[Cross-posted from modsquad.]

As I’ve been arguing in previous posts, Leibniz in 1686 offered an argument that [A] all individual substances express God. As he put the point in the essay “Primary Truths”, “all individual created substances are different expressions of the same universe and different expressions of the same universal cause, namely God” (my italics).

However Leibniz also said, towards the end of the “Discourse on Metaphysics”, that [B] “other substances express the world rather than God, while minds express God rather than the world” (DM 36). Something very similar is in the summary of DM35, and in at least two of Leibniz’s letters to Arnauld (A 2.2.60, 2.2.257). This appears to be in contradiction with [A]. It held that all individual substances express God, whereas this appears to be the view that only some individual substances, minds, express God.

The last four sections of the “Discourse” (34-7) are focused on the distinction between minds and other substances. Even here Leibniz continues to suggest, in places, that all substances express God. Thus in DM 35 we are told that “the whole nature, end, virtue, and function of substance is merely to express God and the universe”. But DM 36 (and indeed the summary of 35) appear to deny that all substances express God.

Setting aside for the moment the question of how Leibniz can claim both [A] and [B], what is it that leads him to assert [B]?

One might try (here’s me trying) to say that [B] is not to be taken literally, saying there’s not really a difference between what minds and other substances express, though there are related differences (about, e.g., whether this expression is accompanied by knowledge). Thus [B] would just be a misleading summary of that point. But, if nothing else, Leibniz says [B] repeatedly, and not just in a section summary, so this looks rather weak. What else might one say here?

Well, one theme in the  discussion is that minds are made in God’s image, in such a way that a mind “does not merely express the world but it also knows it and it governs itself after the fashion of God”. So minds have a sort of resemblance to God that the other substance lack. And for this reason we might say that minds express God, whereas other substances do not. (Many thanks here to Julia Jorati for her thoughts about these passages, especially this aspect of them.)

Back to the question of how this all fits together. One might reconcile [A] and [B] by saying that minds express God in two ways and for two reasons (because he is their cause, and because they resemble him by having intellect and will) but other substances only express him in one way (because he is their cause). But this still doesn’t fit terribly well with the claim that substances other than minds express the world rather than God.

Thinking about it in this way, there look to me to be two views about expression of God in the “Discourse”: the view seen in the later sections, on which minds resemble and thus express God, but other substances don’t do that so well, and merely represent the world; and the one of the earlier sections, on which both sorts of substance express both God and the world. I’m inclined to take this as evidence for something like Catherine Wilson’s reading of the “Discourse” as containing multiple systems that don’t fit perfectly well together.

[Cross-posted from modsquad.]

Leibniz thought (at least sometimes) that substances express God, because they express their causes. But why did he think that substances express their causes? In this post I briefly explore three ways in which we might try to understand his reasons for this.

Version 1: expression and knowledge

The late-1670s note “What is an idea?” (L 207-8, A 6.4.1369-71) provides some possible illumination. In the course of his discussion Leibniz notes that “every entire effect represents the whole cause, for I can always pass from knowledge of such an effect to knowledge of its cause” (L 208). So if we have knowledge of an “entire effect” then we will be able to acquire knowledge of the “whole cause” of that effect. That seems to suggest this argument.

1. If one has knowledge of an (entire) effect, one can acquire knowledge of its (whole) cause.
2. That could only be the case if the effect represented the cause. So
3. All (entire) effects represent their (whole) causes.

Some details about ‘entire’ and ‘whole’ aside, this gets us close to the Discourse’s claim that effects express their causes. Moreover, premise 1 might gain some motivation from widespread views of knowledge and understanding that adhere to or approximate the slogan that to know is to know through causes. On the other hand, this seems not tell us why effects express their causes, even if it does show us that it must be the case that they do. Moreover, this is a text from several years before the Discourse, and it is not so clear that the details of Leibniz’s views of expression (in particular, expression of God) were all that stable over time.

Version 2: the cause-effect relation as a special case of expression

Dan Garber discusses expression in his Leibniz: Body, Substance, Monad (216-24). Among other things, he argues that “The cause/effect relation is a special case of the expression relation” (218) (basically because expression requires a “constant and fixed” relationship, and causation is such a relationship).

Thinking along this sort of line, we might construct another argument for the claim that effects express their causes.

1. The relation of expression holds between two things, A and B, when there is a regular relation between them.
2. The cause-effect relation is an regular relation between two things. So
3. When two things stand in the cause-effect relation, the relation of expression also hold between them. So
4. All effects express their causes.

Evaluating this is largely going to be a matter of deciding whether causation is indeed among the ‘regular’ relations that Leibniz says are required for expression. It doesn’t seem to be one of Leibniz’s usual examples. (Though he does, as in DM15, attempt to explain apparent causal relationships, as between two finite substances, in terms of expression.) On the other hand, the expression of God is not a usual example of expression either.

Version 3: expression and complete concepts

There are yet other Leibnizian reasons to think that an effect will express its cause, if one focuses on the Discourse. Indeed we can I think find a complete Leibnizian reason for the view in the Discourse itself.

Consider in particular the views expressed in DM 8 (about complete concepts, etc). There will be true claims of the form ‘S is P’ that relate any substance to God. Suppose for instance that ‘P’ is ‘ultimately an effect of God’. For any created substance this will be true. Thus, by the view about concepts explained in DM 8, ‘ultimately an effect of God’ will be part of the complete concept of every substance. And, indeed, there will be marks and traces in each substance corresponding to this predicate. So we can at least say that each substance represents God. Though we are some distance from talk of functions and isomorphisms, we are, given that expression more or less is representation, at a point at which we might see why Leibniz would say that all substances express God. Thus, we could understand the view that all substances express their causes as a consequence of other Leibnizian views about substances and language.

The importance of expressing causes might appear to be minimal on this reading: substances turn out to express causes simply because they express everything that stands in any relation to them (not just a regular one, whatever that is). On the other hand, as a reading of the Discourse, or or Leibniz’s views in 1686, this approach has the (slight?) advantage that the resources for explaining why Leibniz thought that substances express their causes are contained in the text itself. This being the reason also fits nicely with the view (that all individual substance express God) being present in Leibniz’s “Primary Truths” essay, which attempts to ground many Leibnizian views in his views about language. And it might also help explain why the expression of God is not a persistent feature of Leibniz’s statements about substances — as the DM8 view tends to disappear, this view of all substances as expressing God might naturally tend to disappear with it.

[Cross-posted from modsquad.]

Leibniz frequently uses the notion of expression. Expression is apparently a sort of representation relation. But what, according to Leibniz, has to happen for one thing to express another? Well, what often seems clear is the requirement that there be a regular relation between the expresser and the expressed. We might understand the debates in the secondary literature on this topic as largely about how exactly to understand Leibniz’s notion of a regular relation. There has been, for example, debate about whether expression is isomorphism. (See among others Kulstad, Mates, Simmons, and Swoyer.)

The most discussed examples of expression are cases like an ellipse expressing a circle and a map expressing a piece of land. But Leibniz puts the notion of expression to a variety of other uses. Among them is his claim that some, or perhaps all, substances express God. Thus in the Discourse on Metaphysics we learn that “God’s Extraordinary Concourse Is Included in That Which Our Essence Expresses…” (DM 16 title); that “our soul … express[es] God and, with him, all possible and actual beings, just as an effect expresses its cause (DM 29); that “Minds Express God Rather Than the World, but That the Other Substances Express the World Rather Than God” (DM 35 title); and that “we may say that, although all substances express the whole universe, nevertheless the other substances express the world rather than God, while minds express God rather than the world” (DM 36).

This issue of the expression of God has been rather less discussed than expression in general. However in one relatively recent discussion, Alan Nelson says that “…spirits express God in virtue of being able to know eternal truths” (“Leibniz on Modality, Cognition, and Expression”, 284). That is, only some substances (spirits) express God. And they do this by being able to know eternal truths. In this post and a couple of following ones I want to consider both the suggested restriction to some substances, and the reasons why substances express God. I pay particular attention to the 1686 Discourse on Metaphysics.

A first question then: why, according to Leibniz, should we think that minds express God? Well, DM 16 tells us that “an effect always expresses its cause and God is the true cause of substances”. Given that, we can construct the following argument:

1. An effect always expresses its cause.
2. Every substance is an effect of God. So
3. Every substance expresses God.

Similarly, Leibniz said — in some comments about expression in a letter written that year to Simon Foucher — that “Each effect expresses its cause, and the cause of each substance is the decision which God took to create it” (WFNS 53; A 2.2, p.91). That suggests a slight variant on the above argument:

1. An effect always expresses its cause.
   2*. Every substance is an effect of God’s resolution to create it. So
   3* Every substance expresses God’s resolution to create it.

Despite some variation in exactly what is said to be expressed — which may not even be real disagreement, without a more detailed understanding of what it means to express God — we have very similar argument in both cases here. Substances express God, because God is their cause. Moreover, all substances do this, not just minds.

More posts to come on this: on why Leibniz thinks that substances express their causes; on the passages in the Discourse that distinguish minds from other substances; and on the extent, if any, to which Leibniz maintained this view over time.