## 1. The Word '*Sophisma*'



Although some medieval theologians -- and humanists even more, of
course, like Vives or Rabelais -- used the words
'sophism' or 'sophist' as a derogatory
designation for quibbling philosophers,
'*sophisma*' in medieval philosophical literature
has a very precise and technical sense. To avoid any confusion with
fallacies and badly-constructed arguments, we shall here use the
original term '*sophisma*' rather than the word
'sophism' (which even nowadays has a pejorative
connotation).


## 2. Description and Characteristics


### 2.1 The *Sophisma* Proper



A *sophisma* has several important characteristics. First of
all, a *sophisma* proper is a *sentence* rather than an
argument. In particular, a *sophisma* is a sentence that


1. is *odd* or has odd consequences,
2. is *ambiguous*, and can be true or false depending on how
it is interpreted (or is taken to be ambiguous when in fact it is
not), or
3. is *puzzling* not in itself but only when it occurs in a
specific context (or "case," *casus*).



Here are some some examples of kind (1), sentences that are odd or
have odd consequences:



> 
> This dog is your father.
>   
> 
> A chimaera is a chimaera.
> 



As examples of kind (2), *ambiguous* sentences that can be true
or false depending on how they are interpreted, consider:



> 
> All the apostles are twelve.
>   
> 
> The infinite are finite.
>   
> 
> Every man is of necessity an animal.
> 



As an example of kind (3), sentences that are not puzzling in
themselves but only when they occur in a definite context
("case," *casus*), consider:



> 
> The sentence 'Socrates says something false', in the case
> where Socrates says nothing other than 'Socrates says something
> false'.
> 



This sentence is paradoxical, and is one of the forms the Liar
paradox. As another example of kind (3) consider:



> 
> 'Every man is an animal', in case no men, or only one man
> or only two men exist(s).
> 


### 2.2 The Aim of the Discussion



Once the odd, ambiguous or puzzling *sophisma*-sentence is put
forward, one should try to understand what it means, what it implies,
and how it fits into or contradicts the particular theory under
consideration. This is called "solving the
*sophisma*," and it is the aim of the entire discussion.
The way solutions are sought and established is similar to the highly
formalized scholastic method for determining a
"question":


1. First, one has to examine the arguments *pro* and
*contra*.
2. Second, one has to present one's own solution to the
problem. (Sometimes this part of the discussion is preceded by certain
theoretical remarks or clarifications that make the terminology more
precise.)
3. Third, one has to refute the arguments supporting the opposite
answer.


#### 2.2.1 Some examples



Our first example comes from Peter of Spain's
*Syncategoreumata*, chapter 4. The *sophisma* runs:



> 
> *Omne animal preter hominem est irrationale.*
>   
> 
> (Every animal but man is irrational.)
> 



In accordance with step (1), the *pro* and *contra*
arguments run:



> 
> 
> Proof: The sentence 'Every animal is irrational' is false,
> and the only counterinstance is man. Therefore the *sophisma*
> is true.
> 
> 
> 
> Disproof: Every animal but man is irrational. Therefore, every animal
> but this man is irrational. And that is false.
> 
> 
> 



This particular *sophisma* is put forward to test the logical
behaviour of the syncategorematic word 'but'
(*preter*), more specifically, to consider the question of what
is excepted when we use an exceptive word.



In accordance with step (2), Peter of Spain solves the
*sophisma* by saying that it is true without qualification, and
that the argument *pro* is sound.



In accordance with step (3), the argument *contra* is rejected
on the grounds that it is a fallacy, because in the sentence it starts
off with, 'Every animal but man is irrational,' the
expression 'man' has simple supposition, that is, it
stands for man in general, whereas in the second sentence,
'Therefore every animal but this man is irrational,' the
expression 'this man' has personal supposition, that is,
it stands for an individual man. The second mistake in the disproof is
that it proceeds from a combination of something less general with the
distributive sign 'every' to a combination of something
that is more general with the distributive sign 'every':
in the first sentence, 'every animal' ranges over every
animal other than man, whereas in the second sentence, the expression
'every animal' comprehends not only all the animals, but
also every man other than this one.



The underlying logical problem in this *sophisma* according to
Peter's exposition is the question of what kind of distribution
is involved in propositions containing an exceptive expression in
combination with the universal sign 'every'. In this case,
the solution to the *sophisma* is quite straightforward, as the
disproof rests on an unwarranted change in distribution throughout the
argument.



Another relatively simple example comes from Albert of Saxony,
*Sophismata*, *sophisma* xi. The *sophisma*
runs:



> 
> *Omnes homines sunt asini vel homines et asini sunt asini.*
>   
> 
> (All men are donkeys or men and donkeys are donkeys.)
> 



In accordance with step (1), here are the *pro* and
*contra* arguments:



> 
> 
> Proof: The *sophisma* is a copulative sentence (in modern
> logical terminology, a conjunction) each part of which is true;
> therefore the *sophisma* is true, since its analysis becomes:
> [All men are donkeys or men] and [donkeys are donkeys].
> 
> 
> 
> Disproof: The *sophisma* is a disjunctive sentence each part of
> which is false; therefore the *sophisma* is false, since its
> analysis becomes: [All men are donkeys] or [men and donkeys are
> donkeys].
> 
> 
> 



This is a *sophisma* of the second kind above, one that rests
on an ambiguity and can be read with a true interpretation or with a
false interpretation. Many such *sophismata*, although not this
one, resist being translated from Latin into another language without
losing the ambiguity. For example, the sentence 'aliquem asinum
omnis homo videt' can be translated by 'Every man sees a
donkey' as well as by 'There is a donkey that every man
sees'. Similarly, in solving *sophismata,* sometimes
Latin word order is used as an arbitrary code for interpreting the
sentence. For example, according to William Heytesbury, when the word
'infinite' is placed at the beginning of a sentence and
belongs to the subject, it has to be interpreted as a syncategorematic
term; in any other case, it is usually interpreted as a categorematic
term (Heytesbury, *Sophismata*, *sophisma* xviii,
fol.130va). Such word-order codes might seem like reasonable
regimentations of language to a Latin-speaker, but in translation they
often seem quite implausible and forced. No such problems arise with
this example. (For clarity, square brackets have been inserted into
the proof and disproof above, in order to indicate the ambiguity of
the *sophisma.*)



In accordance with step (2) above, Albert of Saxony, who discusses
this *sophisma*, solves it by just saying that it is either
true or false depending on which interpretation we choose. He then
takes the opportunity to review the basic principles governing the
truth-value of copulative and disjunctive sentences.



In accordance with step (3), we would normally be required to refute
the opposite answer. In this case, however, there is nothing to
refute, since Albert's solution accepts both the *pro*
and the *contra* arguments (for different readings of the
*sophisma*).



In general, a *sophisma* provided a good opportunity to discuss
problems related to a specific theoretical issue. For example, the
*sophisma* '*Album fuit disputaturum*'
('The white [thing] was about to dispute') in
thirteenth-century Parisian literature elicited discussions of
problems connected with the theory of reference in tensed contexts,
and also provided an opportunity to refute the positions others held
on this very controversial subject. This is why Pinborg 1977 (p. xv)
says, with reference to the body of literature devoted to discussions
of *sophismata*, that at Paris in the thirteenth century,
"the *sophismata* seem -- within the faculty of arts
-- to play a role analogous to the *Quaestiones
quodlibetales* [quodlibetal questions] in the faculty of
theology." The *Catalogue of 13th Century Sophismata*
(Ebbesen and Goubier 2010) provides an extensive list of logical
problems and distinctions that were brought up under the guise of a
*sophisma*. Again, many grammatical problems were also dealt
with in this way.


#### 2.2.2 *Sophismata* and the Roles of Syncategorematic Words



It is important to recognize that many *sophismata* contain
syncategorematic words that are responsible for their odd, ambiguous
or puzzling character. They can be difficult to interpret, especially
when more than one syncategorematic word occurs in one and the same
sentence. In the *sophismata* literature, discussions of
problematic sentences are usually accompanied by an explanation of the
distinctions governing the use of syncategorematic words. In turn such
distinctions can help to interpret the sentence at issue.



An example of such a distinction is the following. The
*sophisma* 'Only God being God is necessary'
('*Tantum deum esse deum est necessarium*')
contains the syncategorematic word 'only'
('*tantum*'). The *sophisma* is solved by
making a distinction between two different functions of the word
'only', in that the exclusion it makes can pertain to the
expression 'God', or to the entire phrase 'God being
God'. In the former case the sentence is true, but in the latter
it is false (Ebbesen and Goubier 2010, vol. I, p. 122). Another
example of a problematic sentence containing the disjunctive
expression 'or' is the *sophisma* 'Every
proposition or its contradictory opposite is true'. Some authors
considered this proposition as true, but others thought it was
ambiguous. In one way, the distribution of 'every' could
be taken as ranging over the disjunction, in which case the
proposition reads 'Any proposition or its contradictory is
true', which is true. In another way, the disjunction could be
taken to cover the distribution, in which case the proposition reads
'Every proposition is true or every contradictory opposite is
true', which is false. A final example of a distinction concerns
the *sophisma* 'The white can be black' (an awkward
translation of the sentence '*Album potest esse
nigrum*'), which can be taken to mean either 'The
thing that is white can be black', which is true, or 'It
can be the case that the white thing is black' (at the same
time, that is), which is false. The truth or falsity of the
proposition then depends on a scope distinction regarding the
expression 'can be'.



The expression 'syncategorematic word' should be taken in
a broad sense here; it includes not only classical syncategorematic
words such as 'and', 'if',
'every', etc., but also expressions such as
'infinite' or 'whole', which can be used both
categorematically and syncategorematically. Thus, the sentence
'*Infinita sunt finita*' ('The infinite are
finite' -- another example of a *sophisma* that
cannot be translated into English without disambiguating it) is false
if 'infinite' is used categorematically, for in that case
it reads, 'Things that are infinite are finite.' But it is
true if 'infinite' is used syncategorematically, for in
that case it reads, 'Finite things are infinite in number'
or 'There are infinitely many finite things' (See
Heytesbury, *Sophismata*, *sophisma* xviii, fol. 130va).
This is another example of the kind of distinction that was used to
solve the *sophisma*.



Many *sophismata* too are what medieval logicians called
'exponible sentences'
('*exponibilia*'); these are sentences that appear
to be simple but actually imply several other sentences into which
they can be decomposed. For example, the sentence 'A
differs from B', was said to be equivalent to
'A exists and B exists and A is not
B', whereas the sentence 'A ceases to be
white', was said to be equivalent either to 'Now A
is white and immediately after this A will not be white'
or to 'Now A is not white and immediately before this
A was white', depending on the theory.


### 2.3 The Main Fields in which *Sophismata* are Discussed



Discussions of *sophismata* were used to disentangle problems
of logic and grammar, but their subject matter included concepts
featured in physics and theology as well. While the problems at issue
in the *sophismata* are taken to be logico-grammatical, it is
possible to distinguish between logical, grammatical and physical
*sophismata*. Furthermore, many standard *sophismata* of
the thirteenth and fourteenth centuries feature God or the Antichrist,
entities that belong to the domain of theology. As Ebbesen points out
(1997, p. 151), these entities could play an interesting role in
sophismatic discussions because they were considered to have unusual
qualities, which could make for intriguing logical puzzles. Yet
theological *sophismata* as such are extremely rare.


#### 2.3.1 Logical *Sophismata*



As seen above, logical *sophismata* are closely connected to
discussions of syncategoremata. The aim of these discussions is to
determine the truth-value of a particular sentence containing (a)
syncategorematic word(s), or the truth-value of some other problematic
sentence (including, for example, sentences involving self-reference),
but also to delve into specific topics exemplified in a
*sophisma*, such as:


* the syntactic and semantic properties of terms (including the
difference between what a term signifies, and what it stands for) in
sentences such as 'Every man sees every man', 'You
are a donkey', and 'I promise you a horse'; we could
compare these kinds of discussions to modern discussions of sentences
such as 'The morning star is the evening star';
* quantification and existential import, as in the sentence
'Every phoenix is';
* the logic of negation and "infinite" words, as in the
sentences, 'Nothing and a chimaera are brothers',
'Nothing is nothing', and 'If nothing is, something
is';
* the problem of universals, as in 'Man is a species'
and 'Man is of necessity an animal';
* the composite and divided senses of a sentence and the scope of
modal operators, as in 'The white can be black' and
'Every man is of necessity an animal', etc.;
* the truth conditions of a *dictum*, as in 'You know
whether of the one who is lying it is false that Socrates is
he';
* scope distinctions in negations, as in 'No one running you
are a donkey';
* scope distinctions in a conditional containing a distributive sign
(quantifier), as in 'Nothing true if Socrates is running is
antecedent to Plato running';
* the truth value of conditional sentences containing an impossible
antecedent, such as 'If you know you are a stone, you do not
know you are a stone';
* the nature of necessity and possibility, as in sentences such as
'The soul of the Antichrist of necessity will be',
'Every grammarian is of necessity a man', and 'It is
possible that every man is an animal', etc.


#### 2.3.2 Physical *Sophismata*



The aim here is to discuss concepts featuring in physics, such as
motion, change, velocity, intension and remission of forms, maxima and
minima, time, etc. Examples of *sophismata* in this domain are
sentences containing the syncategoremata 'begins' and
'ceases', e.g., 'Socrates ceases to be not ceasing
to be', 'Nothing is true except in this instant',
and 'What begins to be ceases to be'. But, as seen above
with the *sophisma* 'The infinite are finite',
problems like these are treated as logical and conceptual problems.
This logico-semantical approach to physical problems is characteristic
of medieval natural philosophy and should be kept in mind when we
wonder to what extent medieval physics can be considered a precursor
to modern physics.



With respect to so-called 'physical *sophismata*,'
special attention should be paid to certain fourteenth-century English
authors known as the "Oxford Calculators", e.g., Richard
Kilvington, William Heytesbury, Thomas Bradwardine, Richard and Roger
Swineshead. These philosophers developed a distinctively
"English-style" of *sophismata.* Based on the
theological doctrine of the absolute power of God, the distinction
between what is physically possible and what is logically possible
(where non-contradiction is the only limit) allowed these authors to
devise imaginary thought experiments. For example, suppose that
A is a distance to be traversed which Socrates cannot traverse,
and that his power is increased until Socrates can traverse distance
A completely, and that Socrates' power is not increased
further: is the *sophisma* 'Socrates will begin to be
able to traverse distance A' true or false? (Richard
Kilvington, *Sophismata*, *sophisma* 27, in Kretzmann
1990, p .60). Thought experiments such as these led these authors to
develop, among other things, a theorem for uniformly accelerated
motion (e.g., Thomas Bradwardine's Mean Speed Theorem).


#### 2.3.3 Grammatical *Sophismata*



In the Middle Ages the label 'grammatical
*sophismata*' was used for the *sophismata* that
dealt with grammatical well-formedness (*congruitas*) and
grammatico-semantic completeness. *Sophismata* such as
'Love is a verb', 'O Master', 'It rueth
me', and 'I run' gave rise to very pointed
discussions concerning grammatical categories and theories. For
example, does a change in word order change the meaning of a
proposition? Can a participle be a subject? How should we interpret
interjections? Can '*est*' ('is') be
used impersonally?



Kneepkens (2015) has drawn our attention to a remarkable collection of
*sophismata*, of French or English origin, presumably dating
from early thirteenth century, which exclusively discusses problematic
sentences taken from biblical, liturgical, and other religious
sources. This collection has the characteristics of grammatical
*sophismata*, but in addition focuses on metaphorical features
of religious language, as well as making use of rhetoric as an
analytical tool (Kneepkens 2015, p. 320).


#### 2.3.4 Theological *Sophismata*



Ebbesen has identified one *sophisma* that deserves the label
'theological' (in the sense, that is, of an
"exception to the general rule that the *sophism* is not
a theological genre" (Ebbesen 1997, pp. 151-152). The
*sophisma* in question runs '*Deus est eodem modo in
dyabolo sicud fuit in beata virgine*'('God is in the
same way in the devil as he was in the Blessed Virgin'). The
reason why this could count as a theological *sophisma* is that
the question that is raised in it, about how God is present in
creatures, is theological in nature. Another theological
*sophisma* investigated by Ebbesen is the sentence,
'*Deus scit quicquid scivit*' ('God knows
whatever he has known'), which was widely discussed in the
standard *sophismata* literature. The sentence elicits
questions pertaining not only to the logical behaviour of the verb
'*scire*' ('to know'), but also to the
specifically theological issue of the object of God's knowledge
(Ebbesen 1997, p. 154ff.).


## 3. The Various Roles of *Sophismata*



The first and most evident role of *sophismata* is pedagogical.
In theoretical treatises, *sophismata* can play various roles.
They can be used to explain a given statement or rule, illustrate a
distinction or an ambiguity, show what would follow if a rule were
violated, or test the limits of a theory.



In addition, although some differences can be identified between the
Paris and the Oxford traditions, *sophismata* are important as
oral exercises (disputations) in a student's training in
philosophy, especially in the first years of universitary education in
the Faculty of Arts. Nevertheless, it is clear that, while
Heytesbury's *Rules for Solving Sophismata* is written
for undergraduate students -- at Oxford
'*sophista*' was the official name given to
students who had disputed "on *sophismata*"
("*de sophismatibus*") for about two years --
this is probably not the case for his *Sophismata*, in which
the discussions are much more complicated.



It is no exaggeration to say that the study of *sophismata* in
the Faculty of Arts was as important as biblical exegesis in the
Faculty of Theology.


## 4. *Sophismata* Literature



In the Introduction of the *Catalogue* (Ebbesen and Goubier
2010, vol. I), we find an elaborate description of the medieval genre
of *sophismata.* This genre was based on disputational
practices in medieval universities. In its most basic form, it
included the discussion of a problematic proposition, beginning with
the presentation of the proposition, followed by a proof, a disproof,
and a solution, sometimes accompanied by a response to the opposing
arguments (see our section 2.2). The joint discsussion of these steps
was known as *corpus sophismatis*. A respondent's
solution to the *sophisma* could be followed by an attack,
leading to yet another exchange of arguments. In other instances the
discussion of the *sophisma* could continue with a discussion
of related problems, the first of which was often dealt with in an
elaborate way. These kinds of *sophismata* are quite long.



*Sophismata* are found in a variety of texts, which scholars
have categorized into different kinds. *Abstractiones*
treatises are collections of *sophismata* arranged by a type of
syncategorematic word (e.g., exceptive words, exclusive words,
conditional words, disjunctive words, and so on), or sometimes by the
distinction that is used to solve them. The material covered in each
*sophisma* is mostly confined to a *corpus*.
*Syncategoremata* are treatises devoted to syncategorematic
words; in these treatises *sophismata* are used to illustrate
or to give more refined explanations of the logical behaviour of the
different syncategorematic words (or kinds of syncategorematic words).
In *Distinctiones* treatises, the starting points are
distinctions or logical rules connected with sentences that contain a
syncategorematic word. The material in these treatises is usually
organized around the type of syncategorematic word at issue. Besides
these different kinds of treatises (the boundaries of which, however,
are not very clear), we also find collections of *sophismata*
that seem to be (fictional or faithful) reports of oral disputations.
These collections can contain grammatical *sophismata*, but the
latter are also found in separate, rather loosely-organized,
treatises. *Sophismata* also play an important role in general
manuals of logic, and in other works -- often written by the same
authors, or by different authors working in the same milieu as the
former collections -- with titles such as *On Exponibles*,
*On Consequences*, *Sophistry*, etc.



Even if there are technical distinctions among these types of
treatises, all of them play the same roles mentioned above: they
provide students with logical skills that can be applied to any
subject whatsoever.