## 1. Life and Work



Very little is known about Crathorn's life. He might have been
born in the village of Crathorne in north Yorkshire. He became a
Dominican friar before going to Oxford, where he lectured on the first
book of Peter the Lombard's *Sentences* in the years
1330-32, a work we can date because of a passage in which
Crathorn mentions an eclipse that we know occurred on July 16, 1330.
His Dominican contemporary, Robert Holkot, also tells us that that he
lectured at the same time (1331-33) as a Dominican named
Crathorn (Courtenay 1978; Schepers 1970 and 1972)



William Crathorn also lectured on the Bible, and Holkot is presumably
responding to Crathorn's arguments in his *Sex articuli*.
A manuscript in Vienna contains what could be Crathorn's
forty-two quodlibetal questions (Richter 1972), but most of these
questions are similar to the ones contained in his *Questions on
the Sentences* (*Quaestiones super librum
sententiarum*).


## 2. Relation to Other Scholars



Crathorn's *Sentences* commentary is of great
philosophical and historical interest for the study of the first
generation of Oxford thinkers after Ockham because he develops his own
provocative positions by discussing the major issues of his day and
criticizing the views of his contemporaries (Courtenay 1978, Gelber
2004). His favorite target was Ockham, but he also argued against the
views of Thomas Aquinas (Krauss 1933), John Duns Scotus, Richard
Fitzralph, and Robert Holkot (Schepers 1970, 1972).



Although Crathorn criticized Ockham, he remained a nominalist (he
admits only individuals in his ontology and subscribes to the same
kind of theory of predication as Ockham). Above all, he worked out
some of the consequences of Ockham's views in epistemology, the
philosophy of language, and ontology, to show what problems they
created. We do not know whether he knew Ockham personally, or only
indirectly, through his younger disciple, Adam Wodeham. Indeed,
Wodeham frequently refers to a Dominican *socius*, who could
have been Crathorn himself or a certain John Grafton, another Oxford
Dominican of this time.


## 3. Epistemology



The problem of knowledge is at the very heart of Crathorn's
thought. Going back to Roger Bacon, he held that the only way the
human mind is able to know the external world is through
*species* that resemble it (I *Sent.* q. 1, concl. 4).
Bacon's theory of the multiplication of species
(*multiplicatio specierum*) was developed to explain causality
using the model of optics. A thing *c* has an effect on another
thing *e* through the multiplication of species *s* from
*c* towards *e*, just as light is multiplied through the
air when it illuminates an object. According to Bacon, the species
*s* is a representative of *c* but with a lesser mode of
being. Thus, the species is multiplied through the medium of air again
and again until it arrives at *e*. The causal power of
*c* is in this way conserved through the medium until it acts
on *e*. The species is therefore both the cause (i.e., the same
thing as the cause but with a diminished mode of being) and a likeness
of that cause. Applying Bacon's theory to epistemology, Crathorn
asserts that we have no direct access to things in the external world
and that we immediately perceive only their mental likenesses or
representations, i.e., their species. These mental entities, whether
we call them 'species" or 'concepts" (the
terms are equivalent for Crathorn), have the same nature as the things
they resemble (*ibid.* concl. 8). Contrary to Bacon, the
Dominican considers that the species has the same mode of being
-- i.e., material being -- outside and inside the mind. As a
consequence, all the species we have in the mind belong to the
category of quality, for no real substance or quantity can exist
materially in the human soul. Since concepts can only belong to the
category of quality according to Crathorn, they must be mental
qualities having the same nature as non-mental qualities and they must
exist subjectively in the mind, which is to say that they exist in
some part of the brain (Pasnau 1997). Crathorn writes, "the word
'cognition' (*cognitio*) stands for the idea
(*verbum*) of the thing known, and that idea is the quality
existing subjectively (*subiective existens*) in the mind or in
some part of the brain" (I *Sent.* q. 1, concl. 1).
Therefore, cognition is nothing but the species itself or the part of
the soul where it is received and stored. From an ontological point of
view, nothing distinguishes sensible cognition, imagination and
intellection except the distinct part of the soul where the species is
received. There is no difference between sensible and intelligible
species.



Crathorn goes on to describe the different parts of the brain and
their functions. As the canonical medieval topology of the brain
suggests, there are three main lobes (*cellulae*) connected by
nerves through which the information conveyed by the species can be
transferred from one lobe to another. The first lobe corresponds to
sensitive imagination (*cellula fantastica*), the second to
conceptualization and discourse (*cellula syllogistica*) and
the third to memory (*cellula memoriale*) (I *Sent.* q.
2, concl. 4).



Crathorn thus had to emend Ockham's theory of evident knowledge,
because intuitive cognition is no more the guarantee of any certitude
regarding the existence of extramental things. In addition, the
cognition of the terms of a proposition -- even a *per se
nota* proposition -- is not sufficient, according to
Crathorn, to ensure the causal mechanism that leads to evidence and
certitude. Indeed, as we shall see below, Crathorn refuses to treat
the species or cognitions as linguistic elements of thought. All
languages are conventional by nature. Therefore, it is possible to
cognize some terms the signification of which remains unknown to the
cognizing subject. As a result, although empirical knowledge of the
things signified by the terms is usually needed, it is necessary to
argue beyond simple and intuitive cognitions, via syllogisms and
demonstrations, to consolidate one's certitude that not only
representations exist. Crathorn thus suggests that we substitute for
the Ockhamist definition of evident cognition his own definition:
evident cognition is a manifest, clear, and not obscure cognition (q.
1, p. 69-70: *notitia evidens est notitia manifesta, clara et
non obscura*), be it simple or complex, intuitive or
abstractive.



Incredibly, Crathorn affirms that whenever one is thinking of a white
thing, the mind of that person actually becomes white. His notion of
similarity is strict and uncompromising. Mental concepts cannot
resemble substances but only qualities of substances (I
*Sent*., q. 1, concl. 7) because the species of substance would
have to be a substance itself and our minds would turn into a new
substance if we thought of it. It also cannot be a pure quantity
because in thinking of infinite magnitudes, our minds would become
infinite, and the same is true for the other categories besides
quality. According to Crathorn, our ability to conceptualize is
therefore limited to natural concepts of qualities, which in being
conceived become qualities of the soul.



Crathorn had to face up to the skeptical consequences of this odd
epistemology. How can we know what is real if our only access to
reality is via representations of its qualitative features? His answer
to this question is quite radical: we cannot be naturally and directly
certain that reality exists as we conceive it since it is not possible
to distinguish qualities inside and outside the mind: as qualities,
they would have precisely the same nature (*ibid.* concl.
10-13). The only solution to skeptical doubt here is the
principle, which he claims is known *per se*, that God does not
produce an effect supernaturally in order to lie or to lead people
into error (*ibid.* q. 1, concl. 14), a principle more famously
used in connection with Descartes' thought experiment of a
*Dieu trompeur* several centuries later.



Crathorn endeavored elsewhere to gather at least a few certitudes,
since one could doubt whether the a priori principle that God would
never deceive us is itself certain. To rebut the skeptic, he turns
back to Augustine's version of the *cogito*-argument to
prove that we can at least be certain of our own mental activity, for
if one were to doubt a proposition such as 'I am', it
would follow that he exists, since he who does not exist does not
doubt. Hence, no one can be in doubt concerning the proposition,
'I am' (I *Sent*., q. 1, concl. 14; translated in
Tachau 1988, p. 273).


## 4. Philosophy of Language



One of the most important debates at Oxford around 1320-30
concerned the proper object of scientific knowledge. When we know
something scientifically, is our knowledge about external things (the
earth interposed between the sun and the moon), propositions
('The moon is eclipsed'), or some other more complex state
of affairs? Crathorn is believed to have participated in the
development of the idea that the proper object of science is neither
the external thing nor the proposition (as Ockham and Holkot had
argued), but the 'total significate' of that proposition
(Tachau 1987). Typically, the total significate would include not only
external things but also the premises and other assumptions that
generate our assent to the proposition as the conclusion of a piece of
demonstrative reasoning.



Another debate concerned the nature of mental language, specifically
whether it is conventional or natural (Gelber 1984; Panaccio 1996)
Ockham had argued that thinking occurs in a universal language made of
concepts acquired naturally, i.e. through natural relations of
causality and similitude. All conventional languages used for human
communication are subordinated to this mental language, which is
shared by everyone. But Crathorn could not accept such a position
because of his cognitive theory according to which there are only
qualities in the mind. So there can be natural signs of extra-mental
qualities. What about substance-terms (the equivalent of proper and
common names), verbs, and syncategorems, i.e., logical particles and
connectives such as 'or', 'but',
'all', and 'if'? Accordingly, Crathorn argues
that except for natural signs of qualities, no natural likeness in the
mind can explain the signification of these terms. Mental language is
therefore as conventional as spoken and written languages and is in
fact derived from conventional languages (I *Sent*., q. 2; Cf.
Panaccio 1996, Perler 1997, Robert 2009b and 2010b). Just as thought
depends on the *species* or likenesses of external things,
mental words are likenesses of conventional words and have exactly the
same semantic properties. Depending upon which language(s) you learn
to speak, your mental language will be a likeness of Latin, English,
French, etc. This does not mean that we do not have natural
representations of the external world, but these mental
*qualia* do not form a language. Crathorn was the only thinker
of his time to affirm that conventional words are prior to their
mental counterparts. Meaning is first given by a community of
speakers; mental language is simply the internalization of these
spoken and written languages. When we think about the world with
propositions and syllogisms, we always think in a conventional
language or, more precisely, in its mental reflection.


## 5. Ontology and Categories



In keeping with his views on knowledge and language, Crathorn
advocated radical changes to traditional Aristotelian ontology. These
are discussed in a sub-treatise on the categories in his
*Commentary on the Sentences* (I *Sent*. qq.
13-18).



Ockham famously reduced the ten Aristotelian categories to two,
substance and quality, treating the other eight as modes of signifying
substances and qualities. For Crathorn, however, the entire
Aristotelian system has to be revised. The human mind naturally knows
nothing but qualities, and we cannot be certain that even they exist
without appealing to the principle that God could not deceive us.
Thinking and reasoning are of no help because, as we saw above, they
are purely conventional.



Instead, Crathorn treats the Aristotelian categories as philosophical
conventions. Following the chapters of Aristotle's
*Categories* step by step, he comes to the conclusion that none
of the ten categories are valid because the reasons Aristotle uses to
distinguish them are inadequate. For example, the category of
substance is distinguished from the other categories by the fact that
it has no contrary and can successively acquire contrary qualities
(Aristotle, *Categories* 5). But Crathorn claims that when we
heat a piece of wood or a man, not only the substance but also its
qualities become hot, such that its qualities change from one state to
their contrary exactly like a substance. Therefore, this crucial
distinction between substance and accidents does not apply. Crathorn
writes, "not only the substance of the wood can receive the
contraries, but also the accidents of the wood ... but if the wood is
hot, not only is the heat attached to the wood hot, but also all the
positive coextensive natures of the wood" (I *Sent*., q.
13, concl. 13). He also affirms that "one and the same thing
numerically can truly be said to be substance and accident in relation
to different things" (*ibid*., concl. 5). Indeed, water
and fire can be considered as natural substances, but one is the
contrary of the other. As a general conclusion, Crathorn asserts that
the very same thing can be called a substance, a quality, a quantity,
a relation and so forth (q. 17, p. 462 and q. 18, p. 476).



Crathorn develops his position mostly by attacking the views of other
philosophers who accepted such distinctions, but unfortunately he is
not always clear about his positive reasons for abandoning
Aristotelian ontology. But, on one hand it is consistent with his
epistemology, for our only direct and natural certitude is that
qualities exist. On the other hand, it is also consistent with his
frequent tendency to materialism. Indeed, we can discern hints of
atomism in his *Commentary on the Sentences*.


## 6. Atomism



Crathorn is less well known than other fourteenth-century atomists
such as the Oxford thinkers Henry of Harclay (d. 1317) and Walter
Chatton (c. 1285-1344), or the Parisians Gerard of Odo
(1290-1349), Nicolas Bonet (d. 1343), and Nicolas of Autrecourt
(1299-1369) (Murdoch 1974, 1982; Grellard and Robert 2009), yet
we find several questions on the divisibility of the continuum in his
*Sentences* commentary (particularly I *Sent*., q. 3,
but also qq. 4 and 14-16). He affirms that a continuum is
divisible into a finite number of atoms that are not mathematical
points but its real, physical parts (I *Sent*., q. 3; for
discussion, see Wood 1988, Robert 2009a). Atoms are thus real singular
entities with discrete magnitude or quantity and a proper nature. For
example, he says that there are atoms of gold and atoms of lead, and
that these are different kinds of things (I *Sent*., q. 14).
Crathorn's atomism is far from that of Democritus.



The most difficult problem for atomists arises from book VI of
Aristotle's *Physics*, where it becomes necessary to
define the contiguity of atoms. Since an atom by definition has no
parts, how can we say that they touch each other? If they are actually
in contact, they should be in one and the same place (if not, then
there is no continuity since continuity requires contiguity). Crathorn
replies by saying that this is a problem only for those who think of
atoms as mathematical points. But since he holds that atoms have a
proper magnitude and that they are defined by the fact that they
occupy a single location (*situs* or *locus*), a
quantity that is simply the place occupied by the quantified thing (I
*Sent*., qq. 3 and 14-15), the contiguity and continuity
of atoms can be explained in terms of the contiguity of places. Atoms
can form a continuous magnitude if all of them are contiguous, i.e.,
if they all occupy contiguous atomic places.



The implications of Crathorn's atomism are truly astonishing.
First, every movement boils down to local motion of atoms in the void.
Thus, Crathorn affirms that a continuous motion has only one possible
speed, which is the greatest speed it could ever reach (Murdoch 1984).
In other words, movement is continuous when an atom changes from one
atomic place to another contiguous atomic place. The proportion of
time and place (i.e., the speed) is always equal to one. So how can he
explain the fact that things appear to move at different speeds? The
answer is quite simple: to every varying speed there corresponds a
discontinuous motion, with times of rest between some of the atomic
places occupied by the moving atoms (I *Sent*., q. 16, concl.
6). For example, the normal speed of an atom *a* corresponds to
its local motion from a place *p1* to another contiguous place
*p2* in a given atomic time. Variation of speed occurs if
*a* moves from *p1* to *p2* but with a time of
rest equivalent to two atoms of time. We may infer that speed can also
vary if *a* goes from *p1* to another place *p3*
that is not directly contiguous with *p1*.



Although Crathorn does not describe himself this way, he seems to be
one of the most radical atomists of the fourteenth century (Robert
2010a), sharing with his Parisian contemporary Nicholas of Autrecourt
much of the same anti-Aristotelian bent in his metaphysics and natural
philosophy. Combined with his epistemology and philosophy of language,
his philosophy is certainly one of the most original forms of
reductionism in later medieval philosophy.