Ashworth, Earline Jennifer. 1967. "Joachim Jungius (1587-1657) and the Logic of Relations." Archiv für Geschichte der Philosophie no. 49:72-85.
"In histories of logic, the sixteenth and seventeenth centuries, at least until Leibniz began his work, are either ignored or are referred to with the utmost brevity as being hardly
worthy of attention (1).
However, there is one name which appears with fair regularity in the literature, and that is the name of Joachim Jungius, whose Logica Hamburgensis is often contrasted
favorably with the Port Royal Logic. Both Bochenski and the Kneales allow this book, published in 1638 for the use of the Classical Schools at Hamburg, to be one of the better textbooks of the period
(2); while Heinrich Scholz in his influential Geschichte der Logik, not only praises it highly, but discusses Jungius's contributions to logic at some length (3). More impressive yet are the
varied tributes paid to Jungius by Leibniz, who called him "one of the most able men that Germany has ever had" (4); compared him with Galileo and Descartes (5); and said that "he surpassed all
others in the knowledge of true logic, not even excepting the author of the Artis Cogitandi [Arnauld]" (6). Of course, much of Leibniz's praise arose from his admiration of Jungius's varied
activities, his career as a medical doctor, his contributions to physics, botany, mineralogy, theology, educational theory, and his foundation of the first-learned society in Germany (7). More
specifically, however, Leibniz admired Jungius for his demonstration that not all inferences could be reduced to syllogistic form, and he praised his logical acuteness in this respect on a number of
occasions (8). The purpose of this paper is to shed some light on a much neglected area of the history of logic by inquiring whether Jungius's treatment of non-syllogistic or, in this context,
relational inferences, is commensurate with the logical distinction which has been claimed for him; and, more briefly, to see whether there are any further factors which set Jungius above other
logicians of the same period." (pp. 72-73)
"In conclusion one may say that although the Logica Hamburgensis shares in all the faults of its age, the superficiality, the lack of metalogical perceptiveness, it also
has merits which are peculiarly its own. The body of truth-functional logic contained in it would alone be sufficient to distinguish Jungius from his contemporaries, and still more impressive, given
the background, is his use of relational inferences. It is true that the argument a divisis ad composita is both unoriginal and unremarkable, despite Scholz's praise; it is true that the
inversion of relations is found in other contemporary logicians; while discussion of the oblique syllogism was quite usual; but the argument a rectis ad obliqua was both original and clearly
presented. Moreover, Jungius seems to have been fully conscious that relational inferences were inferences in their own right, to be treated as such and not to be hidden away among the categories.
Without this realization, any amount of originality in the discovery of actual inferences could have gone for nought. Hence, while the verdict of Heinrich Scholz needs modification, his praise of
Jungius is basically justified, for it was he who brought the logic of relations to the attention of his successors, especially Leibniz." (p. 85)
(1) In this context, it must be acknowledged that historians of thought have been kinder than those devoted strictly to formal logic. For instance, Peter Petersen's seminal work,
Geschichte der aristotelischen Philosophie im protestantischen Deutschland, Leipzig 1921. contains much material of interest to the historian of logic. The publication in 1964 of Dr. Wilhelm
Risse's work, Die Logik der Neuzeit. 1. Band. 1500—1640, Stuttgart-Bad Cannstatt 1964, marks a great step forward in the study of the field.
(2) I. Bochenski, History of Formal Logic, translated and edited by Ivo Thomas, Notre Dame, Indiana, 1961, p. 257, W. & M. Kneale, The Development of Logic,
Oxford 1962, p. 313.
(3) H. Scholz, Geschichte der Logik, Berlin 1931, pp. 41—2.
(4) "Letter to Christian Habbeus, Jan. 1676", Samtliche Schriften und Briefe, edited by the Prussian Academy of Sciences (1923) 1st Series, Vol. I, p. 443.
(5) Opuscules et fragments inédits de Leibniz, edited by L. Couturat, Paris 1903, p. 345.
(6) "Letter to Koch, 1708", quoted by Couturat in La logique de Leibniz, Paris 1901, note 4, p. 74.
(7) The Societas Ereunetica, founded in Rostock in 1622. Unhappily, it lasted at most only two years. For further information on Jungius's life, see the following
G. Guhrauer, Joachim Jungius und sein Zeitalter, Stuttgart und Tübingen 1850; Beiträge zur Jungius-Forschung. Prolegomena zu der von der Hamburgischen Universität
beschlossenen Ausgabe der Werke von Joachim Jungius (1587—1657), edited by A. Meyer, Hamburg 1929; Joachim Jungius-Gesellschaft der Wissenschaften: Die Entfaltung der Wissenschaft. Zum
Gedenken an Joachim Jungius, Hamburg 1957. The second work mentioned contains an extensive bibliography.
(8) Opuscules et fragments inédits, p. 287, p. 330, p. 406.
———. 1968. "Propositional Logic in the Sixteenth and Early Seventeenth Centuries." Notre Dame Journal of Formal Logic no. 9:179-192.
"Until recently, historians of logic have regarded the early modern period with unremitting gloom. Father Boehner, for instance, claimed that at the end of the fifteenth century
logic entered upon a period of unchecked regression, during which it became an insignificant preparatory study, diluted with extra-logical elements, and the insights of men like Burleigh into the
crucial importance of propositional logic as a foundation for logic as a whole were lost.(1) Nor is this attitude entirely unwarranted, for the new humanism in all its aspects was hostile to such
medieval developments as the logic of terms and the logic of consequences. Those who were devoted to a classical style condemned medieval works as unpolished and arid, and tended to subordinate logic
to rhetoric; while those who advocated a return to the original works of Aristotle, freed from medieval accretions, naturally discounted any additions to the subject matter of the
But it would be a mistake to dismiss the logical work of the period too readily. In the first place, the writings of the medieval logicians were frequently published and widely
read. To cite only a few cases, the Summulae Logicales of Petrus Hispanus received no fewer than 166 printed editions;(2) Ockham's Summa Totius Logicae was well known; the 1639
edition of Duns Scotus included both the Grammaticae Speculativae attributed to Thomas of Erfurt and the very interesting In Universam Logicam Quaestiones of Pseudo-Scotus; (3) the
Logica of Paulus Venetus was very popular; and a number of tracts by lesser known men like Magister Martinus and Paulus Pergulensis were printed. Moreover, since logic still played such a
preeminent role in education, contemporary scholars were not backward in producing their own textbooks; and numerous rival schools of logic flourished.(4) The purpose of this paper is to make a
preliminary survey of some of the wealth of material available from the sixteenth and first half of the seventeenth centuries, in order to ascertain how much of the medieval propositional logic had
in fact been retained.(5) It will become clear that the situation was better than has been thought." (p. 179)
(1) See P. Boehner, ''Bemerkungen zur Geschichte der De Morgannsche Gesetze in der Scholastik," Archivâr Philosophie, 4 (1951), p. 145.
(2) See J. P. Mullally, The Summulae Logicales of Peter of Spain (Notre Dame, Indiana, 1945), p. LXXVIII.
(3) In Joannes Duns Scotus, Opera Omnia, edited by L. Wadding (Lugduni, 1639), Vol. I.
(4) For a comprehensive account of the various schools of logic, see Dr. Wilhelm Risse, Die Logik der Neuzeit. I. Band 1500-1640, (Stuttgart-Bad Cannstatt, 1964).
(5) I have limited myself to material in the British Museum and the Cambridge University Library for the purposes of this introductory survey.
———. 1968. "Petrus Fonseca and Material Implication." Notre Dame Journal of Formal Logic no. 9:227-228.
"Little attention has been paid to the question of whether material implication was recognized in the sixteenth and seventeenth centuries, although it has been argued that John of
St. Thomas was aware of the equivalence '(p ⊃ q) ≡ (~p v q)'.(1) The other usual test-case for a knowledge of material implication is '(p ⊃ q) ≡ ~(p . ~q) and I intend to show that the sixteenth
century Jesuit, Petrus Fonseca, whose Institutionum Dialecticarum libri octo was one of the most popular textbooks of the period, (2) was well acquainted with this second equivalence." (p.
"One must conclude that Fonseca was aware both of strict and of material implication." (p. 228)
(1) See Ivo Thomas, "Material Implication in John of St. Thomas", Dominican Studies 3 (1950), p. 180; and John J. Doyle, "John of St. Thomas and Mathematical Logic",
The New Scholasticism 27 (1953), pp. 3-38.
(2) First published in 1564, it went into at least 44 editions. See Wilhelm Risse, Die Logik der Neuzeit, Band I. 1500-1640 (Stuttgart-Bad Cannstatt, 1964), p. 362, n.
———. 1969. "The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries." Archiv für Geschichte der Philosophie no. 51:260-285.
"The purpose of this paper is to make a preliminary survey of some of the wealth of material available from the sixteenth and first half of the seventeenth centuries, in order to
ascertain how much of the medieval propositional logic had in fact been retained.(5) It will become clear that the situation was better than has been thought.
The vocabulary and organization of the textbooks under consideration were fairly standard. The discussion of the proposition [Enuntiatio, Propositio, or, in Ramist texts,
Axioma] followed sections on the predicaments and predicables or the Ramist equivalent, on arguments. Medieval logicians had called the compound proposition 'hypothetical', but sixteenth and
seventeenth century writers more usually referred to enuntiatio conίuncta or composita, sometimes with a note to the effect that it is vulgarly or improperly called
'hypothetical'.(6) Melancthon retained the name 'hypothetical', as did one or two others.(7) The Spanish scholastic, Petrus Fonseca, discussed the whole question in some detail, saying that the name
'hypothetical' most properly applies to conditional propositions, but can also be used of disjunctions, because they imply a conditional.(8) A compound proposition was generally said to consist of
two (or more) categorical propositions, joined by one (or more) of a list of propositional connectives. The assumption that the truth of these propositions depended upon the truth of the parts, the
kind of connective employed, and in certain cases the relationship between the parts usually remained implicit, but the seventeenth century German logician, Joachim Jungius, said explicitly that
truth or falsity depended on "the kind of composition involved";(9) while Alsted had written previously that truth or falsity depended "on the disposition of parts". (10)
There was much agreement as to the kinds of compound proposition to be considered. Conditional, conjunctive, and disjunctive propositions were always mentioned. Those logicians in
the scholastic tradition, like Campanella, Cardillus, Fonseca, Hunnaeus and John of St. Thomas, included causal and rational propositions, as did some outside the tradition like Cornelius Martini and
Jungius, who discussed the causal proposition at length. Only a few, including Fonseca and C. Martini, mentioned the temporal and local propositions which had been discussed by such medieval
logicians as Ockham and Burleigh; but both Ramus and Burgersdijck spoke of 'related' propositions which exhibit 'when' and 'where' among other connectives.(11)
Ramus and those influenced by him added a new kind of compound proposition, the discretive.
Although compound propositions were rarely called 'hypothetical', the traditional title of 'hypothetical syllogism' was usually retained for the discussion of propositional
inference forms. Only a few spoke of syllogismus compositus or coniunctus. (12) In all cases the categorical syllogism was discussed before the hypothetical, and usually such
matters as sorites, example, enthymeme and induction also came first. A few books had, in addition, a section on the rules for valid inference or bona consequeentia.
Melancthon in his Erotemata Dialectices included a chapter entitled De Regulis Consequentiarum after his discussion of sorites and before his discussion of the
hypothetical syllogism. Alsted placed his canons of material consequence in the same position; while the remarks of Caesarius come after his section on the hypothetical syllogism. On the other hand,
the three scholastics, Campanella, Fonseca, and Hunnaeus introduced their rules for good consequence before they discussed the syllogism, thus approaching most closely to the later medieval order of
priorities." (pp. 179-180)
"It is indeed true that the logicians of the sixteenth and early seventeenth centuries failed to appreciate the fundamental importance which the logicians of the later middle ages
had attributed to propositional logic; and a number of the texts I have been concerned with even give instructions for the reduction of hypothetical syllogisms to categorical syllogisms.(88) On the
other hand, the amount of propositional logic retained was by no means negligible, and some authors, such as Fonseca and Jungius, included a great deal. No startling advances were made, but there
were innovations in detail, like Jungius's discussion of the posterior subdisjunctiva, or the linking of the conditional with a negated conjunction.
One may therefore conclude that, while the period is not one of great excitement for the historian of logic, it merits considerably more attention than it has been granted in the
past." (p. 188)
(5) I have limited myself to material in the British Museum and the Cambridge University Library for the purposes of this introductory survey.
(6) Cf. Thomas Campanella, Philosophiae Rationalis Partes quinque. 2. Dialectίca (Parisiis, 1638), p. 334; Augustinus Hunnaeus, Dialectίca seu generalίa logices
praecepta omnia (Antverpiae, 1585), p. 147; and Amandus Polanus, Logicae libri duo (Basileae, 1599), p. 147.
(7) Philippus Melancthon, Erotemata Dialectices, ( ---, 1540?), p. 96. Cf. Johannes Caesarius, Dίalectica (Coloniae, 1559), Tract. IV [No pagination]; and
Cornelius Martini, Commentatiomm logicorum adversus Ramίstas (Helmstadii, 1623), p. 204.
(8) Petrus Fonseca, Institutionum Dialectίcarum libri octo (Conimbricae, 1590), Vol. I, p. 173. Cf. Abelard's discussion of the same point in his Dialectica, edited by de Rijk
(Assen, 1956), p. 488.
(9) Joachim Jungius, Logica Hamburgensis, edited by R. W. Meyer (Hamburg, 1957), p. 98. '([Enuntiatio conjuncta] . . . secundum illam compositionis speciem, veritatis et
falsitatis est particeps".
(10) J. H. Alsted, Logicae Systema Harmonium (Herbonae Nassoviorum, 1614), p. 321. "Compositi axiomatis veritas & necessitas pendet specialiter ex partium
(11) Petrus Ramus, Dialecticae libri duo (Parisiis, 1560), p. 126; and Franco Burgersdijck, Institutionum Logicarum libri duo, (Lugduni Batavorum, 1634), pp.
(12) E.g., Fonseca, op. cit., vol. II, p. 100, refers to ''syllogismus coniunctus"; and Polanus, op. cit., p. 165, refers to "syllogismus compositus".
(88) E.g., Conrad Dietericus, Institutiones Dialecticae (Giessae Hassorum, 1655), p. 312; Fortunatus Crellius, Isagoge Logica (Neustadii, 1590),pp. 243-246; and
Jungius, op. cit., passim.
———. 1970. "Some Notes on Syllogistic in the Sixteenth and Seventeenth Centuries." Notre Dame Journal of Formal Logic no. 11:17-33.
"Although a number of different schools of logic flourished in the sixteenth and seventeenth centuries (2), they seem to have shared a lack of interest in formal logic which
expressed itself in a greater concern for the soundness than for the validity of arguments. An example of this tendency is the emphasis placed upon the Topics, or the ways of dealing with and
classifying precisely those arguments which were not thought to be susceptible of formal treatment, since they depended for their effectiveness upon the meaning of the terms involved.(3) It is true,
of course, that the Humanists and, later, the Ramists, devoted considerably more space to the Topics and to the "invention" of arguments than did the scholastics, the Aristotelians, the Philippists
or followers of Melancthon, or even the eclectics; but this was balanced by the greater devotion of the other schools to the categories, the predicables, the pre-, post-, and even
extra-predicaments.(4) However, there was one subject which was both formal in inspiration and common to all text-books, namely, the syllogism; and as a result it provides a very good test of how
much interest and competence in purely formal matters was retained during these centuries of logical decline." (p. 17)
"In the light of this discussion, I find myself driven to the reluctant conclusion that genuine competence in formal logic was not often to be found in this period, at least where
syllogistic was concerned. One distressing feature is the lack of discussion of issues like the definition of the major and minor terms or the status of singular propositions. Frequently one is left
to guess differences in meta-theory from differences in usage.
And even where there is discussion, it is not always adequate. For instance, a doctrine of the relationship between terms was used to exclude the fourth figure without any
realization that this doctrine could not properly be applied to the first, second or third figures. Another characteristic of logicians of this period was a random introduction of new modes. What
reason could be given for listing only two indirect modes of the second figure, or for allowing singular terms to appear only in third figure syllogisms? Finally, many logicians introduced frankly
extra-logical considerations into their discussions. What was natural, what was fitting, what people tended to say, were all thought to be relevant issues. Only Arnauld and Alsted and, to a lesser
extent, Campanella, present the right doctrines for the right reasons, unencumbered by extraneous material." (pp. 27-28)
(1) This study is based on an examination of printed texts in the British Museum, the Cambridge University Library, and the Bodleian. I do not mention Leibniz because he was not a
writer of logical textbooks.
(2) For a comprehensive account of the various schools, see Wilhelm Risse, Die Logίk der Neuzeίt. I Band. 1500-1640 (Stuttgart-Bad Cannstatt, 1964).
(3) The situation is rather different today. For instance, much of the material discussed under the Topic of genus and species could be dealt with by set theory,
and much of that discussed under the Topic of part and whole could be formalized by the methods of S. Lesniewski. The Topics, as treated by Boethius, Abelard, and Peter of Spain, are
discussed by Otto Bird, in his article "The Formalizing of the Topics in Mediaeval Logic," Notre Dame Journal of Formal Logic, vol. 1 (1960), pp. 138-149.
(4) For a typical account of these matters see Joachim Jungius, Logica Hamburgensis, edited by R. W. Meyer (Hamburg, 1957), Book I.
———. 1972. "The Treatment of Semantic Paradoxes from 1400 to 1700." Notre Dame Journal of Formal Logic no. 13:34-52.
"During the middle ages, semantic paradoxes, particularly in the form of "Socrates speaks falsely", where this is taken to be his sole utterance, were discussed extensively under
the heading of insolubilia. Some attention has been paid to the solutions offered by Ockham, Buridan, and Paul of Venice, but otherwise little work seems to have been done in this area.
My own particular interest is with the generally neglected period of logic between the death of Paul of Venice in 1429 and the end of the seventeenth century; and the purpose of
this paper is to last some light both upon the new writings on paradoxes and upon the marked change in emphasis which took place during the sixteenth century. Although the traditional writings on
insolubilia were available throughout the period, the detailed discussions of the fifteenth and early sixteenth centuries were soon entirely replaced by briefer comments whose inspiration
seems wholly classical. Even the mediaeval word insolubile was replaced by the Ciceronian inexplicabile. In this area at least there is strong evidence for the usual claim that the
insights of scholastic logic were swamped by the new interests and studies of Renaissance humanism." (p. 34)
"Whether any of these solutions is likely to bear fruit today is for the reader to decide. It is, however, clear that the writers of the fifteenth and early sixteenth century were
inspired by a genuine interest in problems of logic and language, and that they handled them with the finest tools available. That their discussions should have been so completely ignored by
subsequent logicians, some of whom were doubtless their pupils, is surprising, given both the availability of their books and the persistence of other traditional doctrines like supposition. (81)"
(81) See my article, "The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries", Archiv fur Geschichte der Philosophie vol. 51 (1969), pp. 260-285.
———. 1972. "Strict and Material Implication in the Early Sixteenth Century." Notre Dame Journal of Formal Logic no. 13:556-560.
"One of the favorite games played by historians of logic is that of searching their sources for signs of the Lewis-Langford distinction between strict and material implication.
There are three ways of going about this, but the first two are often reminiscent of the conjurer searching for his rabbit, and only the third has real merit, for it alone involves the study of what
was said about the conditional as such. I shall look at each way in turn, in relation to writers of the early sixteenth century." (p. 556)
"I think it is fair to conclude by saying that some early sixteenth century logicians were beyond doubt aware of the distinction between strict and material implication; and that no
special pleading is necessary to establish this." (p. 560)
———. 1972. "Descartes' Theory of Clear and Distinct Ideas." In Cartesian Studies, edited by Butler, Ronald Joseph, 89-105. Oxford: Basil Blackwell.
"It is widely agreed that Descartes took ideas to be the objects of knowledge and that his theory of clear and distinct ideas arose from his attempt to find a way of picking out
those ideas whose truth was so certain and self-evident that the thinker could be said to know them with certainty. To say of an idea that it is clear and distinct was, he believed, to say of it both
that it was certainly true and that any claim to know it was justified. No other criterion need be appealed to. It is at this point, however, that most of those who set out to expound Descartes'
theory of knowledge are brought to a standstill. The part played by clear ideas is obvious enough, but what did Descartes mean by `clear and distinct'? This paper is an attempt, not to make an
original contribution to the study of Descartes, but to elucidate his terms and evaluate his criterion in the light of what both he and others have written." (p. 89)
"The fact that Descartes adopted the word ‘idea’ is itself significant. When scholastic philosophers discussed human cognition, they spoke of the mind as containing concepts
(species, intentiones). They claimed that these concepts originated through our sense perceptions, and hence that they stood in some relation to external objects. The term ‘concept’ was
contrasted with the term ‘idea’. Ideas were the eternal essences or archetypes contemplated by God, and the question of their external reference did not arise. They were an integral part of God’s
mind. God could create instances of one of his ideas, but his idea was in no way dependent upon the existence of such instances. Descartes took the word ‘idea’ and applied it to the contents of the
human mind because he wanted to escape the suggestion that these contents must be in some sense dependent on the external world as a causal agent. (9) He wished to establish the logical possibility
that a mind and the ideas contained within it are unrelated to other existents, and can be discussed in isolation from them.
Descartes saw the term ‘idea’ as having a very wide extension.
He said “ . . . I take the term idea to stand for whatever the mind directly perceives,”(10) where the verb ‘perceive’ refers to any possible cognitive activity, including sensing,
imagining and conceiving.(11) Thus a sense datum, a memory, an image, and a concept can all be called ideas. This, of course, leads to the blurring of distinctions. For Descartes, “I have an idea of
red” may mean that I am now sensing something red, or that I have a concept of the colour red, even if I am not now picking out an instance of that concept. Moreover, when Descartes speaks of an
idea, he may be taking it as representative of some object or quality in the physical world, as when he says “I have an idea of the sky and stars,” or he may be referring to the meaning he assigns to
a word, as when he says “I have an idea of substance.” Nor does he make any distinction between “having an idea” and “entertaining a proposition.” Such statements as “Nothing comes from nothing” and
“The three angles of a triangle are equal to two right angles” are categorized as ‘common notions’,(12) and are included among the contents of the mind. Descartes does remark that in some cases an
idea may be expressed by a name, in other cases by a proposition,(13) but he does not bother to pursue this line of inquiry.
One of the characteristics of an idea is 'objective reality’, a scholastic phrase which Descartes adopted, but used in a new way. In scholastic writings the terms ‘subjective’ and
‘objective’ have meanings which are the reverse of the modem meanings. An object like a table exists subjectively or as a subject if it has spatio-temporal existence, if it is real or actual. In
contrast, the concept of a table can be looked at as having two kinds of existence. The concept qua concept has formal existence, but the concept as having some specifiable content is said
to have objective existence, or existence as an object of thought. The concepts of a table and of a chair are formally similar but objectively different. So far as subjective realities were
concerned, the scholastics assigned them different grades of reality according to their perfection and causal power. For instance, a substance is more perfect and causally more efficacious than an
accident, hence a man has a higher grade of reality than the colour red.
It was also held that every effect had a cause with either an equal or a higher grade of reality. These doctrines were not seen as having any relevance to concepts. As formally
existent, a concept has of course to have some cause, but the content of the concept was not seen as having any independent reality. Descartes, however, felt that the objective reality could be
considered independently of its formal reality, and that it must be graded just as subjective reality was graded. The idea of a man, he felt, has more objective reality than the idea of a colour.
Moreover, the cause of the idea containing a certain degree of objective reality must have an equal or greater degree of subjective reality. For instance, the idea of God has so high a degree of
objective reality that only God himself is perfect enough to be the cause of such an idea.(14)" (pp. 91-93)
"Although Descartes struggled to defend his criterion, his struggles ended in an impasse. He had made the mistake of trying to prove too much. He had wanted to develop an
introspective technique by which he could be sure of recognizing those ideas which were objects of certain knowledge; but such an enterprise was doomed from the start. He could only escape from the
objection that nothing about an idea can justify us in making judgment about its external reference by entering into an uneasy and unjustifiable alliance with God; and by such an alliance he negated
his claim that a single criterion for true and knowable ideas could be found." (p. 105)
(9) E. S. Haldane, G. R. T. Ross (eds.) , The Philosophical Works of Descartes, (Cambridge, 1911) [cited as 'HR'] vol. II, 68.
(10) HR II, 67-8.
(11) HR I, 232.
(12) HR I, 239.
(13) C. Adam P. Tannery, Oeuvres de Descartes (Paris 1897-1913) [cited as 'AT'] AT III, 395.
(14) HR I, 161-170.
———. 1973. "Are There Really Two Logics?" Dialogue. Canadian Philosophical Review no. 12:100-109.
"As a historian of logic, I am frequently puzzled by the things which people have to say about the relationship between mathematical logic and some other kind of logic which is
variously described as ‘intentional’ and ‘traditional.’ Part of my puzzlement arises from my failure to understand precisely what kind of system is being offered under the guise of intentional logic.
I have always taken it that logic is concerned with valid inferences, with showing us how we may legitimately derive a conclusion from a set of premisses; yet the validation of inferences seems to be
the least of the concerns of the intentional logician. He says that it can be done, but he does not bother to show us how. My purpose in this paper is to list some of the sources of my puzzlement in
the hope that an exponent of intentional logic will show me how they can be resolved, and how their resolution will contribute to the building of a system (however informal) in which different types
of argument can be validated."
———. 1973. "Existential Assumptions in Late Medieval Logic." American Philosophical Quarterly no. 10:141-147.
"There are three types of existential assumption that are commonly made by logicians: (1) that subject terms refer to non-empty classes; (2) that proper names have referents; and
(3) that formulas are to be interpreted only within non-empty domains. In the standard first-order quantificational calculus with constants, the second and third of these assumptions are retained,
but the first, which is attributed to traditional syllogistic, has been abandoned.
Subject terms may refer to empty classes, and a distinction can be drawn within the system between those inferences which are valid only for non-empty classes and those which are
valid for both empty and non-empty alike. For instance, given the assumption that universally quantified propositions whose subject terms refer to empty classes are true, but that existentially
quantified propositions whose subject terms refer to empty classes are false, it turns out that the inference from "All As are B" to "Some As are B" only holds
with the addition of the premiss, "There is at least one A." More recently, systems have been constructed in which the other two assumptions have also been discarded. Their valid formulas
are valid in both empty and non-empty domains, and non-denoting constants are admitted. Any inference whose validity depends on the assumption that the domain of interpretation is non-empty, or that
a constant denotes, is distinguished from the others by the presence of an extra premiss.(1) Thus, what was an assumption implicitly applied to all cases, is now made explicit and is shown to apply
only to a subset of formulas within the system.
It is frequently assumed that medieval logic operated with a group of implicit existential assumptions similar to those I have mentioned, but this view is erroneous. Late medieval
logicians were just as concerned as contemporary logicians to deal with non-denoting terms within their systems, and to draw explicit distinctions between those inferences whose validity involves
existential assumptions and those whose validity does not involve existential assumptions. It is inappropriate to ask whether they took their formulas to be valid within the empty domain or not, both
because they worked with ordinary language rather than with formal systems, and because they did not use the notion of interpretation within a domain. When they interpreted a sentence such as "All
men are animals," they did not speak of a domain of individuals some of whom were men and some of whom were animals, but only of those individuals who were either men or animals.
However, they explicitly concerned themselves with the other two existential assumptions, and they admitted both non-denoting constants and terms referring to empty classes to their
system. In this paper I intend to examine how some logicians of the late 15th and early 16th centuries interpreted sentences containing non-denoting terms, how they assigned truth values to them, and
how they dealt with those inferences which needed an existential premiss to ensure validity." (p. 141)
"My discussion has been necessarily somewhat sketchy, and I have not examined all the contexts in which constantia was used,(28) but it should have become clear by now not
only that late medieval logicians had clear views about the existential import of various types of sentences, but that they used their initial decisions about the truth and falsity of sentences
containing non-denoting terms to build a consistent system. It is to be regretted that the vast majority of logicians after the third decade of the 16th century ceased to discuss these matters, with
the result that modern readers tend to think of traditional logic as lacking a sophistication which it did indeed possess." (p. 147)
(1) See, for example, W. V. O. Quine, "Quantification and the Empty Domain" in Selected Logic Papers (New York, 1966), pp. 220-223; Hugues Leblanc and Theodore Hailperin,
"Non-Designating Singular Terms," The Philosophical Review, vol. 68 (1959), pp. 239-243; B. C. van Fraassen, "Singular Terms, Truth Value Gaps and Free Logic," The Journal of
Philosophy, vol. 63 (1966), p. 481-495. There is a large and growing body of literature on the topic of logics which are free from existential suppositions.
———. 1973. "Andreas Kesler and the Later Theory of Consequence." Notre Dame Journal of Formal Logic no. 14:205-214.
"In another paper I examined the theory of consequence presented by a number of later fifteenth and early sixteenth century writers, ending with Javellus, an Italian who died in
1538. (1) For this earlier period, there was an abundance of material, containing much sophisticated discussion of semantical issues; but the next hundred years do not offer more than a few sources,
and these are of limited value. The only really outstanding figure, so far as I can see, is that of Andreas Kesler. He was a Protestant theologian who was born at Coburg in 1595, educated at Jena and
Wittenberg, and died in 1643 after a long career in education. In 1623 he published a book entitled De Consequentia Tractatus Logicae which is unique, both for its own time, and as compared
to the products of this earlier period, in that it explicitly subsumes the whole of formal logic under the theory of consequence. The laws of opposition and conversion, the categorical and
hypothetical syllogism, were all seen as different types of consequence. Moreover, no extraneous material was included. Instead of starting with the categories, like the Aristotelians, or with the
invention of arguments, like the Ramists, he devoted his first chapter to the definition of consequence. Topics, informal fallacies and other such subjects found no place, whereas some rarely
discussed matters like exclusive and reduplicative propositions and the modal syllogism did appear. Thus he stands out for his contents as well as for his organization." (p. 205)
"After this brief survey one can only conclude that the theory of consequence suffered an abrupt decline after the first part of the sixteenth century. The one outstanding writer on
the subject was Andreas Kesler, but he stands out for a single insight, rather than for any awareness of the ramifications of the theory. Unlike his sources, he saw that all of formal logic could be
subsumed under the basic notion of consequence, and he was able to exclude extraneous material, but that was as far as he went. About the definition and division of consequence, and about
consequential rules, he had nothing to say but what had been said before him by Fonseca and Regius. Nor did he betray any knowledge of earlier writers, although some at least must have been available
to him in Wittenberg. For once those who deplore the loss of mediaeval insights during the sixteenth century seem to be justified." (p. 210)
(1) See my paper "The Theory of Consequence in the Late Fifteenth and Early Sixteenth Centuries,", to appear in Notre Dame Journal of Formal Logic, vol. XIV (1973), No. 3,
———. 1973. "The Theory of Consequences in the Late Fifteenth and Early Sixteenth Centuries." Notre Dame Journal of Formal Logic no. 14:289-315.
"In this paper I intend to examine the treatment accorded to consequences by a group of writers from the late fifteenth and early sixteenth centuries, although I shall make some
reference to earlier periods. The subject of consequences (or valid inference) is of central importance to the historian of logic because those who discussed it covered such a wide range of logical
issues, including criteria for validity, problems of self-reference, the status of the so-called paradoxes of strict implication, and the systematization of valid inference forms. Indeed, a large
part of semantics and the whole of formal logic could be subsumed under this general heading. Whether the authors themselves fully appreciated that this was so is unfortunately not such an easy
question to answer, for those I am concerned with frequently leave the reader in doubt as to their view of the relation of consequences to the rest of logic. So far as they discussed the matter,
syllogistic was seen to be consequential in nature,(1) but they certainly did not make the subordinate position of the syllogism as clear as Burleigh had in the fourteenth century, or indeed as
Andreas Kesler was to do in the seventeenth century.(2) A good guide to the way they viewed the problem is to see where consequences were discussed.
A very few authors, including J. Major, A. Coronel and J. Almain, devoted a whole treatise to them, but generally speaking they came in on the coat-tails of other topics so far as
separate treatises were concerned.
They appear at the beginning of Dolz's treatise on the syllogism, at the end of Celaya's treatise on supposition and under 'hypothetical propositions' in the treatises on opposition
written by R. Caubraith and F. Enzinas. The best places to look for a discussion of consequence turn out to be commentaries on Peter of Spain, where they appear either as an appendage to the
Parva Logicalia or under the heading of 'hypothetical propositions', and, of course, general textbooks of logic. In these, a separate tract was sometimes devoted to consequences, as it was
by C. Javellus, but more usually they were associated with the syllogism, whether as an introduction to it or, sometimes, as an appendix to it. Savonarola, for instance, said all he had to say of
consequences in a section on the powers of the syllogism.
The bibliography at the end of this paper should give a fairly clear picture of the situation; though it must be noted that the majority of commentaries and textbooks belonging to
the sixteenth century did not mention consequences at all." (pp. 289-290)
(1) Enzinas, Tractatus Syllogίsmorum, fo.I vo, said "syllogismus est consequentia bona et formalis . . . omnis consequentia formalis que non tenet gratia alicuius regule
logicalis tenebit syllogistice." Cf. Heirich Greve, Parva Logicalia nuper disputata, Leipzig (149-).fo. lxxi.
(2) Andreas Kesler, De Consequentia Tractatus Logicus (Wittenberg, 1623). See my paper, '*Andreas Kesler and the later theory of consequence," Notre Dame Journal of
Formal Logic, vol. XIV (1973), pp. 205-214.
———. 1973. "The Doctrine of Exponibilia in the Fifteenth and Sixteenth Centuries." Vivarium no. 11:137-167.
Reprinted as essay IX in: Studies in Post-Medieval Semantics.
"One of the most neglected parts of late medieval logical theory is that devoted to exponibilia, or those propositions which need further analysis in order to lay bare
their underlying logical form and to make clear under what conditions they can be said to be true or false. My main intention in this paper is to examine the rich array of printed sources which are
available to us from the later fifteenth and early sixteenth centuries, but I will consider some texts written before the invention of printing, and I will also give some account of what happened to
the theory in the late sixteenth and seventeenth centuries. The sources fall into three main groups. There are separate treatises on exponibles, especially those written by Peter of Ailly(*) and
later Parisian logicians; there are commentaries on the treatise on exponibles attributed to Peter of Spain; and there are those parts of longer works which were devoted to ‘Proofs of Terms’, as in
Paul of Venice and his followers. These groupings are not, of course, exhaustive. For instance, Marsilius of Inghen and George of Brussels discussed exponibles in the second part of a treatise on
consequences, and Albert of Saxony included exponibles in the part of Perutilis Logica devoted to different kinds of proposition. As might be expected, the authors of the separate treatises
on exponibles were considerably more detailed and careful in their analysis than were those authors who treated exponibles as a subsidiary matter. In my view, the two most outstanding treatises are
those written by Peter of Ailly (d. 1420) and by Domingo de Soto (d. 1560). The latter is not original, but it is a very acute and thorough survey of the doctrines which were current in late
fifteenth and early sixteenth century Paris, where de Soto had studied under and with such logicians as Major, Celaya and Lax, whose names will frequently occur in my text. Outside treatises devoted
to exponibles, good brief treatments are to be found in the anonymous commentator on Marsilius of Inghen, and in George of Brussels, (both of the later fifteenth century) and in Hieronymus of St.
Mark (of the early sixteenth century). The earlier writers are often disappointing.
For instance, although Paul of Venice’s Logica Magna is sometimes described as an encyclopedia of medieval logic, the section on exponibles lacks the precise analysis of
types and sub-types of exponible propositions found in other authors, and the examples are frequently confusing.
Similarly, the treatise wrongly attributed to Peter of Spain lacks detail, and derives most of its value from the remarks of commentators." (pp. 137-138)
"To conclude, one can say that the history of exponible propositions mirrors the history of medieval logical doctrines in general. At the end of the fifteenth and beginning of the
sixteenth centuries there was a sudden surge of activity, during which such topics as exponibilia, insolubilia and suppositiones were analyzed, clarified and elaborated in works
which are highly respectable from the logician’s point of view, even if they contain little that is original. This period of activity was followed by a period of decline, in which medieval doctrines
continued to receive some attention, especially in Spain, but they are clearly subordinated to the main business of expounding Aristotelian logic. By the end of the seventeenth century they cease
ever to be mentioned." (p. 165)
[* Peter of Ailly, Tractatus Exponibilium, Paris c. 1495?]
[** Domingo de Soto, Opusculus Exponibilium, in Introductiones dialectice, Burgis 1529]
———. 1973. "Priority of Analysis and Merely Confused Supposition." Franciscan Studies no. 33:38-41.
"In a recent article John J. Swiniarski discusses William of Ockham's use of merely confused supposition.(1) He claims that, in the case of universal affirmative propositions,
Ockham's method of attributing merely confused supposition to the predicate accomplishes much the same result as Peter Thomas Geach's method of attributing determinate supposition to the predicate
and using a priority of analysis rule, whereby the subject is always analysed first. However, he notes, Ockham's analytical procedures when applied to particular negative propositions can lead to
erroneous results,which are only avoided by the adoption of a priority of analysis rule. Since such a rule renders merely confused supposition unnecessary, he concludes that Geach was right and that
Ockham ought to have employed only distributive and determinate supposition to get her with a priority of analysis rule in his treatment of standard categorical propositions. I do not wish to
criticize what Swiniarski has to say about the interpretation of Ockham. Instead, I wish to make a few remarks about the use of merely confused supposition by sixteenth century logicians in order to
show that it is not in general so easily dispensed with. (2)" (p. 38)
"In the light of these two examples, I conclude that there was good reason for sixteenth century logicians to retain merely confused supposition, and to use Domingo de Soto's
priority of analysis rule rather than Geach's." (p. 41)
(1) Swiniarski, John J., "A New Presentation of Ockham's Theory of Supposition with an Evaluation of Some Contemporary Criticisms," Franciscan Studies, 30 (1970), 209-217.
Those readers who are not familiar with supposition theory should be reminded that merely confused supposition involves an analysis into a disjunctive subject or predicate, whereas distributive
supposition involves an analysis into a conjunction of propositions and determinate supposition involves an analysis into a disjunction of propositions.
(2) For further details about supposition theory in the sixteenth century, see my paper: " The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries, " Archiv für
Geschichte der Philosophie, 51 (1969), 260-285.
———. 1974. "Some Additions to Risse's Bibliographia Logica." Journal of the History of Philosophy no. 12:361-365.
"One of the greatest contributions to the history of logic in recent years was the publication in 1965 of Wilhelm Risse's Bibliographia Logica, Vol. I, which covers the
years from 1472 to 1800. However, despite the fact that Risse's monumental work lists an estimated 8,000 logical works, it is still far from comprehensive, as Mr. Hickman pointed out in an earlier
article in this journal. Why this should be the ease immediately becomes apparent when one starts to work in a library such as the Bodleian at Oxford with its handwritten catalogue of books printed
before 1920 and its lack of any specialized bibliographies such as the British Museum has provided for early printed books. Even in well catalogued libraries such as the University Library at
Cambridge it can be difficult to locate texts, and one often stumbles across a new logical work through the accident of its being bound in the same volume as better known works. As a result of my
researches over the last few years, I have put together a list of works which do not appear in Risse in the hope that other historians of logic may benefit from my discoveries. I cannot, however,
claim that I have exhausted the resources of the libraries which I have visited. Doubtless there are still not only new editions but new authors left to be discovered." (p. 361)
"This paper concerns logic texts published between 1472 and 1800. I list 20 items whose authors do not appear in Risse, 12 items whose authors appear in Risse in connection with
another title or other titles, and 58 items which appear in Risse in another edition or in other editions. I indicate the libraries in which all these items are to be found, and I also list some
useful bibliographical works."
———. 1974. "Classification Schemes and the History of Logic." In Conceptual Basis of the Classification of Knowledge. Proceedings of the Ottawa Conference on the Conceptual
Basis of the Classification of Knowledge, October 1st to 5th, 1971, edited by Wojciechowski, Jerzy A., 275-283. Pullach bei München: Verlag Dokumentation.
———. 1974. "For Riding Is Required a Horse: A Problem of Meaning and Reference in Late Fifteenth and Early Sixteenth Century Logic." Vivarium no. 12:146-172.
Reprinted as essay I in: Studies in Post-Medieval Semantics.
"One of the most interesting features of the works of the logicians associated with the University of Paris in the late fifteenth century and the first part of the
sixteenth century is their application of medieval logical doctrines to the discussion of actual examples. In this paper I intend to present a detailed study of one specific example, "For riding is
required a horse" [Ad equitandum requiritur equus]. I shall first discuss each of the arguments that was used, showing its place in the general body of logical doctrine; then I shall present
three typical texts, together with an analysis of the pattern of argument found in each. One text will deal with the problem in the context of contradiction, one in the context of conversion, and one
in the context of supposition theory.In this way I hope to deepen our understanding both of the theories and of the techniques of medieval and post-medieval logic." (p. 146)
"The claim that the gerund 'riding' implies a reference to particular acts of riding,which can in turn be identified with individual horses, solved the problem of "For riding is
required a horse" at the expense of raising further philosophical problems about both language and the world. However, the claim that the sentence should be regarded as equivalent either to a simple
conditional or to some kind of modal proposition solved all the problems very neatly without, apparently, raising new ones. In the light of such an analysis one could maintain the truth of "For
riding is required a horse" without at the same time having to argue that the sentence had the same truth-value as its contradictory or a different truth-value from its simple conversion, since these
related sentences would have undergone a similar analysis, thus turning out to have the desired truth-values. Whichever solution one prefers, it seems to have been amply demonstrated that the simple
minded approach in terms of personal supposition alone was inadequate. To speak of horses being required for riding is to do more than to make reference, successful or otherwise, to individual horses
or any other identifiableo bjects in the world." (pp. 157-158)
———. 1975. "Descartes' Theory of Objective Reality." New Scholasticism no. 49:331-340.
"In the Third Meditation Descartes, who is at the beginning sure only of his own existence, presents a complex proof for the existence of God which is based on the fact
that he finds within himself an idea of God. I intend to ignore the supplementary proof which deals with the conservation of his existence, and to focus on his discussion of the properties of ideas,
for it is here that Descartes is most difficult to comprehend yet most vulnerable to criticism. With the exception of Gassendi's remarks in the fifth objection, I shall concentrate upon what
Descartes himself had to say, for a thorough survey of all the secondary sources often serves only to obscure the main issue." (p. 331)
"Descartes reinforced his arguments with various claims about the nature of predicates and the way in which we come to understand them. He thought, mistakenly, that one could not
only distinguish between negative and positive predicates, but that one could demonstrate the logical priority of such positive predicates as 'infinite' or 'perfect' by showing that one can only
understand the finite or imperfect in the light of a prior acquaintance with the infinite or perfect. (29) However, although he seems now to be talking about epistemology rather than ontology, it
turns out that his claims rest upon the same assumptions about the content and causation of ideas as are involved in the main proof, so they do not need to be discussed further.
However liberal one is in granting Descartes his desired premises, I think it is fair to conclude that his arguments do not prove what they purport to prove. This seems to be a
strong indication that one will lose nothing by being illiberal from the very beginning." (p. 340)
(29) E. Haldane and G. Ross, The Philosophical Works 0f Descartes (Cambridge, 1968), I, 166.
———. 1976. "I Promise You a Horse. A Second Problem of Meaning and Reference in Late Fifteenth and Early Sixteenth Century Logic (First Part)." Vivarium no.
Reprinted as essay II (first part) in: Studies in Post-Medieval Semantics.
"The logicians associated with the University of Paris in the late fifteenth and the first part of sixteenth century were at one with their medieval predecessors in their attempt to
formulate a unified theory of the reference of such general terms as 'horse'. To be successful, any such theory has to give a plausible account of what happens to general terms in modal and
intentional sentences, and the logicians I am concerned with clearly tried to deal with this problem. However, because of the rather standard way in which logic texts tended to be organized, the
relevant material has to be sought in various places. In an earlier paper, I made a detailed study of the reference the word 'horse' was said to have in the modal sentence, "For riding is required a
horse"; and in order to carry out that study, I had to draw material from the discussion of contradiction, of conversion, and of supposition. (1) In this paper, I intend to make a detailed study of
the reference the word 'horse' was said to have in the intentional sentence "I promise you a horse", and my material will be drawn from the discussion of contradiction, of conversion, of supposition
and of appellation. (2) I shall first examine each of the arguments that was used, showing its place in the general body of logical doctrine; then I shall present four typical texts, together with an
analysis of the pattern of argument found in each.
One text will deal with the problem in the context of contradiction, one in the context of conversion, one in the context of supposition, and one in the context of appellation. In
this way I hope to show what problems intentional sentences were seen to raise for the standard theory of reference, and how these problems were dealt with." (pp. 62-63)
"On the whole, it seems fair to say that the logicians I have examined failed to produce a theory of the reference of general terms which applied with equal success to all contexts.
Some, like Sbarroya, found themselves forced to emphasize the difference between intentional and non-intentional contexts by postulating completely different types of referent. Some, like Heytesbury,
overlooked the difference altogether in their appeal to personal supposition. Some, like Buridan, recognized that terms in an intentional context have a function which goes beyond that of referring
to individual objects; but they were unable to say with precision just how this broader function was to be reconciled with the referential function. However, one thing is common to those who
struggled with the logical problems caused by "I promise you a horse". That is, they managed to save the validity of those inferences they were concerned with, either by so interpreting sets of
sentences that they were not to be counted as instances of the inferences in question, or by so interpreting sets of sentences that they came out to have the desired truth-values, and could no longer
be cited as counter-examples to a general rule. Thus, they were successful as logicians, if not as philosophers of language." (p. 78)
(1) " "For Riding is Required a Horse": A Problem of Meaning and Reference in Late Fifteenth and Early Sixteenth Century Logic". Vivarium, XII (1974) pp. 146-72.
(2) Enzinas, Pardo and de Soto discussed the matter in the context of their discussion of contradiction; Celaya, Coronel (Prima Pars), Sbarroya and de Soto discussed the
matter in the context of their discussion of conversion; Hieronymus of St. Mark and Martinez Siliceo discussed the matter in the context of their discussion of supposition; Tartaretus discussed the
matter in the context of his discussion of descent; and Coronel (Secunda Pars), Dorp, Hieronymus of St. Mark, Major, Manderston, Mercarius and Pardo discussed the matter in the context of
their discussion of appellation. It will be noted that some authors discussed the matter in more than one place. For details of the texts, see the bibliography at the end of the paper. Of the authors
cited, Hieronymus of St. Mark and Sbarroya are not, so far as I know, specifically associated with Paris, though they are clearly influenced by Parisian logicians.
For medieval discussions of the problem, see P. T. Geach, "A Medieval Discussion of Intentionality" in Logic Matters (Oxford, 1972) 129-138, and J. Trentman, "Vincent
Ferrer and His Fourteenth Century Predecessors on a Problem of Intentionality" in Arts Libéraux et Philosophie au Moyen Âge (Montréal/Paris,1969) 951-956.
———. 1976. "I Promise You a Horse. A Second Problem of Meaning and Reference in Late Fifteenth and Early Sixteenth Century Logic (Second Part)." Vivarium no.
Reprinted as essay II (second-part) in: Studies in Post-Medieval Semantics.
Parto Two: Texts and Analyses.
———. 1976. "Agostino Nifo's Reinterpretation of Medieval Logic." Rivista Critica di Storia della Filosofia no. 31:353-374.
———. 1976. "Will Socrates Cross the Bridge? A Problem in Medieval Logic." Franciscan Studies no. 14:75-84.
Reprinted as essay XII in: Studies in Post-Medieval Semantics.
"In their treatises on insolubilia, or semantic paradoxes, medieval logicians frequently mentioned other cases in which the assumption that a proposition was true
led to the conclusion that it was false, and the assumption that it was false led to the conclusion that it was true. Some of these cases were easily solved. If one considers the proposition
"Socrates will enter a religious order" in relation to Socrates' vow, "I will enter a religious order if and only if Plato does," and to Plato's vow, "I will enter a religious order if and only if
Socrates does not," one sees at once that the problem stems from contradictory premises.(1). But not all cases were of this sort. Consider the favourite example, "Socrates will not cross the bridge,"
when said by Socrates, in relation to the two premises, "All those who say what is true will cross the bridge" and "All those who say what is false will not cross the bridge."(2) It is easily
demonstrated that "Socrates will not cross the bridge" is true if and only if it is false, but what is not so easily demonstrated is the source of the paradox. Certainly it is not a paradox just like
"What I am now saying is false," since the key proposition does not speak of its own semantic properties, but the premises do indeed speak of truth and falsity in a way which has implications for the
truth-value of "Socrates will not cross the bridge." The question thus arises whether "Socrates will not cross the bridge" is to be counted as a semantic paradox, to be dissolved in the same way as
the Standard Liar is dissolved, or whether it is to be seen as needing another kind of solution, perhaps less radical in its implications for our common-sense notions about such matters as the
legitimacy of self-reference or the definition of truth." (pp. 75-76)
"In conclusion, I would like to say that Paul of Venice's reputation as the last of the great medieval logicians seems to me to be vastly overrated. Several logicians of the late
fifteenth and early sixteenth centuries, including Bricot, Eckius, Major and de Soto, offer more acute discussions of logical problems and more satisfactory solutions, as I hope I have demonstrated
by this examination of the bridge paradox." (p. 83)
(1) Thomas Bricot, Tractatus Insolubilium (Parisius, 1492) sign. b. viii and sign, c i; Johannes Eckius, Bursa Pavonis (Argentine, 1507) sign, k v; John Major,
Insolubilia (Parrhisiis, 1516) sign, c ii ff. Cf. Albert of Saxony, Perutilis Logica (Venetiis, 1522) fo. 46 vo; Robertus de Cenali, Insolubilia in Liber Prioris
Posterioris (Parisius, 1510) sign, o iiii.
One should note here that vows, promises and the like were treated as propositions with truth-values rather than as performative utterances with no truth-values. This view was
combined with a realization that there are certain conditions which have to be met before a vow is binding. For instance, the vower must genuinely intend to do what he vows to do, and what he vows to
do must be both moral and within his power. These extra conditions were not thought relevant to the question whether "Socrates will enter a religious order" was true or false.
To the slightly different question of whether Socrates would be bound by his vow, Major, for instance, held that he would not, on the grounds that his vow was conditional and that
the condition, given Plato's vow, could not be fulfilled.
For references to Major's text and to other discussions of vows and promises, see below, note 15.
(2) Paul of Venice, Logica Magna (Venetiis, 1499) fol. 198 and Paul of Venice, Tractatus Summularum Logice Pauli Veneti (Venetiis, 1498) sign. e i vo. The latter
work which appeared in many editions, is known as the Logica Parva. See also John Buridan, Sophisms on Meaning and Truth, translated and with an introduction by T. K. Scott (New
York, 1966), pp. 219-220; Cenali, loc. cit.; David Cranston, Tractatus Insolubilium et Obligationum [Paris, c. 1512] sign. e iiii; Eckius, op. cit., sign, k iiii vo; Robert Holkot, Super
Quattuor Libros Sententiarum Questiones (Lugduni, 1497) sign. E ii; Major, op. cit., sign. c ii vo; Peter of Ailly, Conceptus et Insolubilia (Parisius, 1498), sign. b. viii; Peter of
Mantua, Logica (Venetiis, 1492), sign, o vivo; Domingo de Soto, Opusculum Insolubilium in Introductiones Dialectice (Burgis, 1529), fol. cxlvi f. Bricot, op. cit., sign. b. vii vo f. speaks
of giving a penny to the truth-teller rather than of allowing him to cross a bridge, but the principle is the same. Some authors (e.g. Eckius, op. cit., sign. k v) gave both versions of the paradox,
as did Paul of Venice himself (Logica Magna fol. 197 vo f., Lógica Parva, sign. e i f.) It should be noted that there are many variations in the names of the characters and in the phrasing
of the propositions. Some authors substituted "You will throw me into the water" for "Socrates will not cross the bridge."
(15) It is because of this association with promising that we find the bridge paradox and others similar to it discussed in theological works as well as logical, e.g. Holkot, op.
cit., sign. C iiii ff., sign. D viii vo ff.; John Major, In Quartum Sententiarum Questiones ([Paris], 1519), sign. ccxcii vo ff. For general discussions of promising see, e.g., Gratian,
Decretum, Chapter XXII (various editions) and Richard Mediavilla (or Middletown) Scriptum Super Quarto Sententiarum ([Venice], 1489) Book IV, distinction 38.