated into the text of *Posterior Analytics* II 9 and
seems to come from the James translation of the commentary of Alexander
(= Philoponus?). The interpolated text suggests that a formal
definition might serve as the middle term in a demonstration, proving
the material definition of the subject. For example, one might
demonstrate that anger is the boiling of blood around the heart (its
material definition), by using as the middle term the formal definition
of anger, the desire to do harm to another. Of course, one would have
to know a first principle asserting that whatever fits the formal
definition must realize the functioning it expresses in that material
form, and one would have to know what anger really is, in its own
proper form. Again, drawing on Aristotle's example in *Posterior
Analytics* II 8, thunder is a noise made in a cloud (formal
definition), and such a noise, in a cloud, is made (only) when fire is
extinguished in it, and so thunder is the extinction of fire in a
cloud.




A demonstration of the highest sort in mathematics does not, of
course, work out the mechanism by which some function must be
accomplished, so in this case the middle term will be the formal
definition of the subject, stated in terms of its parts (so a
definition of a triangle will be in terms of the lines making it up,
the definition of a number in terms of the units making it up, and so
on). The attribute, rather than a material definition, will simply be
the property proved of the subject.




In both these sorts of demonstration, Grosseteste holds, the major
premise and conclusion are *per se* in the second way, that is,
the subject is somehow presupposed in their predicates. The minor
premise, since it predicates a formal definition of its subject, is
*per se* in the first way (the subject contains the predicate).
So in the case of a natural demonstration, the subject is the causal
outcome of the predicate (the noise, or thunder, results from the
extinction of fire in a cloud), and is presupposed in it inasmuch as
the point of the material events is to produce that outcome. It is as
if one were to say that the construction of an adding machine
presupposes the notion that it adds, because it is in order to do this
that it has a structure which causes addition. Final and efficient
causation does not figure in mathematical demonstrations, but in any
proper demonstration, Grosseteste thinks, the conclusion will not
merely assign a predicate that belongs universally to its subject, but
one that is *commensurately* universal with it. That is, one
won't have identified the real underlying cause why a figure has a
property if it belongs to some larger class of figures that have the
property, unless one demonstrates that this larger class has it, and
then appends, as it were, a note to the effect that the figure falls
within the larger class. That means that a demonstration of the highest
sort will always show a property to belong to something which not only
has it necessarily, but which is also necessary to produce that
property. So the conclusion and the major premise will have to be
*per se* in the second way, for the subject will be the
*necessarily* underlying cause of the property. Nothing else can
produce it.


## 4. The Criticism of Grosseteste by Albert the Great and Thomas Aquinas




The earliest commentary on the *Posterior Analytics* other
than Grosseteste's to gain any general currency in Europe was that of
Albert the Great (ca. 1200-1280), written between 1245 and 1260. His
commentary takes a different form from Grosseteste's. It is composed of
ten Treatises on each of the two books of Aristotle's work, each
treatise approaching a topic as a subject of controversy, on which
Albert reports every view he can find from Arabic and Ancient
commentators, as well as the moderns. It also has different content,
for as an Aristotelian, Albert objected to Grosseteste's metaphysical
views, and this led him to a different reading of the *Posterior
Analytics*.




The most obvious difference is in Albert's views of the
subalternation of one science to another, and the role of mathematics
in the natural sciences. Since Albert does not accept a substantial
form of a thing that acts as an exemplar to preexisting matter, and
does not accept the development of lower forms of individuals from
higher forms in the mind of God, he rejects the notion that
"natural things are founded on mathematical being, and
mathematical being on divine being ... so that the principles of
natural being are mathematical." (Albert the Great,
*Commentary on the Metaphysics*, Book I Chapter 1.) For Albert
the unity of a particular thing is rooted in its particular substantial
form, and does not arise as an expression of a higher, mathematical
unity, nor can any knowledge of particular natures in themselves be
obtained through reflection on being itself, or other higher forms.
Each science must stand on its own, and we cannot even derive the
species from its genus, much less from its mathematically expressible
accidents.The new account of subalternation worked out by Albert was
accepted in general by later Aristotelians (for instance, in Ockham,
*Summa Logicae* III.II 21), and Grosseteste's account was
abandoned.




Consider the science of harmony. Grosseteste had said that it was
subalternate univocally to the science of proportion, for a harmony is
a proportion realized in sounds. Albert objects that in a demonstration
within the science of harmony, the real explanation why it is so does
not occur in the science of proportion, for the subject of the science
is sounds, not proportions, and what is true of proportions cannot be
applied to harmonies directly, as though a sound were a mathematical
entity. Sounds do have certain mathematically expressible accidents,
but the science of proportions does not establish the substance or
nature of sounds. It bears only on those accidents. The two sciences
are not univocal, that is, they do not have the same subject. Rather,
the subject of the higher science is an accident of the subject of the
lower science. So the subject of harmony is a certain kind of sound,
not a certain kind of proportion. To explain why, we will have to trace
the fact, not from the nature of proportionality, striving to introduce
itself into a certain kind of material, but from the nature of sound.
Nature operates by its own principles, and if it accomplishes the aims
of some higher form, this is because God created it so that it would
accomplish those aims of itself. God created it from nothing, rather
than its evolving from a higher form striving to realize itself in
matter.




From this Albert concludes that the science of the human body might
be subalternated to mathematics, after all, and when Aristotle says
medicine is not subalternate to geometry, he only means that the whole
of medicine is not subalternate to geometry in the way that the whole
of optics is, say. Instead, only a few medical demonstrations are
subalternate to geometry. They are, however, subalternate to geometry
in exactly the same way as the demonstrations in optics are, for optics
is the science of light, and geometry bears only on certain accidents
of light, not on light itself, and does not explain why light has those
accidents.




Thomas Aquinas agrees with Albert on these matters. In his literal
commentary on the *Posterior Analytics* (1269-72) he notes that
mathematics bears on matter because of the nature of matter, which
leads it to have mathematical accidents, dimensions, that is, accidents
which can be abstracted from matter and considered on their own in the
mathematical disciplines without relation to matter. It is only in the
intellect, through abstraction, that they become separated from matter,
and their presence in matter is due to the nature of matter, not to any
sort of prior mathematical reality. But there is something here that is
not in Albert, for Albert does not allow the possibility that the
nature of a thing can cause it to have properties that are not part of
its essence. He thinks that every accident in a thing is to be traced
to another accident in the thing, or some accident of something outside
which brings it about that the accident inheres, but that no accident,
not even an attribute, that is, a proper accident necessarily belonging
to that sort of thing, is caused in it by its essence. To Albert's
mind, this would mean that the nature of a thing, considered in itself
and not insofar as it is a particular in particular circumstances,
would efficiently cause its attribute to inhere in it, and that smacks
of Platonism, of the view that separated universals somehow play a
causal role in the world. Thomas argues that a thing's nature
efficiently causes its primary attribute, and that it does so
necessarily and without exception. This means that the primary
attribute is always a propensity or capacity, not an actual inherence
of an occurrent quality, since, of course, the actual inherence of an
occurrent quality depends on the right conditions being in place for
the operation of the capacity to have that quality. Albert allows that
such propensities are necessary in their subjects, and he agrees that
they are not part of the subject's essence, so that they follow
deductively from its nature, but he allows no sort of efficient
causation any role in this process. Efficient causation of this sort is
referred to in later Thomistic writers as
"emanation"--so Cajetan in his commentary on the
*Summa Theologiae* I, questions 54 and 77, and Suarez in his
discussion of efficient causation in *Metaphysical Disputation*
18.3. But such efficient causation is an impossibility for Albert, for
Albert takes it that all efficient causation connects actualities (an
assumption he perhaps got from Averroes), and seems to take
propensities and capacities as nothing more than descriptions how
efficient causality works for one or another kind of thing.




Part of the issue rests on the requirement that first principles,
which assert primary, indemonstrable attributes of their subjects, be
necessary truths. Thomas takes it that they must be strictly necessary,
universally true in every case at every time. Albert thinks the
necessity involved here is of another sort, a conditional necessity, so
that the attribute belongs to its subject necessarily, *if nothing
prevents it*. Thus he can identify an actuality as a primary
attribute, allowing that possession of the attribute by the subject
only occurs "for the most part," and still identify the
first principle asserting this possession of the attribute as a
necessary truth. It seems that Thomas Aquinas was less radically
Aristotelian on this point than his master. The metaphysical difference
led to a notorious and long-lasting dispute over the nature of the
highest sort of demonstration (*demonstratio potissima*).


## 5. The Dispute over the Highest Sort of Demonstration




Thomas Aquinas argued that the highest sort of demonstration had as
its middle term the real definition of the subject term (*Comm. on
PA* II 1.9, 7, 19). This led him to claim that the fourth way in
which something can be per se pertained to demonstration, since it
indicates an efficient causal connection, and the minor premise will be
true in a demonstration because of the efficient causal connection
between the essence of the subject, as expressed in its real
definition, and the attribute proven of it, making it per se in the
fourth way.




Albert the Great, with his more Aristotelian metaphysics, had argued
that a demonstration of the highest sort would have the definition of
the attribute as its middle term. This sort of definition is sometimes
called a causal definition, and is the rough equivalent of a real
definition for an attribute. In actuality, an attribute is an accident,
and so has no proper real definition, indicating what it is
*entirely in itself*, since what it is involves its belonging to
an appropriate subject, and it actually belongs to such a subject only
under favorable conditions. So a "real" definition for the
attribute would have to express things extrinsic to the attribute, its
subject and that which brings it to actuality in the subject. For this
reason, Ockham insists that the definition of an attribute is a nominal
definition, not a real one, and Aquinas holds that the conclusion of a
demonstration of the highest sort will be per se both in the second way
(presupposing the subject) and the fourth (indicating efficient
causation) (Aquinas, *Commentary on P.A.* I 10). Albert's
preference for the definition of the attribute follows Averroes's
opinion that the highest sort of demonstration should demonstrate not a
mere potentiality, but an actual state of affairs. Aquinas and the
others who held to his view recognized that a demonstrable attribute in
a natural thing would have to be a potentiality, though, of course, an
actuality could be demonstrated in a mathematical demonstration, where
efficient causation is not at issue, and an occurrent attribute can be
shown to inhere in the subject necessarily and at every time.




There actually seems to be a good deal more support for Albert's
view than for Thomas's in the *Posterior Analytics*. Albert
relies in particular on Aristotle's reference to the sort of definition
that includes every part of a demonstration, but arranged in a
different order (*Posterior Analytics* II 10), which he takes to
be the definition of the passion which is the middle term in a
demonstration, and on the examples of demonstration discussed in
*Posterior Analytics* II 8. Aquinas finds little support for his
position in the *Posterior Analytics*, and resorts to *De
Anima* I 1 to prove his point, so that much of his more detailed
discussion of demonstration of the highest sort is in fact to be found
outside the commentary on the *Posterior Analytics*.




Albert's position was defended after Aquinas by Giles of Rome, who
wrote an extensive literal commentary on the *Posterior
Analytics* in 1285, with many questions embedded in it, as well as
an opusculum *What is the Middle Term in Demonstration*
(1276-77). Giles follows Albert closely. Thomas had argued that
Albert's candidate for the highest sort of demonstration could not be
accepted, because it assumed as its major premise that the definition
of the attribute belongs to the subject. This, however, is
demonstrable, for the definition of the attribute belongs to the
subject only because of the subject's essential nature, if it in fact
always belongs to the subject, and if it does not always belong to the
subject, then the demonstration needs an additional premise, which is
not a necessary truth at all, to the effect that the external
conditions needed for the subject to have its attribute are present. So
prior to the proposed demonstration is a demonstration that the
definition of the attribute belongs to the subject, because it belongs
to whatever has the real definition of the subject. Giles's objection
to this is that the major premise in such a demonstration is, as it
were, tautologous, there being no real distinction between the subject
and its essence, and so the purported demonstration begs the question.
In order to avoid begging the question, both premisses would have to be
such that there is a real distinction between subject and predicate.
The argument had been made against Albert's position that the
definition of the attribute and the attribute itself were identical, so
that Albert's candidate for demonstration of the highest sort begged
the question, but Giles (and Ockham after him) points out that the
definition of the attribute, being a causal definition of something
whose existence depends on other things, refers obliquely to things
other than the attribute itself, and so is not in fact really identical
with it. The same point cannot be made in defense of the affirmation of
the real definition of the subject of the subject, and so Giles turned
the tables on his opponents.




This was a powerful objection. The standard reply to it is developed
in John of Cornwall's *Questions on the Posterior Analytics*
(1298-1300), and Walter Burleigh's *Questions* and
*Commentary* on the *Posterior Analytics* (1300-10). John
of Cornwall's work was at one time thought to be Scotus's, and it
certainly seems to reflect Scotus's thinking on this point (*Opus
Oxoniensis* I, Distinction 2, Question 2). The defense is to claim
that there are two sorts of concepts possible of a substance,
quidditative concepts, which are captured in the real definition, and
concepts that express the quiddity only confusedly. Someone who does
not know what the quiddity of a lion is nonetheless may have a concept
of lion if he has encountered lions, but his concept is
non-quidditative. To avoid begging the question in a demonstration of
the highest sort, one must assert the quidditative concept of the
non-quidditative concept of a substance. So, if one says that a lion
(as commonly conceived) is in fact an animal with a certain genetic
code, say, this is not a mere tautology, for the notion of the genetic
code is not included in the everyday, non-quidditative concept of lion.
Giles's reply is to the effect that the confused, simple concept of a
substance possessed by the ordinary fellow in fact refers to the same
reality as the real definition does, so that asserting the real
definition of the confused concept simply asserts that the reality is
itself, and so is a triviality, after all. This, of course, is not true
of the definition of an attribute, since it obliquely refers to things
other than the reality that is the attribute, namely its causes. So to
discover the real definition of human and assert it of the simple,
confused concept of human being is not to convey new information. To
see the point of this reply, we must see that the standard way of
identifying the real nature of a human being is simply to place it in
its genus and identify its specific difference, but it is arguable that
doing this in the case of a substance gives us no new information, but
only places the thing in the right spot in a scheme of classification.
It *is* a little hard to see how "a human being is a
rational animal" does anything more than identify what we want to
talk about. Of course, to say that *this* *concrete*
thing is a rational animal is informative, but does it give us any
different information than the assertion that this concrete thing is a
human being? On the other hand, the causal definition of an attribute
really does add to our information about it, as when we find that the
noise-in-the-cloud, i.e. thunder, is a
noise-in-the-cloud-produced-by-the-extinction-of-fire. These two
notions are really distinct, for the one refers obliquely to fire, and
the other does not.




Giles's objection to the view that the definition of the subject is
the middle term in the highest sort of demonstration would be
particularly difficult for Thomas to meet, since Thomas agreed with
Giles on the unicity of substantial form. Ockham and the Franciscan
tradition in general, which rejects this doctrine, might hold that the
real definition of human being, say, does refer to real parts that need
not be referred to in a confused, simple concept of human being.
Scotus, of course, has an additional resource available, for he can
deploy a formal distinction between the individual and its essence here
(which would not be recognized by Ockham or Thomas), even when the
individual has but a single substantial form.


## 6. William of Ockham and the Possibility of Scientific Knowledge




William of Ockham discusses the *Posterior Analytics* and
demonstration in two places, his *Summa Logicae* III.II, *On
Demonstrative Syllogism*, and his *Scriptum in Librum
Sententiarum Ordinatio*, Prologue, Questions 2 through 6 (before
1324). In the latter, he develops an account of demonstration to
discuss the question what, if anything, can be demonstrated of God. In
both places he lays out his views systematically, rather than in
commentarial form.




Ockham agreed with Scotus and Aquinas that the definition of the
subject is the middle term in a demonstration of the highest sort, but
he is no more comfortable with the notion that the subject somehow
efficiently causes an attribute in itself through its essence than is
Albert. Indeed, he insists that nothing of interest follows for a
demonstration from the real definition of a subject giving its genus
and difference. This is because what follows demonstratively follows
on some real structure of really distinct parts within the
subject. This means, first of all, that a genus-difference definition
of a thing, which does not identify really distinct parts in it,
cannot serve as a middle term in demonstration. Moreover, since God
has no real parts, but is perfectly simple, no demonstration
concerning God can be constructed at all. But some definitions of a
subject do identify real parts within it. One case occurs in
mathematics, in which the real definition of a subject obliquely
conveys parts of the subject, for instance, as in the definition of a
triangle, which is not said directly to be identical to its parts, the
lines making it up, say, but is said obliquely to be something
composed *from* those lines. This, for Ockham, is the only
possibility for the highest sort of demonstration (*Summa
Logicae* III.II 40). It alone meets Thomas's criterion for such a
demonstration, i.e. it shows the attribute to belong actually to the
subject necessarily and in every case, Albert's criterion, that the
attribute be occurrent and not merely a capacity, and Giles's
requirement that the attribute be really distinct from the subject, so
that it can reasonably be said that the conclusion is not an immediate
proposition. In another case, one can demonstrate an implicitly
negative attribute of something from the fact that it is composed of
real parts, arguing, for instance, that "Whatever has separable
parts is destructible, every material thing has separable parts,
therefore every material thing is destructible." This, however,
since it shows an attribute which conveys the parts of the subject
negatively, is not a demonstration of the highest sort.




In another type of demonstration, the middle term may be a
definition of a concrete subject obliquely referring to its parts
without any determination, namely in demonstrations concerning animals
and human beings, in which the reality contains a plurality of forms.
Thus a particular human being is able to learn, say, in virtue of the
form which is its rational soul. If, as Thomas held, there is no
plurality of forms here, but every natural substantial form, including
biological forms, is simple, and its rational soul just *is* the
form of the body, then no demonstration is possible at all, for the
ability to learn is immediately in a human being through itself, so
that to say that a human being is rational is to express a first
principle. If there is a plurality of forms, this sort of demonstration
nonetheless falls short of the highest sort, for it concerns only the
*concretum*, the concrete instance that has several forms, not
the substance considered in itself (simply as possessor of the form).
(Note that here *forms* are the parts expressed in the
definition obliquely, so the case differs from mathematical
demonstrations.) Moreover, since the concretum receives the attribute,
the attribute is either learning itself, which is clearly not
demonstrable of every concrete instance of a human being, since some
human beings may fail to realize their capacity to learn, or merely the
ability to learn, which is not an actual occurrent constituting part of
a real fact about the world as it is, but, as Albert insisted, merely a
kind of possibility of an occurent thing. The notion that a kind of
efficient causation produces the capacity for learning, which is to be
taken as something really present in a human being even when the human
being is not learning, is rejected by Ockham, of course, for he takes
it that talk about the capacity is only oblique talk about real events,
using modal propositions. All natural demonstration concerning
efficient causes is reduced to this sort of thing by Ockham, and he
never allows that, for instance, it can be shown that fire is capable
of heating, unless it is taken that we are talking about concrete
instances of fire, in which case the whole essence of a particular fire
can be expressed in the middle term, thus: "Every hot thing is
capable of heating, every concrete instance of fire is (essentially) a
hot thing, therefore every concrete instance of fire is capable of
heating." This is as close as Ockham gets to Thomas's notion of
the highest sort of demonstration.




For Ockham, a demonstration arising from natural efficient causes
takes the following pattern: "When there is no opaque medium
between the moon and the sun, the moon will be illuminated by the sun,
when the moon is in such a place, there will be no opaque medium
between the moon and the sun; therefore the moon is then
illuminated." Here, the attribute "illuminable," an
attribute predicated of its subject without further determination, is
indemonstrable, but the attribute "illuminated when in such a
place" is predicated of its subject with a further determination,
and so can be demonstrated. This form of demonstration agrees closely
with the highest form of demonstration in Albert and Giles of Rome, but
Ockham does not regard it as demonstration of the highest sort, since
its conclusion is hypothetical rather than categorical.




Ockham did not allow any demonstration from final causes on the
pattern of Grosseteste's demonstration of a material from a formal
definition of an attribute, because he did not think that final causes
have any genuine productive power. When a final cause is identified,
the causal power involved is always the efficient causal power of some
agent with a purpose in mind. This raised a problem with the account of
the science of demonstration Ockham inherited from Grosseteste.
Grosseteste expected the science of demonstration to argue from the
function of demonstration to the material structure required to realize
that function. The procedure seems inadmissible to Ockham, since it
does not follow the path of actual (efficient) causation. Thus the
demonstrations making up the science of demonstration seem to be
illegitimate. Ockham responds to this problem by holding on to the
formal structure that Grosseteste had identified for the science of
demonstration, but making demonstration follow the natural (and
reliably functional) efficient causal path from knowledge of its
premisses to knowledge of its conclusion. Thus the conclusion that a
demonstration has necessary premisses cannot be drawn concerning
demonstration defined in terms of its purpose, but only for
demonstration defined in such a way that that sort of thing actually
produces knowledge. So the definition will be "a syllogism with
necessary premisses etc," which, as it happens, supposits for the
same things as "syllogism intended by the artisan, the logician,
to produce knowledge." It is as though we were to define an axe
by describing those aspects of its structure responsible for its
functionality (a handle of a certain shape, a head made of iron with a
sharp edge, etc.), and then deducing from this structure that it will
actually serve that function (actually cut wood) under the right
conditions, and then applying this piece of natural science to the
practical issue by giving the advice to use an axe so defined in the
appropriate way when one wants to cut wood.


## 7. Knowledge of First Principles




It is no doubt clear at this point that a large part of the question
how we gain natural knowledge has not yet been treated, for we have not
yet discussed how it is one acquires knowledge of the first principles
that enter into demonstration. Grosseteste allowed two forms of
knowledge. In first principles per se in the first way (so that the
predicate is contained in the subject) he suggested that through
sensory experience of particulars of a natural kind, one's intellect is
aroused, and comes to a vision of the real nature of the thing which is
expressed in the real definition of the subject. (Aquinas has a similar
view concerning the first principles of a demonstration of the highest
sort. With acquaintance with the real definition of a substantial
nature, one can simply see, intellectually, what its immediate powers
are.) Since the predicate is contained in the subject, once we have a
real definition of the subject in hand, we simply see that the first
principle is true. Roughly speaking, we will simply see what functions
a natural thing has once we understand what it is formally, though we
will not yet see how it manages to execute those functions.




How it executes those functions is expressed in principles per se in
the second way, so that the subject is somehow implicated in the
predicate. It is in these first principles that natural causes are
expressed. Grosseteste supposes that we have a faculty,
*aestimatio*, parallel to the senses, which enables us to simply
see a particular causal connection. This faculty is no more infallible
than are the senses, but after a number of such experiences of a causal
relation the intellect will be aroused, and will begin to seek actively
whether the apparent causal connection is real or not. To do this, it
will attempt to produce experiences in which the apparent cause is
present, but nothing else that might be a cause is. If the effect is
produced in such situations, it will then conclude the first principle,
which will assert the material definition of the attribute to its
formal definition. For instance, through experience we might note that
thunder is caused by the extinction of fire, and express this in the
principle that thunder, considered formally (as a noise in a cloud,
perhaps with a certain function of frightening those in Hades), is in
fact the same as noise in a cloud produced by the extinction of fire
(the material realization of this function of frightening by a loud
noise). Or we might note that anger (as the desire to harm someone) is
in fact, in this world, the same thing as the boiling of blood around
the heart (the material conditions for its realization). Thus he takes
causal principles to describe how a form is realized (made actual)
given certain material resources. To see what material resources in
fact realize the form, sensory experience, aided by reason, is
needed.




Aquinas, it is to be noted, holds that we know all the principles of
a demonstration of the highest sort through an intellectual vision of
the substantial nature of the subject, for this tells us the real
definition, and so reveals the minor premise, per se in the first way,
and it also enables us to see, through the intellect, what primary
attribute arises through *emanatio* from such a thing. Like
Grosseteste, Aquinas thinks that the causal capacities of things (their
functions) must be understood to know what they are, but he sees no
problem in working out how these forms do what they do within the
actual world. In the case of the highest form of demonstration, they
simply *do* it. It is as though we were to say that an adding
machine adds, without concerning ourselves how it must be designed to
do so. Of course, real natural substances are simple, and artificial
things like adding machines are not. An adding machine adds because of
the way it is put together, but it is absurd to say that heat heats or
a person knows, because of the way it is put together, for it is
*not* put together. There must be something for which simply to
exist is to exercise its function, or else we have an infinite regress,
and must explain every functioning as though it were the functioning of
a complex machine, without ever settling on simple parts for the
machine which simply function as they do because of what they are. It
is Aquinas who lies behind Descartes's view that first principles in
the sciences are clearly and distinctly perceived by reason.




Duns Scotus seems to have retained Grosseteste's empiricist bent.
Some causal principles are known per se, for instance, that an opaque
thing placed between something illuminated and its light source will
block the light and leave that thing in the dark. Here, anyone who
knows the definitions of the terms (in the example, of
'opaque') can work out the principle from there. But, like
Grosseteste, he also thought some principles can only be discovered
through experience. So he advances the notion that
"Whatever occurs in many instances by a cause that is not
free is the natural effect of that cause." He seems to assume
that a sufficient number of observations will lead to cases in which
the cause fails, if it ever does. In any case, this seems to continue
Grosseteste's empiricist tendencies, for he apparently assumes that a
simple substance must be observed to function before one can conclude
through reason that it functions as it does. Aquinas would no doubt
say that such observation of the immediate functioning of a simple
substance is necessary in order to acquire a concept of its
substantial nature, and so its real definition. A real definition of a
substance will specify its natural effect, and we do not infer its
functioning from experience, but rather use experience to abstract its
real definition.




Ockham thought that the causal power of a most specific natural kind
(*infima species*) can be known through the observation of a
single instance. So the curative power of an herb, or the ability of
heat to produce heat in something adjacent to it, can be concluded by
reason from a single instance. The principle at work here states that
everything in a given most specific natural kind which acts produces
effects of the same kind. He thus seems to refer to a version of the
uniformity of nature. He is perfectly clear that the real definition of
a simple substance, since it does not signify anything outside the
substance, cannot tell us what its effects are. Here we find the roots
of Early Modern Empiricism.