Empty Reference in Sixteenth-Century Nominalism: John Mair’s Case

1 Signification and Conceptual Representation

John Mair flourished as a scholastic philosopher in the first half of the sixteenth century and his textbooks on logic have been widely influential in that period. They have been redacted, republished, and circulated several times in continuously revised versions.^[5] His logical treatises were divided into the parua logicalia, containing the treatises on suppositions, ampliation, and appellation, and the noua logica, dealing with logical consequences and inferences between analyzed propositions.^[6] Mair outlines his theory of signification in his treatises on the properties of terms, which together with the prologue of his commentary on Peter Lombard’s Sentences form useful starting points to address his terminist semantics.

Clearly, Mair’s theory of signification is rooted in the nominalist variety of logical semantics, but it is well known that diverging accounts of signification have been proposed by his predecessors in that tradition. Notably, William of Ockham’s theory of signification differs from John Buridan’s in a respect that is relevant to assess John Mair’s theory. In Ockham’s view, the relation between vocal signs and concepts is one of subordination, and in virtue of their subordination to concepts, terms latch directly onto the things in the external world that they signify. Ockham regards utterances that instead stand for other concepts or for themselves as non-significative. John Buridan, on the other hand, is known to have emphasized that conceptual mediation is required for the referential functions of language to succeed. Accordingly, Buridan’s account famously distinguishes between mediate and immediate signification, and in his view written utterances immediately signify concepts and mediately (or ultimately) signify things.^[7]

The terminist account of reference is developed in supposition theory, in which supposition accounts for the contextual relationship between terms and things at the level of sentences. In medieval terminology, a term is said to have personal supposition when it stands for things in ordinary sentential uses, whereas material supposition occurs in special cases where terms stand for other mental or written signs. Mair defines supposition as a property of those terms that can be truly predicated of a deictic pronoun pointing to the things they stand for.^[8] The gist of the idea is that, for example, in the sentence “Adam is a human being” the supposition of the terms is established by verifying two singular predications, “this is Adam” and “this is a human being.” That affirmative sentence is true when these predications refer to the same thing, and false otherwise. Part of the rationale for adopting this “pointing-strategy” is that in Mair’s nominalist semantics no appeal is made to states of affairs to act as truth-makers for sentences, and only individuals (the supposits) are ultimately signified.^[9] But while this account aligns closely with Ockham’s theory of supposition, Buridan’s theory, and developments thereof, become more relevant when we shift to signification. Concerning the latter, Mair divides the significate of a term into “ultimate” and “non-ultimate significate” in the following way:

The significate of a term is twofold: one is the ultimate and the other non-ultimate. The ultimate significate is that which the term properly signifies, be it properly in a natural manner or in a conventional manner. The non-ultimate significate is that which the term improperly signifies, that is to say in a common natural manner, or in a conventional fashion and improperly. One can explain this with an example: the uttered word ‘man’ ultimately signifies all men, since it signifies men properly in a conventional manner, and it signifies improperly the written word itself that is similar to it. It represents both the non-ultimate and the ultimate concept.^[10]

What Mair seems to say is that the term “man” properly signifies all men, but together with this it also improperly signifies the concept man.^[11] While the relationship between an utterance and the thing it conventionally signifies is personal supposition, the relation between an utterance and its semantic content, its non-ultimate significate, is described by Mair as a natural and not as a conventional relation. In view of this complex account of signification, Joël Biard claimed that the resulting picture in Mair is rather fragmented and capricious since that it combines in an eclectic fashion elements from Ockham’s and Buridan’s accounts.^[12] But Mair’s account is not confused if we take into consideration a development within nominalist semantics that was uncovered by Elizabeth Karger and Stephen Read, by which the view of material supposition as significative took root in the fourteenth century largely due to Marsilius of Inghen, and was further elaborated by later logicians such as John Dorp of Leiden. Like Marsilius and Dorp, Mair also distinguishes between the “conceptum ultimatum” from the “conceptum non ultimatum,” the latter being a concept or a mental image of the word that is improper and artificial but not altogether arbitrary. As Read has argued, this distinction played an important role to characterize material supposition as unitary and significative.^[13]

But what are the concepts for Mair? Henrik Lagerlund has shown that Peter of Ailly was in this respect very influential on Mair. In a general definition, for Mair, a concept is a sign that is able to signify something or some things (aliquid/aliqua), or that things are in some way (aliqualiter).^[14] The first are the categorematic concepts – namely, common or singular terms which function as subjects of predicates in the sentential context like “human being” – or a syncategorematic constituent – namely a logical term, such as the quantifiers and the connectives. For Mair, only categorematic terms are properly speaking significative.^[15] Mair also says that a term, which signifies something or some things, represents that thing or things in virtue of relations of natural similarity, which he sometimes calls a mental image or simulacrum. Also in line with Peter of Ailly’s theory, concepts are described by Mair as mental acts that involve apprehending something and causing a vital change,^[16] and representation is taken to be solely a function of concepts, the kinds of things that are able to elicit the cognition of something as their likenesses.^[17] But to answer what kinds of things there can be representations of, and how impossibilia can have a place in conceptual thought, we should turn to another key aspect of the medieval theory of signification in which these debates were framed by Mair.

2 Ampliation and the Semantic Value of Empty Terms

3 Impossible Significates and Mair’s Nominalist Semantics

Unlike the Hagenau commentator, when John Mair addresses this issue some decades later, he did not attribute the inclusion of imaginable impossibilities to the domain of signification explicitly to Marsilius. Mair refers instead to John Dorp of Leiden, who wrote a terminist commentary at some point between 1393 and 1396, explicitly on Buridan’s Summulae de Dialectica, but interpolating it in fact with Marsilius’ material.^[35] Very little is known about Dorp’s life, but it is clear that he had made a name for himself among the nominalists and that he was mentioned in the famous 1474 Nominalist manifesto.^[36] John Dorp is Mair’s main source when discussing the question of whether ampliation to imaginable impossibilities should be admitted in semantics. Yet, Mair’s view is Marsilian, granting the truth of such sentences as “a chimera is understood” and “‘chimera’ signifies a chimera,” because intentional predicates and verbs expand the supposition of the subject terms to stand for impossibilities.

Mair also makes clear that although we can signify and conceive impossibilities, this does not mean they do refer to something in the sense of picking out an “aliquid,” since “the chimera or the impossible is imagined, but the chimera cannot be imagined as something.”^[37] What kinds of impossibilities can be imagined? Some of the examples provided by Mair indicate that he had no problem with the idea that absolute impossibilities can be signified. In the context of a critical discussion of Anselm of Canterbury’s ontological argument in his Sentences commentary Mair notes that even such an impossibility as something greater than God – namely, “something greater than that which nothing greater can be thought” – can be imagined, even though such an object is impossible in the strongest sense of impossibility.^[38] Mair remarks that since an intentional context is generated by the verb cogitari in the expression “that than which nothing greater can be thought” (quo maius cogitari non posset), that clause signifies both things that can be or that can be imagined, even though they are impossible in the strongest sense and cannot exist outside the intellect.

We are provided with more details about the kinds of impossibilities that he regards conceivable in his Quaestio de complexo significabili, where Mair deals with the total significates of sentences. As we have seen above, for Mair (and Marsilius) “a human being is a donkey” signifies the complex that a human being is a donkey, and this is an impossible significate, since no human being can be a donkey. But Mair further adds that impossible significates are to be allowed if they do not contain an explicit contradiction. Only those sentences that do involve explicit contradictions lack significates altogether. An example of such sentences is “the non-intelligible is intelligible,”^[39] which cannot have an intelligible sentential significate (since it involves an explicit contradiction of the form p and not-p), whereas the sentences “a human being is a donkey” and “a human being is irrational,” given that they not formally contradictory, do signify intelligible impossibilities.

If a signifiable impossibility is not an item in the ontology and does not pick out an “aliquid,” one question that remains is whether a nominalist violates the traditional principle of theoretical parsimony in admitting such quasi-entities. To be sure, such quasi-entities were clearly posited only for the purpose of accounting for intentional contexts in ampliation theory, but just as it is a contentious matter whether ampliation theory reckons with possibilia, ^[40] similar contention could be made concerning imaginabilia. Mair’s main source for this issue, John Dorp of Leiden, did mention the following potential objection: since there are infinitely many possible objects, and a series of imaginable things would contain and exceed the series of all possible things, then the former infinite series would exceed the latter, which seems to be inconsistent with the concept of infinity.^[41] Aside from taking note of this interesting objection, John Dorp and Mair did not raise further worries concerning the metaphysical status of signifiable impossibilities. Furthermore, the nominalist provenience of the theory need not mean that this expansive strategy in semantics was exclusively held by self-declared Marsilians in the sixteenth century; instead, it seems to have become a default position in terminist semantics. For example, Peter of Crockaert, a Thomist from Mair’s circle who also discussed at length issues pertaining to signifiable impossibilities in his commentary on De ente et essentia and who was often cited by Mair, notes that imaginable impossibilities are quasi-entities that do not belong to any metaphysical category.^[42]

Instead of addressing metaphysical issues about impossibility, Mair focuses on the problems that imaginable impossibilities raise for the theory of signification. One such issue concerns whether the theory of signification becomes incoherent once impossible objects are included in semantics. Mair noted the potential objection that since “signifying” and other intentional verbs ampliate the terms to signify imaginabilia, then anything which can be imagined as falling under such a term, say T, would also be signified by T. It would be true to say, for example, that “‘human being’ signifies donkeys,” since the term “human being” in that sentence is ampliated to imaginable impossibilities, and human beings may be imagined to be donkeys without contradiction.^[43] Replying to this potential objection, Mair resorts to scope distinctions familiar from ampliation theory to say that donkeys are not among the significates of “human being.” For Mair, it is indeed true to say that the term “human being” signifies every “human being that can be imagined” (omnes homines qui imaginantur esse), but it is not the case that it signifies everything that can be imagined as a human being (omnes res quae imaginantur esse homines).^[44] Mair’s point is meant to show that admitting signifiable impossibilities does not render the theory of signification incoherent.

4 Concept Formation and Empty Representations

The problem that Mair seeks to address more extensively in his defense of the Marsilian view articulated in the treatise on ampliations touches on the issue of concept formation. Some potential answers to the question of what kinds of concepts can signify impossibilities were mapped out by the Hagenau commentator as we have seen above, and although it is unclear who the Marsilians mentioned in that text were, John Dorp of Leiden could plausibly be counted among the second group of Marsilians mentioned by the Hagenau commentator, namely those who maintain that impossibilities are signified only by complex concepts. Mair turned to John Dorp when addressing the issue of how we can form concepts of impossible objects and reports his view as follows:

To this argument, Dorp replies well in the end of his treatise on ampliations that such a concept is caused by possible things in this way: since the intellect has the concept of a mountain caused by the mountain, assembled with the concept of gold caused by gold, in such a way that these concepts were caused by possible things, afterwards the intellect unites and combines these concepts with each other taking this whole [composite concept] for a single concept of a golden mountain, the concept of which represents an impossible thing, namely a golden mountain (assuming that a golden mountain is impossible).^[45]

This response strategy further underscores how Dorp and Mair combined Buridan’s and Marsilius’ views. The background motivation for that answer is clearly the position that Buridan articulated, according to which the intellect can only be moved by possible things. Recall that Buridan took impossible concepts to be formed by combining possible ones. By putting possible concepts together “falsity or fiction can emerge,” and hence all impossible concepts are complex. However, instead of holding like Buridan did that chimeras are mere ficta and lack any unitary significate, Mair and Dorp hold that they do signify imaginable impossibilities.

How can they do so? To recall Mair’s account of signification, he claims that concepts are representations and that these in turn were standardly regarded as natural likenesses of things. But as we have seen, not all utterances correspond to concepts of things, namely ultimate concepts, but some correspond instead to non-ultimate concepts, that is concepts that do not signify properly objects in the external world. Mair’s account of signification diversifies the relationships obtained in the semantic triangle and claims that a relation of representation that is neither natural nor wholly conventional obtains between terms and their non-ultimate concepts. That in turn leads to rejecting that all concepts are natural likenesses of things – in particular, impossible concepts are not. When he addresses the issue of how “chimera” can be a term if it does not represent an “aliquid,” Mair’s take on the matter involves distinguishing between two ways that concepts can be called representations, one way representing per se and another representing per accidens:

It is replied that possible concepts always and per se represent possible things, and hence naturally. And per accidens impossible things [are represented], but neither in a proper way naturally, nor conventionally in the way that a vocal term signifies an ultimate concept. Neither naturally nor conventionally I say, or you can paraphrase it thus: that it is as we please [ad placitum] that by the intellect and by free will we put together those concepts of possible things forming [the concept of] one impossible thing, and therefore it is manifest that sometimes we form concepts of impossible things, namely when [the intellect] puts them together affirmatively.^[46]

What this passage describes as per accidens representation is the same kind of relation as that which obtains between utterances and their non-ultimate concepts, in the sense that this relation is neither natural nor conventional. The arbitrary significates of impossible concepts – which are, in Mair’s account, complex and not simple concepts – are made out of possible parts, and those partial concepts are formed by the causal process of abstracting general features from sensory cognition just like in natural cases. But instead of representing their objects per se, forming an impossible concept involves a joint activity of the intellect and the will, for it is only because of the will and not because of sensory cognition that we are able to combine concepts that are incompatible with each other. It is thus in virtue of their parts and per accidents that impossible concepts are said to be representations. Yet, the reason why Mair can claim that “chimera” nonetheless has a unitary significate is that it signifies a non-ultimate concept, and this involves accepting that not all conceptual representations have to be natural likenesses of things. Indeed, by stressing the joint activity of the will in causing such representations, Mair claims that such mental acts, although they do not lack objects altogether, are not caused by them in the same way natural likenesses are.^[47]

5 Conclusions

In this article, I sought to clarify some central debates concerning the semantics of impossibility that were current in Mair’s period. I have proposed an analysis of Mair’s account of empty reference and argued that the reception of the theories of signification proposed by John Buridan and by Marsilius of Inghen is central to understand that account. On the one hand, as we have seen, widening the domain of signification to include imaginable impossibilities attests to the wide-ranging influence that Marsilius’ theory exercised in the sixteenth century. On the other hand, Mair’s approach to necessarily empty terms is shaped by the reception of that theory through John Dorp of Leiden, in which elements of Buridan’s account were also incorporated in the resulting picture of signification. The resulting picture suggests two things. First, widening the domain of signification to include imaginable impossibilities was considered essential to account for intentional contexts and for our ability to conceive impossibilities, which was regarded as a default position in nominalist semantics in that period. Second, the capacity to imagine absolute impossibilities was thought to require a view of conceptual representation that opposes the idea that all conceptual representations are natural likenesses of their objects. These two points illustrate how sixteenth-century nominalists, such as John Mair, sought to critically examine, refine, and develop the ideas of their predecessors in innovative and thought-provoking ways.