Late medieval logic
Late medieval logic
Paul Vincent Spade
I
Medieval logic encompassed more than what we call logic today. It
included semantics, philosophy of language, parts of physics, of
philosophy of mind and of epistemology.
Late medieval logic began around 1300 and lasted through at least
the fifteenth century. With some noteworthy exceptions, its most
original contributions were made by 1350, particularly at Oxford.
Hence the focus of this chapter will be on the period 1300–1500, with
special emphasis on Oxford before 1350.
But first some background concerning the earlier period. The logical
writings of Aristotle were all available in Latin by the mid-twelfth
century.1 In addition, except for the theory of ‘proofs of propositions’2
(see section VIII below), the characteristic new ingredients of medieval
logic were already in place or at least in progress by the end of the
twelfth century or the beginning of the thirteenth.
The theory of inference or ‘consequence’, for example, was studied
as early as Peter Abelard (1079–1142). Again, after about 1120 the
circulation of Aristotle’s Sophistical Refutations in Latin stimulated a
study of fallacies and the many features of language that produce them.
Out of this investigation there arose twelfth- and thirteenth-century
writings on semantic ‘properties of terms’, like ‘supposition’ and
‘ampliation’ (see section VI below).3 At the same time, treatises on
sophismata or puzzle-sentences in logic, theology or philosophy of
nature began to be produced. (A good analogy for this literature may
be found in modern discussions of Frege’s ‘The morning star is the
evening star’.) Likewise, studies were written about the logical effects
of words like ‘only’, ‘except’, ‘begins’ and ‘ceases’ that offer many
opportunities for fallacies and involve complications going far beyond
syllogistic or the theory of topical inferences.4 Treatises on ‘insolubles’
or semantic paradoxes began to appear late in the twelfth century
([17.42], [17.49]). Simultaneously, a literature developed on a new
kind of disputation called ‘obligations’.5 Collectively, these new logical
genres are known as ‘terminist’ logic because of the important role
played in them by the ‘properties of terms’.
These developments continued into the thirteenth century. By midcentury,
authors such as Peter of Spain, Lambert of Auxerre and William
of Sherwood were writing summary treatises (summulae) covering the
whole of logic, including the material in Aristotle’s writings as well as
new terminist developments.6
Then, after about 1270, something odd happened, both in England
and on the Continent. In France, terminism was eclipsed by an entirely
different theory called ‘speculative grammar’, which appealed to the
notion of ‘modes of signifying’ and is therefore sometimes called
‘modism’. This theory prevailed in France until the 1320s, when John
Buridan (b. c. 1295/1300, d. after 1358) suddenly restored the theory
of supposition and associated terminist doctrines. After Buridan,
supposition theory was the leading vehicle for semantic (as distinct
from grammatical) analysis until the end of the Middle Ages.
Modism never dominated England as it did elsewhere; terminism
survived there during its period of neglect on the Continent. Still,
few innovations in supposition theory or its satellite doctrines were
made in England during the last quarter of the thirteenth century.
But then, in the very early fourteenth century, Walter Burley (or
Burleigh, b. c. 1275, d. 1344/5) began to do new work in the terminist
tradition.
This temporary decline of terminism on both sides of the Channel
at the end of the thirteenth century, and its sudden revival shortly after
1300, are mysterious events. But, whatever the underlying causes, when
supposition theory and related doctrines re-emerged in the early
fourteenth century, they were importantly different from how they had
been earlier.7
II
This section will survey the main stages of late medieval logic, and
introduce important names. Later sections will focus on particular
theoretical topics.8
In England,9 logic after 1300 may be divided into three stages: first,
1300–50, when the best work was done. Burley and William of Ockham
(c. 1285–1347) were the paramount figures during this period. Both
made important contributions to supposition theory, and Ockham in
particular developed sophisticated theories of ‘mental language’ and
‘connotation’.
In the next generation, several men associated with Merton College,
Oxford, were influential in specific areas. Richard Kilvington (early
fourteenth century, d. 1361) and William Heytesbury (b. before 1313,
d. 1372/3), among others, applied the techniques of sophismata to
questions in natural philosophy, epistemic logic and other fields.
Thomas Bradwardine (c. 1295–1349) wrote an Insolubles that was
perhaps the most influential treatise on semantic paradoxes
throughout the Middle Ages. Around 1330–2, Adam Wodeham
devised an important theory of ‘complexly significables’ (complexe
significabilia), the closest medieval equivalent to the modern notion
of ‘proposition’. Richard Billingham (fl. 1340s or 1350s) seems to
have originated the important theory of ‘proofs of propositions’. His
treatise Speculum puerorum or Youths’ Mirror will be discussed in
section VIII below.
The second stage of English logic after 1300 lasted from 1350 to
1400. This was a time of consolidation, of sophisticated but no longer
especially original work. The period has not yet been well researched,
but at least three trends can be distinguished. First, there was a
remarkable number of school-manuals written in logic, compilations
of standard doctrine with little innovation. Works of Richard Lavenham
(d. 1399 or after) provide a good example. Gradually, certain of these
school-texts congealed into two collections called the Libelli
sophistarum (Little Books for Arguers), one for Oxford and one for
Cambridge. These were printed in several editions around 1500.
Second, English logic from 1350 to 1400 had a special interest in
the doctrine of ‘proofs of propositions’ associated with Billingham. As
time passed, the labour devoted to this topic grew enormously. John
Wyclif dedicated a large part of his Logic (before 1368) and especially
of his Continuation of the Logic (1371–4) to this theory. So did Ralph
Strode, a contemporary of Wyclif s, in his own Logic. John Huntman
wrote a Logic sometime near the end of the century, showing the
continued expansion of the Billingham tradition.
A third concern of English logic in this period was the signification
of propositions. The most influential work here was probably On the
Truth and Falsehood of Propositions by Henry Hopton (fl. 1357).
There Hopton discussed and rejected several previous views before
setting out his own theory.10 (See section V below.)
Several other English authors during this period should be mentioned,
although their works are not yet fully understood. They include Richard
Feribrigge (fl. probably 1360s), author of an important Consequences
and a Logic or Treatise on the Truth of Propositions. Of lesser
importance are: Robert Fland (fl. 1335–60); Richard Brinkley, the
author of a Summa of logic probably between 1360 and 1373; Thomas
Manlevelt (or Mauvelt), who wrote several treatises around mid-century
that were influential on the Continent; and near the end of the century,
Robert Alington, William Ware, Robert Stonham, and others.
One of the most significant events in English logic late in the century
was the arrival at Oxford in 1390 of the Italian Paul of Venice (c.
1369–1429). Paul studied there for some three years. On his return to
Italy, he taught at Padua and elsewhere, and was an important conduit
through which English logic became known in Italy in the fifteenth
century. His writings include a widely circulated Little Logic (Logica
parva) and the enormous Big Logic (Logica magna).
The third stage of late medieval English logic includes the whole
fifteenth century. This was a period of shocking decline. Except for a
few insignificant figures around 1400, not even second-rate authors
are known. The manuscripts from this period—and by 1500, early
printed books—offer little hope that further research will change this
assessment. The Oxford and Cambridge Little Books for Arguers,
already mentioned, testify to the deterioration of logic during this
period. Medieval logic was effectively dead in England after 1400.
Logic on the Continent during these same two centuries cannot be
so neatly divided into stages. Still, there as in England, the most
important work was done before about 1350. The pre-eminent figure
was doubtless Buridan. His writings include a Consequences, a
Sophismata and a Summulae of Dialectic. Buridan’s students included
many influential logicians of the next generation, among them: Albert
of Saxony (d. 1390), the author of a Sophismata and A Very Useful
Logic, and the first rector of the University of Vienna; and Marsilius of
Inghen (c. 1330–96), the first rector of the University of Heidelberg
and the author of an Insolubles and of treatises on ‘properties of terms’.
On many points, Buridan’s logical views were like Burley’s or
especially Ockham’s in England. There are differences, but the
similarities are more striking, especially when contrasted with logic on
either side of the Channel before 1300. The extent of Ockham’s own
influence on Buridan is doubtful, but Ockham’s confrère Adam
Wodeham was instrumental in transmitting much English learning to
Paris. In particular, Wodeham’s theory of ‘complexly significables’ was
adopted by Gregory of Rimini (c. 1300–58).
The Parisian Peter of Ailly (1350–1420/1) wrote several interesting
logical works, including: Concepts and Insolubles, a pair of treatises
on ‘mental language’ and the Liar Paradox; Destructions of the Modes
of Signifying, against ‘modism’; Treatise on Exponibles (see section
VIII below); and Treatise on the Art of ‘Obligating’ (perhaps by
Marsilius of Inghen instead).
Before 1400, the Italian Peter of Mantua (fl. 1387–1400) wrote a
Logic that already shows knowledge of earlier English work,
particularly that stemming from Billingham. Around 1400 Angelo of
Fossombrone, who taught at Bologna (1395–1400) and Padua (1400–
2), wrote an Insolubles maintaining an elaborated version of
Heytesbury’s theory. About the same time, the newly returned Paul of
Venice spread the gospel of Oxford logic further in Italy. Among his
students, Paul of Pergula (d. 1451/5) wrote a Logic and a treatise On
the Composite and the Divided Sense (on the scope of certain logical
operators) based on Heytesbury’s own work of that name, and Gaetano
of Thiene (1387–1465) wrote detailed commentaries on works by
Heytesbury and Strode. Other authors in Italy and elsewhere continued
to write on logic to the end of the Middle Ages and beyond.11
Even these few names will suffice to show that the logical landscape
after about 1400 was by no means so desolate on the Continent as in
England. Still, on either side of the Channel logical work after 1350
was largely derivative and, while sometimes very sophisticated, not
very innovative. There was certainly no one, for example, with the
stature of Burley, Ockham or Buridan.
III
This and the following sections will concentrate on five important topics
in late medieval logic: (a) the theory of ‘mental language’, (b) the
signification of propositions, (c) developments in supposition-theory,
(d) semantic paradoxes, and (e) connotation-theory and the ‘proofs of
propositions’.
In On Interpretation, 16a3–4, Aristotle stated that ‘spoken sounds
are symbols of affections in the soul, and written marks symbols of
spoken sounds’. These words were translated by Boethius and
interpreted as implying three levels of language: spoken, written and
mental. Through Boethius this three-level hierarchy of language became
a commonplace in medieval logical literature.
Of the three, mental language was regarded as the most basic. Its
semantic properties are natural ones;12 they do not originate from any
convention or custom, and cannot be changed at will. Unlike spoken
and written languages, mental language is the same for everyone.
Careful authors sometimes distinguished ‘proper’ from ‘improper’
mental language. The latter occurs when we think ‘in English’ or ‘in
French’. Thus a public speaker might rehearse a speech by running
through silently the words he will later utter aloud. What goes on there
is a kind of ‘let’s pretend’ speaking that takes place in imagination and
is in that sense ‘mental’. But it is not what most authors meant by
‘mental language’. Since silent recitation varies with the spoken language
one is rehearsing, it is not the same for everyone. Proper mental language
is different. It includes, for example, what happens when one suddenly
‘sees’ the force of a mathematical proof; in that case there is a ‘flash of
insight’, an understanding or judgement that need not yet be put into
words, even silently. This kind of mental language, the theory goes, is
the same for everyone.13
Spoken language, by contrast, has its semantic function parasitically,
through a conventional correlation between its expressions and mental
ones. The arbitrariness of this convention is what allows the multitude
of spoken languages. Written language plays an even more derivative
role, through a conventional correlation between its inscriptions and
the sounds of spoken language. The arbitrariness of this convention
too allows for different scripts among written languages. Only through
the mediation of spoken language, the theory went, are inscriptions
correlated with thoughts in mental language. This view implies that
one cannot read a language one does not know how to speak. Most
medieval authors accepted this consequence.
Following Boethius, the correlations between written and spoken
language and between spoken and mental language were often regarded
as relations of ‘signification’. This claim had theoretical consequences,
since signification was a well-defined notion in the Middle Ages. A
term ‘signifies’ what it makes one think of (‘establishes an understanding
of’=constituit intellectum+genitive).14 While there was dispute about
what occupies the object-pole of this relation, there was agreement
over the criterion. Signification is thus a special case of causality, and
so transitive. (Certain authors added to signification in general the
particular notions of immediate and ultimate signification. The general
relation of signification thus became what modern logicians call the
‘ancestral’ of the relation of immediate signification;15 a term t then
ultimately signifies x if and only if t signifies x and x does not signify
anything else.) Terms in mental language signify (make one think of)
external objects only in the degenerate sense that they are the thoughts
of those external objects.
According to this view, to say that expressions of spoken language
immediately signify expressions of mental language is to say that the
function of speech is to convey thoughts. Certain authors, e.g. Duns
Scotus (c. 1265–1308), Burley and Ockham, regarded this as too
restrictive. For them, spoken (and written) terms may be made to signify
anything, not only the speaker’s thoughts. In fact spoken words do
not always make us think of thoughts; sometimes we are made to think
directly of external objects. For these authors, the relations between
written and spoken language and between either of these and mental
language are not relations of signification. Ockham described them
neutrally as relations of ‘subordination’.16
IV
Although authors since Boethius had recognized mental language, it
was not until the fourteenth century that it began to be investigated in
detail. Ockham was the first to develop a full theory of mental language
and put it to philosophical use. Shortly thereafter, Buridan began to
work out his own view. His theory agrees with Ockham’s on the whole,
although Ockham’s is the more detailed. In the early 1340s, Gregory
of Rimini refined certain parts of the theory, and applied it to a solution
to the Liar Paradox. In 1372, Peter of Ailly’s Concepts and Insolubles
incorporated the work of both Ockham and Gregory.17 Other authors
made contributions to the theory, but these were the major ones. The
presentation below will follow Ockham’s account except as indicated.
Terms in mental language are concepts; its propositions are
judgements. The fact that mental language is the same for everyone
explains how it is possible to translate one spoken (or written) language
into another. A sentence in Spanish is a correct translation of a sentence
in English if and only if the two are subordinated to the same mental
sentence. More generally, any two spoken or written expressions—
from the same or different languages—are synonymous if and only if
they are subordinated to the same mental expression. Again, any spoken
or written expression is equivocal if and only if it is subordinated to
more than one mental expression.
If mental language accounts for synonymy and equivocation in
spoken and written languages, can there be synonymy or equivocation
in mental language itself? The textual evidence is mixed. There are
passages in Ockham (Summa logicae I, 3 = [17.7] OP 1:11; Summa
logicae I, 13 = [17.7] OP 1:44) supporting a negative answer in both
cases. Nevertheless other texts (Ordinatio, I, d. 3, q. 2 = [17.7] OT 2:405;
Ordinatio I, d. 3, q. 3 = [17.7] OT 2:425; Quodlibet 5, q. 9 = [17.7] OT
9:513–18), where Ockham is discussing the semantics of certain
connotative terms (see section VIII below), perhaps imply the existence
of mental synonymy. As for equivocation, Ockham’s theory of tense
and modality, as well as his theory of supposition (see section VI below),
commits him outright to certain kinds of equivocation in mental
language.18 But apart from textual considerations, there are
philosophical reasons for saying that, given other features of Ockham’s
theory, mental synonymy or equivocation makes no sense.19
What is included in mental language? In two passages (Summa
logicae, I, 3 = [17.7] OP 1:11.1–26; Quodlibet 5, q. 8 = [17.7] OT 9:508–
13), Ockham remarks that, just as for spoken and written language,
the vocabulary of mental language is divided into ‘parts of speech’.
Thus there are mental nouns, verbs, prepositions, conjunctions, etc.
But not all features of spoken and written language are found in mental
language. Ockham acknowledges doubts about mental participles (their
job could be performed by verbs) and pronouns (presumably ‘pronouns
of laziness’, as for example in ‘Socrates is a man and he is an animal’).
Moreover, not all characteristics of spoken and written syntax are found
in mental language. While mental nouns and adjectives have case and
number, and mental adjectives admit of positive, comparative and
superlative degrees, they do not have gender and are not divided into
grammatical declensions (like Latin’s five declensions). Mental verbs
have person, number, tense, voice and mood, but are not divided into
grammatical conjugations.
Ockham’s mental language looks remarkably like Latin. This fact
led some modern writers to reject the theory as a foolish attempt to
‘explain’ features of Latin by merely duplicating them in mental
language, which is then regarded as somehow more ‘basic’ ([17.39] §
23). But more is involved than that. Ockham’s strategy is to admit into
mental language exactly those features of spoken or written language
that affect the truth-values of propositions. All other features of spoken
and written language, Ockham says, are only for the sake of decorative
style, or in the interest of brevity. They are not present in mental
language.20
Mental language is thus a logically perspicuous language for
describing the world. It has whatever is needed to distinguish truth
from falsehood, nothing more. In this respect, mental language is
reminiscent of the ‘ideal languages’ proposed by early twentieth-century
philosophers ([17.51]).
How are mental words combined in mental propositions? What is
the difference, for example, between the true mental proposition
‘Every man is an animal’ and the false ‘Every animal is a man’? In
written language, the difference is the spatial configuration of the
words. But the mind does not take up space, so that there can be no
such difference there. In speech the difference lies in the temporal
sequence of the words. But since proper mental language at least
sometimes involves a ‘flash of insight’ that happens all at once, neither
can temporal word order account for the difference between the two
mental propositions.
Because of such difficulties, authors such as Gregory of Rimini and
Peter of Ailly held that mental propositions (although not all of them
for Peter) are simple mental acts not really composed of distinct mental
words at all.21 Ockham too had considered such a theory (In Sententias
II, qq. 12–13 = [17.7] OT 5:279; Exposition of ‘On Interpretation’,
proem = [17.7] OP 2:356). It is hard to reconcile this view with the
claim that mental vocabulary is divided into ‘parts of speech’; distinct
mental words would appear to have no job to do if they do not enter
into the structure of mental propositions.
V
Besides the disagreement over the immediate signification of spoken
and written terms (see section III above), there was a dispute over
ultimate signification. Metaphysical realists, such as Burley, maintained
the traditional view that general terms ultimately signify universal
entities, while nominalists (e.g. Ockham and Buridan) held that they
ultimately signify only individuals.
Some authors extended the notion of signification to ask not only
about the signification of terms but also about the signification of whole
propositions. Do they signify anything besides what their component
terms signify separately? Do they signify, for example, states of affairs
or facts?
Ockham did not explicitly address this question. But Buridan did,
and his answer was no. For him ([17.16] II, conclusion 5), a
proposition—and in general any complex expression—signifies
whatever its categorematic terms signify, nothing more. (‘Categorematic’
terms are those that can serve as subject or predicate in a proposition;
they were regarded as having their own signification. Other words
were called ‘syncategorematic’ and were regarded as not having any
signification of their own; they are ‘logical particles’ used for combining
categorematic terms into propositions and other complex expressions.)
Thus in the spoken proposition ‘The cat is on the mat’, when I hear the
word ‘cat’ I am, on Buridan’s account, made to think of all cats and
when I hear ‘mat’ I am made to think of all mats. That is all the
proposition makes me think of, and so all it signifies.
Elsewhere Buridan maintained a different and incompatible theory
([17.16] II, sophism 5 and conclusions 3–7). The proposition ‘Socrates
is sitting’, for example, signifies Socrates to be sitting. And what is that?
Buridan held that if Socrates really is sitting, then Socrates to be sitting
is just Socrates himself. But if he is not sitting, then Socrates to be sitting
is nothing at all.22 This view bears some similarity to a theory held
earlier at Oxford by Walter Chatton (1285–1344) and discussed as the
first previous view in Henry Hopton’s On the Truth and Falsehood of
Propositions. Similar views were defended by Richard Feribrigge and
John Huntman. The details of their texts have not been thoroughly
investigated, and there is much that is still obscure; it is not certain that
all these authors maintained variants of the same doctrine. Still, the
motivation is the same in each case: to find something to serve as the
significate of a proposition in an ontology that does not allow anything
like facts, states of affairs or ‘propositions’ in the modern sense.
But there were other opinions. As early as Abelard, some authors
held that what propositions signify falls outside the Aristotelian
categories, and is something like the modern notion of ‘proposition’.
Sometimes this new entity was called a ‘mode’, sometimes a dictum.23
In the fourteenth century, such theories continued to find their
defenders. Perhaps a version of it may be seen in the early 1330s in
William of Crathorn. Perhaps too Henry Hopton intended such a theory
as the second previous view he considered, according to which a
proposition signifies a ‘mode’ of a thing, where a ‘mode’ is not a
something but a being-somehow (esse aliqualiter). But an unequivocal
statement can be found in the theory of ‘complexly significables’
([17.38]; see also [17.35] chs 14–15). According to this theory,
complexly significables are the bearers of truth-value. They are not
propositions in the medieval sense, not even mental propositions, but
are what is expressed by propositions. They are the significates of
propositions, and the objects of knowledge, belief and prepositional
attitudes generally. Complexly significables do not exist in the way
substances and accidents do. Before creation, for example, only God
existed. But even then God knew that the world was going to exist.
This complexly significable cannot be identified with God himself, since
God is a necessary being but it was contingent that the world was
going to exist. Yet as distinct from God, it cannot have existed before
creation. Such extralogical considerations were an important motivation
for the theory of complexly significables. Authors such as Buridan and
Peter of Ailly rejected the theory; Peter, for example, claimed that the
argument about God’s knowledge before creation is based on an
illegitimate substitution of identicals in an opaque context involving
necessity ([17.27] 62).
All these theories offered a real entity (even if an odd one, like a
‘complexly significable’) as the correlate of a true proposition, and so
as the ontological basis for a ‘correspondence’ theory of truth. Other
authors took a different approach. They too maintained a
correspondence theory, often expressed as: a proposition is true if and
only if it ‘precisely signifies as is the case’, or if and only if ‘howsoever
[the proposition] signifies, so it is the case’. For them, the proper
question is not what but how a proposition signifies. This ‘adverbial’
notion of signification allowed a correspondence theory without being
obliged to find any ontological correlate for a true proposition to
correspond to. After rejecting earlier views, Henry Hopton’s own theory
was like this. Heytesbury had earlier held a similar view, as did Peter of
Ailly later ([17.22] 61–5; [17.27] 10, 48–54 and nn.).
VI
The theory of ‘supposition’ is a mystery. Although it is central to the
theories of ‘properties of terms’ that developed from the twelfth century
on, it is not clear what the theory was intended to accomplish, or indeed
what the theory as a whole was about.24
Throughout its history, there were two main parts to supposition
theory. One was a theory of the reference of terms in propositions, and
how that reference is affected by syntactic and semantic features of
propositions. The question this part of the theory was intended to
answer is, ‘What does a term refer to (supposit for, stand for) in a
proposition?’ That much is clear. But from the beginning, there was
another part of supposition theory, an account of how one might validly
‘descend to singulars’ under a given occurrence of a term in a
proposition, sometimes combined with a correlative account of ‘ascent
from singulars’. The mystery surrounds this second part.
Before the decline of terminism after 1270, there is some evidence
that the second part of supposition theory, like the first, was intended
to answer the question of what a term refers to in a proposition. The
first part of the theory says what kind of thing a given term-occurrence
refers to, while the second specifies how many such things it refers to
(in much the way one finds even today accounts purporting to say
whether the terms of a syllogism are about ‘all’ or ‘some’ of a class).
The evidence for this is mixed, but even if this was the original intent
of the second part of supposition theory, some authors quite early
realized its theoretical difficulties.
When supposition theory re-emerged with Burley in England and
later with Buridan in France, the two parts of the theory had been
separated once and for all. By that time the theory of descent and
ascent clearly was not about what a term refers to in a proposition.
What it was about instead is uncertain.
The account below will mainly follow Ockham, although other
authors will be mentioned. Their theories differed from his in detail,
sometimes in important detail, but Ockham’s is fairly typical.
The first part of supposition theory divided supposition or reference
first into proper (literal) and improper (metaphorical). The latter is
illustrated by ‘England fights’, where ‘England’ refers by metonymy to
England’s inhabitants. Medieval logic, like modern logic, did not have
an adequate theory of metaphor. Ockham, Burley and a few others list
some haphazard subdivisions of improper supposition, but really
mention it only to set it aside. Their emphasis is on proper supposition.
Proper supposition was divided into three kinds: personal, simple
and material. The origin of these names is unclear, although the term
‘personal’ suggests a connection with the theology of the Trinity and
the Incarnation. But it should not be thought that personal supposition
has anything especially to do with persons.
Personal supposition occurs when a term refers to everything of which
it is truly predicable. Thus in ‘Every man is running’, ‘man’ refers to all
men and so is in personal supposition. But so too ‘running’ refers there
to all things now running, and hence is likewise in personal supposition.
It does not refer there only to some running things, for example, only
to the running men. Again, in ‘Some man is running’, ‘man’ refers to
all men, not just to running ones.
A term has material supposition when it refers to a spoken or written
word or expression and is not in personal supposition. Thus, ‘man’ in
‘Man has three letters’ has material supposition. Although there are
obvious similarities, material supposition is not merely a medieval
version of modern quotation marks. For in ‘It is possible for Socrates
to run’, the phrase ‘for Socrates to run’ has material supposition. But it
refers to the proposition ‘Socrates is running’, of which the phrase ‘for
Socrates to run’ is not a quotation. (For Ockham, there are no states of
affairs or complexly significables that can be said to be possible. Only
propositions are possible in this sense.)
The definition of simple supposition was a matter of dispute,
depending in part on an author’s metaphysical views and in part on
his theory about the role of language in general ([17.46]). As a paradigm,
‘man’ in ‘Man is a species’ has simple supposition. In general, terms in
simple supposition refer to universals. But for nominalists like Ockham,
there are no metaphysical universals; the only universals are universal
terms in language, most properly universal concepts in mental language.
Thus for Ockham terms in simple supposition refer to concepts. It is
they that are properly said to be species or genera. To prevent the term
‘concept’ in ‘Every concept is a being’ from having simple supposition
(it has personal supposition, since it refers to everything it signifies—
to all concepts), Ockham added that a term in simple supposition must
not be ‘taken significatively’, i.e. that it not be in personal supposition.
But for a realist like Burley, terms in simple supposition refer to real
universals outside the mind. It is they that are species and genera.
Furthermore, for Burley and certain others, general terms in language
signify those extramental universals. Thus the term ‘man’ signifies
universal human nature, not any one individual man or group of men,
and not all men collectively. For Burley, therefore, it is in simple
supposition that a term refers to what it signifies. For Ockham, general
terms do not signify universals, not even universal concepts; they signify
individuals. Even a term like ‘universal’ signifies individuals, since it
signifies concepts, which are metaphysically individuals and are
‘universal’ only in the sense of being predicable of many things. Hence
for Ockham, it is in personal supposition, not simple, that a term refers
to what it signifies.
Personal supposition is the default case. Any term in any proposition
can be taken in personal supposition. It may alternatively be taken in
simple or material supposition only if the other terms in the proposition
provide a suitable context. In such cases, the proposition is strictly
ambiguous and may be read in either sense.25
From this first part of supposition theory alone, certain authors,
e.g. Ockham and Buridan, although not Burley, developed a theory
of truth-conditions for categorical propositions on the square of
opposition. Thus, a universal affirmative ‘Every A is B’ is true if and
only if everything the subject term refers to the predicate term also
refers to (although it may refer to other things as well). Truthconditions
for other propositions on the square of opposition can be
derived from this.
Subordinated to this first part of supposition theory was a theory of
‘ampliation’, accounting for the effects of modality and tense on
personal supposition. A term in personal supposition may always be
taken to refer to the things of which it is presently predicable. But in
the context of past or future tenses, the term may also be taken to refer
to the things of which it was or will be predicable. Likewise, in a modal
context (possibility, necessity), the term may also be taken to refer to
the things of which it can be truly predicable. This expansion of the
range of referents was called ‘ampliation’.
Ockham and Burley regarded the new referents provided by
ampliation as alternatives to the normal ones. Thus in the proposition
‘Every man was running’, ‘man’ may be taken as referring either to all
presently existing men or to all men existing in the past. The proposition
is thus equivocal. But on the Continent, Buridan and others regarded
the new referents as additions to the normal ones. For them, in the
proposition ‘Every man was running’ ‘man’ refers to all presently
existing men and all past men as well.26
The second main part of supposition theory, the theory of descent
and ascent, was a theory subdividing personal supposition only, into
several kinds. First, there is discrete supposition, possessed by proper
names, demonstrative pronouns or demonstrative phrases (e.g. ‘this
man’). All other personal supposition is common, and was typically
subdivided into: determinate (e.g. ‘man’ in ‘Some man is running’),
confused and distributive (e.g. ‘man’ in ‘Every man is an animal’), and
merely confused (e.g. ‘animal’ in ‘Every man is an animal’). The details
varied with the author.
Sometimes these subdivisions were described via the positions of
terms in categorical propositions. Subjects and predicates of particular
affirmatives, and subjects of particular negatives, have determinate
supposition. Subjects of universal affirmatives and negatives, and
predicates of universal and particular negatives, have confused and
distributive supposition. Only predicates of universal affirmatives have
merely confused supposition.
More helpful is the description in terms of descent and ascent. For
Ockham (Burley’s and Buridan’s theories are equivalent), a term has
determinate supposition in a proposition if and only if it is possible to
‘descend’ under that term to a disjunction of singulars, and to ‘ascend’
to the original proposition from any singular. The exact specification
of the notions of ‘descent’, ‘ascent’ and ‘singular’ is subtle, but an
example should suffice. In ‘Some man is running’ one can ‘descend’
under ‘man’ to a disjunction: ‘Some man is running; therefore, this
man is running or that man is running’, etc., for all men. Likewise one
can ‘ascend’ to the original proposition from any singular: ‘This man
is running; therefore, some man is running.’ Hence ‘man’ in the original
proposition has determinate supposition.
A term has confused and distributive supposition in a proposition if
and only if it is possible to ‘descend’ under that term to a conjunction
of singulars but not possible to ‘ascend’ to the original proposition
from any singular. Thus in ‘Every man is running’ it is possible to
descend under ‘man’: ‘Every man is running; therefore, this man is
running and that man is running’, etc., for all men. But the ascent from
any singular ‘This man is running; therefore, every man is running’ is
invalid. Hence the term ‘man’ in the original proposition has confused
and distributive supposition.
A term has merely confused supposition in a proposition if and only
if (a) it is not possible to descend under that term either to a disjunction
or to a conjunction, but it is possible to descend to a disjoint term, and
(b) it is possible to ascend to the original proposition from any singular.
Thus in ‘Every man is an animal’ it is not possible to descend under
‘animal’ to either a disjunction or a conjunction, since if every man is
an animal, it does not follow that every man is this animal or every
man is that animal, etc. Much less does it follow that every man is this
animal and every man is that animal, etc. But it does follow that every
man is this animal or that animal or, etc. Again, if it happens that every
man is this animal (i.e. there is only one man and he is an animal), then
every man is an animal. Hence the term ‘animal’ in that proposition
has merely confused supposition.
It is hard to see what this doctrine was intended to accomplish,
particularly with its appeal to odd ‘disjoint terms’ in merely confused
supposition. At first, modern scholars thought it was an attempt to
provide truth-conditions for quantified propositions in terms of
(infinite) disjunctions or conjunctions. But if that was its purpose,
the doctrine is a failure. The predicate of the particular negative ‘Some
man is not a Greek’ has confused and distributive supposition
according to the above definitions, but the conjunction to which one
can descend under ‘Greek’ does not give the truth-conditions for the
original proposition. Suppose Socrates and Plato are the only men.
Then the conjunction ‘Some man is not this Greek [Socrates] and
some man is not that Greek [Plato]’ is true, but the original proposition
is false.
The problem is that rules for ascent always concern ascent from any
one singular, never from a conjunction. Certain later authors, e.g. Ralph
Strode, Richard Brinkley and Paul of Venice, do explicitly discuss ascent
from conjunctions.27 But earlier writers such as Burley, Ockham and
Buridan conspicuously did not.
Another attempt to explain this second part of supposition theory
suggests that the rules for ascent and descent were used in detecting
and diagnosing fallacies. This is doubtless correct as far as it goes, but
does not account for the details in the theory as we actually find it. In
the end, the exact function of this part of the theory in the early
fourteenth century remains a mystery.
VII
Medieval discussions of ‘insolubles’ (semantic paradoxes like the Liar
Paradox, ‘The sentence I am now saying is false’) began in the late
twelfth century. By around 1200, theories on how to solve them can
be distinguished. Thereafter, three periods in the medieval insolubles
literature can be distinguished: (1) c. 1200–c. 1320, (2) c. 1320– c.
1350 and (3) everything after that.
The earliest known medieval theory of insolubles (cassatio or
cancelling) maintained that one who utters an insoluble is simply ‘not
saying anything’, in the sense that his words do not succeed in making
a claim. This view, although it has its supporters today, quickly
disappeared in the Middle Ages. Other early theories rejected some or
all self-reference; these too have their modern counterparts. Still other
early theories sound less familiar to modern ears. A few authors argued
that, despite the surface grammar, the reference in insolubles is always
to some previous proposition. For example, ‘What I am saying is false’
really amounts to ‘What I said a moment ago is false’. The insoluble is
true or false depending on whether I did in fact say something false a
moment ago. Others, e.g. Duns Scotus, appealed to a distinction
between signified acts and exercised acts. This is the distinction between
what the speaker of an insoluble proposition says he is doing (the
signified act) and what he is really doing (the exercised act). Although
the distinction is suggestive, it is far from clear how it solves the
paradoxes.
Many of these early views are cast in the framework of Aristotle’s
fallacy of what is said ‘absolutely’ and what is said ‘in a certain respect’.
Discussing that fallacy in his Sophistical Refutations, Aristotle made
some enigmatic remarks (180a38–b3) that suggested the Liar Paradox
[17.42]. Consequently, many medieval authors tried to treat insolubles
as instances of that fallacy, although there was little agreement on the
details. Some held that insoluble propositions are true ‘absolutely’ but
false ‘in a certain respect’. Some had it the other way around. Others
said they were both true and false, each ‘in a certain respect’. Still
others applied the Aristotelian distinction not to truth but to
supposition, so that they distinguished between supposition absolutely
and supposition in a certain respect. Long after the early period in the
medieval literature, the fallacy absolutely/in a certain respect was
retained as an authoritative framework for many authors’ discussions,
even when the real point of their theories was elsewhere.
These early theories predominated until about 1320; some of them
survived much longer. Burley and Ockham offered nothing new here.
Both maintained a theory that merely rejected problematic cases of
self-reference without being able to identify which those problematic
cases were.
The first to break new ground was Thomas Bradwardine, in the
early 1320s. Bradwardine’s theory was based on a view linking
signification with consequence. He appears to have been the first to
hold that a proposition signifies exactly what follows from it.28 Since
he was also committed to saying that every proposition implies its
own truth (e.g. Socrates is running, therefore ‘Socrates is running’ is
true), this means that the insoluble ‘This proposition is false’ signifies
that it itself is true. Since it also signifies that it is false, it signifies a
contradiction, and so is simply false. The paradox is broken.29
Bradwardine’s view was enormously influential. Buridan later
maintained a broadly similar theory, and others held variants of it to
the end of the Middle Ages; it was one of the predominant theories.
Shortly after Bradwardine, Roger Swyneshed (fl. before 1335, d. c.
1365), an Englishman associated with Merton College, proposed a
theory in which truth is distinguished from correspondence with reality.
For a proposition to be true, it must not only correspond with reality
(‘signify principally as is the case’), it must also not ‘falsify itself, i.e.
not be ‘relevant to inferring that it is false’. (This notion of ‘relevance’
is not well understood.) Swyneshed drew three famous conclusions
from his theory: (1) There are false propositions (namely, insolubles)
that nevertheless correspond with reality. (2) Valid inference sometimes
lead from truth to falsehood. Validity does not necessarily preserve
truth, although it does preserve correspondence with reality. (3)
Sometimes, two contradictory propositions are both false. The insoluble
‘This proposition is false’ is false because it ‘falsifies’ itself. But its
contradictory ‘That proposition is true’ (referring to the previous
proposition) is also false, since it fails to correspond with reality—the
previous proposition is not true. These conclusions generated much
discussion in the later literature. Swyneshed’s theory did not have many
followers, but it had at least one important one: Paul of Venice
maintained a version of Swyneshed’s theory in his Big Logic.
In 1335, William Heytesbury proposed a theory that rivalled and
may have surpassed Bradwardine’s in influence. He maintained that in
circumstances that would make a proposition insoluble if it signified
just as it normally does (‘precisely as its terms pretend’), it cannot signify
that way only, but must signify some other way too. Thus ‘Socrates is
uttering a falsehood’, if Socrates himself utters it and nothing else,
cannot on pain of contradiction signify only that Socrates is uttering a
falsehood, but must signify that and more. Depending on what else it
signifies, and how it is related to the ordinary signification of the
proposition, different verdicts about the insoluble are appropriate.
Heytesbury himself refused to say what else an insoluble might signify
besides its ordinary signification; that could not be predicted. But some
late authors went on to fill in Heytesbury’s silence. They stipulated
that insolubles in addition signify that they are true, thus linking
Heytesbury’s theory with Bradwardine’s.
Heytesbury’s view has an important consequence. Since signification
in mental language is fixed by nature, not by voluntary convention,
mental propositions can never signify otherwise than they ordinarily
do. Given Heytesbury’s account of insolubility, this means that there
can be no insolubles in mental language. Heytesbury himself did not
draw this conclusion, but it is there none the less.
All important developments concerning insolubles between 1320
and 1350 originated with Englishmen and are associated in one way
or another with Merton College. Later writers, in the third and last
stage of the medieval insolubles literature, sometimes developed this
English material in interesting new ways. Thus Gregory of Rimini and
Peter of Ailly took the above consequence of Heytesbury’s theory to
heart. They maintained that there are no insolubles in mental language,
and that insolubles arise in spoken and written language only because
they correspond (are subordinated) to two propositions in the mind,
one true and the other false. Apart from these developments of earlier
views, there seem to be no radically original theories of insolubles in
the Middle Ages after about 1350.
VIII
Ockham’s theory of connotation has antecedents in Aristotle’s remarks
on paronymy (Categories, 1a12–15). It is the most highly developed
such theory in the Middle Ages.
For Ockham, some categorematic terms are absolute; others are
connotative. ‘Bravery’ is absolute since it signifies only bravery, a quality
in the soul. But ‘brave’ is connotative since it signifies certain persons
(brave ones), but only by making an oblique reference to (‘connoting’)
their bravery. Connotative terms have nominal definitions; absolute
terms do not. The notion of a nominal definition is difficult to state
exactly ([17.44]), but all nominal definitions of a connotative term are
‘equivalent’ for Ockham in a sense that is perhaps as strong as
synonymy. Furthermore, it appears that the connotative term itself is
synonymous with each of its nominal definitions, and may be viewed
in fact as a kind of shorthand abbreviation for them. Thus the adjective
‘white’ is a connotative term having the nominal definition ‘something
having a whiteness’ or ‘something informed by a whiteness’. All three
expressions are synonymous for Ockham.
Since Ockham’s ‘better doctrine’ is that there is no mental synonymy,
the elementary vocabulary of mental language (simple concepts)
includes no connotative terms. Mental language contains the absolute
term ‘whiteness’ and syntactical devices to form nominal definitions
like those above. But it does not, on pain of synonymy, contain a distinct
mental adjective ‘white’. (But see section IV, above.)
All primitive categorematic mental terms are thus absolute. This
has important consequences for Ockham’s philosophy. For (barring
miracles) the mind has simple concepts only for things of which it has
had direct experience (‘intuitive cognition’). The supply of absolute
concepts is therefore a guide to ontology.
There is a related theory in Ockham, the theory of ‘exposition’ or
analysis (see [17.34] 412–27). The outlines of this theory were
established by the mid-thirteenth century. In brief, an exponible
proposition is one containing a word (the ‘exponible term’) that
obscures the sense of the whole proposition. It is to be analysed or
‘expounded’ into a plurality of simpler propositions, called ‘exponents’,
that together capture the sense of the original. Thus ‘Socrates is
beginning to run’ might be expounded by ‘Socrates is not running’ and
‘Immediately hereafter Socrates will be running’.
Ockham’s own theory of exposition is not especially innovative,
except that he explicitly links it with the theory of connotation. This is
an attractive move, since whereas the theory of connotation provides
explicit nominal definitions for connotative terms, it is plausible to
view exposition theory as providing contextual definitions of exponible
terms treated as incomplete symbols. Hence, just as the absence of
synonymy in mental language means that it contains no simple
connotative terms, so too it would mean that mental language contains
no exponible propositions, but only their exponents. Since contextual
definitions provide the more general approach, it is not surprising that
connotation theory quickly declined after Ockham, and is treated only
perfunctorily in Strode and Wyclif. Its place is taken there by much
more elaborate treatments of exponibles. Buridan does retain a fairly
full theory of connotation, but it is not so detailed as Ockham’s.30
Although the theory of exposition continued to have a life of its
own, by mid-century it had also been incorporated into the theory of
‘proofs of propositions’.31 Billingham’s Youth’s Mirror was a seminal
work here.
The notion of ‘proof’ involved in this literature was broader than
the Aristotelian demonstration of the Posterior Analytics. It meant any
argument showing that a certain proposition is true. Not all
propositions can be ‘proved’. Some of them serve as ultimate premisses
of all proofs; they must be learned another way. Such elementary
propositions Billingham calls ‘immediate’ propositions, containing only
‘immediate’ terms that cannot be ‘resolved’ into more elementary terms.
Immediate terms include indexicals such as ‘I’, ‘he’, ‘this’, ‘here’ and
‘now’, and very general verbs such as ‘is’ and ‘can’ and their tenses.
Hence a proposition like ‘This is now here’ is immediate.
Other propositions can ultimately be ‘proved’ from immediate
propositions. Billingham recognized three methods for such proofs:
exposition, ‘resolution’ and proof using an ‘auxiliary’ (officialis) term.
Exposition has already been explained. Resolution amounts to proof
by expository syllogism. Thus ‘A man runs’ is ‘proved’ by the inference
‘This runs and this is a man; therefore, a man runs’. But there is a
problem. The premisses of this inference are not immediate, since their
predicates are not immediate terms. And there appears to be no way to
reduce them to yet more basic propositions by any of the three ways
Billingham recognizes.
‘Auxiliary’ terms govern indirect discourse. They include epistemic
verbs such as ‘knows’, ‘believes’, etc., and modal terms such as ‘it is
contingent’. To ‘prove’ a proposition containing an auxiliary term is to
provide an argument spelling out the role of the auxiliary term. One of
the premisses of this argument states how the proposition referred to in
indirect discourse ‘precisely signifies’. Thus ‘It is contingent for him to
run’ is proved by: ‘“He runs” is contingent; and “He runs” precisely
signifies for him to run; therefore, it is contingent for him to run.’
There are still many obscurities in the theory of ‘proofs of
propositions’. But it was very widespread.
IX
Our knowledge of late medieval logic has advanced enormously since
the 1960s. The availability of previously unpublished texts has shed
great light on this fertile period. Yet, as this chapter shows, there is still
much that is unknown. The general reader should regard the claims in
this chapter as tentative. Readers with specialized training or interest
should regard them as an invitation to further research.
NOTES
1 CHLMP, pp. 46, 74–5. See also Chapter 7 above, p. 176.
2 In medieval terminology, a ‘proposition’ is a declarative sentence, often a sentencetoken.
The term was not typically used in its modern sense, to mean what is
expressed by a sentence(-token). I shall use ‘proposition’ in its medieval sense
throughout this chapter except where indicated.
3 De Rijk [17.29], especially vol. 1. On consequentiae in the twelfth century, see
Chapter 7 above, pp. 157–8, 175–6.
4 CHLMP, ch. 11.
5 CHLMP, ch. 16. Despite the name, these disputations had nothing to do with
ethics or morality. They were not about deontic logic. Their exact purpose is still
uncertain.
6 There were also anonymous works of this kind, dating back to the twelfth century.
See De Rijk [17.29].
7 With these last three paragraphs, see Spade [17.50], especially pp. 187–8, and
references there. See also CHLMP, chs 12 and 16B.
8 For information on authors mentioned in this section, see CHLMP, pp. 855–92
(‘Biographies’).
9 On English logic as discussed in this section, see Ashworth and Spade [17.28]
and references there.
10 In the 1494 edition of Heytesbury, Hopton’s treatise is wrongly attributed to
Heytesbury himself.
11 On Angelo, see Spade [17.45] 49–52. For other authors mentioned in this
paragraph, see Maierù [17.34], 34–6.
12 There is potential for confusion here. In twentieth-century philosophy, a ‘natural’
language is one like English, in contrast to ‘artificial’ languages like Esperanto or
the ‘language’ of Principia Mathematica. In medieval usage, the latter would
likewise count as ‘artificial’ languages, but so would English; the only truly natural
language is mental language.
13 See Peter of Ailly [17.27] 9, 19–21, 36–7, and references there.
14 See Aristotle, De interpretatione, 16b 19–21.
15 Something a bears the ancestral of relation R to z if and only if a bears R to
something b that bears R to something c that…that bears R to z.
16 With this section, see CHLMP, ch. 9.
17 For Gregory and Peter, see Peter of Ailly [17.27].
18 Buridan’s theory does not imply this, and Peter of Ailly flatly denies it for
supposition.
19 With these last two paragraphs, see Spade [17.47].
20 See the reply to Geach in Trentman [17.51]. For a critique of Ockham’s strategy,
see Spade [17.47].
21 See Peter of Ailly [17.27] 9 and 37–44, and references there.
22 A similar approach is used in Buridan’s discussion of opaque epistemic and doxastic
contexts. See Sophismata [17.16], IV, sophisms 9–14. With the remainder of this
section, see Ashworth and Spade [17.28].
23 Kretzmann [17.40]. See also Chapter 7 above, pp. 157–8.
24 With this section, see Spade [17.50], and CHLMP, ch. 9.
25 Spade [17.43]. In so far as such contexts can arise in mental language, this view
requires equivocation there. See Spade [17.47].
26 [17.47]. See also n. 18, above.
27 Spade [17.50] n. 78 and the Appendix. For Brinkley I am grateful to M.J.
Fitzgerald.
28 In the ‘adverbial’ sense of prepositional signification, described in section V above.
29 For qualifications and complications, see Spade [17.48].
30 Buridan’s name for connotation is appellatio or ‘appellation’ (Sophismata, IV).
31 With this last part of section VIII, see Ashworth and Spade [17.28] and references
there.
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