The independence of the attributes in Spinoza

According to Spinoza, all of reality—namely, deus sive natura and its modes—can be independently understood under each of (at least) two attributes: thought and extension. Under the attribute of thought, we have a world of ideas, and under the attribute of extesion, we have a world of bodies. There is identity between the two worlds: each idea is about a body. We have a beautiful account of the aboutness relation: the idea is identical to the body it is about, but the idea and body are understood under different attributes.

But here is a problem. It seems that to understand an idea, one needs to understand what the idea is about. But this seems to damage the conceptual independence of the attributes of thought and extension, in that one cannot fully understand the aboutness of the ideas without understanding extension.

I am not sure what to do about this.

Plagiarism and a repeat invitation

I am occasionally asked whether I am not afraid that someone will steal ideas from my blog and publish them. I'm not. If the ideas get published by someone else, that saves me the trouble of writing them up myself. Hopefully they will give credit where credit is due and it won't be theft.

Moreover, I invite anybody competent who wants to coauthor a paper with me by starting with the ideas in a post, working out the details and writing up a first draft. (Check with me first before getting to work, though.) In the philosophical profession, coauthored papers count pretty much the same as single-authored, so plagiarizing would involve unnecessary risk for very minor benefit.

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.

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.