## 1. Historical Survey



William of Sherwood, writing from an Oxford perspective in the 1240s,
identified four properties of terms: "There are four properties
of terms that we intend to distinguish now ... These properties
are signification, supposition, copulation, and appellation"
(tr. Kretzmann, p.
 105).[1]
 A different tradition is represented by Peter of Spain and Lambert of
Auxerre, namely, that of Paris. Lambert identifies five properties of
terms: "there are many properties of a term, namely,
supposition, appellation, restriction, distribution, and relation
... But, because signification is, as it were, the perfection of
a term, and because the properties of a term are founded on
signification, one ought for the sake of clarity in what follows to
see at the outset what the signification of a term is and how it
differs from supposition" (tr. Maloney, p.
 253).[2]
 In his treatment he includes ampliation (a correlative to
restriction) and thereby matches the sections in Peter of
Spain's *Tractatus*: *De suppositionibus* (On
Suppositions), *De relativis* (On Anaphora), *De
ampliationibus* (On Ampliations), *De appellationibus* (On
Appellations), *De restrictionibus* (On Restrictions), *De
distributionibus* (On Distribution).



To these must be added further properties of terms which were
important in the theory's gestation in the twelfth century but
were later no longer included as distinct properties: univocation,
equivocation, adjectivation, substantivation and so on. From the
fourteenth century onwards, other properties were also abandoned, so
that finally the important lasting properties were signification,
supposition, ampliation and restriction, and relation (that is, the
supposition of relatives, i.e., anaphora).



From its beginnings in the twelfth century, the primary distinction
was that between signification, sometimes known as univocation, and
appellation, later known as supposition. As early as Anselm's
*De Grammatico* we find a distinction between *significare
per se* (signify in itself) and *significare per aliud*
(signify relatively). The latter was also known as *appellare*
(to name or appellate). Whereas in the former (*per se*) what
was signified was a form, in the latter (*per aliud*) what was
signified, or appellated, was a thing. A single form is common to a
number of things we call by the same name, so one crucial problem in
the philosophy of language is to understand how the different uses of
a name are unified in the face of the distinctness of the many
individuals talked about. In this way, we can understand the
importance in the twelfth century of univocation in contrast with
appellation. Proper names, naming single items, are contrasted with
appellative names, naming many. Univocation is the signification of a
univocal word, described in the *Fallacie Parvipontane* as
"retaining the signification of the name while varying its
supposition/appellation" (my
 translation).[3]
 Thus a fallacy of univocation occurs when one does not realise that
what were being talked about (the supposita or appellata) change. For
example, to infer 'A dodo lives' from 'A dodo
lived' is a fallacy (of univocation) since the former is false
(there are no living dodos for 'dodo' to stand for) while
the latter is true (for the past tense ampliates 'dodo' to
stand for past dodos - see
 section 4).[4]



Throughout much of the twelfth century, 'supposition'
retained the linguistic sense it had had since at least the time of
Priscian (early 6th century CE), namely, the placing of a name as
 subject.[5]
 The relation of that name as subject to the thing named was called
its appellation. This was the ability of a univocal appellative noun
to name different things. The appellation of a name was not fixed,
however. It could be ampliated or restricted by the predicate. So, for
example, the predicate '*opinabilis*' (credible)
ampliates or extends the appellation of a name such as
'man' to cover a wider range, perhaps of no longer
existing men, or of men who might have existed, or who might exist in
the future. Thus, appellation came to mean the present correct
application of a term (William of Sherwood, ed. Lohr et al., p. 265;
tr. Kretzmann, p. 106), which could be ampliated, or even restricted
by, say, the apposition of an adjective: 'white man'
appellates only white men, not all even presently existing men.



De Rijk (1982, pp. 165-6) identifies the three stages in the
development of the theory of properties of terms: in the first,
appellation takes centre stage; in the second, appellation theory is
extended to capture all uses of terms as subject; in the final stage,
all other properties are grouped under supposition as the overarching
notion and 'appellation' underwent its own transformation.
(See also Kann 2016.) Thus supposition became the leading property of
an occurrence of a term in a proposition (including now predicates,
and even parts of predicates), distinguishing what in particular was
being spoken of on some occasion of utterance by some particular use
of a word (supposition), from that word's general property of
meaning (signification). The term 'man' signifies the form
of man wherever the term occurs, but each occurrence of the term
'man' supposits for the individuals in possibly distinct
classes or groups of men (note that it supposits for the men, not the
classes).



Given the literal meaning of '*supponere*' as
"acting as subject", it is unsurprising that several
authors, even as late as Vincent Ferrer in the 1370s, restricted
supposition to subject terms, preferring to speak instead of
copulation as the corresponding property of the predicate. Those
reservations aside, however, the natural similarity in function of
subject and predicate in picking out varying classes of things while
remaining a univocal term led most authors to extend the notion of
supposition to all terms. Burley (2000, p. 80) says that
"supposition properly so called is a property of a subject term
relative to the predicate". However, "supposition taken
broadly is a property of a term relative to another in a proposition.
In this sense, supposition belongs to the subject as well as to the
predicate, and even to the verb." At the same time, talk of
univocation was superseded by signification, by implication univocal
signification unless equivocation was
 identified.[6]



A major shift in focus occurred in the early fourteenth century,
probably occasioned by Ockham - certainly, he was the leading
figure among the terminists, those who focussed "on terms as the
basic unit of logical analysis" (Ashworth 2010, p. 146). For the
nominalists, signification came to be understood entirely
extensionally, given their antipathy towards real universals.
Accordingly, what was taken to be signified by a term were the things
of which it can be truly predicated instead of a form or property
which they share. For example, whereas hitherto the term
'man' had been taken to signify humanity, and
'white' whiteness, for Ockham the former signifies (all)
men and the latter all white things. From this perspective, the
contrast found in thirteenth century authors between (as Peter of
Spain called it) natural and accidental supposition, becomes less
important. Natural supposition was the term's natural or nomic
extension, accidental supposition that range of things it supposited
for in a particular proposition. For Peter, the term itself signifies
a form, and supposits naturally for a class of objects, whereas an
occurrence of the term supposits accidentally on an occasion of use
for a group of those objects. For Ockham, the term signifies that
class, the form being no more than a *fictum* (a figment of the
mind) or (in his later works) the mental act (of conceiving of those
things) itself.



From the early fourteenth century, signification and supposition came
to dominate among the properties. Ampliation and restriction were
already functions of supposition (or appellation as it had been),
copulation as the naming function of predication was also subsumed
under supposition, and *relatio*, the connection of anaphoric
terms to their antecedents, becamse a matter of the supposition of
those terms. Finally, distribution was treated as a particular mode or
type of supposition, confused and distributive supposition. Indeed, in
the final phase, it could seriously be asked whether supposition was
indeed a property of terms, as does Albert of Saxony (*Quaestiones
circa Logicam*, q. 12). For like many others, following Peter of
Spain (2014, p. 240), he defines supposition as '*acceptio
termini*' (the act of acceptance of a term) of various
kinds, and so supposition is as much a property of the speaker or
hearer as of the term.


## 2. Signification



Signification contrasts with the other properties of terms in one
major respect, for the other properties (perhaps with the exception of
appellation in some authors, and natural supposition) are all
properties of terms relative to their occurrence in particular
propositions - indeed, they are properties of occurrences of
 terms.[7]
 Signification, however, is independent of a term's particular
uses or occurrences: "Signification differs from supposition in
this that signification is prior to supposition" (Lambert, tr.
Maloney, p.
 254).[8]
 Indeed, the other properties are dependent on the signification of
the term. For example, an occurrence of a term can only supposit
personally (see
 section 3)
 for certain objects in virtue of its signifying them, among others,
or signifying some property they share.



A twelfth-century commentary on the *Perihermeneias* reports
Porphyry as saying that at the time of Aristotle, there was a great
debate over the principal signification of utterances: was it
'*res*' (things) or incorporeal natures (Plato) or
*sensus* (sensations) or *imaginationes*
(representations) or *intellectus*
 (concepts)?[9]
 In fact, medieval philosophers of language were heir to two
conflicting semantic theories. According to Aristotle, the greatest
authority from the ancient world, words name things by signifying
concepts in the mind (Boethius translated Aristotle's term as
*passiones animae* - affections of the soul) which are
likenesses abstracted from them. But Augustine, the greatest of the
Church fathers, had held that words signify things by means of those
 concepts.[10]
 This led the medievals to the question: do words signify concepts or
things? The question had already been asked by Alexander of
Aphrodisias and his answer was transmitted to the medievals in
Boethius' second commentary on Aristotle's
*Perihermeneias* (*De Interpretatione*):
"Alexander asks, if they are the names of things, why has
Aristotle said that spoken sounds are in the first place signs of
thoughts ... But perhaps, he says, he puts it this way because
although spoken sounds are the names of things we do not use spoken
sounds to signify things, but [to signify] affections of the soul that
are produced in us by the things. Then in view of what spoken sounds
themselves are used to signify he was right to say they are primarily
signs of them" (tr. Smith, pp.
 36-37).[11]
 So words primarily signify concepts.



But the matter was not settled, other than that whatever view a
medieval philosopher took, it had to be made to accord with the
authority of Aristotle, perhaps *in extremis* by reinterpreting
Aristotle's words. Abelard refers to a distinction between
*significatio intellectuum* (signification of concepts) and
*significatio rei* (signification of the thing), more properly
called nomination or appellation (see De Rijk, *Logica
Modernorum*, vol. II(1), pp. 192-5). Similarly, the
*Tractatus de proprietatibus sermonum* asks whether words
signify concepts or things, and responds: both (*intellectum et
rem*), but primarily a thing via a concept as medium (op.cit. II
(2), p. 707).



A particular novelty of the thirteenth century, however, was to
conceive of the concept itself as a sign. We find this in Lambert of
Auxerre: "The signification of a term is the concept of a thing,
for which concept of a thing (*intellectus rei*) a vocal sound
is imposed at the will of the one instituting it, for, as Aristotle
proposes in Book One of *On Interpretation* vocal sounds are
signs of affections (*passiones*) that are in a soul, that is,
in an intellect, whereas concepts are signs of things" (tr.
Maloney, p.
 253).[12]
 Hence by transitivity, utterances which are signs of concepts which
are signs of things are themselves signs of things: "A vocal
sign that is a sign of a sign ... [will be directly] a sign of
the concept and indirectly a sign of the thing" (tr. Maloney, p.
 254).[13]
 For example, 'man' immediately signifies the concept man,
but by mediation of the concept it signifies the second substance or
form of man. Accordingly, it can supposit for what fall under man,
e.g., Plato and Socrates. But it does not signify Plato or
Socrates.



As noted above, this last distinction was elided by Ockham, in making
the mental act the universal, a name of the things. 'Man',
he says, signifies Plato and Socrates and all men equally, by virtue
of its subordination to the mental act. Once signification is treated
extensionally in this way, its only difference from supposition lies
in its priority: a general term signifies all those things of which it
can be truly predicated (Ockham, *Summa Logicae* I c. 33).


## 3. Supposition and Copulation



Just as signification corresponds most closely - though not
exactly - to contemporary ideas of meaning or sense, so
supposition corresponds in some ways to modern notions of reference,
denotation and extension. The comparison is far from exact, however.
One major difference is that the medievals distinguished many
different modes (*modi*) of supposition. Despite the difference
between different authors' semantic theories, particularly as
they developed over the centuries, there is a remarkable consistency
in the terminology and interrelation of the different modes.



The major division is between material, simple and personal
supposition. Material supposition is when a term stands for a
linguistic item as such. Often, of course, this will be a case of
autonymy, when it stands for itself. William Sherwood writes:
"It is called material when a word itself supposits either [A]
for the very utterance itself or [B] for the word itself, composed of
the utterance and the signification - as if we were to say [A]
'man is a monosyllable' or [B] 'man is a
name'" (tr. Kretzmann, p.
 107).[14]
 Writing in Paris nearly a hundred years later, Thomas Maulfelt put it
like this: "Material supposition is a term standing for itself
or for another similar to it in sound or writing suppositing in the
same way or otherwise which it was not imposed to signify or for some
other sound which is not inferior to it, and which it does not signify
naturally and properly" (my
 translation).[15]
 'Noun' supposits materially for itself when we say
'Noun has four letters' - or 'The term
"noun" has four letters'; it doesn't supposit
materially, but personally for itself, when we say 'A noun is a
part of speech'.



Simple and personal supposition are sometimes grouped together as
"formal supposition" (in contrast to material). Simple
supposition is harder to characterize generally. A common description
is to say it occurs when a term supposits for the universal or form
which it signifies. However, not everyone believed that terms
signified universals. (See the entry on the
 Medieval Problem of Universals.)
 So whereas William of Sherwood wrote "It is simple when a word
supposits what it signifies for what it signifies" (tr.
Kretzmann p.
 107),[16]
 and Walter Burley likewise: "supposition is simple when a
common term or an aggregated singular term supposits for what it
signifies" (tr. Spade p.
 82),[17]
 William of Ockham appears to characterize simple supposition quite
differently: "Simple supposition occurs when a term supposits
for an intention of the soul and is not functioning
significatively" (tr. Loux p.
 190).[18]
 But in fact, the difference between them is not in their theories of
supposition, but rather of signification. As we noted earlier, Ockham
believes that a general term like 'man' signifies
individual men like Plato and Socrates; Burley that it signifies a
second substance (the universal), man. Burley appeals to the authority
of Aristotle: "'man' is the name of a second
substance; therefore, the term 'man' signifies a second
substance. And it does not signify a second substance that is a genus.
Therefore, it signifies a species" (*De Puritate*, tr.
Spade p.
 87).[19]
 Ockham, as a nominalist, however, dismissed real universals, and (at
least in his later theory represented in *Summa Logicae)*
believed the only universals were words, including words of the inner
mental language, mental acts. So for him, a spoken or written term has
simple supposition when it stands non-significatively for the mental
act to which it is subordinated by the conventions of signification,
that is, the mental act and its natural signification abstracted from
those things which the word conventionally signifies.



John Buridan (*Summulae*, tr. Klima, sec 4.3.2, p. 253)
famously eliminated simple supposition altogether, for this very
reason, namely, that universals are words of a mental language, so
terms suppositing for them are suppositing for a kind of linguistic
item, and so such a case should be included under material
supposition.



Material and simple supposition are contrasted with personal
supposition, what we might call the standard case, where a term stands
for ordinary objects - the objects it signifies (for Ockhamists)
or what fall under the universal or form that the term signifies, as
for example, Lambert (ed. Alessio, p. 209; tr. Maloney, p. 259) or
Burley express it: "Supposition is personal when a term
supposits for its suppositum or supposita or some singular of which
the term is accidentally predicated" (tr. Spade p.
 81).[20]
 The contrast is a useful one, as is shown in the following standard
fallacies:




|  |  |
| --- | --- |
| Homo est dignissima creaturarum | (Man is the worthiest of creatures) |
| Sortes est homo | (Socrates is a man) |
| Ergo Sortes est dignissima creaturarum | (So Socrates is the worthiest of creatures). |



The premises are true and the conclusion false, so wherein lies the
fallacy? It is one of equivocation or "four terms":
'homo' ('man') has simple supposition in the
first premise and personal supposition in the second, so there is no
unambiguous middle term to unite the premises. Again:




|  |  |
| --- | --- |
| Currens est participium | (Running is a participle) |
| Sortes est currens | (Socrates is running) |
| Ergo Sortes est participium | (So Socrates is a participle). |



This time, 'currens' ('running') supposits
differently in the two premises, materially in the first and
personally in the second, explaining why putting the two truths
together fallaciously leads to the false conclusion. In earlier times,
these would have been called fallacies of univocation since what
varies is the supposition, not the signification, of 'man'
and
 'running'.[21]



What determines whether a term has material, simple or personal
supposition? One view might be that it depends on the intention of the
speaker; another, that all propositions are ambiguous and the term can
be taken either way. However, the prevailing medieval view was that it
was determined by the predicate, so that, e.g., a predicate like
'is a noun' enforces material supposition for the subject,
while 'is a species' requires simple supposition: "A
subject, on the other hand, sometimes supposits a form separately and
sometimes does not, depending on what the predicate demands, in
accordance with the following [principle]: Subjects are of such sorts
as the predicates may have allowed" (Sherwood, tr. Kretzmann, p.
 113).[22]
 This slogan, *talia subiecta qualia predicata permiserint*
(subjects are such as predicates permit), was commonly attributed to
Boethius; but Sherwood correctly points out that Boethius' point
was different, and his phrase was the converse: *"talia
[predicata] qualia subiecta permiserint"* - see De
Rijk, *Logica Modernorum* II (1), p. 561.



In the fourteenth and fifteenth centuries, it became commonplace to
require a *nota materialitatis* (a sign of the material use)
for a term in material supposition. Such a sign was to prefix
'iste terminus' ('this term') or
'ly' (taken from the French definite article) to the term.
Without such an indication, the term was considered to have personal
supposition by
 default.[23]
 The use of inverted commas is a much later innovation, though some
scribes indicate material supposition (or quotation) by surrounding
the term or phrase with a pair of dots (puncta).



Personal supposition is divided by most authors into discrete and
common supposition, the first that of singular terms (proper names,
demonstrative phrases and so on), the latter that of general terms.
Common personal supposition is again divided, namely, into determinate
and confused, and the latter into confused and distributive and merely
confused supposition. These three modes are well illustrated by the
four categorical forms (see the entry on the
  Traditional Square of Opposition):



> 
> 
> (A) All *A* are *B*.
> 
> 
> 
> (E) No *A* are *B*.
> 
> 
> 
> (I) Some *A* are *B*.
> 
> 
> 
> (O) Some *A* are not *B*.
> 
> 
> 



The subject of (I)- and (O)-, and the predicate of (I)-propositions,
have determinate supposition; the subject and predicate of (E)-, the
subject of (A)-, and the predicate of (O)-propositions have confused
and distributive supposition; and the predicate of (A)-propositions
has merely confused supposition. This is common doctrine; what varies
is how these modes are characterised. "It is determinate",
writes William of Sherwood, "when the locution can be expounded
by means of some single thing" (tr. Kretzmann, p. 108), but he
addresses a doubt: "It seems that when I say 'a man is
running' [i.e. an I-proposition] the term 'man' does
not supposit determinately, since [A] the proposition is indefinite,
and [B] it is uncertain for whom the term 'man' supposits.
Therefore it supposits [A] indefinitely and [B] uncertainly; therefore
indeterminately" (pp.
 115-6).[24]
 But this is simply a matter of terminology, he replies -
determinate supposition means suppositing for one, not for many, but
for no particular one, for that would constitute discrete supposition.
Note, however, that for Ockham, Burley and others, a term with
determinate supposition supposits for everything of which it can be
truly predicated. The sense in which it is true of one, rather than
many, is that the proposition is true if true of one. The term still
supposits for all. As Burley says: "The supposition is called
'determinate', not because a term suppositing
determinately in this way supposits for one suppositum and not for
another. Rather the supposition is called 'determinate'
because for the truth of a proposition in which the common term
supposits determinately it is required that the proposition be made
true for some determinate suppositum" (tr. Spade pp.
 102-3).[25]



All that William of Sherwood can offer to characterize confused
supposition is to say that it is had when a term supposits for many,
then resorting to examples for its divisions. Peter of Spain tries
harder: "Confused supposition is taking a common term in place
of many by means of a universal sign" (tr. Copenhaver, p.
 249),[26]
 and confused and distributive when it supposits for all. But this is
still unclear, and eventually a solution was found in the doctrine of
ascent and descent. Call the individual things falling under a general
term its "inferiors", and call the singular proposition
resulting from a general proposition by replacing a general term (with
its qualifier) by a term with discrete supposition for one of its
inferiors, one of the proposition's "singulars".
Then the inference from a general proposition to one of its singulars
is called "descent", the converse inference,
"ascent". If descent under a term is valid, or at least is
valid without changing the rest of the proposition, it is called
"mobile", otherwise "immobile". Walter Burley,
William of Ockham and their followers could then define the three
modes of common personal supposition as follows:


1. An occurrence of a general term in a proposition has determinate
supposition when one can descend validly from the proposition to the
complete disjunction of its singulars with respect to that term, and
conversely can ascend validly from any singular;
2. Otherwise, it is confused, and (i) is confused and distributive if
one can validly descend from the proposition to the indefinite
conjunction of its singulars with respect to that term; otherwise (ii)
it is merely confused.



In this last case, 2 (ii), Ockham noted: "it is possible to
descend by way of a proposition with a disjunctive predicate and it is
possible to infer the original proposition from any [singular]"
(tr. Loux p.
 201).[27]
 Thus the predicate of an A-proposition has merely confused
supposition since descents 1 and 2 (i) are invalid, but from
'Every man is an animal' one can validly infer
'Every man is this animal or that animal and so on for all
animals', and conversely, from 'Every man is this
animal' (were it ever true) one could infer that every man is an
animal.



A final complication came at the end of the fourteenth century and
subsequently, when it was asked: "Are there only three modes of
common personal supposition?" Some answered, 'Yes';
but others distinguished two modes of merely confused supposition, or
equivalently distinguished a fourth case, 2 (iii), collective
supposition, where descent was permissible to a proposition with a
conjunctive term. The standard example was 'All the apostles of
God are 12', which entails 'Matthew and Mark and so on are
12', with a conjunctive
 subject.[28]



Several recent commentators have asked what the medieval theory of
modes of common personal supposition was for: was it a theory of
inference, of quantification, of truth-conditions, of fallacies, or
what? Asking these questions may help us to come to terms with the
theory; but if pressed too hard, they are unhelpful. The
medievals' theory was none of these things; it was their
theoretical basis with which to pose and answer certain semantic
questions.



All modes of supposition so far described fall under what was
variously called proper supposition or accidental supposition or,
excluding material supposition, formal supposition. Distinct from
these were what Peter of Spain called natural supposition, mentioned
earlier in the discussion of signification, and what Ockham and others
call improper supposition, covering metaphor and other figures of
speech.



Moreover, various authors before the fourteenth century, and at least
one fourteenth century author too (namely, Vincent Ferrer) differed a
little from what has been said in not attributing supposition to
predicate terms, calling the corresponding property of predicates,
"copulation". However, even in the early thirteenth
century, this distinction was fading. William of Sherwood makes it
clearly: substantive names and pronouns supposit, whereas adjectives,
participles and verbs copulate - all those terms which are
attributed to something by means of the copula 'is'. Only
the modes of common personal supposition are repeated for copulation:
"every copulating word signifies in adjunction to a substantive
and thus is copulated personally ... [and] every copulating word
is the name of an accident, but every name of an accident is common;
therefore no copulation is discrete" (Sherwood, tr. Kretzmann,
p.
 121).[29]
 However, even in Lambert and Peter of Spain, there is only an empty
nod towards copulation. Lambert notes that properly speaking,
supposition attaches to substantives, while copulation is appropriate
for adjectival terms. But broadly speaking, he says, supposition
belongs to both (ed. Alessio, p. 208; tr. Maloney, p. 258). The
distinction is clearly unnecessary and useless, and although the term
is preserved in, e.g., Walter Burley's *De Puritate*, his
discussion headed 'On Copulation' is in fact a discussion
of the uses of the copula, 'est'.


## 4. Ampliation and Restriction



Some words have the effect of widening or narrowing the supposition of
other terms in a proposition. For example, by qualifying
'man' with the adjective 'white', we restrict
the supposition of 'man' in 'A white man is
running' to white men; while a verb in the past tense ampliates
the supposition of the subject to include what were its supposita. For
example, 'A white thing was black' means that something
which is now white or was white in the past was black.



Lambert of Auxerre is typical in describing the many aspects of a
proposition which can produce ampliation or restriction. Some are
natural, as when 'rational' restricts 'animal'
to supposit only for men by being adjoined to it; other cases are
'*usualis*' - 'use-governed' in
Maloney's translation (p. 278): for example, when we say
'The king [or better 'A king' (rex)] is
coming', we are taken to mean the king of the country where we
are, so 'king' is restricted to supposit only for that
king. Some ampliation and restriction is effected by consignification,
that is, by an aspect of a word - by the tense of the verb, or
by the gender of an adjective: in 'homo alba', the
feminine ending of 'alba' restricts 'homo' to
supposit only for women, indeed, white women. Other ampliation and
restriction is effected by the signification of words - as in
the case of 'rational animal' just mentioned, or in
"Socrates' donkey", where the possessive restricts
'donkey' to supposit only for Socrates' donkeys.



Peter of Spain (ed. Copenhaver, p. 441) notes that only general terms
can be ampliated or restricted, and only terms having personal
supposition.



Just as the past tense ampliates the subject to include past as well
as present supposita, modal verbs ampliate the subject to possible
supposita, as do verbs such as 'understand',
'believe', and indeed, notes Albert of Saxony, verbal
nouns ending in '-bile': 'possible',
'audible', 'credible', 'capable of
laughter' and so on. Albert (*Perutilis Logica* II 11,
ed. Berger, p. 380) realises that even 'supposit'
ampliates the subject: when we say 'This term supposits for
something', what it supposits for need not actually exist, but
might be past, future, possible or merely intelligible. According to
Buridan, 'must' ampliates for possible supposita, for
'*A* must be *B*' means 'It is not
possible that *A* not be *B*', contradictories
must clearly ampliate in the same way, and 'It is possible that
*A* not be *B*' ampliates for possibilia.
Ampliation over possibles means care is needed in inferences from
'is' to 'can': '*A* can be
*B*' need not follow from '*A* is
*B*', for '*A* can be *B*'
means that what is or can be *A* can be *B*, and even if
*A* is *B*, not everything which can be *A* might
be capable of being *B*. For example, 'Every planet
lighting our hemisphere can be the sun' is false even though it
is in fact the sun which lights it, since the moon might light our
hemisphere but the moon cannot be the
 sun.[30]



It is an interesting fact that almost alone among terminist logicians,
Ockham does not speak of ampliation and restriction. (See Priest and
Read 1981.) The reason appears to be that he disagrees with the
truth-condition given above for 'A white thing was black',
and similar cases. This proposition, he says, is ambiguous. Rather
than meaning that what is or was white was black, it equivocates
between 'What is white was black' and 'What was
black was white': "in the case of every proposition of the
past and of the future in which the subject is a general term or a
demonstrative pronoun with a general term or a discrete term referring
to some composite, we must distinguish [two
 senses]".[31]
 Whether Ockham realized that his theory improved on the ampliative
theory is unclear; nonetheless, his account seems to accord better
with intuition. For the ampliative account is disjunctive: it says
that the proposition is true if either what was white was black or
what is white was black. Then it is true if either disjunct is true;
whereas on Ockham's account it has two different senses, and can
be false on one while true on the other - true because something
now white used to be black but false if nothing which used to be white
was ever black. For a clearer case, take the first sex-change
operation - for the first time, say, a woman was a man. But no
one who was a woman had ever been a man, so it was (also) false that a
woman was a man. The proposition 'A woman was a man' is
ambiguous and "*est distinguenda* " (i.e.,
different senses must be distinguished, one true, one false).



Ockham also eschews talk of ampliation in giving his account of modal
propositions. Does 'A white thing can be black' mean that
what is or can be white can be black, i.e., that either what is white
can be black or what can be white can be black, as the ampliative
account demands? - cf., e.g., Albert of Saxony: "For
'A white thing can be black' signifies that what is white
or what can be white can be black" (my
 translation).[32]
 No, for this loses the sense in which it is self-contradictory to
suggest that it is possible that a white thing be black. The
proposition is ambiguous, in one sense self-contradictory, in the
other true, Ockham notes (*Summa Logicae* II 10), because
'This is black' can be true if uttered pointing to
something white: "'A white thing can be black' is
true, because 'This is black' is possible, pointing to
something for which 'white' supposits; but 'A white
thing is black' is
 impossible".[33]


## 5. Appellation



Perhaps the term with the most varied history is
'appellatio', though even so, one can discern a common
thread running through it. It starts, we saw, as an equivalent of
'nominatio' in Anselm and Abelard, and by the thirteenth
century is used to pick out the present extension of a term, that of
which it can be truly predicated in the present tense: "So now
one should know that appellation is spoken of in four ways ... In
the fourth way, appellation is said to be the acceptance of a term for
a suppositum or supposita existing actually, and our present focus is
on appellation spoken of in this fourth way" (Lambert, tr.
Maloney pp.
 261-2).[34]
 In Burley, at the turn of the fourteenth century, it almost usurps
the place of 'copulatio', being for him the relation of
the predicate to its inferiors: "Thus, just as supposition taken
strictly is a property of the subject insofar as it is matched with
the predicate, so appellation is a property of the predicate matched
with the subject or with an inferior" (*De Puritate*, tr.
Spade p.
 131).[35]
 There are shades too, of Abelard: "a univocal general term
appellates its inferiors but does not signify
 them".[36]
 But the crucial phrase which runs through the history of the term
appears here too: "the predicate appellates its form"
(ed.Boehner, p. 48: "praedicatum appellat suam
formam"). What Burley says he means by this is that the
predicate should be truly predicable at some time, in the present
tense, of the supposita of the subject.



It is ampliation and restriction which distinguish this property of
the predicate from properties of the subject. For, on the standard
account, the subject may be ampliated, or restricted, by the predicate
(or by the copula or other signs), but the predicate itself is never
ampliated or restricted: as we saw above, 'A white thing was
black' is true only if 'black' has at some time been
truly predicable of the supposita of the subject, namely, of what is
or was white. In contrast, 'A white thing is black' may
never have been true - indeed, in this case, it never will have
since it is self-contradictory. So the subject does not always
"appellate its form", that is, one must use a
demonstrative to give the truth-conditions of such propositions (see
Panaccio 2012, SS2 esp. p. 144-5). A consequence pointed out by
John Buridan, among
 others,[37]
 is that conversion needs application with care in such cases.
Consider 'The just will be justly damned': this can be
true, if those who are just sin in the future. But 'Justly will
the just be damned' is false, for 'Justly are the just
damned' will never be true. Similarly, 'Socrates
approaching you know' can be true while 'You know Socrates
approaching' (the "hooded man" fallacy from
Aristotle's *De Sophisticis Elenchis* 179b1-3) may
be false (for you know Socrates, but do not recognize him
approaching). It is explained by reason of the fact that the predicate
appellates its form (for 'You know Socrates approaching'
requires that the predicate 'know Socrates approaching' be
true of you and so is false), whereas 'Socrates approaching you
know' requires only that 'Him you know' be true,
referring to Socrates, and it is true. The doctrine of appellation
could thus be used to diagnose familiar fallacies.



Scott, in his discussion of Buridan's treatment of the sophism,
'You know the one approaching' (pp. 42-9), claims
that Buridan's concept of appellation (which he misleadingly
translates as 'connotation') in his diagnosis is novel,
and Spade follows him in his commentary on Peter of Ailly (p.109
n.188). But the notion is clearly continuous with Burley's in
that 'appellating its form' requires true predication via
a demonstration. Indeed, it is continuous with Lambert's usage,
for 'chimera' has no appellata precisely because
'hoc est chimera' ('This is a chimera') is
false whatever is demonstrated. Admittedly, Buridan explicitly
restricts appellation to appellative terms, that is, "every term
connoting something other than what it supposits for"
(*Summulae de Dialectica: Treatise on Suppositions*, tr. Klima,
p. 291), and it "appellates that which it connotes as pertaining
to that which it supposits for". Thus 'white'
connotes whiteness and supposits for white things. What appears to be
novel in Buridan is the extension of the doctrine to intentional
verbs, which, Buridan says, cause the terms following them (the
predicate, or part of the predicate) to appellate their
*rationes*, that is, the concepts by which they signify what
they do. Thus in 'You know Socrates approaching', the
expression 'Socrates approaching' appellates its concept,
the *ratio* 'Socrates approaching', and so the
proposition is false unless you are aware who it is; whereas in
'Socrates approaching you know', the subject
'Socrates approaching' appellates its concept only under
disjunction to the *rationes* of other possible substituents in
the same grammatical position, and so it suffices that 'Him you
know' be true, where 'him' refers to Socrates under
some concept or
 other.[38]


## 6. Relation



Lambert of Auxerre (tr. Maloney, p. 290) speaks explicitly of relation
as a property of terms, but most authors describe the phenomenon as
the supposition of relatives. The relation in question is that between
anaphoric terms and their antecedents. Most treatises consist of a
repetition of a standard taxonomy: there are relatives of substance
and relatives of accident, relatives of identity and relatives of
diversity. For example, relatives of substance and of identity are
'who', 'he', 'his', and among
these, reciprocal relatives such as 'himself'; of
diversity are 'another' and 'someone else'.
The latter are said to refer back (*referre*, past participle
*relatum*) to their antecedent but to supposit for something
different, as in, e.g., 'Socrates is running and someone else is
debating'. Relatives of accident include, first, those of
identity, 'such as', 'like',
'when', and those of diversity, 'in another
way', 'other'; in, say, 'Socrates is running
and Plato is other', 'other' refers back to
'running'; in what way it differs will depend on the
author's account of predicates.



In contrast to the extensive taxonomy, medieval discussions of
relatives before the mid-fourteenth century seem rather short on
theory, dealing with puzzles more by common sense and description than
in any unified way. For example, the prevailing view is that relatives
of identity preserve the supposition of their antecedent. Why, then,
can they usually not replace the antecedent? Consider, e.g.,
'Every man sees himself'. Does 'himself' have
the same supposition as 'man' (or 'every man')
and if so, why can the antecedent not replace it? - for
'Every man sees every man' has a very different
signification. Lambert (tr. Maloney, p. 299) claims that in the case
of reciprocal relatives the reciprocal pronoun can replace the
antecedent unless the antecedent is taken universally, as in
'Every man sees himself'. In this case, it still supposits
for the same as its antecedent, but in a different way, namely,
discretely. Ockham spells it out: "in 'Every man sees
himself', 'himself' supposits for every man by means
of confused and distributive mobile supposition: but it does this
singularly since it is not possible to descend without altering the
other extreme ... thus, 'Every man sees himself, therefore,
Socrates sees Socrates'" (tr. Loux p.
 218).[39]



Ockham claims that, although non-reciprocal relatives of identity
always supposit for that for which their antecedent supposits, those
whose antecedent is a general term occurring with personal supposition
can never be replaced by their antecedent and result in an equivalent
proposition. For example, 'A man runs and he disputes' is
not convertible with 'A man runs and a man disputes'.
Buridan has two rules to explain what is happening (*Summulae*,
tr. Klima pp. 283-4):


1. A relative of identity "refers back to its antecedent only
with respect to those of the antecedent's supposita for which
the categorical proposition in which its antecedent occurred was
verified"
2. A relative of identity "supposits or is taken in a
proposition as is its antecedent, namely, materially if materially,
personally if personally, distributively if distributively,
determinately if determinately, merely confusedly if merely
confusedly", except as in 1.



Hence, in e.g., 'Man is a species and it is predicable of
many', or 'Socrates runs and he disputes', the
relative can be replaced without loss of meaning by its antecedent.
But in 'A man runs and he disputes', it cannot, for the
supposition would change. 'He' supposits only for men who
are running, whereas 'a man', if it replaced it, would
supposit for all men.



Another issue concerned identifying the contradictory of a proposition
containing a relative. A categorical containing a relative of identity
such as '*A*, which is *B*, is *C*'
is equivalent to '*A* is *B* and *A* is
*C*'. Hence its contradictory, '*A*, which
is *B*, is not *C*', says Albert of Saxony, is
equivalent to '*A* is not *B* or *A* is not
*C*': "The second rule: a negative categorical
proposition in which a relative term occurs is equivalent to a
disjunctive proposition: e.g., 'Socrates, who is running, is not
disputing' has the same truth-value as 'Socrates is not
running or Socrates is not disputing'. And therefore such a
proposition has two causes of truth, each of which is sufficient on
its own for its truth. Hence 'Socrates, who is running, is not
disputing' is true either because Socrates is not running or
because Socrates is not disputing. Hence because by the first rule the
affirmative is equivalent to a conjunction, it follows that the
negative contradictory to it is equivalent to a disjunction composed
from the contradictories of the conjuncts, since conjunctions and
disjunctions with contradictory parts contradict one
 another".[40]


## 7. Conclusion



The medievals did not have a solution to every semantic puzzle with
which they were faced, any more than do contemporary philosophers. But
their theory of properties of terms was the basis of a rich semantic
theory within which they were able to develop complete and fruitful
theories which yielded significant insights - both for them and
for us - into a broad range of semantic issues.