## 1. Life and Works




History is written by the winners. Most of what we know of William of
Champeaux's life and work has been refracted down to us through the
prism of a man who hated him. Peter Abelard lost almost every battle
with William, his teacher and political enemy, yet he tells us that
William was a discredited, defeated, jealous, and resentful man.
Abelard claims to have humiliated William in debate, driving him from
the Paris schools. He alleges that, in defeat, William cast himself in
the role of monastic reformer only to advance his political career by
an unearned reputation for piety. Still, even Abelard recognized that
William was no fraud, calling him "first in reputation and in fact,"
and relocating to study under his tutelage (HC; trans. Radice
1974).




On the scholarly front, Abelard presents only half the story. He brags
of forcing William to abandon a firmly-held realist theory of
universals, but, rather than come over to Abelard's vocalist or
nominalist cause, William developed a second, more sophisticated,
realist view. So what might have appeared as an expression of
intellectual honesty and academic rigor on William's part, Abelard
presents as somehow shameful. What Abelard leaves out is how much he
learned from William. Now that more of William's work has become
available, it is clear that William prodded Abelard to give up
naive vocalism and develop the complex semantic theory we now
associate with Abelard's nominalism.




The extent of William's and Abelard's involvement on opposite sides of
the major political struggles of the day is also beginning to come to
light. William was a man of considerable influence in the monastic
reform movement. Abelard was a man of considerably less influence
allied with the opposite faction. It is probably true that Abelard
attracted the better students and so precipitated William's move from
Paris to St. Victor. But far from retiring in shame, William became a
statesman, ambassador, and confidant to the Pope, all the while
retaining enough political clout to prevent Abelard from either
holding his former chair as canon of Notre Dame or establishing a
school in Paris. One recent biographer of Abelard points out that in
1119, while Abelard was recovering from his castration and was soon to
be facing charges of heresy, William was a bishop acting as papal
negotiator to the court of Emperor Henry V. Unfortunately for
William's reputation, it was Abelard whose writings captured the
imagination of readers in later centuries (Clanchy 1997: 296ff).




Very little is known about William's early life and education. The
date usually assigned for his birth is 1070, but this may be off by as
much as a decade. In 1094 leaders of the monastic reform movement
appointed William as Master of Notre Dame. If this date is correct, he
would have been only 24 at the time, and this was a crucial moment for
the reformers. In 1094 King Philip I had been excommunicated for his
"illegal marriage," and any person appointed to be Master at Notre
Dame would have to have been an established scholar with considerable
political influence, something not usually found in 24
year-olds. Thus, a date of 1060 or earlier may not be unlikely for
William's birth (Iwakuma forthcoming c).



 Little is known of William's education before he took this important
post. He is known to have studied with Anselm of Laon and a certain
Manegold, but it is unclear whether this was the theologian, Manegold
of Lautenbach, or the grammarian, Manegold of Chartres. It is even
suspected that William studied with the vocalist Roscelin of
Compiegne.



 Early in the first decade of the twelfth century, probably in 1104,
William became archdeacon of Paris. In 1108 the reformist party
received a setback when King Luis VI, King Philip's son by his
"illegal marriage" ascended the throne. William resigned as archdeacon
to move to the abbey of St. Victor and the Paris suburbs, where he
continued to teach and remained an influential reformer. Both Hugh of
St. Victor and Bernard of Clairvaux were among William's
proteges from this period at St. Victor.



 In 1113, he was appointed bishop of Chalons-sur-Marne. He
continued to act as papal legate and negotiator and remained
influential in the reform movement, particularly through his patronage
of Bernard of Clairvaux. His continued scholarly reputation is
demonstrated in the somewhat ludicrous tale of Rupert of Duetz, who,
in 1117, set himself on a quest to challenge William of Champeaux and
Anselm of Laon to intellectual combat (Clanchy 1997: 143). On January
18, 1122, William took the habit of a Cistercian and died at Clairvaux
eight days later.



 William's corpus of writings is not widely available and a great deal
more textual work needs to be done before any assessment can be made
about his broader philosophical significance. Nevertheless, his basic
philosophical commitments and some of his characteristic views are
known. The texts we do have indicate that he started his career as a
realist in matters of logic and metaphysics and that his commitment to
realism grew stronger with the appearance of the vocalists and early
nominalists. Thanks to Abelard's criticisms, William is best known for
his realist theories of universals. In response to the vocalist
challenge, he seems to have held something like the *Cratylus*
theory of language: the nature of words is intimately tied to the
nature of the things they name. In logic, some vocalists claimed that
the force of inference arises from words or ideas, but William argued
that this is to be found instead in some thing or relation between
things, which he identified as the *locus* or *medium* of
argument. He interpreted Aristotle's *Categories* as ten
general things, not ten general words as the vocalists
maintained. These and other claims suggest a broadly realist
philosophical outlook. It is possible that fragments and excerpts of
William's work passed down to us by his near contemporaries are those
in which he was debating with the vocalists, and so we do not know
whether they represent William's deepest commitments or only brief
forays into an important debate.



 William's views are known mostly through references in contemporary
works, especially those of Abelard. Though several of William's works
have been identified, very few have been edited, and none has been
translated into English. The *Introductions* --
*Introductiones dialecticae secundum Wilgelmum* 
(ISW)  and *Introductiones dialecticae secundum magistrum G.
Paganellum* (IGP) -- are very early works, possibly dating
from William's arrival in Paris in 1094. Edited with these two
*Introductions* are two brief discussions of *media* or
*loci*, and the beginning of an early commentary on Porphyry,
all likely by William (Iwakuma 1993; ISW is also in de Rijk 1967).
These texts defend some of William's characteristic doctrines, but in
1094 the vocalist movement had not yet begun to exert any real
influence in Paris, and so it is likely that he had not yet been
forced to articulate his views in response to serious criticism.



 Some of William's later works have also been identified. Although no
editions have been published, several articles contain extensive
excerpts. William is known to have written commentaries on Porphyry's
*Isagoge*, Aristotle's *Categories* and *De*
*Interpretatione*, Boethius' *De* *Differentiis*
*Topicis*, and Cicero's *De* *Inventione* and
*Rhetorica ad Herennium*. Some of his theological writings,
along with those of other leading French theologians, were compiled in
the later twelfth century under the title *Liber*
*Pancrisis.* These have been edited as the
*'Sententiae' of William of Champeaux* (Lottin
1956). The *Liber* *Pancrisis* is thought to be a
compilation of the best Parisian theology of the period, and so it is
likely to represent William's most advanced views.


## 2. Universals




The history of philosophy remembers William for his two theories of
universals, **material essence realism** and **indifference
realism**. These theories emerge from the writings of Peter
Abelard, where they are paired with Abelard's decisive arguments
against them. Indeed, Abelard's critique was so powerful that when
John of Salisbury wrote his famous catalogue of twelfth-century
theories of universals, William is not even mentioned
(*Metalogicon* II 17-20; Abelard LI Por.: 10-16, trans. Spade
1994: 29-37; see also
 John of Salisbury,
 Peter Abelard, and
 King 2004)



 Material essence realism proposes that there are ten most general
things or essences: one most general thing corresponding to each of
Aristotle's ten categories. These essences are universal things:



> It should be seen that there are ten common things which are
> the foundations of all other things and are called the most general
> things - as for example this common thing, substance, which is
> dispersed through all substances, and this thing, quantity, which is
> dispersed in all quantities and so on. And just as there are ten common
> things which are the foundations of all other things, so also there are
> ten words which, thanks to the things they signify, are said to be the
> foundations of all other words (C8; Marenbon 1997: 38).


 
 These ten genera exist and are to some degree unformed. They are
formed into subalternate genera and species by the addition of
differentia. Species are formed into individuals by the addition of
accidental forms: "a species is nothing other than a formed genus, an
individual nothing other than a formed species" (P3; Marenbon 2004:
33; Iwakuma 2004: 309; Fredborg 1977: 35). This is how the view gets
its name. The genus exists as the matter. The difference forms the
genus "into a sub-altern genus which in turn becomes the matter for an
inferior sub-altern genus or species. The addition of accidental forms
divides the species into discrete individuals" [*et fiant res
discretae in actu rerum*] (C8; Iwakuma 1999: 103). The
individuals in a species or genus thus share a single material
essence.



 Everything in the created world is an accidentally differentiated
individual, but this is an incidental feature of the created world,
and by no means a commitment to concretism. Universal essences exist;
they are simply never found except as accidentally differentiated, qua
individuals.



> In actuality genera and species have their being in
> individual things. I can, however, consider by reason the same thing
> which is individuated with its accidents removed from its make-up, and
> consider the pure simple thing, and the thing considered in this way is
> the same as that which is in the individual. And so I understand it as
> a universal. For it does not go against nature for it to be a
> pure thing if it were to happen that all its accidents were removed.
> But because it will never happen in actuality that any thing exists
> without accidents, so neither in actuality will that pure universal
> thing be found. (P3; Marenbon 2004: 33)




This mental exercise of stripping away forms does not merely produce a
universal concept. It reveals the underlying metaphysical
reality. There is a real universal thing corresponding to our
universal concepts. It is this principle of a single universal
substance individuated by accidents that Abelard reduces to
absurdity.



 When faced with Abelard's arguments against material essence realism,
William gave up his belief in universal essences but refused to accept
that universals are simply words or concepts. Indifference realism
rejects the core principle of material essence realism by rejecting
the notion that there are shared essences and holding that individuals
are completely discrete from one another.



 The words 'one' and 'same' are ambiguous,
William says: "when I say Plato and Socrates are the same I might
attribute identity of wholly the same essence or I might simply mean
that they do not differ in some relevant respect." William's newfound
ambiguity is the seed of his second theory of universals. The stronger
sense of 'one' and 'same' applies to
Peter/Simon and Saul/Paul (we would say Cicero/Tully), who "are one
and the same according to identity" (Sen 236.123). As for Plato and
Socrates:



> We call them the same in that they are men [*in hoc quod
> sunt homines*], ['same'] pertaining with regard to
> humanity. Just as one is rational, so is the other; just as one is
> mortal, so is the other. But if we wanted to make a true confession, it
> is not the same humanity in each one, but a similar [humanity],
> since they are two men. (Sen 236.115-120)




So, although Plato and Socrates have no common material--matter,
form, or universal essence--they are still said to be the same
because they do not differ. This leads to the claim that Abelard finds
so disturbing. Each individual is both universal **and**
particular:



> 
> Those things which *per se* are considered many and wholly
> diverse in essence are one considered in general or specific nature.
> That is, they do not differ in being man (*esse*
> *hominem*).
> 
> 
> 
> 
> One Man is many men, taken particularly. Those which are one
> considered in a special nature are many considered particularly. That
> is to say, without accidents they are considered one *per*
> indifference, with accidents many.
> 
> 
> 
> 
> It should never be said that many men make one Man. Rather it should
> be said that many men agree in being, in what it is to be a man
> (*in esse hoc quod est esse homo*). Nevertheless, they are
> wholly diverse in essence (P14; Iwakuma 1999: 119).
> 
> 
> 



 Indifference realism is not a complete departure from material
essence realism because William still accepts accidental
individuation. When the accidents are stripped away, Plato and
Socrates are still one and the same although in the weaker sense of
'one' and 'same'. They do not share a material
essence, though they each have the same state or *status* of
being a man. William's indifference realism holds that when
individuating accidents are stripped away from two individuals, what
you are left with may be numerically distinct but it is not
individually discernible (you can't tell which one is Socrates). What
is left then are pure things--there are no individuating
characteristics. In this sense, each thing is itself a universal.


## 3. Logic and Philosophy of Language




With so few of William's works identified and even fewer properly
edited and published, any serious discussion of his views on logic is
years away. What follows is a brief presentation of William's thoughts
on various issues. In many cases, these are gleaned from references in
other texts, mostly by Abelard. These references indicate that
William was a wide-ranging and serious thinker, but much as with the
Pre-Socratics, we have just seen just the tip of the iceberg as far as
his actual writings are concerned.


### 3.1 Signification




Logic is the art of discerning truth from falsehood and of making and
judging arguments (ISW I 1.1; IGP I 1.1). The study of logic must
therefore begin with the study of words. The *Introductions*,
ISW and IGP, first define sounds, significant sounds, words, phrases
(*orationes*), and sentences, then proceed to detailed
discussion of complex hypothetical and categorical sentences and
syllogisms. William's approach here became a model for twelfth-century
logic textbooks.




William accepts the standard medieval definition of signification: a
sound is significant if it generates an understanding in the mind of a
hearer. Judging by William's discussion, there was some debate at the
end of the eleventh century as to whether signification required that
a spoken word actually, as opposed to merely potentially, generate an
understanding in the mind of a hearer. Actual signification is too
strong a criterion, but every sound potentially generates an
understanding, even if only in the mind of the person uttering
it. William argues that once a word is imposed--and a convention
established--the word is significant because it is apt to signify
whenever it is uttered (Iwakuma 1999 p109; forthcoming b). William's
views on the conditions for imposing words are not yet fully
known. The vocalists seem to have held that absent a linguistic
convention, there is no connection between any sound and what it is
imposed to signify, a view shared by Abelard (see Guilfoy 2002). On
the other hand William held that "there is such an affinity between
words and things that words draw their properties from things and so
the nature of words is shown more clearly through the nature of
things" (P14; Marenbon 1996: 6).




William clearly invites controversy by claiming that the only
significant sounds, that is, the only words, are those that are
imposed to name presently existing things:



> 
> 
>  That word is significant which is imposed on an existing thing, like
> 'Man'; that word is not significant which is imposed on a
> non-existing thing, like 'chimaera', 'blictrix', and
> 'hircocervus' (IGP I 2.2).
> 
> 
> 
>  A significant word is one whose *significatum* is found among
> existing things (ISW I 1.4).
> 
> 
> 




To claim that 'chimaera' is the equivalent to
'blictrix' implies that 'chimaera' is equally
meaningless. The view that significant words must name existing things
presents obvious and difficult cases because we can utter true or
false sentences about things that never existed or that no longer
exist. In such cases, William claims that words have a figurative
signification. 'Chimaeras are imaginary' figuratively
expresses the sentence 'Some mind has the imagination of a
chimaera' (Abelard D 136.32; Kneale and Kneale 1962:
207). 'Homer is a poet' is properly understood
figuratively as 'Homer's work, which he wrote in his role as
poet, exists' (H9; Iwakuma 1999: 113; Abelard D 136.14ff,
168.11ff).




Abelard attributes to William the view that words signify all things
that they were imposed to name (Abelard D 112.24). Other texts
indicate that William might have believed this. An anonymous text
attributes to William the view that 'all' signifies all
things simultaneously (H13; Iwakuma 1999: 111). However, it is also
possible that Abelard misunderstood or misrepresented William (Iwakuma
1999: 107).




It is reported that William held a similar view of infinite terms.
William is said to have argued that an infinite term, e.g.,
'non-man', signifies all those things that are not men
(H13; Iwakuma 1999: 109). However, William's own discussion of
infinite terms is available. In the *Introductions* William
argues that the signification of infinite terms can be taken
affirmatively, negatively, or correctly (ISW I 4.2). Taken
affirmatively 'non-man' positively signifies every thing
that is not a man: each rock, flower, and squirrel. The affirmative
account allows one to substitute 'stone' for
'non-man' in syllogisms with absurd results. Taking
infinite terms negatively solves this problem by claiming that
infinite terms do not signify any existing thing, but William cannot
accept this because it would mean that infinite terms are not
significant. Rather, he argues that the imposition of infinite terms
is related to the imposition of their correlative terms.



> 'Animal' and 'man' signify the
> very same thing, animal and man, by imposition [*ponendo*],
> 'non-animal' and 'non-man' by remotion
> [*removendo*]. But because infinite terms signify by remotion,
> there is nothing which can be concluded by imposition. So it is not
> possible to conclude 'stone' from 'non-animal'
> (ISW I 4.2).




Because the remotive imposition of the infinite term
'non-animal' is related to the positive imposition of the
term 'animal', the infinite term does not signify stone in the
way the word 'stone' would. So although William holds that
the same thing is signified, the mode of signification would preclude
substitution of positive and infinite terms.




Abelard criticizes William for "doing such abuse to language" that he
allowed 'rational' and 'rational animal' to
signify the same thing (Abelard D 541.24). Again, another anonymous
source confirms that William thought that a definition and the term
defined, that is 'rational mortal animal' and
'man', signify the same thing (Green-Pedersen 1974,
frag. 6). Both are consistent with William's theories of universals
and may reflect William's commitment to words signifying presently
existing things. William may well have thought that
'rational' and 'rational animal' have the same
signification because each thing signified by 'rational'
is signified by 'rational animal', and conversely. Such a view
would involve a fairly simplistic theory of meaning, but this alone
does not mean it was not William's view.




Some aspects of William's theory of signification are considerably
more complex. He developed a theory of two modes of signification of
quality terms:



> 
>  One mode by imposition another by representation. 'White'
> and 'Black' signify the denoted substance by imposition,
> because they are imposed on this substance. They signify the
> qualities whiteness and blackness by representation. The substance
> they signify according to imposition is signified secondarily. They
> principally designate those qualities which they signify by
> representation.(C8; Iwakuma 1999 p.107)




Abelard confirms that William made this sort of distinction. As
Abelard describes it, William held that 'white' signifies
the white individual and also whiteness. 'White' signifies
the subject (*fundamentum*) by denoting (*nominando*)
it. It signifies whiteness by determining it in the subject
(*determinando circa fundamentum*) (Abelard LI Top:
272.14). But at the present time, not enough material is available to
begin to flesh out William's account of signification by denotation
and signification by determination.


### 3.2 Multiple Senses of Sentences




William had several different views on the interpretation of different
kinds of sentences. That he held the views is not much in dispute;
they are attributed to him by several contemporaries and some are
found in his own works. But the possible philosophical relation
between them is a matter of speculation.


 William held that sentences have two senses, a grammatical sense
and a dialectical sense. Taken in the grammatical sense, the verb in
sentences such as 'Socrates is white' marks an
intransitive copulation of essence: the same thing is denoted by the
subject and predicate. In the dialectical sense, the verb in
'Socrates is white' marks a predication of inherence: what
is denoted by the predicate inheres in what is denoted by the
subject. To the grammarian, 'Socrates is white' and
'Socrates is whiteness' have different senses and
different truth conditions. 'Socrates is white' says that
Socrates is a subject of whiteness. 'Socrates is
whiteness' says that Socrates is essentially whiteness. To the
dialectician, however, the two sentences have the same sense, since
they both say that whiteness inheres in Socrates. The dialectical
sense is more general (*generalior*, *largior*,
*superior*) because it does not distinguish between essential
and accidental inherence. But the grammatical sense is more precise
(*determinatior*). Taken in the dialectical sense,
'Socrates is white' and 'Socrates is
whiteness' would both be true. So, while the dialectical sense
has some use for dialecticians, sentences are true and false in the
grammatical sense (Abelard LI Top: 271-273; GP 1974 Frag 9; de Rijk
1967 II.I: 183-85).




According to William, maximal propositions contain or signify all the
propositions under them. Thus, the maxim, 'Of whatever the
species is predicated the genus is also predicated' signifies or
contains the sentences 'If it is a man it is an animal',
'If it is a rock it is a substance', etc. Only the most general
form is truly a maximal proposition, but it is the more precise
(*certior*) sentences contained under the maxim that provide
the inferential force for particular arguments. William may have
developed this view in response to the vocalists. Abelard explains
that multiple senses are needed given William's view that things, not
words, warrant inference; only the more precise formulations can
signify the things themselves (Abelard LI Top: 231.26-238.34). An
anonymous author confirms Abelard's understanding of William's
view. The argument, 'Socrates is a man therefore Socrates is an
animal' is warranted by the topical maxim noted above. It is not
the maxim itself but the more precise version contained in it,
'If it is a man it is an animal', that provides the force for
this particular inference. According to this text, William argued that
it is not the words (*voces*) or the sense
(*intellectus*) of the more precise sentence that provides the
inferential force, but the fact that the more precise sentence
signifies relations (*habitudines*) between things
(Green-Pedersen 1974: Frag 8;10;12).




William divides the standard A, E, I, and O sentences according to
what he calls the matter of the sentence *materia
propositionis*). The matter of the sentence is determined by the
relationship between what is signified as the subject and the
predicate. Each standard-form sentence is found in one of three
matters: natural, contingent, or remotive. In a sentence of natural
matter the predicate inheres universally in the subject: 'All
men are animals'. In a sentence of contingent matter the
predicate inheres in the subject, but not universally: 'All men
are white'. In sentences of remotive matter the predicate in no way
inheres in the subject: 'All men are stones'. The validity
of direct inferences between contraries, subalterns, etc. depends on
the matter of the sentences involved. In all matter, contraries cannot
both be true. So regardless of the matter, if an A sentence is true
the corresponding E sentence is false. In natural and remotive matter,
if either the A or E sentence is false the other must be true: if
'No men are animals' is false then 'All men are
animals' must be true. However, in contingent matter both
sentences may be false. It is possible for both 'All men are
white' and 'No men are white' to be false. William
gives a similar treatment for contradictories, subcontraries, and
subalterns (ISW I 3-3.3; II 1.1-1.3; IGP I 5.4-5.6).


### 3.3 Argument, Conditionals, and Loci




Contemporary logicians recognize a difference between arguments and
their corresponding conditionals. But they accept that an
argument:



> 
>  (1) Premise 1; Premise 2; therefore, Conclusion
> 




and its corresponding conditional:



> 
> 
> (2) If (Premise 1 and Premise 2) then Conclusion




are equivalent by the deduction theorem. (2) in turn is interderivable
with:



> 
>  (3) If Premise 1 then (if Premise 2 then Conclusion)




These logical relationships were all in dispute during the twelfth
century. (Iwakuma 2004b presents these distinctions and discusses
William's role in the debate.) Logicians at that time attributed much
more significance to the distinction between arguments and
conditionals, and most did not accept what we would now recognize as
the formal rules of material implication. Along these lines, several
views were attributed to William as characteristic of his logical
program, but his arguments in the available texts do not reflect what
others say about him. So, once again, the extent of William's
influence is unclear.




William accepted that (1) and (2) are equivalent, but not for any
metalogical reason. He thought that syllogisms were phrases
(*orationes*) that contain the senses of several other
sentences. The view attributed to William is that syllogisms and
arguments are, as he puts it "subcontinuatives"
[*subcontinuativa*] containing other sentences. 'Socrates
is a man; therefore, Socrates is an animal' contains the sense
of the sentences 'Socrates is a man', 'Socrates is
an animal' and, 'If Socrates is a man, then Socrates is an
animal' (B9 2.1 ed. Iwakuma 2004b: 102; this is the same text as
Green-Pedersen 1974, frag 2). William calls the contained sentences
'continuatives [*continuativa*]'. He also treats
all syllogisms as conditionals of type (2) rather than type (3). There
is no argument for his preference, at least not in the Introductions,
and none of the available sources give his reasons. At present all
that can be said is that William seems to have had a hand in the
origins of a debate that raged during the twelfth century and was not
revived until the twentieth.




William introduces several novelties in his discussion of loci. Most
significantly, he limits his discussion of the traditional Boethian
topics to the loci from the whole, part, opposites, equals, and
immediates. He also introduces loci from the subject and from the
predicate into his discussion of categorical arguments. Both moves
were controversial.




William sometimes refers to the locus as 'the medium', by which
he does not necessarily mean the middle term but rather the thing that
acts as a link between the extremes of an argument. He also called the
locus 'the argument', by which he means that the locus provides
the argumentative or inferential force. But whichever name he chooses,
William's realist commitment is evident.



> The same thing is the argument and the locus according to
> Master W. but the locus is the force of the argument [*sedes*
> *argumenti*], and so this thing is the force of the
> argument. (Green-Pedersen 1974: frag 1)




In the Introductions, William calls loci "words" [*voces*], but
they are words denoting the things themselves or their relations
(*habitudines*) (IGP I 7). But William is not clear about the
importance of this distinction between things and relations. Fragments
of his later work report that he was quite careful to distinguish his
view from any brand of vocalism. He distinguished the word
(*vox*), the understanding or meaning of the word
(*intellectus*), and the thing itself denoted by the word, and
held that the thing itself is the locus. (Green-Pedersen 1974: frag
3,4)




In categorical syllogisms, William introduces the locus from subject,
predicate, both subject and predicate, and from the whole (ISW II 2.2;
IGP I 8ff; see Stump 1989: 117ff). Thus, the argument



> 
> All men are animals  
> 
> No animal is a stone  
> 
> Therefore, no man is a stone
>  




is warranted by the locus from the predicate. The predicate of the
first sentence is the link or medium between the extreme terms in the
conclusion. In this case, *animal* (presumably the universal
thing itself) is the locus or seat of the argument. The rule is, if
something is predicated of some subject universally, then whatever is
removed universally from the predicate is removed universally from the
subject (William provides a lengthy set of rules describing the
logical relations that hold between subjects and predicates). As
described above, William holds that such maximal propositions contain
the sense of those propositions that fall under them. The rule
contains sentences signifying the relations between man and animal and
between animal and stone (IGP I 8.4). The relations of *animal*
to the extremes warrant the inference.




William provides a similar account of hypothetical syllogisms. He
introduces several loci and rules, but these are not formal
rules. What ultimately warrants any hypothetical syllogism is the same
sort of derivative signification of an extra-mental thing or
relation. Provided Socrates is risible, 'Socrates is a
man' is true. The following hypothetical syllogism is warranted
by the locus from the consequent:



> 
>  (Socrates is a man - Socrates is an animal) - (Socrates is
> risible - Socrates is an animal)




The rule is: whatever follows from the consequent follows from the
antecedent. In this case, the consequent is 'Socrates is a
man', and the antecedent is 'Socrates is
risible'. This looks like a formal rule:



> 
>  (A-B)-((B-C)-(A-C))
> 



 but William does not present it as such. 'Socrates is risible
- Socrates is a man' is warranted by the locus from equals,
and 'Socrates is man - Socrates is an animal' is
warranted by the locus from the part (IGP I 9.2). The conclusion,
'Socrates is risible - Socrates is an animal', is
arrived at via topical reasoning, not by formal rules of
inference. This is the basis for much of the later criticism of his
work. Abelard in particular derives contradictions from his views by
treating William's loci as formal rules of inference (see Martin
2004).


### 3.4 Modality




Abelard reports that William thought that all modality was *de
dicto* (or, in Abelard's terminology, *de sensu*)



> 
> 
> Our teacher taught that modal sentences descend from simple sentences
> because modal sentences are about the sense of simple sentences. So
> that when we say 'It is possible (or necessary) that Socrates
> runs', we are saying that what the sentence 'Socrates
> runs' says is possible or necessary. (Abelard D 195.21; see also
> Mews 2005: 49; Knuuttila 1993: 87; Kneale and Kneale 1962:
> 212).



 The extent to which this attribution is accurate is unclear. The view
is at least superficially inconsistent with William's realism and
anti-vocalism in all other areas. Additionally, Abelard was among the
first to recognize the importance of the *de dicto* / *de
re* distinction; the issue may be fairly confused in William's
work, as it was in many others. On the other hand, several anonymous
texts attribute to William the claim that 'possibly' and
other modal terms modify the signification of other words in a
sentence. Thus, 'bishop' signifies actual and existing
bishops, but 'possible bishop' has a figurative sense
signifying all those things whose nature is not repugnant with being a
bishop (Iwakuma 1999: 112). This is not necessarily a rejection of
*de re* modality, but again, more of William's work needs to be
studied.


## 4. Ethics




William's ethics starts with two generally accepted early medieval
claims: (1) evil is not any positively existing thing but only the
privation of good (Sen 277.1); (2) every act or event that occurs is
performed or condoned by God and therefore good (Sen 277.11-15). These
lead William, among others, to situate moral good and evil in the
human mind.




To this end, William names the elements of a fairly complex moral
psychology: vice, desire/lust, pleasure, will, intention, and consent.
Any or all of these elements might play a role in sinful behavior.
Vice itself is not necessarily bad, since the vices are not acquired
habits but inborn dispositions. Vices incline us to bad behavior but
do not necessarily compel the will: there is no sin unless we consent
to the behavior the vice inclines us toward (Sen 278.10). Carnal
desire, lust, and pleasure, on the other hand, are always morally
bad. William writes extensively about sexual lust and pleasure,
especially as they are involved in the transmission of original
sin. Before the fall, sex was no more pleasurable than "putting your
finger in your mouth" (Sen. 254). In our fallen condition, however,
lust and pleasure can never be removed from the act. Because our
"ability" to experience this pleasure is the result of original sin,
the pleasure itself is always culpable. Consent to a sexual act under
the proper circumstances--e.g., between lawful spouses for the
purpose of procreation--only lessens the gravity of the sin (Sen
255; 246). In William's moral psychology, will, intention, and
consent are the undifferentiated elements of voluntary action. These
play the most significant role, but sin is not exclusively in the
will, consent, or intention.




Our best hope to avoid sin is to will what is right for the right
reasons. However, when it comes to discovering what is right, and
therefore what ought to be willed, we start out at a disadvantage. The
human mind naturally has the power to discern good and evil (Sen
253.10; IGP II 4), but one of the effects of the Fall is that our
rational capacities have been clouded and diminished. Before the Fall
the senses were subject to reason; after the Fall this is reversed
(Sen 253.12-15), for since then the mind has become more closely
attached and even enslaved to the body. This is the *fomes* of
sin, a carnal weakness that clouds our reason and makes us more
inclined to sin (Sen 246.39). Fear, not reason, is the key for
William, since "fear is the beginning of all wisdom"
(Sen. 276.1). William describes three kinds of fear (Sen
276.17-34). First is the natural fear of danger and pain; even Jesus
was subject to this fear. Second is fear of losing material things or
the fear of punishment in hell. This fear shows that one values
comfort and material things more that goodness and justice. People
motivated by this second fear will act rightly out of fear of losing
material goods or fear of the torments of hell, but not out of good or
right intention: "he does not merit grace who serves not his love of
justice but his love of things or his fear of punishment" (Sen
261.23-25). Third is the fear that arises from respect for God's
justice and power. This respectful fear of God, with knowledge of our
own weakness and fallibility, "is better called the love of God" (Sen
276.39-43). This humble fear of God should be our guide to what is
right.




William's influence on Abelard here is obvious. Primarily, William and
perhaps others from the school of Anselm of Laon were responsible for
the delineating the complex moral psychology that is at the core of
Abelard's ethics. The major differences are with regard to reason and
responsibility. Because of our fallen state, William has little regard
for the ability of human reason to correctly discern what is
good. William is also content to prove that evil is no thing by
situating its source somehow in the human mind. He is not interested
in showing that we are responsible, only that we, and not God, are
accountable. Our will, like our mind and body, is defective and we
suffer the consequences of its failures. It is Abelard who takes this
moral psychology and develops from it a theory of moral
responsibility.


## 5. Philosophical Theology




William is committed to the belief that the mysteries of faith are
beyond the scope of human reason, but this does not prevent him from
discussing the issues philosophically and using his skill as a
logician to prove his point.




The problem of free will and divine foreknowledge is familiar: if
God's foreknowledge is infallible, then future events, including the
actions of human beings, all happen of necessity; on the other hand,
if future events,including the actions of human beings, could occur
otherwise, then God's foreknowledge would fallible. William denies
both propositions. With regard to the first he offers two
arguments. He claims that God foresees the whole range of possible
choices and infallibly foreknows which option free creatures will
choose (Sen 237; 238). The event itself is not necessary; in fact, God
infallibly foresees that the event is not necessary. He then adds an
interesting claim about future contingent propositions: they are
determinately true or false, but it is the infallibility of divine
foreknowledge that makes them so. The future event itself which the
proposition is about does not yet exist and is indeterminate
(*eventus rerum de quibus agitur indeterminate*) (Sen
238.36). William seems to hold both that the future is indeterminate
and that God's foreknowledge is determinately true or false.




The second proposition, 'if future events, including the actions
of human beings, could occur otherwise, then God's foreknowledge is
fallible', was interpreted in several ways by William's
contemporaries. Some held that if the event could occur otherwise God
would be fallible. Others held that because the event could occur
otherwise God actually is fallible (see Mews 2005: 135). The former
would reject the claim that the event could occur otherwise, but the
latter would simply reject divine infallibility, arguing rather that
God is just very lucky epistemically. Both views are theologically
suspect, of course, and William argued that both inferences are
invalid. But he does so by introducing an unexplained modal intuition
that in context looks question-begging: the inference from 'the
event could occur otherwise' to 'God is or could be
deceived' is not necessary. It is possible that the former be
true and the latter false because "it is never necessary that the
impossible follow from the possible, and it is impossible for God to
be, or to have been, deceived" (Sen 237.68).




William deftly avoids the overreaching that got philosophers like
Roscelin and Abelard into such trouble. He outlines a theory of
metaphorical language for describing God, and argues that the
fundamental relations of the Trinity are beyond the powers of the
human mind to comprehend.




Predicates such as good, just, etc.,when applied to God have a
metaphorical rather than their usual literal meaning. As described
above, William argued that all significant words are imposed to name
existing things in the world and these words generate sound
understandings of those things they were imposed to signify. When we
impose the word 'just' or 'good' to name a
just or good person, we do so because justice or goodness is in some
way a quality of that person or her actions. God, on the other hand,
is goodness itself and justice itself. The dignity and power of God
cannot be grasped by human reason and so we cannot even conceive of
God sufficiently to accurately impose words that name divine
attributes: "words imposed for human use are used metaphorically for
speaking about God" [*ad loquendum de Deo transferuntur*] (Sen
236.46).




Whenever he discusses the Trinity, William associates the Father with
power, the Son with wisdom and the Holy Spirit with love. But this
metaphor is not intended to help us toward rational understanding of
the Trinity, or to provide a clear delineation of properties of the
three ersons in any way that would allow an explanation of their
relations and differences. William argues that there is nothing like
the Trinity in the created world and so there is nothing the human
mind is able to comprehend that could be used as an analogue for
explaining the fundamental relation of the Trinity, three persons
irreducibly present in one substance: "I do not see by what quality I
would be able to explain this, since nothing similar can be found in
the nature of any thing" (Sen 236.86). William rejects Augustine's
metaphors of the sun and sunshine and the mind and reason. Sunshine is
an accident of the air and is no part of the substance of the
sun. Likewise, reason is a power of the mind and not its substance
(Sen 236.101). William also explains that neither of his theories of
universals can be applied to explain the sameness and difference of
the divine persons. Material essence realism would imply that the
persons in the Godhead are accidentally individuated, and this is
unacceptable. The indifference theory would require the non-identity
of three separate substances, which is also contrary to the teaching
of the faith. What is William's ultimate conclusion? "Because no
likeness <to any created thing> could be described, the Trinity
must be defended by faith alone" (Sen 236.91).