Divine thought simplicity

One of the motivations for denying divine simplicity is the plausibility of the claim that:

1. There is a multiplicity of divine thoughts, which are a proper part of God.

But it turns out there are reasons to reject (1) independent of divine simplicity.

Here is one reductio of the distinctness of God and God’s thoughts.

2. God is distinct from his thoughts.

3. If x’s thoughts are distinct from x, then x causes x’s thoughts.

4. Everything caused by God is a creature.

5. So, God’s thoughts are creatures.

6. Every creature explanatorily depends on a divine rational decision to create it.

7. A rational decision explanatorily depends on thoughts.

8. So, we have an ungrounded infinite explanatory regress of thoughts.

9. Ungrounded infinite explanatory regresses are impossible.

10. Contradiction!

Here is another that also starts with 2–5 but now continues:

11. God’s omniscience is identical with or dependent on God’s thoughts.

12. None of God’s essential attributes are identical with or dependent on any creatures.

13. Omniscience is one of God’s essential attributes.

14. Contradiction!

Virtual parts, compressed files and divine ideas

Suppose I record some video to a file on my phone. The video on my phone then is made up of frames, say, 30 of them per second. The frames are parts of the video that it sure seems like we can quantify over. But what is a frame of the video? Well, it's natural to say: The file consists of a sequence of bits implemented as flash memory states arranged spatially in the flash memory of the phone (though not always in the "logical" order, because of wear-leveling and filesystem issues). A frame then would seem to be a subsequence of these flash memory states. But that is in general false. Video files are typically compressed. While some frames--the "key frames"--are stored as a whole as a discrete sequence of bits, typical frames are not stored as a whole. Instead, what is stored is basically a set of instructions on how to modify one or more other frames in order to get the current frame. For instance, if you are panning smoothly across a static object from left to right, the non-key frames will presumably say something like: "Take most of the previous frame, shift it over a little, and then add such and such pixels on the right." But we cannot identify the bits of an instruction like that with the video frame itself, because the video frame does not supervene on the instruction: it supervenes on the instruction and the previous frame.

Even a liberal materialist ontology with unrestricted composition that allows for fusions of arbitrary disconnected sequences of bit-encoding states, the parts of the video do not exist. Noentheless, we correctly (and truthfully) say in ordinary language that the video is made up of frames as parts.

This is a rather nice illustration, I think, of the Thomistic concept of virtual parts. Virtual parts are not fundamental ingredients in the ontology. Nonetheless it is correct (and truthful) to talk of them in ordinary language. There are other such illustrations in computing. For instance, images and sounds are compressed by algorithms that transform them from spatial or temporal sequential data to frequency data or wavelet coefficients. The "natural" parts of the image or sound (say, "the left half", or "the last third") will typically not correspond to a physical part of the device memory storage.

A more homely example is, I am pretty sure, the human visual system. I see an image composed of a variety of parts. There is a lit-up rectangular part (the laptop screen), which has a left half and a right half, and so on. But even without looking up any brain research, I am willing to bet quite a lot that the disjoint spatial parts of the visual image do not correspond to particular things in my brain: I do not have an array of pixels in the brain whose parts correspond to the parts of the image (I do not even have an array of pixels in the retina corresponding to the parts of the image, as the image is stitched together by the brain over time from a variety of images produced by eyes that are constantly moving across the image).

(Can the Platonist avoid talking of virtual parts, insisting that videos and pictures are abstract objects? But even if videos and pictures are abstract objects, I doubt that they have frames and subpictures as parts.)

One thing I would like to use this story for is divine ideas. God is fundamentally simple. But we can meaningfully and truthfully talk of a multiplicity of divine ideas, in much the way that we can talk of the parts of the visual image, which are all encoded in God's one idea of all possibility. And this grounds worlds, propositions and the like.

Divine Belief Simplicity

Divine Belief Simplicity is the thesis that all of God's acts of belief are the same act of belief, the same belief token. While my belief that 2+2=4 seems distinct from my belief that the sky is blue, God's believings are all one. This is a special case of divine simplicity.

Here is an argument for Divine Belief Simplicity. The primary alternative to Divine Belief Simplicity is:

• Divine Belief Diversity: God's act of believing p is distinct from God's act of believing q whenever p and q are different.

But Divine Belief Diversity is false. The argument may be based on an anonymous referee's objection to a paper by Josh Rasmussen—I can't remember very well now—or to some comments by Josh Rasmussen. Here are some assumptions we'll need:

1. For any plurality, the Fs, there is a distinct proposition that the Fs exist or don't exist.

For instance, there is the proposition that the world's dogs exist or don't exist, and the proposition that the French exist or don't exist, and so on. Next:

2. Separation: Given any plurality, the Fs, and a predicate, P, that is satisfied by at least one of the Fs, there is a plurality of all and only the Fs satisfying P.
3. Plurality of Believings: If Divine Belief Diversity holds, then there is a plurality of all divine acts of believing.

But this is enough to run a Russell paradox.

Say that a divine believing b is settish provided that there is a plurality, the Fs, such that b is a believing that the Fs exist or don't exist. For any settish divine belief b, there is the plurality of things that b affirms the existence or nonexistence of. Say that a divine believing b is nonselfmembered provided that b is settish and is not in the plurality of things that b affirms the existence or nonexistence of. By (1), Separation and Plurality of Believings, let p be the proposition that affirms existence-or-nonexistence of the nonselfmembered believings. Now p is true. So there is a divine believing b in p. This is settish. Moreover, this b either is among the nonselfmembered believings or not. If it is, then it's not. If it's not, then it is. So we have a contradiction.

Moreover, this argument does not need to take propositions ontologically seriously. It only needs divine believings to be taken ontologically seriously.

Denying Divine Belief Diversity, however, denies that there is such a thing as the plurality of things that b affirms the existence or nonexistence of.

More on Spinoza on error

Spinoza's main theory of intentionality is simple. What is the relationship between an idea and what it represents? Identity. An idea is, simply, identical with its ideatum. What saves this from being a complete idealism is that Spinoza has a two-attribute theory to go with it. Thus, an idea is considered under the attribute of thought, while its ideatum is, often, considered under the attribute of extension. Thus, the idea of my body is identical with my body, but when we talk of the "idea" we are conceiving it under the attribute of thought, and when we talk of "body" we are conceiving it under the attribute of extension.

But there is both a philosophical and a textual problem for this, and that is the problem of how false ideas are possible. Since presumably an idea is true if and only if what it represents exists, and an idea represents its ideatum, and its ideatum is identical with it, there are no false ideas, it seems. The philosophical problem is that there obviously are! The textual problem is that Spinoza says that there are, and he even gives an account of how they arise. They arise always by privation, by incompleteness. Thus, to use one of Spinoza's favorite examples, consider Sam who takes, on perceptual grounds, the sun to be 200 feet away. Sam has the idea of the sun impressing itself on his perceptual faculties as if it were 200 feet away, but lacks the idea that qualifies this as a mere perception. When we go wrong, our ideas are incomplete by missing a qualification. It is important metaphysically and ethically to Spinoza that error have such a privative explanation. But at the same time, this whole story does not fit with the identity theory of representation. Sam's idea is identical with its ideatum. It is, granted, confused, which for Spinoza basically means that it is abstracted, unspecific, like a big disjunction (the sun actually being 200 feet away and so looking or the sun actually being 201 feet away and looking 200 feet away or ...).

Here is a suggestion how to fix the problem. Distinguish between fundamental or strict representation and loose representation. Take the identity theory to be an account of strict representation. Thus, each idea strictly represents its ideatum and even confused ideas are true, just not very specific. An idea is then strictly true provided that its ideatum exists, and every idea is strictly true. But now we define a looser sense of representation in terms of the strict one. If an idea is already specific, i.e., adequate (in Spinoza's terminology) or unconfused, then we just say that it loosely represents what it strictly represents. But:

• When an idea i is unspecific, then it loosely represents the ideatum of the idea i* that is the relevant specification of i when there is a relevant specification of i. When there is no relevant specification of i, then i does not loosely represent anything.

Here, we may want to allow an idea to count as its own specification—that will be an improper specification. When an idea is its own relevant specification, then the idea loosely represents the same thing as it strictly represents, and it must be true. I am not sure Spinoza would allow a confused idea to do that. If he doesn't, then we have to say that specification must be proper specification—the specifying idea must be more specific than what it specifies, it must be a proper determinate of the determinable corresponding to the unspecific idea i.

An idea, then, is loosely true provided that it loosely represents something. Otherwise, it is loosely false. Error is now possible. For there may not exist an actual relevant specifying idea. Or, to put it possibilistically, the relevant specification may be a non-actual idea.

What remains is to say what the relevant specification is. Here I can only speculate. Here are two options. I am not proposing either one as what Spinoza might accept, but they give the flavor of the sorts of accounts of relevance that one might give.

1. A specification i* of i is relevant provided that the agent acts as if her idea i were understood as i*.
2. A specification i* of i is relevant provided that most of the time when the agent has had an idea relevantly like i the ideatum of an idea relevantly like i* exists (i.e., an idea relevantly like i* exists), and there is no more specific idea than i* that satisfies this criterion (or no more specific idea than i* satisfies this criterion unless it is significantly more gerrymandered than i*?).

I think Spinoza would be worried in (1) about the idea of acting as if a non-existent idea were believed. This is maybe more Wittgensteinian than Spinozistic. I think (2) isn't very alien to Spinoza, given what he says about habituation.

Loose truth and loose representation may be vague in ways that strict truth and strict representation are not. The vagueness would come from the account of relevant specification.

I don't know that Spinoza had a view like I sketch above. But I think it is compatible with much of what he says, and would let him hold on to the insight that fundamental intentionality is secured by identity, while allowing him to say that privation makes error possible by opening up the way for ideas which are sufficiently inspecific in such a way that they have no correct relevant specification.

Plurality of divine ideas

I've been suspicious of divine ideas, but now I like what St Thomas does in S. Th. I.15. St Thomas seems to be insisting that the sentence "There are many divine ideas" gets a semantics according to which it is made true not by some plurality in things, but by God's understanding himself in this way, and in that way, and so on, without these being separate acts of understanding. It is possible, I suspect, for an experienced physicist to understand light as a stream of particles and as a wave simultaneously and without there being two separate acts of understanding here. Likewise, then, God simultaneouosly, and without a multiplicity of acts of understanding, understands himself as something that can be participated in by a donkey, and as something that can be participated in by an oak tree, and as something that can be participated in by an angel, and he does this with a single indivisible (and the indivisibility may not be present in the physicist's case) act of understanding that suffices to make true all of these particular claims about what God understands. So the apparently quantified claim "There are many divine ideas" is made true by a single indivisible entity.

I see Aquinas' project here and in his discussion of the Trinity and the Incarnation as an attempt to provide a semantics compatible with divine simplicity for hard to avoid philosophical truths (this case) or orthodox theological doctrines (the other two cases). This semantics must make the right sentences true, and it must also be plausible.