Notes on; Look, B. (2000)  'Leibniz and the Substance of the Vinculum Substantiale' . In Journal of the History of Philosophy 38 (2):  203--20. Online:

Dave Harris

Look defines the vinculum substantiale} as the 'substantial bond'.  The context was Leibniz trying to explain transubstantiation to a Jesuit correspondent.  The notion of the bond is supposed to explain the reality underneath transformations, and how things get realized or reified.  Look says that Leibniz used the term to explain the reality of composite substance, which had become a problem in his monadology.  He develops the concept to mean all of substantial form, relation, composite substance, and 'separate, substance-like thing'(205), and it is the last one which is used most consistently.  Roughly, the problem is, that composite materials are made up of the activities of thousands of separate monads, and the problem then is to explain how these monads unite together.  In transubstantiation, a particular aggregate of monads is replaced by God with another aggregate that looks exactly the same, but which now contains the body of Christ: nothing is changed in the phenomenon, but a new substance comes into being.  More generally, the vinculum is what turns a mere aggregate into a genuine composite.  The substantiation in the composite can be altered by God in transubstantiation. 

What is at stake is a whole sub discussion about what composites are.  Sometimes Leibniz seems to be arguing that only minds are substances, while bodies are {real} phenomena, although he also has another schema which suggests that animated bodies are substances, and composites are unities {substances are unities?}.  The issue is to explain whether bodies as composites have a reality, or whether it is only the monads that do, producing bodies as phenomena.  {Solid bodies in general, with all the things that solid bodies apparently demonstrate like extension}.  This is where Leibniz considers whether the bond uniting all the monads that constitute bodies produces some emergent substantial reality, some real unity, involving a process of realization.  One possibility might be the emergence of an automaton from a unity of monads, an organism: Leibniz discussed this in terms of a relation of dominance among the monads, but the vinculum offers another possibility, that a unified real thing emerges, a 'new substantiality', or 'organic whole', something more than just a relation among monads.

Look goes on to discuss what the vinculum actually is, having discussed what it does.  There seem to be different conceptions again.  It is either the bound substance itself or the bond, for example; it can be something added to the monads, or it can be a substantial form.  The underlying issue is whether the substance that emerges is produced by combining monads, or whether it is something completely independent.  But behind this is a further discussion about what a substance is: it is something that is not modified, or it can be the source of modifications itself.  The vinculum is the latter, something truly 'in the subject' {in this case the thing that modifies} but as a substantial form.

Look thinks that the most likely definition is that the vinculum is the corporeal composite, a body in its own right, a multiplicity of monads, a unity in 'secondary matter', from the point of view of the dominant monads.  There is a link with Scholastic notions of substance 'the complete being, the composite of matter and form, or the composite of monads in a corporeal substance'(213).  This is a new substance after all: there is something more than just the monads and their aggregates, a new composite, something real, something which '"realizes" the phenomena'.

This still causes problems with the debate with the Jesuit {and because it does look like a bit of a bolt on}.  Here, Leibniz runs into difficulties because he says that the vinculum has to be something completely external to the monads if it is really going to change the substance of the bread.  He seems to have persisted with this view after all.  Later work suggests that the vinculum is particularly connected to the dominant monad.  It has to be something that works with monads and is compatible with them, but it is external to them and detachable from them {almost a force of nature, or dynamic potential in substance itself}.  It is the real relations between monads in the vinculum that produce our thoughts about relations between them.

There is one final possibility—that the vinculum is the relation between the monads, the specific relation found in composites.  There would be problems in explaining how this relation works, though, and there is less textual support.

Overall, Look says that the notion of the vinculum is not very satisfactory, and is inconsistent with other arguments in Leibniz: it seems to have no perception of its own, for example, and it seems to imply there is some causal action after all in uniting the monads.

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