Stanford University

Richard Kilvington (Stanford Encyclopedia of Philosophy)

1. Life and Works

Richard Kilvington (we know almost seventy different spellings of his
name) was born at the beginning of the fourteenth century in the
village of Kilvington, Yorkshire. He was the son of a priest from the
diocese of York. He studied at Oxford, where he became Master of Arts
(1324/25) then Doctor of Theology (ca. 1335) (for bibliographical
details, see Kretzmann and Kretzmann 1990b, Jung-Palczewska 2000b).
His academic career was followed by a diplomatic and an ecclesiastical
one, working in the service of Edward III and taking part in
diplomatic missions. His career culminated in his appointment as Dean
of St. Paul’s Cathedral in London. Along with Richard Fitzralph,
Kilvington was involved in the battle against the mendicant friars, an
argument that continued almost until his death in 1361.

Other than a few sermons, all of Kilvington’s known works stem
from his lectures at Oxford. None is written in the usual commentary
fashion, following the order of books in the respective works of
Aristotle. In accordance with the fourteenth-century Oxford practice,
the number of topics discussed was reduced to certain central issues,
which were fully developed with no more than ten questions in each
set. The reduction in the range of topics is counterbalanced by deeper
analysis in the questions chosen for treatment. Some of
Kilvington’s questions cover fifteen folios, which in a modern
edition yield about 120 pages. His philosophical works, the
Sophismata and Quaestiones super De generatione et
, composed before 1325, came from his lectures as a
Bachelor of Arts; the Quaestiones super Physicam (1325/26)
and Quaestiones super Libros Ethicorum (1326/32) date from
his time as an Arts Master; after he advanced to the Faculty of
Theology, he produced ten questions on Peter Lombard’s
Sentences, composed before 1334. Of these works, only the
Sophismata has been edited, translated, and studied in full
(see Kretzmann and Kretzmann 1990a-b; for the titles of other
questions and their manuscripts, see Jung-Palczewska 2000b).

2. Method in Science

Like many other English thinkers, Kilvington was a leader in three
main disciplines: terminist logic, mathematical physics, and the new
theology. Methods and insights developed in the first two disciplines
were used in the third. The application of the terminist logic and the
refutation of the Aristotelian prohibition against metabasis
resulted in Kilvington’s broad use of logic and mathematics in
all branches of scientific inquiry to emphasize certitude in knowledge
and bring into play four types of measurement. The predominant form of
measurement by limit, i.e., by the beginning and ending of successive
or permanent things (incipit/desinit), by the first and last
instants of the beginning and ending of continuous processes (de
primo et ultimo instanti
), and by the intrinsic and extrinsic
limits of capacities of passive and active potencies (de maximo et
), does not appear to be straightforwardly mathematical,
though it raises mathematical considerations insofar as it prescribes
measure for natural processes. The second type of measurement, by
latitude of forms, describes processes in which accidental forms or
qualities are intensified or diminished in terms of the distribution
of natural qualities such as heat or whiteness or moral qualities such
as love, grace, sin, will, or desire. In his measurement of the
intension and remission of forms, Kilvington is interested in
determining how the highest degree of a quality can be introduced into
a subject already possessing the same quality to a certain degree by
undergoing an alteration, and consequently in establishing the
possibility of a most intense or diminished degree of, e.g., heat and
cold, or virtue and vice. The third type of measurement, the strictly
mathematical, employs a new calculus of compounding ratios to measure
speed in local motion or speed in the distribution of love. Finally,
the fourth type of measurement describes a ‘rule’
permitting the comparison of infinities, treated as infinite sets
containing infinite subsets, and determining which of them is equal,
less, or greater.

Kilvington employs all types of measurement to describe events both
real and imaginable. Having adopted Ockham’s ontological
minimalism, Kilvington claims that absolutes, i.e., substances and
qualities, are the only subjects that can be changed. Therefore, no
term used to describe change, such as motion, time,
latitude, and degree has any representation in
reality. Thus, he contrasts things that are really distinct with
things distinguishable only in reason, i.e., in the imagination.
Imaginary cases are descriptions of hypothetical situations. The
elements of the description and not the situation itself are, in fact,
of primary concern for Kilvington. He is interested in the coherence
of a theory that describes all imaginable cases and not in one that
describes only observable phenomena; to be imaginable means to be
possible, i.e., not to generate a contradiction. Everything imaginable
must be logically possible within a natural framework. Therefore,
although we can imagine a void and formulate rules of motion in it, we
can only say that a void might have existed if created by God’s
absolute power, though it does not actually exist anywhere in the

There are four levels in Kilvington’s secundum
analyses. These levels may be classified according
to their increasing abstraction and decreasing probability. On the
first level, there are imaginary cases which are potentially
observable and which might occur in nature, such as Socrates’
becoming white. On the second level are imaginary cases which cannot
be observed, even though they belong to the natural order. These cases
illustrate the necessary consequences of the application of rules
properly describing natural phenomena—the best example being
Earth’s rectilinear motion, which is caused by its desire to
unite the center of gravity with its own center. On the third level
are cases not observable but theoretically possible, such as reaching
infinite speed in an instant. The fourth level concerns cases that are
only theoretically possible. Kilvington uses the last two groups of
imaginable, i.e., hypothetical cases to reveal inconsistencies in
received theories, especially from Aristotle, demonstrating
mathematically the paradoxes that arise from Aristotle’s laws of
motion. If hypothetical cases do not involve contradiction, there is
no reason to reject them or exclude them from the realm of

Kilvington’s secundum imaginationem analyses go
together with his ceteris paribus method: he assumes that all
circumstances in the case being considered are the same, and that only
one factor, which changes during the process, causes changes in the

3. Logic

Kilvington’s Sophismata, written before 1325, is his
only logical work. A sophisma or sophism is neither a
standard paradox of disputation nor a sophistical argument but a
statement the truth of which is in question. The first sophism
Kilvington discusses typifies the basic structure: a statement of the
sophism sentence followed by a case or hypothesis, arguments for and
against the sophism sentence, the resolution of the sophism sentence
and reply to the arguments on the opposing side, ending with an
introduction to the next sophism sentence.

Kilvington’s sophisms are meant to be of logical interest, but
they also pose important questions in physics or natural philosophy.
In constructing his sophisms, Kilvington sometimes makes use of
observable physical motion and at other times appeals to imaginable
cases that have no reference to outside reality. Although the latter
cases are impossible physically, they are theoretically possible,
i.e., they do not involve a formal contradiction. At one point he

Even though the hypothesis supposed there is impossible in
fact…it is nevertheless possible per se; and for purposes of
the sophism, that is enough.

[unde licet casus idem positus sit impossibilis de
facto…tamen per se possibilis est; et hoc sufficit pro
] (S29: 69; tr. Kretzmann and Kretzmann 1990b:

The first eleven sophisms deal with the process of whitening, in which
the motion of alteration is conceived as a successive entity
extrinsically limited at its beginning and end. There is no first
instant of alteration, claims Kilvington, but only a last instant
before the alteration begins; likewise, there is no last instant of
alteration, but only the first instant at which the final degree has
been introduced. There is no minimum degree of whiteness or speed
gained in motion, but rather smaller and smaller degrees ad infinitum
down to zero, since the qualities change continuously. Integers are
potentially infinite because one can always find a higher integer, but
not actually infinite since there is no single infinite number. In
Kilvington’s view, since any continuity—e.g., time, space,
motion, heat, whiteness—is infinitely divisible, it can be
spoken of quantitatively and measured in terms of infinite sets of
integers. The subjects of sophisms 29–44 reveal
Kilvington’s special interest in local motion with respect to
causes, i.e., active and passive potencies, and effects, i.e., time,
distance traversed, and speed in motion. He considers both uniform and
difform motion caused by voluntary agents and points out the
questionable measure of instantaneous speed through the comparison of
speed in uniform and accelerated motion (see Kretzmann 1982)

The last four sophisms are ostensibly connected with epistemology and
the logic of knowledge, i.e., sentences on knowing and doubting
involving intentional contexts, such as S45: “You know this to
be everything that is this”. The most interesting among them is
S47, “You know that the king is seated”, where Kilvington
calls some rules of obligational disputation into question (see
Kretzmann and Kretzmann 1990: 330—47; d’Ors 1991). In the
opinion of Stump, “what Kilvington has done in his work on S47,
by his change in the rule for irrelevant propositions, is to shift the
whole purpose of obligations” (Stump 1982: 332).

4. Natural Philosophy

Although, Kilvington does not enjoy the reputation in natural
philosophy that he does in logic, recent research reveal that his
questions on Aristotle’s De generatione et corruptione
and Physics inspired Thomas Bradwardine’s theory of
motion and his famous rule of velocities in motion (see
Jung-[Palczewska] 2000b; Jung 2002a; 2002b). Both works stemmed from
lectures Kilvington delivered in the Arts Faculty before 1328, i.e.,
before Bradwardine’s treatise On the Proportion or
Proportions of Velocities in Motions

Like most medieval natural philosophers, Kilvington accepts
Aristotle’s general rules of motion:

  1. “everything that is moved is moved by another”;
  2. “there cannot be a motion without an active capacity
    (virtus motiva) and a passive capacity (virtus
    )”, because without resistance, motion would not
    be temporal.

While accepting substance and quality as the only two absolute
realities, Kilvington states that the reality of motion is limited to
what is in motion: the places, qualities, and quantities it
successively acquires. Consequently, he is more interested in
measuring local motion in terms of the actions of the causes of
motion, the distance traversed, and the time consumed, than in the
intensity of speed. In his commentaries on De generatione et
and the Physics, Kilvington tries to
formulate the differences between generation, alteration, and
augmentation; determine rules for actions that are causes of change;
find rules for the division of different types of continua;
and find a mathematically coherent rule of motion. He considers the
problem of the motion of two angels with regard to its causes and
effects in several ways: how is their power to be bounded if it is
active or passive? Is it subject to weakening? Is it mutable or
immutable? How do we determine the boundaries of an active potency if
a body moves in a medium that is uniformly resistant or not uniformly

Kilvington’s discussion of the measure of motion with respect to
causes, or what we would call his ‘dynamic’ analysis, has
a physical aspect involving relations between forces and resistances,
and a mathematical aspect, involving concepts of continuity and
limits. The mathematical character of Kilvington’s theory can be
seen in his use of two kinds of limit for continuous sequences: an
intrinsic boundary (when an element is a member of the sequence of
elements it bounds: maximum quod sic, minimum quod sic) and
an extrinsic boundary (when an element which serves as a boundary
stands outside the range of elements which it bounds: maximum quod
non, minimum quod non
). Although he did not formulate strict
rules about the different types of division of continua, his
‘study cases’ reveal that he approved the following
conditions for the existence of limits:

  1. There must be a range in which the capacity can act or be acted
    on, and another range in which it cannot act or be acted on; and
  2. The capacity should be capable of taking on a continuous range of
    values between zero and the value which serves as its boundary, and no
    other values.

According to Aristotle (Physics VIII), motion occurs only if
the ratio of acting capacity (a force F) to passive capacity (a
resistance R) is a ratio of major inequality, i.e., when it is
greater than 1. Kilvington affirms that every excess of force over
resistance suffices for motion; thus, whenever force is greater than
resistance, there is motion. This assumes that force (an active
capacity) is bounded by a minimum upon which it cannot act
(minimum quod non), i.e., by the resistance that is equal to
it. For a passive capacity of resistance, Kilvington accepts the
minimum quod sic limit “with respect to
circumstances”; he agrees with Aristotle and claims that to
establish a passive limit for Socrates’ capacity of vision, we
should point to the smallest thing he can see. However, it is not only
that we cannot see a small thing, like a grain, but also a large one,
such as a cathedral, if we are close to it. Therefore, passive
capacity cannot be described by a minimum quod non limit in
each case.

It seems that Kilvington’s belief in the potential power of
mathematics also allowed him to formulate a new rule of motion. He
agrees that the proper way of measuring the speed of motion is to
describe its variations by a double ratio of force (F) and
resistance (R) as defined by Euclid. Speed of motion thus
varies arithmetically whereas the proportion of force to resistance
determining these speeds varies geometrically. Thus, when the
proportion of force to resistance is squared, the speed will be
doubled. Kilvington is aware that the proper understanding of
Euclid’s definition necessitates a new interpretation of
Aristotle’s rules of motion and concludes that when he is
talking about a power moving half of a mobile, Aristotle means
precisely the subdouble ratio of F to R, but when he is
talking about power moving a mobile twice as heavy, he means the
square of the ratio of F to R. Kilvington’s
function provided values of the ratio of F to R greater
that 1:1 for any speed down to zero, since any root of a ratio greater
that 1:1 is always a ratio greater that 1:1. He thereby avoids a
serious weakness in Aristotle’s theory, which cannot explain the
mathematical relationship of F to R in very slow

Kilvington applies his new rule of motion to describe both natural and
violent motion, such as the uniform and difform motions of mixed
bodies and the motion of simple bodies both in a medium and in a
vacuum. Reading Kilvington, we must keep in mind that temporal motion
is possible only if there is some resistance playing the role of a
virtus impeditiva. The simplest example is the violent and
natural motion of a mixed body in a medium, when the acting power has
to overcome the external resistance of the medium as well as the
internal resistance of an element being moved away from its natural
place. The local motion of a simple body in a medium is not
problematic either, since it can be explained by its natural desire to
attain the natural place determined by its heaviness or lightness and
the external resistance. Nor does Kilvington have a problem with
explaining the natural motion of a mixed body in a vacuum, which is
caused by the relative levity and gravity of its elements. Since there
is no external resistance in a void, only internal resistance can
permit motion in time. Kilvington here seems to follow Ockham, who
argued that if a void existed, it would be a place. Since place in the
Aristotelian sense is something natural that has essential qualities,
it determines the natural motion of elementary bodies and, moreover,
their inclination to remain at rest in their natural place.
Accordingly, one could imagine a void in four natural spheres, which
although empty preserve the proper qualities characteristic of the
natural places of earth, water, air, and fire. Hence, the temporal
motion of a mixed body in such a void is the result of the natural
inclination of heavy or light elements to move to their natural
places. The heaviness and lightness play the roles of force and
resistance, respectively. Although there would be no external
resistance in a vacuum, the motion of a mixed body could occur without
any difficulty.

Kilvington’s most perplexing explanation concerns temporal
motion of a simple body in a vacuum. In the opinion of Averroes, a
simple body such as a piece of earth has an elementary form, prime
matter, and different quantitative parts because it can be divided
into parts. Because form cannot resist matter, no resistance can come
from its qualitative parts. But there can be resistance from its
quantitative parts resisting one another. Kilvington maintains that
the temporal motion of a simple body in a vacuum is made possible by
the internal resistance that results when the peripheral parts of a
simple body offer resistance to the central parts because each part is
seeking the center. Such an internal resistance produces motion and
does not impede it; nevertheless, it guarantees temporal motion.
Consequently, if a vacuum existed, the natural motion of a simple body
would be possible. Moreover, the speed of such a motion would be the
fastest, since there is no resistance to be overcome.

In the dynamic aspect of motion, when the speed is proportional to the
F to R ratio, one only determines its value in an
instant. Like all later Calculators, Kilvington does not consider
speed to be a quality, so there is no real, existential referent for
instantaneous speed. Therefore, speed has to be measured by distances,
latitudes of quality (formal distance), or quantities traversed, and
such traversals take time unless the speed is infinite. In order to
characterize changes in the speed of motion, one must analyze the
problem of local motion in its kinematic aspect. Kilvington’s
discussion of the measure of motion with respect to its effect
concentrates on measuring motion by such quantities as distance
traversed and time. His attempt to understand the effect of motion as
caused by smaller and greater resistances brings him to a distinction,
also made by Bradwardine, between the rarity and density of a medium,
which causes motion to be fast or slow, and its extent, determining a
longer or shorter time consumed in motion. Kilvington correctly
recognizes that to measure the speed of a uniform motion that lasts
some time, it is enough to establish relations between time and
distance traversed. In his opinion, the same distances traversed in
equal intervals of time characterize uniform motion. Accelerated
motion is described by the same distance traversed in a shorter
interval of time, and decelerated motion is characterized by the same
distance traversed in a longer time. It is also possible to describe
difform motion by, for example, unequal distances traversed in unequal
intervals of time.

Although Kilvington never abandoned Aristotelian physics, he
frequently goes beyond Aristotle’s theories in order to resolve
the paradoxes resulting from his laws, creating the impression that
behind the facade of Aristotelian principles and terms, Kilvington is
an Ockhamist. Despite the fact that Kilvington never explicitly
mentions Ockham, it is beyond doubt that he not only knew the opinions
of the Venerable Inceptor but also accepted them as a natural way of
understanding the works of the Philosopher.

5. Ethics

The third Aristotelian work on which Richard Kilvington commented
during his regency in the Arts Faculty was the Nicomachean
. The commentary on the second and tenth books of the
Ethics takes a form of ten questions, which deal only with
selected issues that were the subjects of Kilvington’s lectures
at Oxford: e.g., creating and destroying moral virtue, free acts of
volition, the behavior of honest people and the delight taken in their
actions (or conversely, the punishment of those who act evilly), and
questions concerning particular virtues such as courage, generosity,
magnanimity, justice, and prudence. As Michałowska has shown,
Kilvington uses terminist logic and mathematical physics to solve
ethical problems (see Michałowska 2011, 2016). Michałowska
also shows that, just as he did in his questions on the
Physics, Kilvington follows Ockham’s minimalist ontology
by treating ethical qualities—i.e., vices and virtues, cognition
and wisdom, good and evil—as volition-like objects, calling them
the res. Being real things and not merely mental concepts, they
can be measured by addition, subtraction, and division into parts, for
they undergo change via increase or decrease and so have varying
degrees of intensity. Such changes—e.g., undergoing punishment
for an evil act—cannot be instantaneous and must happen in time.
Each change is the result of overcoming resistance by an acting power.
In the case of moral acts, the changes do not produce any external
effects but internal modification in terms of the intensity of virtues
and vices. When a vice acts upon a virtue, it causes its continuous
change, and so a man’s courage can vary in intensity. Virtues
and vices are opposed in Kilvington’s physical theory, so it is
impossible for a man to be vicious and virtuous at the same time,
although it is possible for him to be generous at one time, miserly at

The increase or decrease of a moral quality is either an effect of the
impact of the opposite quality (or a change in the degree of intensity
of the same quality), or else the result of human external acts. For
example, frequent generous actions towards others leads to an increase
of generosity. Performing morally good actions intensifies the
virtues, whereas the constant practice of evil diminishes them.
Virtues and vices can be described in terms of different degrees of
intensity, so one can say that a man can be more or less generous
during his lifetime. And just like physical qualities, Kilvington
states that the intensity of a moral quality has only an extrinsic
limit, so that one cannot perfect one’s virtue infinitely.

Virtues and vices have absolute or relative character, and can be
possessed absolutely (simpliciter) or in a certain respect
(secundum quid). There are highest—i.e., most
perfect—degrees of intensity of our moral virtues, but there are
no absolutely greatest degrees, like Platonic ideas. In
Kilvington’s opinion, a man is never absolutely generous or
virtuous. The ultimate perfection, i.e., the highest degree of moral
virtue, is the product of a man’s natural dispositions,
socializations, and moral acts. But since people relevantly differ,
each of us is virtuous in our own way. So too, the highest degree of
moral virtue is unique in each of us. In Kilvington’s opinion,
if a man is prudent in the highest degree, he must have all other
virtues in the highest degree as well (see Michałowska 2011,

For Kilvington, prudence is one of the primary virtues. It is a habit,
which cooperates with right reason (recta ratio) in the process
of making good or bad decisions. Even though Ockham is not mentioned
by name, his theory of the relation between prudence and moral
knowledge is present in Kilvington’s discussion. Ockham
distinguishes two types of moral knowledge. The first, which concerns
universal truths, is gained through learning; the second, which
concerns particular statements and particular situations, is gained
through experience. Prudence is understood in two ways: as knowledge
about singular propositions and as universal practical knowledge. In
his opinion, both types of prudence are gained only through
experience, the former concerning singular statements and the latter
universal practical statements. The former is properly called
prudence, whereas the latter is commonly known as prudence. In
Ockham’s view, the first kind of knowledge—i.e., of
universal truths—must be distinguished from prudence concerning
singular statements. The second type of knowledge, however, is the
same as prudence, since it is also gained through experience
(Quaestiones q.6, a.10). Kilvington identifies two kinds of
moral knowledge. The first is called scientia necessaria, which
is composed of general statements and refers to universal truth. The
other is called scientia ad utrumlibet, which comprises
particular statements. The scientia necessaria, achieved by
means of deduction, is not sufficient to make good moral decisions and
so it must be complemented by a reference to scientia ad
, achieved by experience (see Michałowska 2016,
13). Gaining knowledge through experience is an indispensable part
becoming prudent. Kilvington states that a man can err with regard to
a moral choice even though he possesses certain and complete knowledge
about universal moral truths; a skilled logician is not necessarily a
moral person. To make good moral decisions, one needs a
fully-developed prudence, which is the same as scientia ad
. Kilvington claims that a man who possesses moral
knowledge is not automatically prudent, but a prudent man is always
wise (see Michałowska/Jung 2010, 109–111).

Good choices are possible only when the will is supported by prudence.
The problem of free will and free choice is fully elaborated in
Kilvington’s Ethics, where he presents his
theory—what Michałowska calls a “dynamic
voluntarism”. Kilvington distinguishes three types of human
volitional acts: willing, nilling, and not-willing. Willing always
wills, and can never be passive or in potency. Even when the will
wants nothing (velle nihil), it is willing, and so it cannot
rest and is always determined to an act of willing. Here Kilvington
seems to be directly influenced by Scotus, who claims that the will
cannot be suspended (Ord. I d.1). The will is absolutely free
in its acts of willing, and the free will of volition is the primary
principle in the genus of contingent propositions. Since the will is
active all the time, it must decide between its three acts of volition
(velle volitionem), nolition (velle nolitionem), or
non-velle. With regard to its own internal acts, the will is
absolutely free. With regard to its external acts, however, it chooses
between wanting something (velle aliquid) and not wanting
something (nolle aliquid). In these cases, the will is also
absolutely free to make such a choice.

For Kilvington it is obvious that prudence plays an essential role in
producing good moral acts. When the habit of prudence is not fully
developed, the will is indecisive. Repeated good moral decisions makes
it hesitate (non-velle) less, so that the agent is able to
reach a decision in any context, whether affirmatively velle or
negatively nolle. Supported by fully developed prudence, the
will makes proper and good moral choices more easily or even
effortlessly (see Michałowska 2016, 14). Kilvington, however, is
of the opinion that most of us rarely make good moral decisions
because we often remain in doubt, stuck in the state of

6. Theology

In theology, Kilvington applied the new methods of terminist logic and
mathematical physics to typical fourteenth-century topics such as
human and divine love, fruition, human will and freedom, God’s
absolute and ordained power, and divine knowledge of future
contingents. Nothing is considered separately from the Creator;
therefore, Kilvington relates each human action to God.

Kilvington accepts Scotus’s distinction (Ord. I, d. 44,
q. u.) between the absolute and ordained power of God. The established
order of nature is the result of God’s ordained power, but God
can also act against this order by his absolute power:

God’s power is called ordained insofar as it is a principle for
doing something in conformity with a right law with regard to the
established order. God’s power is called absolute insofar as it
exceeds God’s ordained power, because thanks to it he can act
against the established order. The jurists commonly use the terms
de facto and de iure, e.g., they say that a king can
do de facto anything that is not in accord with ordained

Although Scotus never explicitly says that God’s ordained and
absolute power can be considered separately, that is how Kilvington
interprets him, as he proceeds to claim that

  1. God’s powers are intensively infinite simpliciter,
  2. God’s absolute power is infinitely greater than, i.e.,
    infinitely more powerful than, his ordained power, since it is only by
    his absolute power that God could have annihilated the world.

The world’s annihilation would not be less just than its
continued existence, since God’s justice stems from his essence,
which, like his power, is absolute and ordained. There are also
actual, ‘dependent’ (secundum quid)
infinities created by God, such as the intensively infinite capacity
of the human soul to love, to experience joy, and to suffer.

Like Scotus, Kilvington is convinced that potentia dei
is a power that really is or can be actualized by God.
Miracles would be examples of God acting against the natural order.
Individual situations also show that God can deviate from laws
established in the natural order, reflecting God’s particular
judgment. But in his Sentences commentary, there are also
many places where Kilvington follows the Ockhamist conception of
absolute power in terms of logical possibility, i.e., hypothetical
situations that have never become actual. Nevertheless, Kilvington
criticizes Ockham (Tractatus contra Benedictum III, 3) when
he analyzes hypothetical, imaginary cases (potentia dei
) ruled by logic alone, in which the only principle that
must be followed is that of non-contradiction.

Kilvington’s theory of potentia dei absoluta et
serves to underline the contingency of creation and the
freedom of divine will. Here Kilvington abridges Scotus’s
opinions (Lectura I, dist. 39) and reorders his arguments,
taking into account only those most useful for his own theory.
Kilvington formulates nine conclusions in order to ‘save the
phenomena’ and emphasize God’s absolute freedom of choice.
He claims that God’s knowledge, existence, and will are the same
as God’s essence. However, with regard to God’s absolute
knowledge, assertoric statements about the past and present and
contingent statements about the future have the same certitude since
they are absolutely necessary, whereas with regard to the God’s
ordained knowledge, they have only ordained necessity. Everything
revealed absolutely by God happens necessarily with absolute
necessity, because otherwise he could make himself incapable of
picking up a stick, and this is a contradiction. Everything revealed
by God’s ordained power—e.g., articles of
faith—depends on God’s will and could be changed. Once
revealed, however, they would have ordained necessity, and so they
would form a new law. Everything that does not depend on God’s
free will comes with ordained necessity, but nothing that depends on
God’s free choice is absolutely revealed by God’s ordained
power. If something is revealed absolutely, it is absolutely credible,
because such a revelation derives from ordained necessity. If
something is revealed under conditions, it is certain only with regard
to those conditions.

Kilvington’s affinity to Scotus may also be seen in his
conception of future contingents. He is in agreement with Scotus
(Lectura I, dist. 39, qq. 1–5) in saying that only an
instant in time is present since only ‘now’ exists.
Therefore, Aquinas’s analogy to God sitting at the center of a
circle and being present with all time fails, whereas Scotus’s
concept of a radius sweeping out the circumference of the circle is
correct, since the entire circle does not exist all at once.
Consequently, ‘now’ moves from past to future like a point
on the circumference of a circle. Kilvington, like Scotus, also
rejects the view that God knows future contingents via Ideas because
Ideas necessarily represent what they represent, as in the sentence,
“Socrates is Artus”, where it is said that Socrates is
Artus. Although Kilvington does not explain his position clearly, it
seems that he takes for granted Scotus’s explanation. Scotus
says that perhaps Ideas could represent simple or complexes terms
necessarily, although, as Chris Schabel puts it:

They could not represent contingent complexes (…), which we can
call X. If God had the Idea only, eternally he would know only
the part of a contradiction, and there would be no contingency. If He
knew both parts, X and ~X , He would know
contradictories to be true simultaneously. Second, since Ideas
represent both futures that are possible but will not exist, and
futures that are possible and will exist, one needs to posit a way to
distinguish between what will exist and what will not exist. (Schabel
2000, 42)

Kilvington is also in agreement with Scotus when he says that
secondary causes cannot originate any contingency because of the
necessity in a chain of causes. Therefore, a contingency observed in
the action of secondary causes must be routed to the first cause,
which is God. To know contingents, God first has to choose one of two
contrary statements, since otherwise, i.e., when God had an act of
knowledge before his act of will, he would have had only necessary
ordained knowledge about natural order, which he already established,
and he would not know contingents. Consequently, God would have only
partial knowledge about one side of a contradiction (i.e., he would
know only one of two contradictory statements, e.g., “Antichrist
will be” or “Antichrist will not be”), and his will
would not be absolutely free. Therefore, contingency must be placed in
God’s will and not in God’s intellect. Again following
Scotus, Kilvington claims that at the same instant in which the divine
will wills A, it is able not to will A. Like Ockham,
Kilvington accepts Scotus’s synchronic contingency. Again, as
Chris Schabel writes:

This is not to say that God’s determinate knowledge of the
proposition makes that proposition about future contingents as
determinately true as those about the past or present. For although in
the latter there is determinate truth—even necessary
truth—so that it is impossible for them to be false, with
respect to future contingents God’s determinate knowledge is
such that allows for enough indetermination that it is still in the
power of their cause to do the opposite. In the whole process of
divine willing and knowing there is no time involved and no discursive
knowledge. (Schabel 2000, 45)

To save God’s absolute free will and at the same time to avoid
the prospect of mutability in God’s decision-making, Kilvington
asserts that by his absolute power God can make himself not to will
A, while A is what God, by his ordained power, wills in
that particular instant, and this happens in eternity. This argument
proves that there is no change in God’s will. In the opinion of
Kilvington, future contingent events are such because God knows that
they are future contingent and not vice versa. God’s accepting
(beneplacitum) will, with respect to future contingents, is
naturally prior to God’s knowledge, because the following
consequence is true, “God wants A to happen; therefore,
God knows it will happen,” whereas this is false, “God
knows it will happen (viz., that Socrates will sin); therefore, he
wants him to sin”.

In Kilvington’s commentary on Sentences, the opinions
of both Scotus and Ockham are much in evidence, as in
Kilvington’s other works. However, while Scotus is often cited
by name, Ockham remains in the background. Still, knowledge of both
Scotus and Ockham is crucial to understanding Kilvington’s
thought, as his own contributions are often the result of blending
these two strands of fourteenth-century Franciscan theology. A good
example is the concept of God’s absolute and ordained powers,
which serves Kilvington to prove that unequal infinities are present
not only in God but also in the created world.

6. Impact and Influence

Besides the particular topics he discussed, Kilvington’s
extensive use of sophisma argumentation, his mathematization
of ethics and theology, and his frequent use of hypothetical
(secundum imaginationem) cases, place his thought in the
mainstream of fourteenth-century English philosophy and theology. His
teachings on logic were influential both in England and on the
Continent. Richard Billingham, Roger Rosetus, William Heytesbury, Adam
Wodeham, Richard Swineshead were among the English scholars who
benefited from Kilvington’s Sophsimata. His
Quaestiones super De generatione et corruptione was quoted by
Richard Fitzralph, Adam Wodeham, and Blasius of Parma, and his
Quaestiones super Physicam was familiar to the next
generation of Oxford Calculators, John Dumbleton and Roger Swineshead
(who also may have influenced Parisian masters such as Nicolas Oresme
and John Buridan). But Thomas Bradwardine was perhaps the most famous
student of Kilvington’s theory of motion. In his renowned
treatise On the Ratios of Velocities in Motions, Bradwardine
included most of Kilvington’s arguments for a new function
describing the relation of motive power and resistance.
Kilvington’s views on future contingents were discussed by
masters at the University of Vienna in the first decade of the
fifteenth century such as Nicholas of Dinkelsbühl, John Berwart
of Villingen, Peter of Pulkau, and the Carmelite Arnold of Seehausen.
His questions on the Ethics and the Sentences
enjoyed a reputation not only in Oxford but also Paris and were
frequently quoted by Adam Junior, John of Mirecourt, Johanes de Burgo,
and Thomas of Krakow (see Jung-[Palczewska] 2000b).

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