## 1 Four Different Meanings of Unity

Meinertsen writes (Meinertsen 2020, p.7):: “ The problem of unity, i.e. how to account for the unity of a state of affairs (how its constituents are unified into it), is in my view the main problem of states of affairs ontology.”

The metaphysical problem of the unity of complexes, in general, is, of course, an old problem that stems from Parmenides. It could be called “Parmenides’ Challenge ‘’ because he tried to show that there can be no complexes. Aristotle treats it thoroughly. As is usual with him, he begins his metaphysical investigations with the distinction of the different meanings of a crucial term. In Book X of his Metaphysica (Aristotle 1987), he deals with the meanings of unity. He argues that all meanings of unity can be reduced to four: 1. the connected, 2. the whole, 3. that which is one in number and 4. what is one in kind. A unifier, as Meinertsen calls it, is meant to be an entity that creates unity. If there are four kinds of unity there could correspondingly be four different unifiers. They should be different because the four kinds of unity are very different. Unity1 is connectedness, unity2 is being a substance with its essence and its properties. Unity3 is to be numerically one. Unity4 is being of the same kind. I would argue that due to their disparity a unifier would not be able to create more than one kind of unity. Moreover, it seems to me that only unity1 and unity3 are relevant for Meinertsen’s problem. Finally, I think that an entity that creates unity where it is lacking or would be lacking without the unifier makes sense only for unity1 and for unity2. Some entity that is not numerically one cannot be made one by some other entity. Unity1 (connectedness) could be created by a connector. Aristotle refers to “the things which are unified by glue or nails or by being tied together” (Aristotle: Metaphysica 1052a22ff.). Thus he thinks of spatial complexes, such as a bundle of wooden sticks held together by a string. The string would be the connector and unifier1. However, what a unifier1 creates is a connection, not unity3, i.e., not numerical oneness. Meinertsen thinks otherwise and his view is common with respect to spatial complexes. When we bundle objects we take for granted that we thereby have created a new and additional entity. We thus think to have created unity3 by applying a unifier1. This may satisfy the standards of Common Sense but not the standards of ontological analysis. The ontologist will wonder with respect to the bundle of wooden sticks whether it is no longer one entity when the string around the sticks becomes loose. Thus, there is a problem of fuzziness of spatial complexes and of their existence.

## 2 Spatial Complexes and States of Affairs

Not only is it doubtful whether connecting things into a spatial complex creates an additional entity, but there is also the question of whether what makes sense for spatial complexes makes also sense for Meinertsen’s states of affairs. They are not meant to be literally spatial complexes. The idea of a connector between the constituents that creates a complex seems to me a technomorphism, an overextended analogy between concretely constructed spatial complexes and states of affairs. The latter are not made. However, as was mentioned, Meinertsen does not speak of “connectors” but of “unifiers”. Nevertheless, he is thinking of a relation or connection. He holds that relations connect. With respect to Aristotle’s four meanings of unity, a unifier need not be a relation, When the term is applied to wholes one could consider essences as unifiers, as unifiers2. Insofar as the essence contains the properties of a substance, although in potency only, it could be understood as a unifier of all those properties. That though cannot be transferred to Meinertsen’s ontological analysis of states of affairs. His unifier is not specific to the respective particular and universal like the essence is to the properties. Therefore, I will continue to assume that Meinertsen’s unifier is a connector between particulars and universals although in the literal sense only spatial complexes can have a connector.

Armstrong, whose analysis of states of affairs Meinertsen adopts to a certain extent avoids this difficulty in his later ontology, where he denies that particulars and universals are proper parts. Armstrong rather considers them to be mere abstractions thus taking a state of affairs to be basically simple, according to Heil’s interpretation of Armstrong (Heil, 2012, 13). Meinertsen in contrast relies on Mertz with his general ontology of complexes that seems to me to be based on a spatial paradigm (Meinertsen, 2018, 133 f.). To revert to this paradigm seems natural. Even Parmenides takes it for granted that complexity is spatial. However, his spatial complexes are more compact than Aristotle’s unities1. Parmenides assumes that the parts have common and coinciding boundaries that are the source of the difficulties which lead him to deny that there are any complexes.

With his Tractatus, Wittgenstein did a lot to establish states of affairs (Sachverhalte) and facts (Tatsachen) as crucial categories of ontology. In his Philosophische Grammatik (Wittgenstein, 1973 p. 199 ff.) he emphasises the difference between a spatial complex and a fact. Although he argues from ordinary usage while I think that “facts” and “states of affairs” are technical terms of philosophy I would nevertheless accept his point. Moreover, Wittgenstein’s view that states of affairs do not have a connector (Wittgenstein, 1963, 2.03) may be taken to vindicate indirectly my claim that only spatial complexes have connectors. I suppose that he rejected connectors because he saw that facts/states of affairs must not be conceived as spatial complexes but that there is a strong tendency to do so particularly in logical atomism which takes facts/states of affairs to be represented by sentences of a symbolic language. Those sentences are, indeed, spatial complexes.

## 3 Connectors

Now it was Gustav Bergmann in his middle period in the 1960ies who forcefully championed connectors in facts (Bergmann, 2003 vol.III p.3ff). He claims that almost all of the ontological tradition does not acknowledge connectors and therefore cannot have a clear conception of complexes. Bergmann subsumes those traditional ontologies under the term “function ontologies”. He thinks that what the fact ontologist takes to be a complex with constituents is for the function ontologist just the value of a Fregean function with a collection of entities as an argument. A function can have a simple value for ordered n-tuples as arguments, that is to say, for an ordered multitude as an argument. According to Bergmann functions are the alternatives of connectors in ontology, i.e., they serve to analyse the same phenomena but the function analysis comes down to denying complexity.

In the frame of his own ontology, Bergmann tries to show with an example that a connector is necessary for a fact as a complex. He considers a case in which we see two spots, a green and a red one. We see which spot is green and which spot is red. We are given in this perception the connection between spot and colour and thus an entity that connects both and which is called by Bergmann “the nexus of exemplification”. (Bergmann, 2003, Vol III. p. 47 f.)

Note that Bergmann first advances the argument for the nexus of exemplification and other connectors when he still refuses to accept facts. The argument may be sound for ontologies without facts but I think that it is not sound also for ontologies with facts. According to such ontologies we have in the situation of Bergmann’s example not only the two spots and the two colours but also two facts. Moreover, Bergmann insists that we perceive facts. So, the difference of Bergmann’s example could be ontologically analysed by the lack of the facts that the first spot is red and that the second is green. However, Bergmann continues with his earlier analysis according to which in those two cases there is no connector.

The Later Bergmann no longer assumes a connector in facts. Rather, he holds that the core of a fact is a pair of diverse (numerically different) entities. This complex of diversity is taken to exist per se. The two entities are separated as well as attracted to each other by their diversity, so to speak. The former term for a connector, namely “exemplification”, now stands for the way of togetherness which is an entity that “clings to” the complex of diversity (Bergmann, 2003 vol. II, p.338). This new use of the term “exemplification” seems odd since the complex to which exemplification clings has of itself already a way of togetherness and a different one, namely that of pairs diversity which are in Bergmann’s ontology, not facts. Moreover, an entity that confers “a way of togetherness” sounds suspiciously like a connector.

## 4 The Connector’s Regress

After having made his case for the necessity of a connector in his book Realism (Bergmann, 2003 vol.III, p.47 f.) it suddenly strikes Bergmann that the presence or absence of the connector is not sufficient at all. What matters is rather the “circumstance” that the connector connects a certain spot with a certain colour or does not do that. This hint is not really satisfactory since circumstances are not a category of his ontology. Moreover, they closely resemble Bergmann’s facts. At any rate, it turns out that Bergmann’s “unifier” which is to provide like that of Meinertsen cohesion to the fact cannot play its role because it leads essentially back to another fact or fact like entity. To assume a “unifying” entity is not enough. The fact that it unifies is also required, more precisely, the fact that the “unifier” /connector connects as a constituent of the respective fact the other constituents. It would be some relational fact with the other constituents as relata. This unifying relational fact needs another fact to connect and unify it. So a regress similar to Bradley’s is started that is vicious because the unity (connectedness) of each fact in the series depends on that of the next. Bergmann did not notice that. Presumably, due to talking of a “circumstance” rather than of a “fact”. As circumstance is no category of his ontology Bergmann doesn’t notice that he needs to give an explicit ontological analysis. The regress indicated is different from Bradley’s. It does not arise from a requirement for the connector to be connected to what it connects but rather from the distinction between the connector and the connected constituents. Bergmann thinks he has taken care of Bradley’s regress by assuming that connectors are particularly dependent on and in this way connected to what they connect.

Bergmann did not recognise and discuss those difficulties in his book Realism, nor in later publications. But he changed his analysis of facts in such a way that the difficulties no longer arise. The Later Bergmann no longer assumes a connector in facts, as was mentioned already.

For the same reason, it does not come to Bradley’s regress. Meinertsen has an important and simple solution to the problem of Bradley’s regress. He argues that no further unifier/connector/relation is necessary because the unifying and connecting relation relates itself to its relata. The solution of the Middle Bergmann was different. The connectors in contrast to ordinary relations belong to a different category than the connected entities and the members of that category are all dependent on the connected entities. That dependence binds them to the connected entities, Bergmann assumes. Thus there is also a similarity to Meinertsen’s self-relating unifier.

There are two ways in which one can meet the claim of a connector/unifier regress:

1. 1.

One can argue that the connector connecting/unifying the spot s, green, and itself and the spot s being green are one and the same. I think that s is green, the is-connector connects s and green, and the is-unifier unifies s, green and itself are clearly different facts or states of affairs.

2. 2.

One can hold that the connecting of s and green is not a fact and that the unifying of s, green is not a state of affairs.

However, the ontological categories of fact and states of affairs are the only ones that come into question. If connecting is not a fact and unifying not a state of affairs they are not entities at all. This conclusion shows in my view that introducing activities such as connecting and unifying is misplaced. An ontological explanation is structural, not genetic.

5. Non-Mereological Complexes.

Meinertsen advances the following argument for the cruciality of the unity problem:” Why is this such a serious problem that I consider it the main problem of the state of affairs ontology? The reason has to do with states of affairs having non-mereological existence conditions. What this means can be seen from the following. Call the ordinary, uncontroversial constituents of a state of affairs its ‘material constituents’ (as opposed to its ‘formal constituents’, if any), e.g. a, b, and R of the state of affairs R(a, b). The mere existence of the material constituents of a state of affairs does not entail the existence of the state of affairs. For if, to take a monadic example, (i) a is F, and (ii) a distinct particular b is G, and (iii) a is not G, then a and G coexist, but a is not G. Since a and G coexist, the (mereological) sum of them exists, but since a is not G, a’s being G does not exist. Similarly in other cases. Because of this difference in existence conditions between sums and states of affairs, I shall say that states of affairs are ‘non-mereological complexes’ and that sums are ‘mereological complexes’. “(p.7) More pointedly still on page 26: “… while mereological complexes exist ‘automatically’ given the existence of other entities (those that happen to be their ‘constituents’), such that any one of them exists ‘automatically’ given these entities, something more is needed for any state of affairs to exist. As implied by my abovementioned answer to the problem of unity, I believe it is the relating of a unique relation that is needed.”

Thus what Meinertsen calls “mereological complexes” are his paradigmatic complexes and he finds the fault with states of affairs insofar as they do not correspond to the paradigm. His aim is to amend states of affairs to turn them into mereological complexes.

I would argue that what Meinertsein calls “mereological complexes” are no existents and thus no complexes at all because they are not entities in addition to their constituents which is the precondition for their existence. If the complex exists “automatically” when its constituents exist it reduces ontologically to its constituents. Non-existents have no place in ontology. That was Parmendes’ main point.