St Andrews Institute of Mediaeval Studies |
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Medieval Logic Research Group |
Principal Investigator: Stephen Read
Research Fellow: Barbara Bartocci
| Paul of Venice's treatise on "Insolubles" from his Logica Magna was published on 25 October 2022 in the edition and English translation by Barbara Bartocci and myself. |  |
The project was funded by a Leverhulme Research Project grant to Professor Read, which ran from 1 August 2017 until 31 July 2021. The project continues as we complete the planned volumes.
The main and most direct aim is scholarly and historical, to provide scholars and students with access to important and interesting texts from the 14th century on the logical paradoxes. The logical paradoxes have played a significant role in the development of philosophical ideas, not just in logic but also in philosophy of language, epistemology, metaphysics and even ethics and political philosophy, throughout the 20th and 21st centuries. They played a no less significant role in later medieval philosophy and were the subject of much debate and the spur to original ideas, arguably reaching their zenith in the 14th century. Much has been learned about the medieval debate in the past fifty years, in the writings of John Buridan, Thomas Bradwardine and others. But other interesting treatises remain unedited, many only surviving in contemporary manuscripts. We have now completed and published the treatise on insolubles (logical paradoxes) by Paul of Venice, summarizing and developing theories and solutions from his predecessors in the 14th century, constituting the final treatise of his Logica Magna. Seven of the treatises from this huge work were edited and translated into English between 1978 and 1991. But the treatise on insolubles was not among them. It has now appeared in print, consisting of an edition of the Latin text, together with an English translation and commentary (October 2022). We continue to prepare editions and English translations of two treatises on insolubles from earlier in the 14th century, those by Walter Segrave and John Dumbleton, writing in Oxford in the second quarter of the century. Paul mentions them, and they contain rich ideas about alternative solutions, restrictio and cassatio respectively. Publication of these texts will allow a better overview of the development of solutions to the paradoxes through the 14th century, as well as giving further insight into the nature of the paradoxes and their possible solution.
Walter Segrave was writing in Oxford in the 1320s or ’30s, defending a restrictivist theory explicitly in response to Bradwardine’s criticisms. His treatise is preserved in three mss, one incomplete (Spade 1975, pp.113-15). It constitutes an extensive and detailed response to Bradwardine, defending restrictivism by presenting a well-thought out reason for the restriction of supposition required to avoid contradiction. Where Burley, and Bradwardine, both attributed the fallacy in insolubles to what Aristotle described as the fallacy of the conditional and the unconditional (simpliciter et secundum quid), Segrave attributed it to the fallacy of accident, turning on a variation in the supposition of the middle term and the extremes in what might otherwise appear to be a sound syllogism. (Note: the material in this section is taken from Stephen Read, "Walter Segrave's ‘Insolubles’: A Restrictivist Response to Bradwardine".)
The heart of Segrave’s solution is that whoever asserts a proposition asserts that it is true, as Burley and many others also claimed. Consequently, the restriction on supposition that Segrave maintains is that
“the extremes of a proposition only supposit for those things about which the whole can mean that it itself is true, assuming that it exists, and those extremes do not supposit for those things about which the whole, assuming that it exists, would mean that it itself is false. And this is what I claim.”
The reason Segrave gives is that
“it is because the extremes take their supposition from the copula, whose significate is that the proposition is true, as was said, so the extreme does not supposit for anything about which the whole would mean that it itself is false or is not true, because this would be inconsistent with the significate of the copula, and so the extremes should be restricted by the meaning of the copula.”
Consider, e.g., he says
A falsehood exists,
call it A, and suppose there is no other falsehood—perhaps God has annihilated all other propositions, or all other existential propositions.
“But it is evident that this:
A falsehood exists,
does not signify that no other falsehood exists. For it always signifies in one way for its own part, since it is not a knowing agent . . . But on the contrary: this inference is necessary:
A is false, therefore no other falsehood than A
exists,
because if there were another falsehood, then A would be true, so whatever implies or signifies the premise signifies the conclusion, so from the opposite, the premise does not signify what the conclusion does not signify.”
Indeed, at a couple of points Segrave appears to endorse Bradwardine’s second postulate (P2), that a proposition signifies everything implied by what it signifies. According to Bradwardine, A signifies that A is false, since that follows ut nunc (as a matter of fact, given no other falsehood exists) from A—or rather, from what A signifies, namely, that a falsehood exists. But if A is false then no other falsehood exists, for, Segrave observes, if there were another falsehood, A would be true. So, by Bradwardine’s postulate, since A signifies that A is false, it signifies that no other falsehood exists. But we agreed that A does not signify that, so it follows that it does not signify that it itself is false, either.
One might wonder whether Segrave is really endorsing and using Bradwardine’s postulate (P2) in his own person here. For this would seem to be an argument against Bradwardine, and so arguably simply ad hominem. But Segrave also appeals to (P2) a little earlier in providing justification for Burley’s claim that every proposition signifies (or at least, for Burley, asserts) its own truth. Recall that Bradwardine’s main conclusion applies only to insolubles, that is, propositions signifying their own falsehood. Segrave bases his stronger claim on the role of the copula, referring to Aristotle’s remark that “the ‘is’ in a statement also means that the statement is true and ‘is not’ that it is not true” and Averroes’ comment that “ ‘being’ here signifies nothing but truth.”
From this, Segrave draws his only postulate:
“The postulate is this: that every proposition means things to be in reality as it signifies. This is self-evident and is clear from the Philosopher and the Commentator in comment 14 on the fifth book of the Metaphysics and throughout the text of that comment: for the copula
in the proposition signifies being true, as is elucidated there . . . From this what was claimed follows ostensively in this way: every proposition not involving a contradiction signifies things’ being in reality as it signifies, and does not signify their not being in reality as it signifies. But things’ being in reality as the proposition signifies, and not their not being in reality as it signifies is for a proposition to be true and not false, provided the proposition exists; so every proposition not involving a contradiction, assuming it exists, signifies itself to be true and not false.”
Segrave takes an example: suppose you are sitting. Then:
“For this inference is valid:
Things are in reality wholly as the proposition ‘You are sitting’ signifies, and it exists, therefore this proposition is true and not false,
and the same is true of other propositions. Therefore, every proposition not involving a contradiction, assuming it exists, signifies itself to be true and not false.”
The caveat “assuming it exists” reflects the fact that the medievals took propositions to be concrete, individual utterances which could not be true or false unless they actually existed. What is striking is that Segrave, taking ‘You are sitting’ as an arbitrary example, and generalizing it to represent any proposition, infers that any such non-contradictory proposition signifies itself to be true and not false. He is here clearly invoking Bradwardine’s second postulate, that signification is closed under implication, so that if from any non-contradictory proposition it follows that it is true and not false, then that is part of what it signifies.
Burley and Bradwardine agree on one thing: that insolubles commit the fallacy of the conditional and the unconditional (secundum quid et simpliciter). They take this from Aristotle’s treatment in his De Sophisticis Elenchis of the example of the man who swears that he is forsworn. Segrave says they are mistaken: according to him, insolubles commit the fallacy of accident.
The fallacy of accident is the first of the fallacies described by Aristotle in De Sophisticis Elenchis as those “independent of language,” and discussed at some length in ch.24. The classic example is the Hidden Man puzzle: you know your father (or Coriscus), your father (or Coriscus) is the man approaching, but you don’t know the man approaching (since he is wearing a mask, or too far away to recognise, etc.). Aristotle’s diagnosis was that one or more of the two properties attached to Coriscus (being known by you and being the man approaching) is accidental (or incidental) to him and so there is no essential connection to support the necessity required correctly to infer the conclusion from the premises.
It has to be said that Aristotle’s discussion of the fallacy of accident is neither clear nor convincing. What he says about examples such as the Hidden Man appears to clash with the principle of expository syllogism (or ecthesis), stated in De Sophisticis Elenchis ch.6, and arguably invoked by Aristotle in the Prior Analytics to give an alternative proof of Darapti:
“The demonstration [of Darapti] can also be carried out per impossibile [i.e., by indirect reduction] or by ecthesis [i.e. setting out]. For if both terms belong to all S and one chooses one of the Ss, say N , then both P and R will belong to it, so that P will belong to some R.”
Buridan claims, pace Aristotle, that
“[e]very affirmative syllogism holds by virtue of the principle ‘what things are said to be universally identical with one and the same thing are also said to be identical between themselves’,”
that is, the very principle Aristotle states in ch.6 of De Sophisticis Elenchis, and negative syllogisms by a corresponding principle of difference. Yet the Hidden Man can be put in exactly the form Aristotle describes as ecthesis:
Being known by you is said of Coriscus
Being the man approaching is said of Coriscus
So being known by you is said of the man approaching.
How then can the premises be true and the conclusion false?
One medieval attempt to clarify the fallacy of accident so as to accord with Aristotle’s theory of the syllogism is found in Giles of Rome. The fallacy arises, he said, when there is a variation in the supposition of the middle term:
“That the major term, if it is true of the middle [term], must then be true of the minor term, only happens in the case of those middle [terms] which are indifferent according to substance, because it requires the middle [term] not to vary or be diverse if the conclusion is to follow of necessity.”
Giles attempts to square this with what Aristotle says in De Sophisticis Elenchis:
“It should be said that it is not Aristotle’s intention to deny that in no way are the unknown and the known the same; but he means that this fallacy is almost argued in four terms and always has diversity of middle [term]; so he says that the same is not known and unknown, because ‘Coriscus’ is used in different ways and almost has the power of two terms, as he is placed with respect to knowledge and as he is approaching.”
Burley extends the idea of variation of the supposition of terms to include the extremes:
“In this fallacy there should be assigned three, namely, the attribute, the accident and the subject thing. And according to Giles, the major extreme is always the attribute and the middle term the subject thing and the minor extreme the accident. But this is not a big worry, for it suffices for there to be this fallacy that some term is not included but is compared to two other terms in the argument. Whence it should be realised that the fallacy of accident sometimes results from a variation of the middle term and sometimes from a variation of the major or minor extreme.”
It is not quite so straightforward, says Burley, to identify the fallacy in the Hidden Man puzzle:
“According to this fallacy, the paralogism is given in this way:
The one approaching is known by you, Coriscus is the one approaching, hence etc.
Or like this:
Coriscus is known by you and is the one approaching, hence etc.
And it is usually said that it is a fallacy of accident from the variation of this term ‘Coriscus’, for concerning Coriscus in that he is known by you it is not included that he is the one approaching. But on the contrary: it seems that this is not a fallacy. For from the opposite of the consequent we may with the minor [premise] infer the opposite of the major [premise] syllogistically. For this syllogism is correct:
No one approaching is known by you, Coriscus is the one approaching, hence etc.
Then it seems that in the first argument there is no fallacy of accident in respect of this conclusion, ‘the one approaching is known by you’, and Aristotle understood this, but it is a fallacy of accident in respect of the reduplicative conclusion, or in respect of this conclusion, ‘the one approaching insofar as he is approaching is known by you’, and then it is not a fallacy of accident from the variation of the middle term, but from the variation of the minor extreme, because this term ‘the one approaching’ is taken in different ways in the minor [premise] and in the conclusion.”
Typical cases of reduplication employ the expressions ‘qua’ or ‘insofar as’, e.g., ‘I know Coriscus qua the one approaching’. The medievals often used reduplication as a test for whether the fallacy of accident was present. So, e.g., Ockham complains that it is commonly said that the hidden man paralogism is shown to commit a fallacy of accident since “it is not included that Coriscus is approaching insofar as he is known by you.”
Segrave spells this out in response to an objection that Aristotle does not seem to attribute the fallacy of accident to insolubles:
“Finally, one can argue like this: if these paralogisms were to be solved by the fallacy of accident, then since it not likely that they passed unnoticed by Aristotle, he would have solved such paralogisms, where he does solve them, by the fallacy of accident.”
Segrave responds:
“To the final argument I say that where Aristotle solves the paralogisms by the fallacy of accident, he shows how to solve paralogisms of this kind, because they have the same defect, as was proved before (in ch.4). For in insolubles the supposition of the middle or extreme term always varies; and this is to commit the fallacy of accident. Thus these paralogisms are similar to insolubles where the middle term being ‘this something’ the extremes are not connected. For one argues like this in insolubles, just as here:
Coriscus is known by you, Coriscus is approaching, therefore the one who is approaching is known by you,
for the term ‘approaching’ is taken, or at least should be understood, reduplicatively, and so the supposition of the extreme varies.”
Segrave recognises that to diagnose a fallacy or paralogism one needs not only to show that the reasoning involved is invalid; one must also show why it appears to be valid and so tempts people to commit the fallacy. Insolubles are so called, he says, not because it is impossible to solve them, but because solving them is difficult. Once again, he is here in agreement with Bradwardine.37 But he goes on to claim that insolubles are particularly difficult to solve since “having filled in the middles from which they derive their evidential force, they seem to differ in no way from good syllogisms”:
“For they have the same syntactic arrangement both in mood and figure, e.g.,
No falsehood is said by Socrates, this is a falsehood, so this is not said by Socrates.
Therefore, since they have the greatest causes of appearing to be good syllogisms, which are just the same as those of a good syllogism, for this reason they are the most difficult to solve. Hence they are deservedly called insolubles par excellence because of their outstanding argumentative strength.”
He explains:
“Insolubles commit the fallacy of accident because by arguing like this:
This is said by Socrates and this is a falsehood, so a falsehood is said by Socrates,
the term ‘falsehood’ supposits in the minor premise for something it does not supposit for in the conclusion. Similarly, in arguing like this:
No falsehood is said by Socrates, this is a falsehood, so this is not said by Socrates,
there is a variation in the middle term because the term ‘falsehood’ supposits for one thing in the major premise and another in the minor, according to those advocating this solution. And thus it is clear that they have to solve these kinds of paralogisms according to the fallacy of accident, namely, from a variation of the middle term or of an extreme term.”
Segrave supports this diagnosis with a brief discussion of supposition theory. Terms only have supposition in the context of a proposition, and only supposit for what they signify—but often not for all their significates. For example, in
A rational animal is a man
‘animal’ supposits only for men, not for all animals, because its range of supposition is restricted by adjoining the expression ‘rational’. Indeed,
“The extremes of a proposition take supposition from such a coupling. To supposit for its supposits is to signify them to be the extremes of that union in reality which the copula signifies. They do this sometimes conjunctively, sometimes disjunctively, insofar as they receive a different mode of suppositing from what is adjoined to them.”
The ground has now been laid for Segrave to solve the insolubles by the fallacy of accident. He illustrates his solution in part by responding to Bradwardine’s extensive arguments against restrictivism.
In addition, five of the mss contain five further chapters, one on Insolubles, the others making up a short introduction to supposition theory, obligations and other logical issues, a Summulae as it is often known. (The treatise on Obligations was edited by Kretzman and E.Stump from one manuscript, in ‘The anonymous De Arte Obligatoria in Merton College Ms.306’, in E. P. Bos (ed.), Mediaeval Semantics and Metaphysics, Studies Dedicated to L. M. de Rijk, Ph.D. on the Occasion of his 60th Birthday, Ingenium, Nijmegen, 239–80.) The additional chapters are arguably by Dumbleton himself, or by a follower of his, for the doctrine is consistent with the Summa Logicae itself.
Paul Spade argues (Heytesbury 1979, p.73) that Cajetan’s identification (in his 15th-century commentary on Heytesbury’s Insolubles) of the second view criticised by Heytesbury, and consequently the eighth discussed by Paul of Venice, as Dumbleton’s cannot be right, since Dumbleton’s treatise itself argues against Heytesbury’s view. But this is a weak argument, for Heytesbury, Swyneshed, Dumbleton and others were all working together in Oxford in the 1330s and would have been aware of each others’ ideas and so could easily end up criticising each other.
The known manuscripts and early printed texts to be used are as follows:
[Updated 17 January 2023]