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 works:
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.
"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 Organon.
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),
(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
———. 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. 227)
"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. 395.
———. 1969. "The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries." Archiv für Geschichte der Philosophie
"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".
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.
"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
(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.
(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 dispositione''.
(11) Petrus Ramus, Dialecticae libri duo (Parisiis, 1560), p. 126; and Franco Burgersdijck, Institutionum Logicarum libri
duo, (Lugduni Batavorum, 1634), pp. 166-167.
(12) E.g., Fonseca, op. cit., vol. II, p. 100, refers to ''syllogismus coniunctus"; and Polanus, op. cit., p. 165, refers to
(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.
"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
(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
———. 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)" (p. 45)
(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.
"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
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.