## 1. Life and Works: Some Comments on the Historiography



Peter of Spain has been established as the medieval author of a work
that became widely known as *Summule logicales magistri Petri
Hispani* (Collection of Logic Matters of Master Peter of Spain).
The great number of manuscripts and printed editions is evidence of
the enormous success this work met with throughout European
universities well into the seventeenth century. An interpolated
version of his *Tractatus*, by then known as the *Summulae
logicales*, was used by John Buridan as a basic text to comment
upon. But finding out the true identity of the author of this
influential *Tractatus* has proved to be a difficult task. For
a long time it was assumed that he was a Portuguese who became Pope in
1276, under the name of John XXI. There is also another, earlier
tradition, according to which the author of the *Tractatus* was
regarded as Spanish, and a member of the Dominican order. Yet another
attribution, dating from the fifteenth century, was to a Petrus
Ferrandi Hispanus, who died between 1254 and 1259; this attribution
would be consistent with the idea that Peter's works on logic
originated from the first half of the thirteenth century. According to
still another attribution, the *Summule* was compiled by a
Black Friar no earlier than in the late thirteenth or early fourteenth
century.



The 'Dominican-thesis' can be divided into three
traditions:


1. The general view that Peter of Spain, author of the
*Tractatus*, is someone who belonged to Order of Black
Friars,
2. The more specific view that the author of the *Tractatus*
was a frater Petrus Alfonsi Hispanus O.P.,
3. Another specific view that the Peter of Spain who created the
*Tractatus* was the same Peter of Spain as the one who wrote
the *Legenda sancti Dominici* and the Office of the
Saint's Feast, namely Petrus Ferrandi Hispanus O.P., who died in
the 1250s.



Current research on the identity of Peter of Spain has once again
taken up the idea that he must have been a member of the Dominican
Order instead of Pope John XXI (D'Ors 1997, 2001, 2003).
However, we are still in the dark about the true identity of Peter of
Spain. The most recent information we have on this score is that a
number of the Dominican candidates recently suggested as the author of
the *Tractatus* can be deleted from the list (Tugwell 1999,
2006). The lack of further information also makes it difficult to
establish the dates and specifics of his carreer.



It is still not possible to establish the date of origin of the
*Tractatus*, the work that has enjoyed such enormous success.
Recent scholarship suggests that it could have been written any time
between the 1220s and the 1250s (Ebbessen 2013, 68-69). It has
universally been recognised as a work by Peter of Spain. Another work
that has been identified as Peter of Spain's is a
*Syncategoreumata* (Treatise on Syncategorematic Words), which
was probably written some years after the *Tractatus*.
Considering the fact that in all the thirteenth-century manuscripts
the *Syncategoreumata* directly follows the *Tractatus*,
and given the number of similarities between doctrinal aspects of
these two works on logic, it is almost certain that they were written
by the same author. Both works seem to have originated from Southern
France or Northern Spain, the region where we also find the earliest
commentaries on these treatises.



An extensive list of writings ascribed to an author by the name of
Petrus Hispanus is provided by Meirinhos (2018). Besides the two works
on logic, the Petrus Hispanus in the *papa*-tradition is the
supposed author of a famous medical work *Thesaurus pauperum*,
as well as fourteen other works on medicine. Writings by (a) Peter of
Spain in the field of natural philosophy include a *Scientia libri
de anima*, and commentaries on Aristotle's *De
anima*, *De morte et vita*, *De sensu et sensato*,
*De animalibus*, and theological works include commentaries on
works by pseudo-Denys the Areopagite as well as a collection of
sermons. As yet there is no certainty about whether the author of
these treatises also wrote the *Tractatus* and the
*Syncategoreumata*, or about the dates of their origin.



Another Petrus Hispanus, referred to as *Petrus Hispanus
non-papa*, has been identified as the author of the *Summa
'Absoluta cuiuslibet'*, a late twelfth-century
handbook on syntax closely linked with Priscian's
*Institutiones grammatice, libb.* XVII and XVIII, which became
very popular later in the Middle Ages under the name *Priscianus
minor* (Kneepkens 1987). The chronology of this work seems to rule
out that this Peter of Spain is the same author as the author of the
*Tractatus*.


## 2. Origins of Peter's Works on Logic



Peter's logic seems to have its origin in the continental
tradition. Evidence of the educational carreer of the
*Tractatus* appears from two commentaries (see De Rijk 1968,
pp. 23-34 and De Rijk (ed.) 1972, Introduction, pp. LXXff.),
which contain short lemmata and a number of questions
(*questiones*) together with their solutions. The tracts as
contained in these texts are very similar to the ones in the
*Tractatus.* The *Tractatus* has features that are
typical of the Paris tradition, such as the separate treatment of
ampliation, restriction and distribution, as well as several other
doctrinal elements (see De Rijk (ed.) 1972, pp.
LXXXIV-LXXXVIII). We do not know whether Peter had any
connection with Paris, nor can we say anything definitive about the
identity of his teachers. Earlier sources for Peter's works on
logic can be traced back to Boethian-Aristotelian logic, and
authorities in the field of grammar such as Priscian and Donatus.



Like the *Tractatus*, the *Syncategoreumata* also
displays a continental origin. It appears to have continued along the
lines of a similar work by Johannes Pagus. This work, which has been
dated between 1225 and 1235, was later on further developed by
Nicholas of Paris, who wrote his *Syncategoreumata* between
1240 and 1250 (see Braakhuis 1979, Vol. I, p. 248).


## 3. The *Tractatus*



The *Tractatus* can be divided into two main parts. One part
deals with doctrines found in the so-called *logica
antiquorum*--i.e., the *logica vetus* (old logic) and
*logica nova* (new logic)--and the other contains
doctrines covered by the *logica modernorum*--viz. the
tracts that discuss the *proprietates terminorum* (properties
of terms).



The first main part of the *Tractatus* divides into five
tracts. The first tract, *De introductionibus* (On introductory
topics), explains the concepts used in traditional
logic--*nomen* (noun), *verbum* (verb),
*oratio* (phrase), *propositio* (proposition)--and
presents the divisions of and the (logical) relationships between
propositions. The second tract, *De predicabilibus* (On the
predicables), covers matters dealt with in Boethius's accounts
of Porphyry's *Isagoge*. It gives an account of the
concept *predicabile* and the five
predicables--*genus*, *species*,
*differentia*, *proprium*, *accidens*--i.e.,
the common features of and differences between the predicables, as
well as of the terms '*predicatio*' and
'*denominativum*'. Tract three, *De
predicamentis* (On the categories), discusses the ten Aristotelian
categories, as well as some items already dealt with in the previous
treatise. The fourth tract, *De sillogismis* (On syllogisms),
mainly goes back to Boethius's *De syllogismis
categoricis* (On categorical syllogisms). It gives an explanation
of the basic element of the syllogism, i.e., *propositio*, and
of the syllogism, and then goes into mood and figure, the proper forms
of syllogisms, and briefly deals with what are called paralogisms. The
fifth tract, *De locis* (On topical relationships), is derived
from Boethius's *De topicis differentiis* (On different
topical relationships) I and II. This tract starts off with an
explanation of the notions *argumentum* and
*argumentatio*, and then proceeds to deal with the species of
argumentation: syllogism, induction, enthymeme, and example. Next, it
gives a definition of *locus* (the Latin translation of the
Greek *topos*): a *locus* is the seat of an argument
(i.e., the *locus* is supposed to warrant the inference by
bringing it under some generic rule.) The intrinsic *loci* (=
the kinds of *locus* that occurs when the argument is derived
from the substance of the thing involved) are covered first, followed
by the extrinsic *loci* (= the kinds of *locus* that
occur when the argument is derived from something that is completely
separate from the substance of the thing involved) and intermediary
*loci* (= the kinds of *locus* that occur when the
argument is taken from the things that partly share in the terms of
the problem and partly differ from it). Examples are:
intrinsic--the *locus* "from definition":
'a rational animal is running; therefore a man is
running'; extrinsic--the *locus* "from
opposites": 'Socrates is black; therefore he is not
white'; intermediary--'the just is good; therefore
justice is good'.



The second part of the *Tractatus* comprises subjects that were
of major importance in the doctrine of the properties of terms. In the
sixth tract, *De suppositionibus*, the theory of supposition is
dealt with. The treatise begins with an exposition of
*significatio*. The definition of *significatio* runs:
*significatio* is the respresentation of a thing by means of a
word in accordance with convention. Next it gives a definition of the
related terms *suppositio* and *copulatio*, and the
differences between the terms *significatio*,
*suppositio* and *copulatio*. Of these three
*suppositio* and *significatio* are the most important
in Peter's semantics. *Suppositio* is defined as the
acceptance of a substantive verb for some thing. *Suppositio*
is dependent on *significatio*, because supposition can only
occur via a term that already has some *significatio*. Put in
other words, *significatio* pertains to a word by itself, and
*supposition* to a term as actually used in some context.



The tract concludes with a division of *suppositio*. The first
division is into *suppositio communis* (common supposition) and
*suppositio discreta* (discrete supposition)--e.g., the
terms *homo* (man) and *Sortes* (Socrates)
respectively.



The second division, *suppositio communis*, is divided into
*naturalis* (natural) and *accidentalis* (coincidental).
*Suppositio naturalis* is described as the acceptance of a
common term for all those things that can share in the common
universal nature signified by the term in question--e.g.,
*homo* ('man') taken by itself by its very nature
is able to stand for all men, whether in the past, present or future;
*suppositio accidentalis* is the acceptance of a common term
for those things for which the term in question requires an additional
term--e.g., in *homo est* ('A man is') the
term *homo* stands for present men, whereas in *homo
fuit* ('A man has been') and in *homo erit*
('A man will be') it stands for past men and future men
respectively, owing to the additional terms *fuit* and
*erit*.



The third division, *suppositio accidentalis*, is divided into
*suppositio simplex* (simple supposition) and *suppositio
personalis* (personal supposition). *Suppositio simplex* is
the acceptance of a term for the universal 'thing' it
signifies, as in *homo est species* ('Man is a
species', *animal est genus* ('Animal is a
genus'), in which the substantive terms *homo* and
*animal* stand for the universal man and animal, and not for
any one of their particulars. *Suppositio simplex* can occur
both in the subject- and in the predicate-term--e.g., *homo
est species* ('Man is a species') and *omnis homo
est animal* ('Every man is an animal') respectively.
*Suppositio personalis* is the acceptance of a common term for
one or more of its particulars, as in *homo currit* ('A
man is running').



The fourth division, *suppositio personalis*, is subdivided
into either *derterminata* (determinate = standing for a
certain particular) or *confusa* (confused = standing for any
individual falling under that name). *Suppositio determinata*
occurs when a common term is taken indefinitely or in combination with
a particular sign--e.g., *homo currit* ('Man is
running') or *aliquis homo currit* ('A/some man is
running'). *Suppositio confusa* occurs when a common term
is taken in combination with a universal sign ('Every man is
running').



The tract on supposition winds up with the discussion of a few
questions regarding the attribution of supposition in a few cases.



The seventh tract of the *Tractatus*, on fallacies, which forms
part of the Aristotelian-Boethian logic, is written in the tradition
of the *Fallacie maiores* (Major fallacies). The eighth tract,
*De relativis* (On relatives), deals with the relative pronouns
as defined by Priscian in his *Institutiones grammaticae.* The
relative pronouns are devided into: relatives of substance, such as
*qui* (who), *ille* (he), *alius* (another), and
relatives of accident, such as *talis* (of such a kind),
*qualis* (of what kind), *tantus* (so much),
*quantus* (how much). The former are subdivided into relatives
of identity (*qui* and *ille*) and relatives of
diversity (such as *alter* and *reliquus*, both of which
can be translated as 'the other'). The relative of
identity is defined in terms of supposition as what refers to and
stands for the same thing. These relatives are either reciprocal or
non-reciprocal. With regard to the relatives of identity, Peter adds a
dicussion of a number of questions about the rationale for using
demonstrative pronouns, and some problems concerning how the fallacy
of a relative having two diverse referents comes about.



The tract on relatives continues with a brief discussion on the
relatives of diversity, accompanied by a rule about the supposition of
the relative when it is added to a superior and an inferior in a
premiss and a conclusion, as in *aliud ab animali*; *ergo
aliud ab homine* ('Something other than an animal; therefore
something other than a man'). With regard to relatives of
identity a rule of the "ancients", who deny that a
proposition introduced by a relative can have a contradictory
opposite, is discussed and rejected. Another rule is given about the
identity of supposition of a non-reciprocal relative and what it
refers to. The tract concludes with short accounts of relatives of
accident.



The ninth, tenth, eleventh, and twelfth tracts of the
*Tractatus*, i.e., the short tracts *De ampliationibus*
(On ampliation), *De appellationibus* (On appellation), *De
restrictionibus* (On restriction) and *De distributionibus*
(On distribution), are in fact elaborations of the theory of
supposition. Ampliation is an extension of the supposition of a term.
It occurs when an expression is combined with a modal term--e.g.
*homo potest esse Antichristus* ('A man can be the
Antichrist'), and *homo necessario est animal* ('A
man is necessarily an animal')--in which case the
supposition of the term 'man' is extended to more than
just individuals existing in the present. The tract on
*appellationes* is very short: appellation is considered no
more than a special case of restriction, i.e., the restricted
supposition brought about by a present-tense verb. In this tract the
rules of appellation are in fact specific kinds of rules of
restriction. The subject of restriction in general is discussed in the
eleventh tract. The rules of restriction are the same ones as were
presented in the early Parisian textbooks on logic (see de Libera
1982, pp. 176-177). The final tract, on distribution, deals with
the multiplication of common terms as a result of their being combined
with universal signs. These universal signs are either distributive of
substance (such as *omnis*, *nullus*), or of accidents
(such as *qualiscumque*, *quantuscumque*). In this
description 'substance' is defined as substistent modes of
being, and 'accident' as accidental modes of being.
Separate attention is given to the universal sign *omnis*
('all' or 'every') along with a discussion of
the common rule that the use of *omnis* requires three
*appellata* (particular things). The most frequently cited
example in these discussions in the thirteenth century was the
sophisma *omnis phenix est* ('Every phoenix is').
According to Peter of Spain, the use of *omnis* does not call
for at least three *appellata*; an exception to this rule is
found in cases in which there is only one *appellatum*, as is
the phoenix-case. The tract also pays attention to a number of
tongue-twisting sophisma-sentences.


## 4. The *Syncategoreumata*



Peter's treatise on syncategorematic words forms part of a
separate genre that developed from the beginning of the thirteenth
century. The term *syncategorema* comes from a famous passage
in Priscian's *Institutiones grammatice* II, 15, which
introduces two types of wordclasses (*partes orationis*)
distinguished by logicians, viz. nouns and verbs on the one hand, and
*syncategoremata*, or *consignificantia*, on the other.
The latter are defined as words that do not have a definitive meaning
on their own, but acquire one only in combination with other,
categorematic words.



Like the treatises of the *Tractatus* kind, the
*Syncategoreumata* were developed from the (twelfth-century)
theories on fallacies, as well as from grammatical doctrines (from the
same period). From the second half of the twelfth century, there was a
growing interest in the linguistic elements that are considered to lie
at the basis of ambiguity and fallacious reasoning. Hence the increase
of treatises presenting a systematic account of these terms. The
connection between these treatises and Priscian's grammar can be
gathered from the attention different authors pay to the *signa
quantitatis* (or quantifiers) and their interest in the meaning
and function of syncategorematic terms.



The list of words to be included among the *syncategoreumata*
was not always the same. Generally speaking it comprised exclusive
words *tantum* (only), *solus* (alone), exceptive words
such as *preter* (except), *nisi* (unless), consecutive
words such as *si* (if) and *nisi* (if not), the words
*incipit* (begins) and *desinit* (ceases), the modal
terms *necessario* (necessarily) and *contingenter*
(contingently), the conjunctives *an* (or), *et* (and),
*nisi* (unless), *in eo quod* (in that), and
*quin* (that not). In Peter's work we also find a
discussion of the terms *quanto* ('how much' or
'as much as') *quam* ('than' or
'as') and *quicquid* (whatever). Unlike that of
some other authors (such as William of Sherwood and Robert Bacon), his
list does not include the word *omnis*.



In the opening of his *Syncategoreumata*, Peter presents his
rationale for this investigation, viz. that there is a close link
between the use of these kinds of words in sentences and their
truth-value. His idea is that the *syncategoreumata* must have
some sort of signification, but not the same as the categorematic
words. For this special kind of signification he uses the words
*consignificatio* and *dispositio*.



The first two separate chapters of the *Syncategoreumata* are
devoted to the words *est* and *non* respectively, which
are said to be implied in all other syncategorematic words.
Peter's account of the first word focuses on the notion of
*compositio* (composition), which is explained in great detail,
by looking into the signification of nouns and verbs (signifying a
composition of a quality with a substance, and that of an act with a
substance respectively). Considerable attention is given to the
composition featuring in the verb 'is', in the form of the
question of whether the composition involved can be counted among
beings or not, considering the fact that it can be used to express
different kinds of states of affairs. The chapter on negation
introduces the important distinction between an act as conceived of or
in the manner of a concept (*ut concepta sive per modum
conceptus*) and an act as carried out (*ut exercita*) (see
Nuchelmans 1988). Among the former type we acts as expressed by the
noun 'negation' and the verb 'to deny, whereas an
act of the latter type is what is expressed by the negative particle
'not'. The remainder of this chapter deals with the
function of the negation, which is to remove the composition found in
whatever it covers, and discusses some well-known sophisma-sentences
which turn on the specific function of negation.



The third chapter of the *Syncategoreumata* discusses the
exclusive words *solus* and *tantum*. They are called
exclusives because they carry out an exclusion, not because they
signify one. An exclusion, furthermore, requires four things, namely,
what is excluded, what is excluded from, the respect in which it is
excluded, and the act of exclusion. The kinds of exclusion are divided
into general and specific: the former involves an exclusion from
something generic, whereas the latter from something specific.
Questions that come up in this section have to do with the results of
adding an exclusive term to different kinds of words, such as to a
term falling under the category of Substance: does it exclude only
other substances, or does it also exclude from things listed under
another category? And what if it is added to a term listed under the
category of Accident (such as colour, quantity, and so on)? The next
question deals with the sorts of terms that can be meaningfully
associated with an exclusion. For example, is it possible to exclude
something from 'being' (as in 'Only being is,
therefore nothing other than being is')? The tract proceeds with
the kinds of things that can qualify for an exclusion. The fourth
chapter, which deals with exceptive words, is compiled in a similar
manner.



The fifth chapter is about the word *si*, which is said to
signify causality in or via antecedence. The chapter also discusses
the kinds of consecution or consequence, problems of inference
connected with the referents of terms used in consecutive sentences,
and how to contradict a conditional sentence. Special attention is
given to the problem whether from an impossible antecedent anything
follows.



The chapter on 'begins' and 'ceases' is a good
example of the way in which extra-logical considerations found their
way into medieval treatises on logic. Thus, apart from the semantics
and inferential problems connected with the use of these words in
propositions, the chapter also looks into the notions of motion and
time. An important part of Peter's ontological views can be
gathered from chapter seven, which covers issues connected with the
use of modal terms. Chapter eight discusses the signification and use
of connectives, and the final chapter on syncategorematic words proper
is concerned with the expressions *quanto*, *quam* and
*quicquid*. A very short, concluding chapter of Peter's
*Syncategoreumata* deals with a somewhat isolated topic, i.e.,
the proper modes of response in an argument. The topics looked into
are solution, the quantity and quality of syllogisms, and the ways to
go about proving a syllogism.


## 5. Doctrinal Elements in Peter's Logic



One of the most important elements in Peter's logic concerns the
doctrine of supposition. The theory of supposition has its origins in
the twelfth century, when the medievals showed a growing interest in
the ways in which words function in different contexts. This way of
dealing with the semantics of terms has been dubbed the
"contextual approach" (see de Rijk 1962-67, Vol. II,
Part I, pp. 113-117).



The primary semantic property of a word is its *significatio*,
in Peter's definition, the "representation of a thing by a
word in accordance with convention". It is a natural property of
a word, the presentation of some (universal) content to the mind. The
*significatio* of a word depends on its imposition, i.e., the
application originally given to the word in question. A word can have
more than one *significatio*, if it was originally applied to
two or more distinct (universal) natures.



The counterpart of *significatio*, the formal constituent of
every meaning, is the word's capacity to "stand for"
different things (even though its *significatio* remains the
same), depending on the context in which it is used. In the early
stages of the development of the theory on the properties of terms,
this feature of a word was called *appellatio*. For instance,
the words 'man' and 'horse' can be used to
stand for different individual men or horses. But they can also stand
for themselves, e.g., when they are used in sentences such as
'man is a noun', or 'horse is a noun'.
Moreover, their meaning can differ according as the words are used in
combination with verbs of different tenses.



In the final stages of the development of the theory, the notion of
supposition becomes the general label that covers all the uses of a
noun (substantive or adjectival), to which other recognised properties
of terms (*appellatio*, *ampliatio* and
*restrictio*) are subordinated.



The theory of properties of terms shows a radical inconsistency, which
has been explained as "the persistent hesitation of medieval
logicians between the domains of connotation (universals) and
denotation (individuals)" (De Rijk 1982, pp. 167-168).
This inconsistency runs throughout Peter's account of
supposition, and comes to the fore most prominently in what he says
about natural supposition (*suppositio naturalis*). The main
problem is in what way the property of natural supposition is related
to a term's *significatio*, which was defined as the
acceptance of a word for a thing (*res*). By this definition,
the *significatio* of the term 'man' covers both
its intension and extension, i.e., the universal nature of man and the
individuals that have this nature in common. *Suppositio
naturalis*, on the other hand, is described as "the
acceptance of a common term for all those things that can share in a
common universal nature"; for example, the term
'man' taken by itself by its very nature stands for all
the individuals that fall under it, whether they existed in the past,
exist in the present or will exist in the future. From this definition
and the example just presented it appears that the extensional
features of *significatio* and *suppositio naturalis*
overlap. The latter kind of *suppositio* has been explained by
interpreters as the natural capacity of a significative word to stand
for something.



There is a more telling difference between *significatio* and
*suppositio naturalis*, however. *Significatio* is the
natural property of any significative term to represent things, owing
to its original imposition, whereas a term's supposition only
enters the scene when it is used. The expression "taken by
itself" (*per se sumptus*) found in Peter's account
of *suppositio naturalis*, does not mean that no context is
required, as is the case in *significatio*, but it merely
indicates that for the moment the actual context is being disregarded.
The link between *significatio* and *suppositio* is the
following. When some word has acquired a signification by an
*impositor* (= someone who bestows a meaning upon a word), then
it connotes a univeral nature or essence, and acquires a natural
capacity to stand for all the actual and possible individuals that
share in this common nature; it owes this capacity to its
*significatio*. If, however, we disregard for a moment the
actual context in which the term in question is used and look upon the
term as taken by itself (*per se sumptus*), then its
supposition covers its entire extension. If we take the factual
context in which the term is used into consideration, then its
extension becomes limited, owing to the context. The context, or more
precisely, the added significative term, can be of three kinds: the
added significative term can be a predicate of a proposition in which
the term at issue occurs, the added significative term can be an
adjective, or the context can be of a social nature (see de Rijk 1971
and de Rijk 1985, pp. 183-203).



The distinction between *significatio* and *suppositio
naturalis* persisted throughout the thirteenth and fourteenth
centuries. Behind it is the fundamental view that regardless of
whether a word is used in some context or not, it always has a
*significatum*, i.e., the universal nature or essence it
signifies, which can be separated from what the word comes to mean in
a specific context.



Besides *suppositio naturalis*, Peter's (and other
medievals') conception of *suppositio simplex* also seems
to hover between connotation and denotation. In the expression
*homo est species* the term *homo* has *suppositio
simplex*, but this is precisely too what the term *homo*
signifies. So there scarcely seems reason to separate signification
from supposition on this score. The specific use of *suppositio
simplex* found in Peter of Spain and other medieval authors, as
the representation of a universal nature, is rejected later on by
authors such as William of Ockham. For the latter, the term
*homo* in the example just given has *suppositio
simplex* (for Ockham a special case of *suppositio
materialis*) in that it stands for the mental concept of man
(Kneale & Kneale 1978, pp. 268-269).



Peter of Spain's logical works are commonly characterised as
revealing a moderately 'realistic' outlook. To explain the
contents of linguistic expressions and the function of logical terms,
he is inclined to focus on their relationships to some extra-mental
reality. This can be shown from the way in which he discusses the use
of the word *est* (is), his account of *suppositio
simplex*, and the way he analyses the occurrence of the word
'necessarily' in propositions. Moreover, his conception of
the consecutive expression 'if' clearly shows his tendency
to put the domains of reality and language on a par. (However, not all
linguistic expressions are connected with extramental reality.
Although ontology always plays a role in his accounts of language, it
would appear that Peter is especially interested in the contents of
linguistic epressions. In that regard it seems more appropriate to
speak of an intensionalist semantics.)



In his *Syncategoreumata*, Peter analyses the significative
function of the word 'is'. To a certain extent his
findings are not confined to that term alone, but cover all verbs, in
which the verb 'is' is always understood. The most
remarkable feature about his discussion of 'is' is his
focus on the notion of composition. What he is particularly interested
in is the kinds of things affirmative propositions featuring that verb
can refer to, in his words, the type of composition involved in such
propositions.



The notion of 'composition' plays a prominent role in
Peter's semantics. Before embarking on the specifics of the word
'is', he first looks into the *compositiones*
involved in the noun and the verb. When it comes to the composition
involved in the use of 'is', the starting-point for his
account is the question whether the expression 'is' in a
proposition of the form 'S is P' implies the
'being' of the composition. Whether it does or not depends
on how we consider the composition. If we are talking about any
composition whatsoever, in his words, the composition in general, the
composition can indiscriminately be connected with beings and
non-beings. This is because we can talk about both things that are and
things that are not by making use of the same affirmative
propositions. Hence anything expressed by a proposition of the form
'S is P' is a being in a certain sense (*ens
quodammodo*). The type of composition he is referring to here is
the mental content of some affirmation, which is something that only
has being to a certain degree. However, the composition in general,
that is, the state of affairs involved in such expressions, is
primarily connected with being rather than non-being. It is when we
talk about non-beings, such as chimaeras, that being in a certain
sense once again enters the scene. Hence a distinction of the types of
being referred to, or the types of composition involved in affirmative
propositions into being in the absolute sense (*ens
simpliciter*) and being in a certain sense (*ens
quodammodo*). The difference between these two types of being is
illustrated by the distinction between two types of inference: from
'A man is an animal', in which the composition involved is
a being in the absolute sense, it follows 'Therefore a man
is', but from 'A chimaera is a non-being', in which
the composition is a being in a certain sense only, it does not follow
'Therefore a chimaera is'.



The counterpart of Peter's discussion of composition is the
section on negation. Peter specifically goes into the question of what
it is the negation denies. In his words, the negation removes the
composition. The composition in this connection is identified with the
affirmed state of affairs (*res affirmata*). What the negation
removes is not the state of affairs, but the affirmation that goes
along with it. The basis of both composition and negation turns out to
be the same state of affairs, i.e., something that is formulated in
the mind, to which we can assent or which we can deny to be the
case.



The focus on matters of ontology is evidenced in other portions of
Peter's logic as well. For Peter, as for Henry of Ghent (who
also wrote a *Syncategoreumata*) the expression *homo*
(man) in *homo est animal* ('Man is an animal') has
simple supposition: it stands for the universal nature of humanity.
Accordingly, the expression is necessarily true, even if no man should
exist. The term 'necessarily' thus has ampliative force:
it enables the subject term 'man' to refer to individuals
not only existing in the present ( which is the normal case when a
present-tense verb is used), but also to those of the past and the
future. This analysis runs contrary to what is found in some other
*Syncategoreumata* authors, like Johannes Pagus and Nicholas of
Paris, who maintain that the term 'necessarily' does not
have ampliative force. Hence the expression *homo necessario est
animal* ('A man is necessarily an animal') is only
true on the condition that a man exists.



A similar point is made in connection with the use of modal terms. For
Peter of Spain, logical necessity is based upon ontological necessity,
or, the necessity of propositions has its foundation in the necessity
of the things spoken about. Necessity is associated with different
types of things, such as the relationships between certain concepts
(such as genera and species), and the specific things the notions of
which we come across in the different kinds of (scientific) knowledge
(such as mathematical entities and their properties). His outlook on
necessity is clearly revealed in his analysis of the inference
*homo necessario est animal*; *ergo Sortes necessario est
animal* ('A man is necessarily an animal; therefore Socrates
is necessarily an animal'). In his view the inference is not
valid, because a transition is made from necessary being to a being at
a certain time. For Peter then, the notion of necessity ultimately
refers to a necessary state of affairs in reality, something that is
always the case.



A fusion of the domains of language and reality also turns up in
Peter's account of the consecutive 'if', which he
explains as signifying causality. Like his contemporaries he looks
into the question whether from something impossible anything follows.
In his account, the notion of 'impossibility' can be taken
in two ways, viz. impossibility as such (or absolute impossibility),
which amounts to nothing, or some impossible state of affairs, that is
a combination of notions that do have a real foundation but are
incompatible. From the latter type of impossibility, such as 'A
man is an ass', something, but not anything can follow, e.g.,
'Therefore a man is an animal'. From impossibilities as
such, e.g., 'You know that you are a stone', nothing can
follow. The fundamental idea is that in order for something to follow
from an antecedent, the antecedent in the consecutive relationship
must be a something (*res*) of some sort (see Spruyt 1993, pp.
161-193).