What does God have to do with fourteenth-century logic? This paper sets out first to remind us of a most remarkable and revolutionary idea put forward by Thomas Manlevelt: that substance does not exist.Footnote 1 Second, it offers a few words on the role played by things divine in the development, initial acceptance and eventual rejection of this idea that substance does not exist—an outcome which has to do with the theological limits set to logic. Third, it offers a general sketch of the diverse roles that things divine play in Manlevelt’s logic. Finally, we return to the non-existence of substance. I suggest that Manlevelt makes clever use of the very limits set by theology to logic to draw the conclusions he likes best.

In handbooks of philosophical history, the name of Thomas Manlevelt is linked to a set of widely-used logical treatises: the so-called parva logicalia.Footnote 2 These short tracts on supposition, confusion and consequencesFootnote 3 were presumably composed in Paris around 1330 and spread all over the European continent during the fourteenth and fifteenth centuries. They were in use as textbooks and commented upon at universities in Germany and beyond: in Leipzig, Erfurt, Prague, Vienna, Uppsala and Kraków.

In the 30s or 40s of the fourteenth-century, this same Manlevelt spent some 200,000 words on a huge commentary on the so-called Old Logic. That is to say, he spent them writing a commentary on Aristotle’s little work on the Categories, which is preceded by a commentary on the Isagoge, Porphyry’s third-century introduction to Aristotle’s Categories.Footnote 4 It is not known whether Manlevelt also did a commentary on the third integral part of the Old Logic, De interpretatione.Footnote 5

Manlevelt’s Questiones libri Porphirii is a study on Porpyry’s five universals: genus, species, differentia, proprium and accidens. The main subject matter of Manlevelt’s Questiones super Predicamenta is, of course, the ten categories: substance plus the nine accidents (quality, quantity, relation, action, undergoing, place, time, situation and having). To the medieval mind, these categories were both the ten most basic logical concepts and the most basic ontological constituents of reality. In short, they were the building blocks for both rationality (ratio) and reality (res).

As was quite usual for medieval logicians, these two commentaries—on Aristotle’s booklet on the categories and on Porphyry’s introductory text to Aristotle’s booklet—discuss the most fundamental questions about logic and its ontological relation to reality.

But what did logic look like in Manlevelt’s eyes? And where may this logic have met its boundaries (if any)? Medieval logic, of course, was not modern symbolic logic. Basically, it was the old Aristotelian syllogistics gradually enlarged with specifically medieval developments in the field of terminist logic, to which we reckon the theories of supposition, syncategoremata, consequences, insolubles and obligationes.Footnote 6

Fundamental to all of this is the theory of the categories. In the Aristotelian categories of being, items are collected and ordered by which we can name reality (for instance, man or white) or form complex wholes (for instance, white man) or even form propositions (for instance, men are white) with which we can speak about reality and refer to it as we want. What now is the nature of the members of the categories? Are these primarily terms which refer to something in reality? Or are these the things themselves insofar as they are captured in a linguistic expression or thought? And is the general nature or universality of a term reflected in any way by a kind of general nature or universality of things existing in the outside world?Footnote 7

To Manlevelt himself, the matter of what logic is about had already been settled. To him, William of Ockham had basically laid out the plan for this in his nominalistic approach to all things logical.Footnote 8 That is to say, everything in reality is strictly individual in nature, and generality is to be found in concepts only insofar as these refer to the things in reality.

Medieval thinkers had the sometimes-annoying habit of referring to other philosophers, whether colleagues or adversaries, not by name but by preferably rather vague descriptions: e.g., ‘some say’, ‘old-fashioned ones would say’ or ‘according to the opinion of the moderns’, etc. At one point, Manlevelt mentions those who maintain that everything there is must be either a substance or a quality.Footnote 9 Thus, he makes a vague reference to those thinkers who came to be called Ockhamists. We are safe to surmise that he numbered himself with them.

In what manner, then, does Manlevelt follow in the footsteps of William of Ockham? Manlevelt does take Ockham’s nominalism as an indisputable starting point. Of course, being a medieval philosopher, he never mentions Ockham’s name, but he does make honorary mention of Ockham in references to ’the Master’,Footnote 10 and ’the major father of the modernists’.Footnote 11 This last one is an honorific title I have never encountered in any other writer. And indeed, like William of Ockham, he fully endorses the idea that all things which exist in the outside world are individuals and that generality is found in concepts only insofar as these refer to things in reality. However, I think he even goes a step further than William of Ockham in several directions.

The most spectacular step has to do with his reduction of the number of categories. The world around us is built up of substances and their accidents. So, if everything that is is either a substance or a quality, this means that every accident is a quality. This is precisely the stance of Ockham and the followers of his nominalistic way of thinking. The categories in medieval ontology comprised all those vindicated by Aristotle: substance plus the nine accidents (quality, quantity, relation, etc.). Eight of the categories fell victim to Ockham’s razor. In Ockham’s ontology, only substance and quality remain as distinct entities; all of the other categories are merely aspects of substances or qualities or ways of talking about these substances or qualities.

To Manlevelt’s mind, however, Ockham did not go quite far enough in stopping short at substance and quality as the basic ontological constituents of reality. Manlevelt’s claim to fame, at the present stage of investigation, would seem to be his denial of substance.

Manlevelt claims that fire can exist without heat, which means that quality is separable from its substance.Footnote 12 He even suggests that substance does not exist. To be precise, he claims that, physically speaking, it can be argued that there is no substance anywhere in the world, whether terrestrialFootnote 13 or celestialFootnote 14—that is to say, so long as the opposite is not to be demonstrated, which it indeed is not.Footnote 15

He not only argues that substance is unnecessary for explanatory purposes but, taking the consecrated host as evidence, he also explains how natural phenomena may be understood in the absence of substance: accidents support and adhere to each other.Footnote 16

However, Manlevelt does not unequivocally stick to this thesis of the non-existence of substance, as he is at the same time willing to argue that what everyone else holds—namely, that substance does exist after all—can reasonably be held as possible. Of course, this is what the theologians say as well, for if there is no substance, how could there be a transubstantiation in the consecrated host?

Manlevelt holds that both the existence and non-existence of substance can be held probabiliter. This does not mean that both hypotheses are equally probable but that both can be argued for: the non-existence of substance on logical grounds, the existence of substance on authoritative grounds.

And it may well be that it is precisely here that we stumble upon the boundaries of logic’s domain. There is logic on the one hand, and there are the authoritative grounds of theology and communis opinio on the other hand. To Manlevelt, there is a strict border between matters logical and theological.

On the other hand, Manlevelt’s text contains an abundance of references to God and theological matters. The truth of faith is set off against the truth of reason.Footnote 17 Logical rules are explicitly said to not always hold in theological matters.Footnote 18 Theologians do get their say in Manlevelt’s text,Footnote 19 and what the theologians have to say does not necessarily tally with what the logician or the natural philosopher has to say.Footnote 20 When he touches upon the subject matter of the unity of the Son of God and His assumed nature, he explicitly says that such matters are to be decided elsewhere.Footnote 21

So, logic meets its boundaries in theology. Does theology also meet its boundaries in logic? The fact is that, with Manlevelt, God, the Trinity, the Blessed Virgin, the Antichrist and the consecrated host keep popping up within the domain of logic. And these manifestations of things divine are often accompanied by the expressly stated opinions of ‘the theologians’.

The roles God plays in Manlevelt’s commentary are diverse. Sometimes, God is brought in as just another example to illustrate a point that could have been made just as well without divine interference. At other times, God makes a more substantial appearance. His role is often precisely to sharpen the dividing line between logic (and sometimes the natural sciences) on one side and theology on the other side. In some cases, God’s role goes even further. His divine presence then seems to push the train of logical reasoning itself in a certain direction.

An example in which God plays a mere illustrative role is when the word God is said to have equivocal reference to both the real God and to God in a painting, just as the words man, stone, etc. refer equivocally to the real thing and the painted thing.Footnote 22

Sometimes God is invoked for the sake of argument to provide an example that may sound rather awkward in itself—if not inappropriate—as when it is said that God is a more perfect substance than a fly.Footnote 23

God makes a more substantial appearance in the very first questio of Manlevelt’s commentary on the Isagoge, which is to say, He appears right at the start of Manlevelt’s huge commentary on the old logic as a whole. There, our feeble and limited human knowledge is compared unfavourably with God’s supreme and infinite, indivisible, simple knowledge as the prima scientia, which is in fact the basis for all human knowledge. God is given full honour as being the First Science and First Cause without Whom no knowledge whatsoever would be possible.Footnote 24 And of course, as God is the First Cause, nothing at all in the universe could exist without God. So, when it comes to the categories as the basic constituents of logic and reality, we see a complete dependency on the ratio side. We also see this on the res side, however, because everything is dependent on God, both for our knowledge of it and for its bare existence.

If all we know is dependent on God’s wisdom, and if God’s wisdom is limitless while our wisdom is not, we should not be surprised if there are things that seem to make perfect sense in a divine context (which is the domain of the theologians) but are difficult if not impossible to grasp given our limited intellectual capacities.

The Trinity (being the Father, the Son and the Holy Ghost) is the prime instance for which things theological and things logical tend to drift apart. Yes, a sharp borderline is drawn between logic and faith at the Trinity.

Here is a logical puzzle about the Trinity: ‘This is the Father’ and ‘This is not the Father.’ A more blatant contradiction is hard to find. Yet if we take the subject of the first proposition (‘This is the Father’) to be the divine essence and the subject of the second proposition (‘This is not the Father’) to be the Son, both propositions are true. For ‘The divine essence is the Father’ is true, and ‘The Son is not the Father’ is also true. But still the two propositions are two mutually contradicting contradictories, for they are two singular propositions about the same subject and with the same predicate. They refer to exactly the same thing, for between the Son and the divine essence there is not the slightest difference.Footnote 25

Even Manlevelt has to admit that things like this are incomprehensible to the human intellect. For it is only by faith that we can maintain that one most simple thing (God) can be really distinct things (Father, Son and Holy Ghost).Footnote 26

Here is a second specimen of God-related logic: there is one; therefore, there is the First Cause; therefore, there is the effect of the First Cause; therefore, there are two. In short: there is one; therefore, there are two. The decisive step here is this: There is one; therefore, there is the First Cause.

Manlevelt has to admit that ‘there are two’ is a necessary conclusion here—albeit not a formal logical conclusion. But in this case, the non-formal theological necessity of the consequence happens to be challenged—not on logical grounds but on precisely theological grounds. For the theologians may deny the decisive intermediate entailment: “There is one; therefore, there is the First Cause”. For according to them, God may exist without being the First Cause. Before the creation of the world, He was God but not the First Cause.Footnote 27

Thus, even within logic, there seems to be some degree of compulsiveness for theological considerations. That is to say, this is one of those cases in which God’s role goes a bit further than providing just a convenient example for some sort of logical reasoning. His divine presence here truly seems to push the train of logical reasoning itself in a certain direction. There are many other examples of things divine being used as building blocks for Manlevelt’s reasoning—too many to make even a passing note of them all here. In fact, it is almost uncanny to come across God so often in a work of logic.

Let us take a closer look now at some argumentation surrounding Manlevelt’s denial of substance. How does the presence of things divine work out in this special case? Has Manlevelt really accepted that, logically speaking, there is no reason to accept the existence of substance but that one has to accept the existence of substance for theological reasons and as a matter of plain common sense after all? Taking his explicit word for it: yes. But seeing how he proceeds in the remainder of his commentary on the Categories, one cannot refrain from the suspicion that, in his heart, Manlevelt thought otherwise.

At one point in this commentary, he gives a precise description of what it is, not for a substance but for a quality, to be receptive of contraries. Not surprisingly, it is the consecrated host which he again takes as his starting point. If exactly the same set of qualities (whiteness, roundness, tasting-of-bread, etc.) can first belong to a piece of bread as its substance and a moment later belong to the body of Christ as its substance, do these qualities really need a substance? What if the transubstantiation can do without substance after all? Although the whiteness in the consecrated host receives warmth and cold, says Manlevelt, it does so not as the subject of warmth and cold. For why should one quality be the subject of another quality and not the other way around? And in the end, all qualities whatsoever are sustained miraculously by God anyway. But in this case, the whiteness of the consecrated host is said to take on the warmth because the whiteness was there first and the warmth came to join the whiteness later and thus came to coexist with the whiteness.Footnote 28

Here we have a clear picture of diverse qualities sticking to one another without any need of a substance to underlie them. If this can be true for the consecrated host, however, then we may safely extrapolate this state of affairs to the world at large. Qualities sticking together to make up the myriad of individual items in this world do not need substance as their physical groundwork. Therefore, there is no necessity to posit substance as an explanation for all things in the world.

So, instead of dismissing the miracle it takes to have a consecrated host without a substance, Thomas Manlevelt seems in the end to heartily endorse this very miracle. If there is no substance in the consecrated host, this is because God miraculously makes it so. As a consequence, all similar appearances of qualities sticking together without substance must be miraculously wrought thus by God as well. Thus, the whole world is one big wonder, kept together by none other than God Himself.