## 1. Life and Works


### 1.1 Life



Abelard's life is relatively well-known. In addition to events
chronicled in the public record, his inner life is revealed in his
autobiographical letter *Historia calamitatum* ["The
Story of My Troubles"] and in his famous correspondence with
Heloise.



Abelard was born into the lesser nobility around 1079 in Le Pallet, a
small town in Brittany near Nantes. He received early training in
letters, and took to his studies with enthusiasm; his later writings
show familiarity with Cicero, Horace, Juvenal, Ovid, Lucan, Seneca,
and Vergil. Abelard eventually renounced his inheritance, including
its attendant knighthood, to pursue philosophy. He did so by
travelling to study with well-known philosophers, most notably
Roscelin and William of Champeaux.



During the first years of the twelfth century, Abelard felt confident
enough to set himself up as a lecturer, first at Melun and then at
Corbeil, competing mainly with William of Champeaux (Paris) for
students and reputation. The strain proved too
much--Abelard's health failed, and he returned to Brittany
for several years.



Abelard returned to Paris sometime between 1108 and 1113 with his
health restored and his ambition intact. He attended William of
Champeaux's lectures, and entered into debate with William over
the problem of universals. According to Abelard's report, he
bested his teacher in debate, and gained his reputation as a
dialectician of note, teaching at several schools. Around 1113 Abelard
decided to study theology; he sought out the most eminent teacher of
theology of his day, Anselm of Laon (not to be confused with Anselm of
Canterbury), and became his student. It was not a good choice:
Anselm's traditional methods did not appeal to Abelard, and,
after some back-and-forth, Abelard returned to Paris to continue on
his own. It would be the last time he studied with anyone.



Upon returning to Paris, Abelard became scholar-in-residence at Notre
Dame, a position he held until his romantic entanglement with
Heloise led to his castration, at which point he entered
the Benedictine monastery of Saint Denis and Heloise
entered the convent of Argenteuil. After his recovery, Abelard resumed
teaching at a nearby priory, primarily on theology and in particular
on the Trinity. His method of philosophical analysis was seen as a
direct challenge to more traditional approaches, and a synod, convened
in Soissons to examine Abelard's writings, condemned them and
required Abelard to make a public avowal of faith, an experience he
found humiliating; shortly afterwards he was allowed to settle in a
wild and uninhabited section of land, to devote himself to
contemplation.



It was not to be. Abelard says that poverty forced him to resume
teaching. He and the students who flocked to him in droves constructed
an oratory named the Paraclete, where he continued to write, teach,
and research. This idyll came to an end around 1126, when Abelard
accepted an invitation to become abbot of the monastery of Saint
Gildas de Rhuys in Brittany; shortly afterwards he handed over the
Paraclete to Heloise and the other nuns, whose convent had
been expropriated. Abelard found the monks of Saint Gildas difficult
and obstructive--even dangerous--and he claims that there
were several attempts on his life while in residence. During this
period he wrote the *Historia calamitatum* and corresponded
with Heloise.



By the mid-1130s Abelard was given permission to return to Paris
(retaining his rank as abbot) and to teach in the schools on the Mont
Ste.-Genevieve. It was during this time that his theological treatises
were brought to the attention of Bernard of Clairvaux, who objected to
some of Abelard's conclusions as well as to his approach to
matters of faith. After some inconclusive attempts to resolve their
differences, Abelard asked the archbishop of Sens to arrange a public
dispute between himself and Bernard on 3 June 1140, to settle their
disagreements. Bernard initially refused the invitation on the grounds
that one should not debate matters of faith, but then accepted it and,
unknown to Abelard, arranged to convene another commission of enquiry
to review Abelard's works on suspicion of heresy. When Abelard
discovered that there was no debate but instead a kangaroo court, he
refused to take part, announcing his intention to appeal to the Pope
directly. He walked out of the proceedings and began travelling to
Rome. The Council condemned nineteen propositions it claimed to find
in his works and adjourned. Bernard launched a successful campaign
petitioning the Papal Court before Abelard was out of France; a letter
from the Pope upholding the decision of the Council of Soissons
reached Abelard while he was at Cluny; Abelard was ordered to silence.
By all accounts Abelard complied immediately, even meeting peacefully
with Bernard in reconciliation. Peter the Venerable, the abbot of
Cluny, wrote to the Pope about these matters, and the Pope lifted
Abelard's sentence. Abelard remained under the protection of
Peter the Venerable first at Cluny, then at St. Marcel, as his health
gradually deteriorated. Abelard died on 21 April 1142. His body was
interred at the Paraclete, and today is (with Heloise) in
Pere Lachaise cemetery in Paris.



Abelard's students were active as kings, philosophers, poets,
politicians, theologians, and monks; they include three popes and
several heads of state. Explicit references to Abelard's
thinking in the later Middle Ages are few, likely because of the cloud
cast by the verdict of the Council of Soissons, but it is clear that
he had a seminal influence on twelfth-century philosophy and perhaps
on later fourteenth-century speculation as well.


### 1.2 Works



The dates of composition and even the number of Abelard's
writings remain largely obscure and a matter of controversy among
scholars. One reason for this is that Abelard constantly revised and
rewrote, so that several distinct versions of a given work might be in
circulation; another reason is that several of his writings might
represent 'teaching notes' constantly evolving in courses
and seminars. Hence it is not clear that 'date of
composition' is a well-defined notion when applied to the body
of Abelard's work that we now possess. Apart from
Abelard's correspondence, which can be dated with relative
precision, Abelard's extant work falls into three
categories.



The first category consists of Abelard's works on
*dialectic*--works concerned with logic, philosophy of
language, metaphysics, and philosophy of mind. His two masterworks
are:


* *Logica* '*ingredientibus*',
"Logic" (starting with the words 'To those
beginning...').
* *Dialectica*, "Dialectic."



Both of these works follow the pattern of the *logica vetus*,
the "old logic" inherited from antiquity: Porphyry's
introduction to Aristotle, the *Isagoge*; Aristotle's
*Categories* and *On Interpretation*; Boethius's
*Introduction to the Categorical Syllogism*, *Categorical
Syllogisms*, *Hypothetical Syllogisms*, *On Topical
Difference*, and *On Division*. Abelard's works cover
the material presented in the old logic, though they do so in
different ways. His *Logica*
'*ingredientibus*' is a close textual commentary on
the old logic, though only some of it survives, namely the
commentaries on the *Isagoge*, the *Categories*, *On
Interpretation*, and *On Topical Differences*; his
*Dialectica* is an independent treatise on dialectic that
treats the same material thematically, though neither the beginning
(covering the *Isagoge* and the start of the
*Categories*) nor the ending (on division and definition) have
been preserved. In addition, there are four lesser works on
dialectic:


* *Introductiones parvulorum*, "Introductory
Logic."
* *Logica* '*nostrorum petitioni
sociorum*', "Logic" (starting with the words
'At the request of our friends...').
* *Tractatus de intellectibus*, "A Treatise on
Understandings."
* *Sententiae secundum Magistrum Petrum*, "Master
Peter's Views."



The first of these is a series of elementary commentaries on the old
logic (though again not completely preserved); their simple level has
led some scholars to think they must come from early in
Abelard's career, others to deny that they are Abelard's
work at all. Second, the *Logica* '*nostrorum
petitioni sociorum*' is something of a work-in-progress: it
assumes knowledge of Abelard's earlier *Logica*
'*ingredientibus*' and discusses advanced points
not dealt with there, but for long stretches it is also a
straightforward paraphrase of or commentary on Porphyry's
*Isagoge*; it has textual parallels with some of
Abelard's other works and shows some knowledge of theology. The
third work deals with concepts, or 'understandings', from
both the point of view of logic (roughly as providing the meanings of
terms) and from the point of view of the philosophy of mind (as
vehicles for mental content). The last work may be no more than a
report of some of Abelard's lectures, and is concerned with
logical and metaphysical puzzles about wholes and parts.



The second category consists of Abelard's works on ethics:


* *Ethica seu Scito teipsum*, "Ethics, or, Know
Yourself."
* *Collationes*, "Conversations" a.k.a.
*Dialogus inter Philosophum, Iudaeum, et Christianum*,
"The Dialogue of a Philosopher with a Jew and a
Christian".



The *Ethics* offers an analysis of moral worth and the degree
of praise or blame that should attach to agents and their actions; it
breaks off at the beginning of the second book. The
*Conversations* is a pair of debates (among characters who
appear to Abelard in a dream) over the nature of happiness and the
supreme good: the Philosopher, who claims to follow only natural
reason, first debates with the Jew, who follows the Old Law; the
Philosopher then debates the Christian, who defends Christian ethics
from a philosophical point of view. Abelard also wrote a slight work
of practical advice for his son:


* *Carmen ad Astralabium*, "Poem for
Astralabe."



Moral advice and edifying sentiments are found in this series of
distichs.



The third category consists of Abelard's works of philosophical
theology. His three main works are devoted to a philosophical analysis
of the Trinity, the several versions representing successive stages of
his thought and his attempts at orthodoxy (each rewritten several
times):


* *Theologia* '*summi boni*'.
"Theology" (that begins with the words 'The highest
good...').
* *Theologia christiana*, "Christian
Theology."
* *Theologia* '*scholarium*',
"Theology" (that begins with the words 'In the
schools...').



The first version of the *Theology* seems to have been the work
condemned at the Council of Soisssons, the last the work condemned at
the Council of Sens. In addition to these three works, in which
problems in philosophical theology are treated thematically, Abelard
also wrote several commentaries:


* *Expositio orationis dominicae*, "Analysis of the
Lord's Prayer."
* *Expositio symboli Apostolorum*, "Analysis of the
Apostle's Creed."
* *Expositio fidei in symbolum Athanasii*, "Analysis of
Faith in the Athanasian Creed."
* *Hexaemeron*, "Commentary on *Genesis*
1-2:25."
* *Commentaria in Epistolam Pauli ad Romanos*,
"Commentary on St. Paul's Letter to the
Romans."



The first three commentaries are brief, but Abelard's
discussions of the first verses of *Genesis* and of
Paul's letter are extensive and detailed (the latter also
relevant to Abelard's ethical theory). Abelard also took up
questions about faith and reason in a short work:


* *Soliloquium*, "Soliloquy."



This brief inner dialogue, modelled on Augustine's
*Soliloquies*, has "Peter" talking things over with
"Abelard." Theological questions of a more practical
nature were raised by Heloise in a series of questions she
asked on her behalf and on behalf of the nuns of the Paraclete:


* *Problemata Heloissae cum Petri Abaelardi
solutionibus*, "Heloise's Problem-List
(with Abelard's Solutions)."



Practical issues are also addressed in Abelard's sermons, hymns,
and lamentations (*planctus*). Finally, Abelard composed an
extremely influential theological work that contains no theoretical
speculation at all:


* *Sic et non*, "For and Against."



Abelard assembles a series of 158 questions, each of which is
furnished with patristic citations that imply a positive answer
(*sic*) to the question and other patristic citations implying
a negative answer (*non*). Abelard does not attempt to
harmonize these apparently inconsistent remarks, but in his preface he
lays down rules for proper hermeneutic investigation: look for
ambiguity, check the surrounding context, draw relevant distinctions,
and the like.



Abelard's students and disciples also record many of his views,
though this material has yet to be explored carefully. There are
references in Abelard's extant works to other works we do not
have: *Grammatica*, "Grammar"; *Rhetorica*,
"Rhetoric"; a commentary on *Ezekiel* written at
the beginning of his studies in theology; and others. It is possible
some of these works may yet be found.


## 2. Metaphysics



Abelard's metaphysics is the first great example of nominalism
in the Western tradition. While his view that universals are mere
words (*nomina*) justifies the label, nominalism--or,
better, irrealism--is the hallmark of Abelard's entire
metaphysics. He is an irrealist not only about universals, but also
about propositions, events, times other than the present, natural
kinds, relations, wholes, absolute space, hylomorphic composites, and
the like. Instead, Abelard holds that the concrete individual, in all
its richness and variety, is more than enough to populate the world.
Abelard preferred reductive, atomist, and material explanations
whenever possible; he devoted a great deal of effort to pouring cold
water on the metaphysical excesses of his predecessors and
contemporaries.



Abelard defends his thesis that universals are nothing but words by
arguing that ontological realism about universals is incoherent. More
exactly, he holds that there cannot be any real object in the world
satisfying Boethius's criteria for the universal, namely
something present as a whole in many at once so as to constitute their
substance (i.e. to make the individual in which it is present what it
is). Hence, Abelard concludes, universality is not an ontological
feature of the world but a semantic feature of language.



Suppose universals were things in the world, so that one and the same
item is completely present in both Socrates and an ass at the same
time, making each to be wholly an animal. Abelard points out that then
the same thing, *animal*, will be simultaneously rational (due
to its role in constituting the species *human being*) and
irrational (due to its role in constituting the species *ass*).
But then contraries are simultaneously present in the same thing as a
whole, which is impossible.



To the rejoinder that rationality and irrationality are not actually
present in the same thing, Abelard offers a twofold reply. First, he
rejects the claim that they are present only potentially. Each species
is actually informed by a contrary, and the genus is actually present
in each as a whole; hence it is actually informed by one contrary in
one species and by the other in the other; since it is wholly one and
the same in each, it is therefore actually informed by contraries, and
the contradiction results. Second, Abelard undertakes to establish
that contraries will be present not merely in the genus but even in
the selfsame individual. For Socrates is (an) animal, and so is
Brunellus the Ass; but by transitivity--since each is wholly and
completely *animal*--Socrates is Brunellus, and hence both
rational and irrational. Put a different way, each is essentially an
animal, and furthermore essentially rational and essentially
irrational.



If we object to this last piece of reasoning, on the grounds that
individuals are unique in virtue of their non-essential features,
Abelard replies that this view "makes accidents prior to
substance." That is, the objection claims that individual things
are individual in virtue of features that contingently characterize
them, which confuses things with their features.



Prospects are no better for realism if the universal is identified not
with a single thing but with a collection of things. Abelard points
out that collections are posterior to their parts, and, furthermore,
the collection is not shared among its parts in the way a universal is
said to be common to many. Nor does it help to try to identify the
universal with the individual in some fashion, for example in claiming
that Socrates *qua* human is taken as the universal *human
being*; Abelard argues that if the universal really is the
individual, then we are stuck with the consequence that either
individuals such as Socrates are common to many, or there are as many
universals as there are individuals, each of which is absurd.



Abelard concludes that universality is merely linguistic, not a
feature of the world. More precisely, Abelard holds that common nouns
(such as 'animal'), verbs, and negative names (such as
'not-Socrates') are correctly predicable of many, and so
count as universals. These terms are semantically general, in that
their sense applies to more than one thing, but they do not thereby
name some general thing; instead, they distributively refer to each of
the individuals to which the term applies. For example, the term
'animal' has the sense *living substance*, which is
inherently general, and it refers to each individual animal since each
is a living substance--as Abelard puts it, since each has the
status of being a living substance. But this is to leave the domain of
metaphysics for semantics; see the discussion of Abelard's
philosophy of language in
 Section 4.



Abelard maintains that everything in the world apart from God and
angels is either form, matter, or a composite of form and matter. The
matter of something is that out of which it is made, whether it
persists in the finished product (as bricks in a house) or is absorbed
into it (as flour in bread). Ultimately, all material objects are
composed of the four elements earth, air, fire, and water, but they do
not retain their elemental forms in most combinations. In general, the
form of a material object just is the configuration of its material
parts: "We call the form strictly what comes from the
composition of the parts." The form of a statue, for example, is
its shape, which is no more than the arrangement of its
matter--the curve of the nose, the size of the eyes, and so on.
Forms are therefore *supervenient* on matter, and have no
ontological standing independent of it. This is not to deny that forms
exist, but to provide a particular explanation of what it is for a
form to inhere in a given subject, namely for that subject to have its
matter configured in a certain way. For example, the inherence of
shape in the statue just is the way in which its bronze is arranged.
Hence material things are identical with what they are made
of--with one exception: human beings, whose forms are their
immaterial (and immortal) souls. Strictly speaking, since human souls
are capable of existence in separation form the body, they are not
forms after all, though they act as substantial forms as long as they
are joined to the body.



Material composites of form and matter, humans excepted, are integral
wholes made up of their discrete material parts as configured in a
given way. Abelard countenances many types of integral wholes:
collections, no matter how their members are selected; structured
composites, whether naturally unified (such as Socrates and his limbs)
or artificially unified (such as the walls, floor, and roof of a
house); continuous quantities that are homogeneous material
'substances,' namely stuffs, such as water or gold;
geometrical objects, such as lines, defined by the relative position
of their parts; temporal wholes, such as a day and the hours that make
it up. Most of these wholes are ontologically nothing beyond their
material parts. Whether structured composites have any independent
ontological standing depends on the status of their organizing
forms.



Abelard's theory of substantial integral wholes is not a pure
mereology in the modern sense, since he holds that there are
privileged divisions: just as a genus is properly divided into not
just any species but its proximate species, so too the division of a
whole must be into its principal parts. Intuitively, some wholes have
a natural division that takes precedence over others; a sentence, for
example, is divided into words, syllables, and letters, in precisely
that order. According to Abelard, the principal parts of a whole are
those whose conjunction immediately results in the complete whole. His
intent seems to be that the nature of the composition (if any) that
defines the integral whole also spells out its principal parts. A
house consists of floor, walls, and roof put together in the right
way. It is an open question whether each principal part (such as the
wall) requires the existence of all of its subparts (every brick). The
principal parts of a collection, for example, are just each of the
members of the collection, whatever may be the case with any given
member's subparts; the principal parts of an aggregation are the
members located in proximity to one another.



Individuals have natures, and in virtue of their natures they belong
to determinate natural kinds. But an individual's nature is not
something really shared with or common to other individuals;
Abelard's refutation of realism has shown that this is
impossible. Instead, Abelard takes a natural kind to be a well-defined
collection of things that have the same features, broadly speaking,
that make them what they are. Why a given thing has some features
rather than others is explained by how it got that way--the
natural processes that created it result in its having the features it
does, namely being the kind of thing it is; similar processes lead to
similar results. On this reading, it is clear that natural kinds have
no special status; they are no more than discrete integral wholes
whose principle of membership is similarity, merely reflecting the
fact that the world is divided into discrete similarity-classes of
objects. Furthermore, such real relations of similarity are nothing
themselves above and beyond the things that are similar. The division
into natural kinds is, presumably, a 'shallow fact' about
the world: matters could have been otherwise had God ordained them
differently; fire might be cold, heavy bodies fall upwards, frogs
reason. If these causal powers were different, then natural kinds
might be different as well, or might not have been as sharply
differentiated as they are now. Given how matters stand, natural kinds
carve the world at its joints, but they are the joints chosen by
God.


## 3. Logic



Abelard was the greatest logician since Antiquity: he devised a purely
truth-functional propositional logic, recognizing the distinction
between *force* and *content* we associate with Frege,
and worked out a complete theory of entailment as it functions in
argument (which we now take as the theory of logical consequence). His
logical system is flawed in its handling of topical inference, but
that should not prevent our recognition of Abelard's
achievements.



Abelard observes that the same propositional content can be expressed
with different force in different contexts: the content *that
Socrates is in the house* is expressed in an assertion in
'Socrates is in the house'; in a question in 'Is
Socrates in the house?'; in a wish in 'If only Socrates
were in the house!' and so on. Hence Abelard can distinguish in
particular the assertive force of a sentence from its propositional
content, a distinction that allows him to point out that the component
sentences in a conditional statement are not asserted, though they
have the same content they do when asserted--'If Socrates
is in the kitchen, then Socrates is in the house' does not
assert that Socrates is in the kitchen or that he is in the house, nor
do the antecedent or the consequent, although the same form of words
could be used outside the scope of the conditional to make such
assertions. Likewise, the distinction allows Abelard to define
negation, and other propositional connectives, purely
truth-functionally in terms of content, so that negation, for
instance, is treated as follows: not-*p* is false/true if and
only if *p* is true/false.



The key to the theory of argument, for Abelard, is found in
*inferentia*, best rendered as 'entailment', since
Abelard requires the connection between the propositions involved to
be both necessary and relevant. That is, the conclusion--more
exactly, the sense of the final statement--is required by the
sense of the preceding statement(s), so that it cannot be otherwise.
Abelard often speaks of the sense of the final statement being
"contained" in the sense of the preceding statement(s),
much as we speak of the conclusion being contained in the premisses.
An entailment is complete (*perfecta*) when it holds in virtue
of the logical form (*complexio*) of the propositions involved.
By this, Abelard tells us, he means that the entailment holds under
any uniform substitution in its terms, the criterion now associated
with Bolzano. The traditional four figures and moods of the
categorical syllogism derived from Aristotle, and the doctrine of the
hypothetical syllogism derived from Boethius, are all instances of
complete entailments, or as we should say, valid inference.



There is another way in which conclusions can be necessary and
relevant to their premisses, yet *not* be formally valid (not
be a complete entailment). The necessary connection among the
propositions, and the link among their senses, might be a function of
non-formal metaphysical truths holding in all possible worlds. For
instance, human beings are a kind of animal, so the consequence
'If Socrates is a human being, Socrates is an animal'
holds of necessity and the sense of the antecedent compels that of the
consequent, but it is not formally valid under uniform substitution.
Abelard takes such incomplete entailments to hold according to the
theory of the topics (to be forms of so-called topical inference). The
sample inference above is validated by the topic "from the
species", a set of metaphysical relations one of which is
expressible in the rule "Whatever the species is predicated of,
so too is the genus" which grounds the inferential force of the
entailment. Against Boethius, Abelard maintained that topical rules
were only needed for incomplete entailment, and in particular are not
required to validate the classical moods of the categorical and
hypothetical syllogism mentioned in the preceding paragraph.



Abelard spends a great deal of effort to explore the complexities of
the theory of topical inference, especially charting the precise
relations among conditional sentences, arguments, and what he calls
"argumentation" (roughly what follows from conceded
premisses). One of the surprising results of his investigation is that
he denies that a correlate of the Deduction Theorem holds, maintaining
that a valid argument need not correspond to an acceptable conditional
sentence, nor conversely, since the requirements on arguments and
conditionals differ.



In the end, it seems that Abelard's principles of topical
inference do not work, a fact that became evident with regard to the
topic "from opposites": Abelard's principles lead to
inconsistent results, a result noted by Alberic of Paris. This led to
a crisis in the theory of inference in the twelfth century, since
Abelard unsuccessfully tried to evade the difficulty. These debates
seem to have taken place in the later part of the 1130s, as Abelard
was about to become embroiled with Bernard of Clairvaux, and his
attention was elsewhere.


## 4. Philosophy of Language



Much of Abelard's philosophy of language is devoted to analyzing
how a given expression or class of expressions function logically:
what words are quantifiers, which imply negation, and the like, so
that the logic described above may be applied. To do so, he relies on
the traditional division, derived from Aristotle, that sees the main
linguistic categories as *name*, *verb*, and their
combination into the *sentence*.



Abelard takes names to be conventionally significant simple words,
usually without tense. So understood there are a wide variety of
names: proper and common names; adjectives and adverbs; pronouns,
whether personal, possessive, reflexive, or relative; conventional
interjections such as 'Goodness!'; and, arguably,
conjunctions and prepositions (despite lacking definite
signification), along with participles and gerundives (which have
tense). Abelard usually, though not always, treats compound names such
as 'street-sweeper' reductively. Even so his list is not
general enough to catalogue all referring expressions. In point of
fact, much of Abelard's discussion of the semantics of names
turns on a particular case that stands for the rest: common names.
These are at the heart of the problem of universals, and they pose
particular difficulties for semantics.



When Abelard puts forward his claim that universality is only a
linguistic phenomenon, so that universals are "nothing more than
words," he raises the objection that unless common names are the
names of common items, they will be meaningless, and so his view is no
better than that of his teacher Roscelin (who held that universals
were mere mouth noises). In reply Abelard clearly draws a distinction
between two semantic properties names possess: reference
(*nominatio*), a matter of what the term applies to; and sense
(*significatio*), a matter of what hearing the term brings to
mind, or more exactly the informational content (*doctrina*) of
the concept the word is meant to give rise to, a causal notion. A few
remarks about each are in order.



Names, both proper and common, refer to things individually or
severally. A name is linked with that of which it is the name as
though there were someone who devised the name to label a given thing
or kind of thing, a process known as "imposition"
(modelled on Adam's naming the animals in Genesis 2:19), rather
like baptism. This rational reconstruction of reference does not
require the person imposing the name, the "impositor", to
have anything more than an indefinite intention to pick out the thing
or kind of thing, whatever its nature may be:



> 
> The inventor [of names] intended to impose them according to some
> natures or distinctive properties of things, even if he himself did
> not know how to think correctly upon the nature or distinctive
> property of a thing.
> 



A name "has a definition in the nature of its imposition, even
if we do not know what it is." Put in modern terms, Abelard
holds a theory of *direct reference*, in which the extension of
a term is not a function of its sense. We are often completely
ignorant of the proper conceptual content that should be associated
with a term that has been successfully imposed.



A proper name--the name of a primary substance--signifies a
concrete individual (*hoc aliquid*), picking out its bearer as
personally distinct from all else. Therefore, proper names are
semantically singular referring expressions, closely allied to
indexicals, demonstratives, and singular descriptions (or descriptive
terms). Common names, by contrast, are semantically allied with
expressions that have what Abelard calls "plural
signification". On the one hand, common names are like plural
nouns; the common name 'man' is grammatically singular but
operates like the plural term 'men'--each refers to
every man, although the plural term signifies individuals as part of a
collection, whereas the common name distributively refers to each
individual. On the other hand, common names are like terms such as
'trio' or 'pair' in that they pick out a
determinate plurality of individuals, but only on an occasion of use,
since their extension is variable.



Thus a common name distributively refers to concrete individuals,
though not to them *qua* individuals. Instead, it severally
picks out those individuals having a given nature: 'human
being' refers to Socrates and to Plato, in virtue of each of
them being human. This is not a shared feature of any sort; Socrates
just is what he is, namely human, and likewise Plato is what he is,
namely human too. Abelard states his deflationary position clearly in
his *Logica* '*ingredientibus*':



> 
> Now it seems we should stay away from accepting the agreement among
> things according to what is not any thing--it's as though
> we were to unite in nothing things that now exist!--namely, when
> we say that this [human] and that one agree in the human status, that
> is to say: in that they are human. But we mean precisely that they are
> human and don't differ in this regard--let me repeat: [they
> don't differ] in that they are human, although we're not
> appealing to any *thing* [in this explanation].
> 



Socrates and Plato are real; their agreement is real, too, but it
isn't to be explained by appealing to any thing--their
agreement just is their each being human. From a metaphysical point of
view they have the same standing as human beings; this does not
involve any metaphysically common shared ingredient, or indeed appeal
to any ingredient at all. That is the sense in which there is a
"common reason" for the imposition of a common name. 



For all that signification is posterior to reference, names do have
signification as well. Abelard holds that the signification of a term
is the informational content of the concept that is associated with
the term upon hearing it, in the normal course of events. Since names
are only conventionally significant, which concept is associated with
a given name depends in part on the psychological conditioning of
language-users, in virtue of which Abelard can treat signification as
both a causal and a normative notion: the word 'rabbit'
ought to cause native speakers of English to have the concept of a
rabbit upon hearing it. Abelard is careful to insist that the
signification is a matter of the informational content carried in the
concept--mere psychological associations, even the mental images
characteristic of a given concept, are not part of what the word
*means*. Ideally, the concept will correspond to a real
definition that latches onto the nature of the thing, the way
'rational mortal animal' is thought to be the real
definition of 'human being', regardless of other
associated features (even necessary features such as risibility) or
fortuitous images (as any mental image of a human will be of someone
with determinate features). Achieving such clarity in our concepts is,
of course, an arduous business, and requires an understanding of how
understanding itself works (see the discussion of Abelard's
philosophy of mind in
 Section 5).
 Yet one point should be clear from the example. The significations of
some names, such as those corresponding to natural-kind terms, are
abstractions in the sense that they include only certain features of
the things to which the term refers. They do not positively exclude
all other features, though, and are capable of further determinate
specification: 'rational mortal animal' as the content of
the concept of 'human being' signifies all humans,
whatever their further features may be--tall or short, fat or
thin, male or female, and so on.



What holds for the semantics of names applies for the most part to
verbs. The feature that sets verbs apart from names, more so than
tense or grammatical person, is that verbs have connective force
(*vis copulativa*). This is a primitive and irreducible feature
of verbs that can only be discharged when they are joined with names
in the syntactically appropriate way, reminiscent of the
'unsaturatedness' of concepts in Frege. Sentences are made
up of names and verbs in such a way that the meaning of the whole
sentence is a function of the meaning of its parts. That is,
Abelardian semantics is fundamentally compositional in nature. The
details of how the composition works are complex. Abelard works
directly with a natural language (Latin) that, for all its
artificiality, is still a native second tongue. Hence there are many
linguistic phenomena Abelard is compelled to analyze that would be
simply disallowed in a more formal framework.



For example, Abelard notes that most verbs can occur as predicates in
two ways, namely as a finite verbal form or as a nominal form combined
with an auxiliary copula, so that we may say either 'Socrates
runs' or 'Socrates is running'; the same holds for
transitive predication, for instance 'Socrates hits Plato'
and 'Socrates is hitting Plato.' Abelard argues that in
general the pure verbal version of predication is the fundamental
form, which explains and clarifies the extended version; the latter is
only strictly necessary where simple verbal forms are lacking. (The
substantive verb 'is' requires special treatment.) Hence
for Abelard the basic analysis of a predicative statement recognizes
that two fundamentally different linguistic categories are joined
together: the name *n* and the simple verbal function
*V*( ), combined in the well-formed sentence
*V*(*n*).



Abelard argues that sentences (*propositiones*) must signify
more than just the understandings of the constituent name and verb.
First, a sentence such as 'Socrates runs' deals with
Socrates and with running, not with anyone's understandings. We
talk about the world, not merely someone's understanding of the
world. Second, sentences like 'If something is human, it is an
animal' are false if taken to be about understandings, for
someone could entertain the concept *human* without
entertaining the concept *animal*, and so the antecedent would
obtain without the consequent. Third, understandings are evanescent
particulars, mere mental tokenings of concepts. But at least some
consequential sentences are necessary, and necessity can't be
grounded on things that are transitory, and so not on understandings.
Sentences must therefore signify something else in addition to
understandings, something that can do what mere understandings cannot.
Abelard describes this as signifying what the sentence says, calling
what is said by the sentence its *dictum* (plural
*dicta*).



To the modern philosophical ear, Abelard's *dicta* might
sound like propositions, abstract entities that are the timeless
bearers of truth and falsity. But Abelard will have nothing to do with
any such entities. He declares repeatedly and emphatically that
despite being more than and different from the sentences that express
them, *dicta* have no ontological standing whatsoever. In the
short space of a single paragraph he says that they are "no real
things at all" and twice calls them "absolutely
nothing." They underwrite sentences, but they aren't real
things. For although a sentence says something, there is not some
thing that it says. The semantic job of sentences is to *say*
something, which is not to be confused with naming or denoting some
thing. It is instead a matter of proposing how things are, provided
this is not given a realist reading. Likewise, the truth of true
sentences is not a property inhering in some timeless entity, but no
more than the assertion of what the sentence says--that is,
Abelard adopts a deflationary account of truth. A sentence is true if
things stand in the way it says, and things make sentences true or
false in virtue of the way they are (as well as in virtue of what the
sentences say), and nothing further is required. The sentence
'Socrates runs' is true because Socrates runs, which is
all that can be said or needs to be said.


## 5. Philosophy of Mind



Aristotelian philosophy of mind offers two analyses of intentionality:
the conformality theory holds that we think of an object by having its
very form in the mind, the resemblance theory that we do so by having
a mental image in the mind that naturally resembles the object.
Abelard rejects each of these theories and proposes instead an
adverbial theory of thought, showing that neither mental images nor
mental contents need be countenanced as ontologically independent of
the mind. He gives a contextual explication of intentionality that
relies on a linguistic account of mental representation, adopting a
principle of compositionality for understandings.



The first Aristotelian analysis takes understanding to be the
mind's acquisition of the form of the object that is understood,
without its matter. For an understanding to be about some
thing--say, a cat--is for the form of the cat to be in the
mind or intellective soul. The inherence of the form in matter makes
the matter to be a thing of a certain kind, so that the inherence of
the form *cat* in matter produces an actual cat, whereas the
(immaterial) inherence of the form *cat* in the mind transforms
the mind into an understanding of a cat: the mind becomes (formally)
identical with its object. Since the 'aboutness' of
understanding is analyzed as the commonness or identity of form in the
understanding and the thing understood, we may call this approach the
*conformality theory* of understanding. This theory captures
the intuition that understanding somehow inherits or includes
properties of what is understood, by reducing the intentionality of
understanding to the objective identity of the form in the mind and
the form in the world.



The second Aristotelian analysis takes understanding to be the
mind's possession of a concept that is a natural likeness of, or
naturally similar to, that of which it is a concept. For an
understanding to be about some thing, such as a cat, is for there to
be an occurrent concept in the mind that is a natural likeness of a
cat. The motivation for calling the likeness "natural" is
to guarantee that the resemblance between the understanding and what
is understood is objective, and that all persons have access to the
same stock of concepts. (The conformality theory does this by
postulating the objective existence of forms in things and by an
identical process in all persons of assimilating or acquiring forms.)
We may call this approach the *resemblance theory* of
understanding: mental acts are classified according to the distinct
degree and kind of resemblance they have to the things that are
understood.



The resemblance theory faces well-known problems in spelling out the
content of resemblance or likeness. For example, a concept is clearly
immaterial, and as such radically differs from any material object.
Furthermore, there seems to be no formal characteristic of a mental
act in virtue of which it can non-trivially be said to resemble
anything else. To get around these difficulties, mediaeval
philosophers, like the British Empiricists centuries later, appealed
to a particular kind of resemblance, namely pictorial resemblance. A
portrait of Socrates is about Socrates in virtue of visually
resembling Socrates in the right ways. And just as there are pictorial
images that are about their subjects, so too are there mental images
that are about things. These mental images, whether they are concepts
or are contained in concepts, explain the way in which a concept is
'about' an object. For an understanding to be about a cat
is for it to be or contain a mental image of a cat. The phenomenon of
mental 'aboutness' is explicated by the more familiar case
of pictorial aboutness, itself reduced to a real relation of
resemblance.



Despite their common Aristotelian heritage, the conformality theory
and the resemblance theory are not equivalent. The transformation of
the mind through the inherence of a form is not necessarily the same
as the mind's possession of a concept. Equally, natural likeness
or resemblance need not be understood as identity of form; formal
identity need not entail genuine resemblance, due to the different
subjects in which the form is embodied.



The standard way to reconcile the conformality theory and the
resemblance theory is to take the mind's possession of a concept
to be its ability to transform itself through the inherence of a form,
construing formal identity as natural likeness, where having a form in
the mind that is identical to the form of the object understood just
is to have a mental image of that very object.



Abelard argues against conformality as follows. Consider a tower,
which is a material object with a certain length, depth, and height;
assume that these features compose its form, much as the shape of a
statue is its form. According to Aristotelian metaphysics, the
inherence of a form in a subject makes the subject into something
characterized by that form, as for instance whiteness inhering in
Socrates makes him something white. The forms of the tower likewise
make that in which they inhere to be tall, wide, massive--all
physical properties. If these forms inhere in the mind, then, they
should make the mind tall, wide, and massive, an absurd conclusion:
the mind "cannot extend itself in length or width." Yet it
is a cardinal thesis of the conformality theory that the mind has the
identical form that is possessed by the external object, the tower,
although the form of (say) length is by its very nature physical.
Thus, Abelard concludes, conformality is incoherent.



Abelard's main objection to the resemblance theory is that
mental images *qua* images, like any sign, are inert: they
require interpretation. A sign is just an object. It may be taken in a
significative role, though it need not be. Abelard notes that this
distinction holds equally for non-mental signs: we can treat a statue
as a lump of bronze or as a likeness. Mental images are likewise
inert. For a sign to function significatively, then, something more is
required beyond its mere presence or existence. But the resemblance
theory doesn't recognize the need to interpret the mental image
as an image, and thereby mistakenly identifies understanding with the
mere presence of a mental image in the mind. Abelard concludes that
mental images have only an instrumental role in thought, describing
them as "intermediary signs of things" (*intersigna
rerum*). Intentionality derives instead from the act of attention
(*attentio*) directed upon the mental image. Proof is found in
the fact that that we can "vary the understanding" simply
by attending to different features of the mental image: the selfsame
image--say, a fig tree--can be used to think about this very
fig tree, or trees in general, or plant life, or my lost love with
whom I sat under it, or anything whatsoever. There is no intrinsic
feature of the mental image in virtue of which it is about any given
thing; if there were, Abelard notes, we could determine by inspection
what a sign is about--but we can't. Mental images,
therefore, can't explain the intentionality of understanding,
because their role is merely instrumental. We think with them, and
cannot avoid them; but they do not explain intentionality.



Abelard draws the conclusion that intentionality is a primitive and
irreducible feature of the mind, our acts of attending to things.
Different acts of attention are intrinsically different from one
another; they are about what they are about in virtue of being the
kind of attention they are. Hence Abelard adopts what is nowadays
called an *adverbial* theory of thought.



Given that intentionality is primitive, Abelard adopts a contextual
approach to mental content: he embeds these irreducible acts of
attention in a structure whose articulation helps define the character
of its constituent elements. The structure Abelard offers is
linguistic, a logic of mental acts: just as words can be said to
express thoughts, so too we can use the articulated logic of language
to give a theory of understanding. In short, Abelard gives something
very like a linguistic account of mental representation or
intentionality. To this end he embraces a principle of
compositionality, holding that what an understanding is about is a
function of what its constituent understandings are about. The unity
of the understanding of a complex is a function of its logical
simplicity, which is characterized by the presence of what Abelard
calls "a single dominant conjunction" (the logical
operator of greatest scope). Hence the understanding of a complex may
be treated as a complex of distinct understandings, aggregated in the
same thought, with its (logical) structure flowing from the
'dominant conjunction' over the other logical operations
governing its constituent understandings. Abelard's acts of
attention thus display the logical structure of the understanding they
express, and thereby give the semantics of written or spoken language.
Much of Abelard's writings on logic and dialectic are given over
to working out the details as a scheme for explicating mental
content.


## 6. Ethics



Abelard takes the rational core of traditional Christian morality to
be radically *intentionalist*, based on the following
principle: the agent's intention alone determines the moral
worth of an action. His main argument against the moral relevance of
consequences turns on what contemporary philosophers often refer to as
moral luck. Suppose two men each have the money and the intention to
establish shelters for the poor, but one is robbed before he can act
whereas the second is able to carry out his intention. According to
Abelard, to think that there is a moral difference between them is to
hold that "the richer men were the better they could become
... this is the height of insanity!" Deed-centred morality
loses any kind of purchase on what might have been the case. Likewise,
it cannot offer any ground for taking the epistemic status of the
agent into account, although most people would admit that ignorance
can morally exculpate an agent. Abelard makes the point with the
following example: imagine the case of fraternal twins, brother and
sister, who are separated at birth and each kept in complete ignorance
of even the existence of the other; as adults they meet, fall in love,
are legally married and have sexual intercourse. Technically this is
incest, but Abelard finds no fault in either to lay blame.



Abelard concludes that in themselves deeds are morally indifferent.
The proper subject of moral evaluation is the agent, via his or her
intentions. It might be objected that the performance or
nonperformance of the deed could affect the agent's feelings,
which in turn may affect his or her intentions, so that deeds thereby
have moral relevance (at least indirectly). Abelard denies it:



> 
> For example, if someone forces a monk to lie bound in chains between
> two women, and by the softness of the bed and the touch of the women
> beside him he is brought to pleasure (but not to consent), who may
> presume to call this pleasure, which nature makes necessary, a fault?
> 



We are so constructed that the feeling of pleasure is inevitable in
certain situations: sexual intercourse, eating delicious food, and the
like. If sexual pleasure in marriage is not sinful, then the pleasure
itself, inside or outside of marriage, is not sinful; if it is sinful,
then marriage cannot sanctify it--and if the conclusion were
drawn that such acts should be performed wholly without pleasure, then
Abelard declares they cannot be done at all, and it was unreasonable
(of God) to permit them only in a way in which they cannot be
performed.



On the positive side, Abelard argues that unless intentions are the
key ingredient in assessing moral value it is hard to see why
coercion, in which one is forced to do something against his or her
will, should exculpate the agent; likewise for ignorance--though
Abelard points out that the important moral notion is not simply
ignorance but strictly speaking negligence. Abelard takes an extreme
case to make his point. He argues that the crucifiers of Christ were
not evil in crucifying Jesus. (This example, and others like it, got
Abelard into trouble with the authorities, and it isn't hard to
see why.) Their ignorance of Christ's divine nature didn't
by itself make them evil; neither did their acting on their (false and
mistaken) beliefs, in crucifying Christ. Their non-negligent ignorance
removes blame from their actions. Indeed, Abelard argues that they
would have sinned had they thought crucifying Christ was required and
did *not* crucify Christ: regardless of the facts of the case,
failing to abide by one's conscience in moral action renders the
agent blameworthy.



There are two obvious objections to Abelard's intentionalism.
First, how is it possible to commit evil voluntarily? Second, since
intentions are not accessible to anyone other than the agent,
doesn't Abelard's view entail that it is impossible to
make ethical judgements?



With regard to the first objection, Abelard has a twofold answer.
First, it is clear that we often want to perform the deed and at the
same time do not want to suffer the punishment. A man wants to have
sexual intercourse with a woman, but not to commit adultery; he would
prefer it if she were unmarried. Second, it is clear that we sometimes
"want what we by no means want to want": our bodies react
with pleasure and desire independently of our wills. If we act on such
desires, then our action is done "of" will, as Abelard
calls it, though not voluntarily. There is nothing evil in desire:
there is only evil in acting on desire, and this is compatible with
having contrary desires.



With regard to the second objection, Abelard grants that other humans
cannot know the agent's intentions--God, of course, does
have access to internal mental states, and so there can be a Final
Judgement. However, Abelard does not take ethical judgement to pose a
problem. God is the only one with a right to pass judgement. Yet this
fact doesn't prevent us from enforcing canons of human justice,
because, Abelard holds, human justice has primarily an exemplary and
deterrent function. In fact, Abelard argues, it can even be just to
punish an agent we strongly believe had no evil intention. He cites
two cases. First, a woman accidentally smothers her baby while trying
to keep it warm at night, and is overcome with grief. Abelard
maintains that we should punish her for the beneficial example her
punishment may have on others: it may make other poor mothers more
careful not to accidentally smother their babies while trying to keep
them warm. Second, a judge may have excellent (but legally
impermissible) evidence that a witness is perjuring himself; since he
cannot show that the witness is lying, the judge is forced to rule on
the basis of the witness's testimony that the accused, whom he
believes to be innocent, is guilty. Human justice may with propriety
ignore questions of intention. Since there is divine justice, ethical
notions are not an idle wheel--nor should they be, even on
Abelard's understanding of human justice, since they are the
means by which we determine which intentions to promote or discourage
when we punish people as examples or in order to deter others.



There is a sense, then, in which the only certifiable sin is acting
against one's conscience, unless one is morally negligent. Yet
if we cannot look to the intrinsic value of the deeds or their
consequences, how do we determine which acts are permissible or
obligatory? Unless conscience has a reliable guide, Abelard's
position seems to open the floodgates to well-meaning
subjectivism.



Abelard solves the problem by taking obedience to God's
will--the hallmark of morally correct behaviour, and itself an
instance of natural law--to be a matter of the agent's
intention conforming to a purely formal criterion, namely the Golden
Rule ("Do to others as you would be done to"). This
criterion can be discovered by reason alone, without any special
revelation or religious belief, and is sufficient to ensure the
rightness of the agent's intention. But the resolution of this
problem immediately leads to another problem. Even if we grant Abelard
his naturalistic ethics, why should an agent care if his or her
intentions conform to the Golden Rule? In short, even if Abelard were
right about morality, why be moral?



Abelard's answer is that our happiness--to which no one is
indifferent--is linked to virtue, that is, to habitual morally
correct behaviour. Indeed, Abelard's project in the
*Collationes* is to argue that reason can prove that a merely
naturalistic ethics is insufficient, and that an agent's
happiness is necessarily bound up with accepting the principles of
traditional Christian belief, including the belief in God and an
Afterlife. In particular, he argues that the Afterlife is a condition
to which we ought to aspire, that it is a moral improvement even on
the life of virtue in this world, and that recognizing this is
constitutive of wanting to do what God wants, that is, to live
according to the Golden Rule, which guarantees as much as anything can
(pending divine grace) our long-term postmortem happiness.



The Philosopher first argues with the Jew, who espouses a
'strict observance' moral theory, namely obedience to the
Mosaic Law. One of the arguments the Jew offers is the Slave's
Wager (apparently the earliest-known version of Pascal's Wager).
Imagine that a Slave is told one morning by someone he doesn't
know whether to trust that his powerful and irritable Master, who is
away for the day, has left instructions about what to do in his
absence. The Slave can follow the instructions or not. He reasons that
if the Master indeed left the instructions, then by following them he
will be rewarded and by not following them he will be severely
punished, whereas if the Master did not leave the instructions he
would not be punished for following them, though he might be lightly
punished for not following them. (This conforms to the standard payoff
matrix for Pascal's Wager.) That is the position the Jew finds
himself in: God has apparently demanded unconditional obedience to the
Mosaic Law, the instructions left behind. The Philosopher argues that
the Jew may have other choices of action and, in any event, that there
are rational grounds for thinking that ethics is not a matter of
action in conformity to law but a matter of the agent's
intentions, as we have seen above.



The Philosopher then argues with the Christian. He initially maintains
that virtue entails happiness, and hence there is no need of an
Afterlife since a virtuous person remains in the same condition
whether dead or alive. The Christian, however, reasons that the
Afterlife is better, since in addition to the benefits conferred by
living virtuously, the agent's will is no longer impeded by
circumstances. In the Afterlife we are no longer subject to the body,
for instance, and hence are not bound by physical necessities such as
food, shelter, clothing, and the like. The agent can therefore be as
purely happy as life in accordance with virtue could permit, when no
external circumstances could affect the agent's actions. The
Philosopher grants that the Afterlife so understood is a clear
improvement even on the virtuous life in this world, and joins with
the Christian in a cooperative endeavour to define the nature of the
virtues and the Supreme Good. Virtue is its own reward, and in the
Afterlife nothing prevents us from rewarding ourselves with virtue to
the fullest extent possible.


## 7. Theology



Abelard held that reasoning has a limited role to play in matters of
faith. That he gave reasoning a role at all brought him into conflict
with those we might now call *anti*-dialecticians, including
his fellow abbot Bernard of Clairvaux. That the role he gave it is
limited brought him into conflict with those he called
"pseudo-dialecticians," including his former teacher
Roscelin.



Bernard of Clairvaux and other anti-dialecticians seem to have thought
that the meaning of a proposition of the faith, to the extent that it
can be grasped, is plain; beyond that plain meaning, there is nothing
we can grasp at all, in which case reason is clearly no help. That is,
the anti-dialecticians were *semantic realists* about the plain
meaning of religious sentences. Hence their impatience with Abelard,
who seemed not only bent on obfuscating the plain meaning of
propositions of the faith, which is bad enough, but to do so by
reasoning, which has no place either in grasping the plain meaning
(since the very plainness of plain meaning consists in its being
grasped immediately without reasoning) or in reaching some more
profound understanding (since only the plain meaning is open to us at
all).



Abelard has no patience for the semantic realism that underlies the
sophisticated anti-dialectical position. Rather than argue against it
explicitly, he tries to undermine it. From his commentaries on
scripture and dogma to his works of speculative theology, Abelard is
first and foremost concerned to show how religious claims can be
understood, and in particular how the application of dialectical
methods can clarify and illuminate propositions of the faith.
Furthermore, he rejects the claim that there is a plain meaning to be
grasped. Outlining his method in the Prologue to his *Sic et
non*, Abelard describes how he initially raises a question, e.g.
whether priests are required to be celibate, and then arranges
citations from scriptural and patristic authorities that at least seem
to answer the question directly into positive and negative responses.
(Abelard offers advice in the Prologue for resolving the apparent
contradictions among the authorities using a variety of techniques:
see whether the words are used in the same sense on both sides; draw
relevant distinctions to resolve the issue; look at the context of the
citation; make sure that an author is speaking in his own voice rather
than merely reporting or paraphrasing someone else's position;
and so on.) Now each authority Abelard cites seems to speak clearly
and unambiguously either for a positive answer to a given question or
for a negative one. If ever there were cases of plain meaning, Abelard
seems to have found them in authorities, on opposing sides of
controversial issues. His advice in the Prologue amounts to saying
that sentences that seem to be perfect exemplars of plain meaning in
fact have to be carefully scrutinized to see just what their meaning
is. Yet that is just to say that they do not have plain meaning at
all; we have to use reason to uncover their meaning. Hence the
anti-dialecticians don't have a case.



There is a far more serious threat to the proper use of reason in
religion, Abelard thinks (*Theologia christiana* 3.20):



> 
> Those who claim to be dialecticians are usually led more easily to
> [heresy] the more they hold themselves to be well-equipped with
> reasons, and, to that extent more secure, they presume to attack or
> defend any position the more freely. Their arrogance is so great that
> they think there isn't anything that can't be understood
> and explained by their petty little lines of reasoning. Holding all
> authorities in contempt, they glory in believing only
> themselves--for those who accept only what their reason persuades
> them of, surely answer to themselves alone, as if they had eyes that
> were unacquainted with darkness.
> 



Such pseudo-dialecticians take reason to be the final arbiter of all
claims, including claims about matters of faith. More exactly, Abelard
charges them with holding that (a) everything can be explained by
human reason; (b) we should only accept what reason persuades us of;
(c) appeals to authority have no rational persuasive force. Real
dialecticians, he maintains, reject (a)-(c), recognizing that
human reason has limits, and that some important truths may lie
outside those limits but not beyond belief; which claims about matters
of faith we should accept depends on both the epistemic reliability of
their sources (the authorities) and their consonance with reason to
the extent they can be investigated.



Abelard's arguments for rejecting (a)-(c) are
sophisticated and subtle. For the claim that reason may be fruitfully
applied to a particular article of faith, Abelard offers a particular
case study in his own writings. The bulk of Abelard's work on
theology is devoted to his dialectical investigation of the Trinity.
He elaborates an original theory of identity to address issues
surrounding the Trinity, one that has wider applicability in
metaphysics. The upshot of his enquiries is that belief in the Trinity
is rationally justifiable since as far as reason can take us we find
that the doctrine makes sense--at least, once the tools of
dialectic have been properly employed.



The traditional account of identity, derived from Boethius, holds that
things may be either generically, specifically, or numerically the
same or different. Abelard accepts this account but finds it not
sufficiently fine-grained to deal with the Trinity. The core of his
theory of identity, as presented in his *Theologia christiana*,
consists in four additional modes of identity: (1) essential sameness
and difference; (2) numerical sameness and difference, which Abelard
ties closely to essential sameness and difference, allowing a more
fine-grained distinction than Boethius could allow; (3) sameness and
difference in definition; (4) sameness and difference in property
(*in proprietate*). Roughly, Abelard's account of
essential and numerical sameness is intended to improve upon the
identity-conditions for things in the world given by the traditional
account; his account of sameness in definition is meant to supply
identity-conditions for the features of things; and his account of
sameness in property opens up the possibility of there being different
identity-conditions for a single thing having several distinct
features.



Abelard holds that two things are *the same in essence* when
they are numerically the same concrete thing (*essentia*), and
essentially different otherwise. The Morning Star is essentially the
same as the Evening Star, for instance, since each is the selfsame
planet Venus. Again, the formal elements that constitute a concrete
thing are essentially the same as one another and essentially the same
as the concrete thing of which they are the formal constituents:
Socrates is his essence (Socrates is what it is to be Socrates). The
corresponding general thesis does not hold for parts, however. Abelard
maintains that the part is essentially different from the integral
whole of which it is a part, reasoning that a given part is completely
contained, along with other parts, in the whole, and so is less than
the quantity of the whole.



Numerical difference does not map precisely onto essential difference.
The failure of numerical sameness may be due to one of two causes.
First, objects are not numerically the same when one has a part that
the other does not have, in which case the objects are essentially
different as well. Second, objects are numerically different when
neither has a part belonging to the other. Numerical difference thus
entails the failure of numerical sameness, but not conversely: a part
is not numerically the same as its whole, but it is not numerically
different from its whole. Thus one thing is essentially different from
another when either they have only a part in common, in which case
they are not numerically the same; or they have no parts in common, in
which case they are numerically different as well as not numerically
the same. Since things may be neither numerically the same nor
numerically different, the question "How many things are
there?" is ill-formed as it stands and must be made more
precise, a fact Abelard exploits in his discussion of the Trinity.



Essential and numerical sameness and difference apply directly to
things in the world; they are extensional forms of identity. By
contrast, sameness and difference in definition is roughly analogous
to modern theories of the identity of properties. Abelard holds that
things are *the same in definition* when what it is to be one
requires that it be the other, and conversely; otherwise they differ
in definition.



Finally, things are *the same in property* when they specify
features that characterize one another. Abelard offers an example to
clarify this notion. A cube of marble exemplifies both whiteness and
hardness; what is white is essentially the same as what is hard, since
they are numerically the same concrete thing, namely the marble cube;
yet the whiteness and the hardness in the marble cube clearly differ
in definition--but even so, what is white is characterized by
hardness (the white thing is hard), and conversely what is hard is
characterized by whiteness (the hard thing is white). The properties
of whiteness and hardness are "mixed" since, despite their
being different in definition, each applies to the selfsame concrete
thing (namely the marble cube) as such and also as it is characterized
by the other.



The interesting case is where something has properties that
"remain so completely unmixed" that the items they
characterize are *different in property*. Consider a
form-matter composite in relation to its matter. The matter out of
which a form-matter composite is made is essentially the same as the
composite, since each is the entire material composite itself. Yet
despite their essential sameness, they are not identical; the matter
is not the composite, nor conversely. The matter is not the composite,
for the composite comes to be out of the matter, but the matter does
not come to be out of itself. The composite is not the matter, since
"nothing is in any way a constitutive part of or naturally prior
to itself." Instead, the matter is prior to the composite since
it has the property *priority* with respect to the composite,
whereas the composite is posterior to its matter since it has the
property *posteriority* with respect to its matter. Now despite
being essentially the same, the matter is not characterized by
posteriority, unlike the composite, and the composite is not
characterized by priority, unlike the matter. Hence the matter and
composite are different in property; the properties *priority*
and *posteriority* are unmixed--they differ in
property.



Now for the payoff. Abelard deploys his theory of identity to shed
light on the Trinity as follows. The three Persons are essentially the
same as one another, since they are all the same concrete thing
(namely God). They differ from one another in definition, since what
it is to be the Father is not the same as what it is to be the Son or
what it is to be the Holy Spirit. The three Persons are numerically
different from one another, for otherwise they would not be three, but
they are not numerically different from God: if they were there would
be three gods, not one. Moreover, each Person has properties that
uniquely apply to it--*unbegotten* to the Father,
*begotten* to the Son, and *proceeding* to the Holy
Spirit--as well as properties that are distinctive of it, such as
*power* for the Father, *wisdom* for the Son, and
*goodness* for the Holy Spirit. The unique properties are
unmixed in Abelard's technical sense, for the Persons differ
from one another in their unique properties, and such properties do
not apply to God; the distinctive properties are mixed, though, in
that God is characterized by each (the powerful God is the wise God is
the good God). Further than that, Abelard holds, human reason cannot
go; but reason validates the analysis (strictly speaking only a
"likeness" or analogy) as far as it can go.