The incoherence of Spinoza's mode ontology

According to Spinoza, I am a mode and God is the only substance. But I am not directly a mode of God. I am a mode of a mode of a mode of … a mode of God, with infinitely many “a mode of” links in between.

This is incoherent. It is an infinite chain with two ends, one being me and the other being God. But any infinite chain made of direct links has at most one end: it would have to be of the form 1:2:3:4:…, with one endpoint, namely zero. We can stick on another chain running in the other direction, like …:iv:iii:ii:i, and get the two ended sequence 1:2:3:4:…:iv:iii:ii:i. But this two-ended sequence is not a chain, because there is no connection between any of the arabic numbered nodes and any of the roman numbered nodes.

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.

Priors, justification and rationalism

The rationalism of Leibniz and Spinoza worked like this: We figure out fundamental necessary metaphysical principles, and these principles determine everything else of necessity (with some qualifications on the Leibniz side as to the type of necessity).

But another rationalism is possible: We figure out fundamental necessary metaphysical principles, and these principles determine the basic probabilistic structure of reality. In Bayesian terms, the fundamental metaphysical principles yield the prior probabilities. A version of this was Descartes’ project in the Meditations.

And there is reason to engage in this probabilistic rationalist project. We cannot get out of the need to have something like prior probabilities. Moreover, priors need epistemic justification. Consider an empirical claim p that we assign a high enough credence for belief to, say 0.99, on the basis of total evidence e. Thus, P(p|e)=0.99. It follows by the axioms of probability that P(p ∨ ¬e)≥0.99. Hence we have a high enough prior credence for belief in p ∨ ¬e. Surely assigning a credence of 0.99 to something requires epistemic justification. Moreover, surely (though people who don’t like closure arguments may not like it) if we have posterior justification when we believe p, we have posterior justification when we believe the obviously entailed claim p ∨ ¬e. But this justification did not come from e. For P(p ∨ ¬e|e)=P(p|e)=0.99 and we have seen that P(p ∨ ¬e)≥0.99, so e is not evidence for p ∨ ¬e (in face, typically e will be evidence against this disjunction). Since e is our total evidence, the justification had to be there in the first place.

Thus we need epistemic justification for our priors. The priors encode genuine information about our world, information that we are justified in possessing. Where do we justifiedly get this information from? We don’t get it through logic, pace logical probability accounts. Metaphysics is one potential answer to this question and exploring this answer gives us good reason to engage in the probabilistic rationalist project. Another option is that the priors are a kind of innate knowledge built into our nature—my Aristotelian Bayesianism is a version of this.

Two kinds of pantheism

There are two kinds of pantheism. One might call them: reductive pantheism and world-enhancing pantheism.

Reductive pantheism says that the world is pretty much like it seems to us scientifically (though it might opt for a particular scientific theory, such as a multiverse one), and that God is nothing but this world. In so doing, one will be trying to find a place for the applicability of divine attributes for the world.

World-enhancing pantheism, however, says that there is more to the world than meets the eye. There is something numinous pervading us, our ecosystem, our solar system, our galaxy, our universe and all reality, with this mysterious world being a living organism that is God. World-enhancing pantheism paints a picture of a divinized world.

World-enhancing pantheism is a genuine religious view, one that leads to distinctive (and idolatrous!) practices of worshipful reverence for the world around us. Reductive pantheism, on the other hand, is a philosophers' abstraction.

It is an interesting question which version of pantheism is Spinoza's. His influence on the romantics is surely due to their taking him to be a world-enhancing pantheist, and he certainly sometimes sounds like one. But it is not clear to me that he is one. Though it may be that Spinoza has managed to do both: we might say that under the attribute of extension, we have a reductive pantheism, but the availability of the attribute of thought allows for a world-enhancing pantheism.

World-enhancing pantheism is idolatrous, while reductive pantheism is just a standard atheistic metaphysics with an alternate semantics for the word "God".

Creative suggestion to improve my Leibniz and Spinoza seminar

I looked at my teaching evaluations from the fall.  There were some useful suggestions.  And one that was particularly amusing: background mood music.

Adverbial ontology and dispensing with parts

Once one has an adverbial ontology, like the one I used to help with the Incarnation, one no longer needs the parts of a substance in one's ontology. "I have two hands." That's made true by my being two-handed. "My right hand has five fingers." That's made true by my having a right hand five-fingeredly. More explicitly, there is a mode m in virtue of which I have a right hand. (According to my Incarnation post, I have m indirectly, as m is a mode of my humanity.) Then we have two moves we can make. We could say that there are five modes of m, which each of which is a different way of the hand's being fingered. If we go that route, then we are forced into identity of indiscernibles for fingers, and by extension for any other parts. I welcome that consequence myself, since I'm anyway pulled to identity of indiscernibles by my theory of transworld identity. But alternately we could simply posit a mode of being five-fingered, perhaps a mode relational to the number five.

To my mind there are three main uses of parts:

1. Some properties of wholes are grounded in properties of parts. "I have the property of having heart-beat in virtue of having as a part a heart that in turn has the property of beating."
2. Parts have location and help explain partial location. "I am partly in this room and partly in that, because one of my legs is here and the other there."
3. Some parts are widely thought to be able to move between substances. "Several hours after you ate the apple, a carbon atom that used to be a part of an apple tree has become a part of you."

The adverbial mode ontology does the first two tasks well.

1: There is a mode in virtue of having which I have heart-beat. But I have that mode indirectly: that mode modifies my being hearted, which in turn modifies my humanity. So properties are divided up. But an advantage of the mode way is that we get to uniformly divide properties not just by parts, but by functional subsystems. Some functional subsystems correspond to parts, but likely not all. In a computer running several processes at once on the same processor core, the processes may correspond to different functional systems—say, one doing Fourier transforms of microphone data and another watching for user input events—but the processes may be implemented by overlapping sets of physical parts (and a computer has no others), and we could easily imagine that there is no distinct set of parts corresponding to each process. It seems likely that something like that happens in the brain, and even if it does not, the possibility should be accounted for in our ontology. The adverbial mode ontology apportions properties had in virtue of a functional subsystem in the same way that it apportions those properties had in virtue of a physical part, and that strikes me as exactly right.

2: This is really just a special case of 1. "My right leg is located in this room" is true in virtue of my being right-leg-possessed this-roomly.

But unless we posit that modes can move between substances—I've heard Rob Koons speculate in that direction and Aquinas's account of transsubstantiation famously allows modes to survive the destruction of their underlying substance—it's harder to handle 3. On general Aristotelian grounds, I think one can just bite the bullet. The identity of a part, if there are parts, is going to be dependent on the whole. There is no carbon atom that was a part of the apple tree and is now a part of you. There are (in the eternalist sense of "are"), at best, two carbon atoms, one that was identity dependent on the tree and the other that is identity dependent on you, and the first caused the second. This is counterintuitive.

So what our adverbial ontologists should say about 3 is that the apple tree has some mode m₁ that makes it count as having had a certain carbon atom once, and you have some mode m₂ that makes you count as having a certain carbon atom. There is a continuity of location (see 2) between the one mode (perhaps with some other intervening modes, depending on the ontological status of the apple as such) and the other. Moreover, m₁ is a cause of m₂. Or, if we prefer (and I think we should), the apple tree as modified by m₁ caused you to have m₂. I.e., there is a mode c₁ of causation had by m₁, which is a causation of m₂, or of me as having m₂. But the numerical identity of the particles, that we need to give up on. However, since giving up on parts dissolves the problem of material constitution, and since every other solution to the problem of material constitution has something else counterintuitive about it, we are in this regard no worse off here than any view on which there are parts.

A challenge for the view is to distinguish between those modes that correspond to parts and those modes that don't. But one might just reject the distinction. Or one might go like this. It might be that all and only the modes that have a location mode are parts. But don't non-part subsystems have a location mode? Maybe not. Rather, they may be modes--or joint modes (maybe a mode can be a mode of more than one mode--or maybe even more than one substance--and maybe that is how relations are to be handled)--of one or more parts, and the parts are what have a location mode. The non-part subsystems, then, have a location in a derivative sense.

The incarnation and adverbial ontology

Christ is God and Christ is a human. God is unchanging and humans are changing. God is omnipresent and humans are spatiotemporally delimited. God is all powerful and the power of humans is limited. All praise be to Christ on this Christmas day!

Yet such theological claims appear to lead to contradiction: is Christ unchanging or change? is he limited or unlimited? Since we have excellent reason to think the claims are all true, we have excellent reason to think the claims are not contradictory. A traditional way to resolve the apparent contradiction is to introduce a qua or as qualifier:

1. Christ is unchanging, omnipresent and omnipotent as God, but as human he changes, and is limited in presence and power.

Such answers do work logically speaking, but it would be good to have a little bit more to say about what the "as" does.

I want to suggest something that may not be original[note 1] but that I found enlightening. Start with the observation that there is no contradiction at all in this sentence:

2. Sam is quick as a reader and slow as a runner.

And there is an obvious and easy way to understand (2) that removes all appearance of contradiction:

3. Sam reads quickly and runs slowly.

No contradiction results from contradictory adverbs being attached to different predicates. From Sam reading quickly we can deduce that Sam does something quickly, but that does not contradict his doing something else slowly.

Now we can make the same move in regard to (1). We will need two base predicates which are then adverbially modified. The ones that come to mind are "is God" and "is human". Then (1) becomes:

4. Christ is God unchangingly, omnipresently and omnipotently, but he is human changingly and limitedly in presence and power.

So far that's just words. But now make it into ontology. The ontology takes a cue from Spinoza's nesting of modes. (Other philosophers have nested modes, but I think it is only in Spinoza that the nesting is really central.) When Sam reads quickly, there is Sam, who reads, and Sam's reading, which is quick. If Sam reads excessively quickly, there is Sam, who reads, and Sam's reading, which is quick, and the quickness of Sam's reading, which is excessive. All of these, other than Sam himself, are modes (Spinoza wrongly thinks Sam is a mode, too). We can now talk of a mode being directly or indirectly a mode of something. Thus, the quickness of Sam's reading is directly a mode of Sam's reading and indirectly a mode of Sam. The excessiveness of Sam's quickness of reading is directly a mode of Sam's quickness of reading and indirectly a mode of Sam's reading as well as of Sam.

Next theorize that a mode m is an essence of an individual x if and only if m is directly a mode of x. This could simply be a necessary "if and only if" or, more ambitiously, it could be an account of what it is to be an essence, essences being nothing but direct modes. Observe that this is a non-modal account of essence—here we are talking of essence in the ancient and medieval sense, not in the modern modal sense (such a distinction was pointed out by Fine, but the best account in print is by Michael Gorman).

Thus all our accidental modes are indirectly modes of us, through our essence. My present typing of this post is a mode of my humanity: I am human typingly. And Christ, unlike us, has (at least[note 2]) two essences: humanity and divinity. Thus any mode of his is one of his essences or is a mode of one of his essences. (Sometimes our words will be ambiguous. Thus when we say that "Christ is wise", that is ambiguous whether he is divine in a wise manner or is human in a wise manner or both.)

This account makes it plausible that analogy will be a central concept. Adverbs apply analogically across predicates. The "quickly" in "Sarah runs quickly" and "Sarah thinks quickly" is to be understood analogically. In general, I suspect cross-essence predications are to be understood analogically. That is a Thomistic aspect in the theory.

Another Aristotelian aspect is that we can make sense of "necessary accidents". Thus, Aristotle thinks it is an accident of a human that the human have a capacity for laughter, but he also thinks this is a necessary accident—every human necessarily has a capacity for laughter. It is insufficient for a mode to be an essence that the mode is necessary: it must be directly a mode of the individual. But just as it is indirectly a mode of me that I be laughing—I am human laughingly when I laugh (which differs from, say, being an alien or angel laughingly)—it indirectly but necessarily a mode of me that I have a capacity for laughter—I am a human with a capacity for laughter ("with..." is one of the many ways of indicating adverbial modifiers).

There is a serious theological difficulty. Does not the account contradict divine simplicity? After all, does not (4) posit a mode of God, namely divinity, and modes of a mode of God, namely omnipresence of divinity, omnipotence of divinity and unchangingness of divinity? Yes, but that only contradicts divine simplicity if these modes are all distinct. But they aren't distinct. Divinity, omnipresence of divinity and all the others are all just God. Thus God is his own mode in this technical vocabulary. But since predication of God is analogical, what this means it that God is related to himself in a way analogical to our relationship to our modes. (Compare: the person who loves herself is related to herself in a way analogical to the way someone who loves another is related to that other.) It's important not to take "mode" to mean "accident", but that was already something necessary from the fact that essences are modes.

Of course, this is not a complete account of divine simplicity yet. Something needs to be said about apparently contingent modes of God, such as creating Adam. (I think claims like "God creates Adam" should not be taken as predicating a mode of God. Why not, with the medievals, take the claim as predicating a mode of Adam? Or as predicating being creator of all contingent beings of God and contigency of Adam?)

This reconciliation with divine simplicity does, however, mean that I cannot simply define a substance as something that isn't a mode. For God on this reconciliation is a substance and a mode. (And that is Thomistic, too, though the vocabulary of "mode" is not. God is both substance and that substance's pure act.) We might define a substance as something that isn't a mode of anything else. Or we might say that x is a substance if and only if the proposition that x exists has a truthmaker which is x and has no other truthmaker.

Finally, I leave it as an exercise to the reader to extend my "metaphysically Aristotelian quantification" to this context. At the same time, some of my cross-level uses of "is" in this post will need some charitable analogical reading.

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.

Spinoza and Kant on reason and universalizability

Spinoza writes (Ethics, Scholium to 4P72):

The question may be asked: "What if a man could by deception free himself from imminent danger of death?  Would not consideration for the preservation of his own being be decisive in persuading him to deceive?"  I reply in the same way, that if reason urges this, it does so for all men;  and thus reason urges men in general to join forces and to have common laws only with deceitful intention;  that is, in effect, to have no laws in common at all, which is absurd.

This not only agrees exactly with Kant's position that lying is always wrong, but the form of reasoning is rather Kantian.  So the first form of the Categorical Imperative precedes Kant not just in doctrine but also in rationale: if reason tells me to do something, it tells everyone this.

And, while I agree the conclusion that lying is always wrong is correct, Spinoza's version of the reasoning just doesn't work.  For defender of lying to save innocent life does not say that reason says that one ought always deceive or even that one ought deceive whenever it is to one's advantage, but the claim is more narrow, say that one should lie to unjust aggressors in order to protect their victims.  And the universalization of this narrow claim does not lead to the sort of absurd social situation Spinoza points out, though it leads to the kind of contradiction that Kant is worried about: if everyone lied to unjust aggressors when this would save lives, unjust aggressors wouldn't believe the claims of those who speak to them, and there would be no point to the lie.

That said, I am in general kind of dubious of universalization arguments.  There is, after all, the classic example of playing tennis Saturday night because the courts are free.

Spinoza on truth and falsity

In Actuality, Possibility, and Worlds, I attribute to Spinoza the view that no belief is false (though I think i also emphasize that nothing rides on the accuracy of the historical claim).  Rather, there are more or less confused beliefs, and in the extreme case there are empty words--words that do not signify any proposition.

I was led to the attribution by a focus on passages, especially in Part II of the Ethics and in the Treatise on the Emendation of the Intellect, that insist that every idea has an ideatum, that of which it is the idea, and hence corresponds to something real.  The claim that every idea has an ideatum is central to Spinoza's work.  It is a consequence of the central 2 Prop. 7 (which is the most fecund claim outside Part I) which claims that the order and connection of ideas is the order and connection of things, and it is also a consequence of the correspondence of modes between attributes.

These passages stand in some tension, however, to other passages where Spinoza expressly talks of false ideas, which are basically ideas that are too confused to be adequate or to be knowledge (the details won't matter for this post).

I think it is easy to reconcile the two sets of passages when we recognize that Spinoza has an idiosyncratic sense of "true" and "false".  In Spinoza's sense, an idea is true if the individual having the idea is right to have it, and it is false if the individual having it is not right to have it (cf. Campbell's "action-based" view of truth, but of course Campbell will not go along with Spinoza's internalism), where the individual is right to have the idea provided that she knows the content, or knows it infallibly.  And Spinoza, rationalist that he is, has an internalist view of knowledge, where knowledge is a matter of clarity and distinctness and a grasp of the explaining cause of the known idea.

Hence, Spinoza uses the words "true" and "false" in an internalist sense.  But we do not.  "True" as used by us expresses a property for which correspondence to reality is sufficient, and "false" expresses a property incompatible with such correspondence.  Since every belief has an idea (in Spinoza's terminology) as its content, and according to Spinoza every idea corresponds to reality, namely to its ideatum, it follows that in our sense of the word, Spinoza holds that every belief is true and no belief is false.

The ordinary notion of truth includes ingredients such as that correspondence to reality is sufficient for truth and that truth is a good that our intellect aims at.  Spinoza insists on the second part of this notion, and finds it in tension with the first (cf. this argument).  But the first part is, in fact, the central one, which is why philosophers can agree on what truth is while disagreeing about whether belief is aimed at truth, knowledge, understanding or some other good.

So, we can say that in Spinoza's sense of "true", it is his view that some but not all beliefs are true.  And in our sense of "true", it is his view that all beliefs are true.  The sentence "Some beliefs are false" as used by Spinoza would express a proposition that Spinoza is committed to, while the sentence "Some beliefs are false" as used by us would express a proposition that Spinoza is committed to the denial of.

This move of distinguishing our sense of a seemingly ordinary word like "true" from that of a philosopher X is a risky exegetical move in general. Van Inwagen has argued libertarians should not hold that compatibilists have a different sense of the phrase "free will".  But I think there are times when the move is perfectly justified.  When the gap between how X uses some word and how we use it is too great, then we may simply have to concede that X uses the word in a different sense.  This is particularly appropriate in the case of Spinoza whose views are far from common sense, whose philosophical practice depends on giving definitions, and who expressly insists that many disagreements are merely apparent and are simply due to using the same words in diverse senses.  (Actually, I also wonder if van Inwagen's case of free will isn't also a case where the phrase is used in diverse senses.  Even if so, we should avoid making this move too often.)

Addendum: This reading is in some tension with 1 Axiom 6 which says that a true idea must agree with its ideatum. While strictly speaking, this sets out only a necessary condition for a true idea, and hence does not conflict with what I say above, it is not unusual for Spinoza to phrase biconditionals as mere conditionals. If we read 1 Axiom 6 as a biconditional, then maybe we should make a further distinction, that between the truth of an idea and truth of a believing. We take the truth of a believing to be the same as the truth of the idea (or proposition) that is the object of the believing. But Spinoza distinguishes, and takes more to be required for the truth of a believing. We then disambiguate various passages. The problem with this is that on Spinoza's view, the believing is identical with the idea. But nonetheless maybe we can distinguish between the idea qua believing and the idea qua idea?

Spinoza's argument for internalism about truth

Internalism about truth holds that a belief's being true is a function of things internal to the mind of the believer. Coherentism and Spinoza's extreme rationalism are two kinds of internalisms about truth. Spinoza's argument in the Treatise for the Emendation of the Intellect is basically:

1. If internalism is not correct, truth is not worth having.
2. Truth is worth having.
3. Therefore, internalism is correct.

For (1) to be at all plausible, we need "worth having" to mean intrinsically worth having, and that makes (2) less plausible, though I think (2) remains true. But I deny (1), with or without the qualification, because some things can be intrinsically worth having without being internal or intrinsic to the person. Thus, it is worth having one's friends do well, even though my friends' doing well is not internal or intrinsic to me. Of course my friends' doing well tends to affect me. But not always: my friend could be doing well in my absence, without any contact we me, and that directly makes me better off.

One can also run the argument in terms of knowledge instead of truth. (I think for Spinoza the two come to the same thing! Spinoza thinks knowledge is true belief, but he has high standards for what counts as true belief—beliefs not justified up to Cartesian standards need not apply.)

Self-organization: Another step in the dialectics

Suppose that it turns out that, given laws of nature like ours, all sorts of neat self-organization—like what we see in evolution—will follow from most sets of initial conditions. Does this destroy the design argument for the existence of God? After all, that there is complexity of the sort we observe appears to cease to be surprising.

A standard answer is: No, because we still need an explanation of why the laws of nature are in fact such as to enable this kind of self-organization, and theism provides an excellent such explanation.

But what if it turns out, further, that in some sense most laws, or the most likely laws (maybe simpler laws are more likely than more complex ones), enable self-organization processes. So not only is it unsurprising that we would get initial conditions that are likely to lead to self-organization, it is also not unlikely that we would have laws that lead to self-organization. It seems that this undercuts the modified design argument.

But I think there is a further design argument. The result that most, or the most likely, laws would likely lead to self-organization would have to be a very deep and powerful mathematical truth. What explains why this deep mathematical truth obtains? Maybe it follows from certain axioms. But why is it the case that axioms such as to lead to that truth obtain? Well, we can say that they are necessary, but that isn't a very good explanation: it is not an informative explanation. (If it turned out that modal fatalism is true, we still wouldn't be satisfied with explaining all natural phenomena by invoking their necessity. Spinoza certainly wasn't, and this he was right about, though he was wrong that modal fatalism is true.) Theism provides a family of deeper and more informative answers: mathematics is grounded in the nature of a perfect being, and hence it is unsurprising that mathematics has much that is beautiful and good in it, and in particular it is unsurprising that mathematics includes self-organization theorems, since self-organization theorems are beautiful and good features of mathematical reality.

I said that theism provides a family of answers, since different theistic theories give different accounts of how it is that mathematical truth is grounded in God. Thus, one might think, with St Augustine, that mathematical truth is grounded in God's intellect. On the theory I defend in my Worlds book, necessary truths—and in particular, mathematical truths—are grounded in the power of God.

There is, of course, an obvious argument from the beauty of mathematics to the existence of God along similar lines. But that argument is subject to the rejoinder that the beauty of mathematics is a selection effect: what mathematics mathematicians are interested in is to a large degree a function of how beautiful it is. (Mathematicians are not interested in random facts about what the products of ten-digit numbers are.) However, I think the present argument side-steps the selection effect worry.

The fecundity of Spinoza's claims

Say that the fecundity of a claim in a logically interconnected text, like Spinoza's Ethics, is the number of claims that logically depend on it. Using the Tredwell adjacency data, I sorted the claims in Spinoza's Ethics in order of decreasing fecundity. We can measure the fecundity in percentages: the percentage of the claims that depend on the given claim.

The result is here. (The explanations of what the items are are here, from Tredwell.) Fecundity is a measure of how fundamental a given claim is to the system.

The twelve most fecund claims, with their number of dependants, are:

1. 1A04: 300 (77.3%)
2. 1D03: 296 (76.3%)
3. 1D04: 295 (76.0%)
4. 1D05: 292 (75.3%)
5. 1A06: 291 (75.0%)
6. 1A01: 291 (75.0%)
7. 1P01: 290 (74.7%)
8. 1A05: 290 (74.7%)
9. 1P04: 290 (74.7%)
10. 1P02: 289 (74.5%)
11. 1P03: 289 (74.5%)
12. 1P05: 289 (74.5%)

Unsurprisingly, they're all from Part I of the Ethics, and unsurprisingly the first six are all axioms or definitions.

The most fecund is Axiom 4, that the cognitio (understanding?) of the effect depends on the cognitio of the cause, which, through Spinoza's overreading of it (it sounds like a weak claim, and that's why we are tempted to agree, but in fact it is a strong claim), becomes the root of the epistemologically central 2 Proposition 7, which says that the order and connection of things is the order and connection of ideas. In fact, it is largely through this 2P07 that Axiom 4 gets its fecundity: 2P07 has a fecundity of 60%, and assumes nothing other than 1A04.

The most fecund derived claim is 1 Proposition 4, that distinct things must differ in attribute or mode.

Unsurprisingly, the ontological argument is central: the fecundity of 1 Proposition 11, that God exists, is 73%.

The most fecund claim from outside of Part 1 is the aforementioned 2 Proposition 7, whose centrality cannot be denied.

There are 103 propositions that have zero fecundity.

Axiom 2 of Part I has zero fecundity in the database I am using, as do 5A02 and 2A08. Due to the limitations of my method, axioms and definitions with zero fecundity don't appear in the results I linked to, though I may fix that eventually. The case of Axiom 2 of Part I interesting and surprising, since it basically states Spinoza's version of the Principle of Sufficient Reason. My feeling is that it is implicitly used all over the place.

The least fecund axiom that actually gets used is 5A01, about contrary actions, which has only one dependent. The next, somewhat more fecund axiom is 4A01, at 4% fecundity, which says that for any thing, there is a stronger thing which can destroy it.

Surprisingly to me, the least fecund axiom from Part 1 is 1A03, at 8%, which basically affirms that causation is deterministic. This may initially suggest that Spinoza's causal determinism is not as central to his thought as it is normally thought to be. But that might be too quick, because I suspect that much if not all of the deterministic import of 1A03 is found in 1A04, especially as interpreted by 2P07 and with the understanding the the logical connections between ideas are always entailment relations.

Axiom/definition dependencies in Spinoza's ethics

Using the Tredwell adjacency data, I generated a list of axiom/definition dependencies for all the propositions in Spinoza's ethics. See the Tredwell adjacency data site for a key to what the nodes (e.g., "2P07") are.

Spinoza graphs

R. F. Tredwell has the data for generating a logical dependency graph of Spinoza's Ethics. I converted the data into DOT format so it can be used with GraphViz, and used GraphViz's dot to generate visual representations.

Here is a giant zoomable graph of the whole Ethics.  (There a "View original" link there, to download the original jpeg.)

Potentially more interesting are the individual graphs of the five parts of the Ethics.  Each graph includes the items from the part in question, as well as the dependencies from earlier parts.  (Again, there is a "View original" link for each which downloads the jpeg file.)

• Zoomable Part 1 [Printable PDF]
• Zoomable Part 2 [Printable PDF]
• Zoomable Part 3 [Printable PDF]
• Zoomable Part 4 [Printable PDF]
• Zoomable Part 5 [Printable PDF]

Here is some additional material:

• All my DOT files, including a plain text version of Tredwell's adjacency data and a perl script to generate the DOT file, and a bash script to generate the svg and jpeg files.
• SVG versions of the graphs: full Ethics, Part 1, Part 2, Part 3, Part 4 and Part 5.

Spinoza and reductionistic determinism

According to some presentist theories of time, facts about the future are grounded in facts about the present and in the laws of nature. What grounds the fact, if it is a fact, that tomorrow the sun will rise is that the present conditions together with the laws of nature entail that the sun will rise tomorrow. Alan Rhoda played with a similar view in regard to the past: facts about the past are grounded in facts about God's present memories.

Suppose determinism holds and there is an initial time t₀. Let L be the laws. Then we can imagine a view which we might call initialism in the place of presentism. According to initialism, facts about what happens at a time t>t₀ reduce to facts about what the laws are and what the initial conditions are. More precisely, if I is the initial conditions of the world at t₀, according to initialism, what it is for a state of affairs to obtain at a time t>t₀ is for I and L to jointly entail that it obtains at t. Thus, what it is for there to be humans in the world is for the world to have had initial conditions and laws such as to guarantee the arising of humans.

According to initialism, none of us are substances, because facts about our existence reduce to facts about the initial conditions and laws. In Spinozistic terminology, we are modes of laws and initial conditions or of whatever grounds the laws and initial conditions.

Initialism has some obvious problems. It assumes that determinism holds and that there is an initial time t₀. But determinism is in tension with quantum mechanics, and probably the best interpretation of the Big Bang is that although the universe has finite age, there was no initial moment.

There is a strong resemblance between initialism and Spinoza's metaphysics. To make the resemblance closer, we will make some modifications.

Modification 1: Take time to discrete. Thus, there is a finite number of moments of time between t₀ and the present. If we do this, we can get a nested view closer to Spinoza's. Instead of reducing the conditions at time t_n to the laws and the conditions at t₀, we reduce them to the conditions at t_n−1 and the laws. Now our present time slices are modes of modes of ... modes of the initial conditions and laws.

The second move we can make is to remove the initial time t₀. Instead, there is a doubly infinite sequence of times ...,t₋₂,t₋₁,t₀,t₁,t₂,.... How things are at each time reduces to the laws and how they were at the preceding time. Thus, in Spinozistic terminology, we are modes of modes of modes of ....

The third move is to reintroduce something outside of the whole sequence of modes, in which the sequence of events is grounded. After all, the idea of a sequence of modes without any substance seems absurd. One move would be to take that which is outside the sequence to be the lawmaker of L—that entity in virtue of which L is law, the truthmaker of the proposition that L is law. We may perhaps call this entity "Natura Naturans", nature naturing, or if we are pantheistically inclined like Spinoza, "Deus sive Natura" (though the latter identification would be taking a stand on whether Spinoza's Deus is Natura Naturans or the whole shebang of nature, in favor of the former). If we like, we can call the mereological sum of the modes "Natura Naturata", nature natured. The Natura Naturans, then, is the substance of which the temporal modes are ultimately (though with an infinite chain intervening) are modes.

The final move, to make the view be more like Spinoza's, is to take out the reference to times. Instead, we just have a sequence of entities—objects and/or events—that are each reduced to previous ones.

I think one puzzle about this view is how the Natura Naturans is related to the sequence of temporally qualified, "determinate", modes. We could take this relationship to be one of reduction once again: the whole infinite sequence of times reduces to the laws. This fits with much of what Spinoza says. It is, however, in some tension with Spinoza's idea that from the idea of God qua eternal, and it is this which seems to fit best with this eternal lawmaker, temporally determinate facts do not follow.

This exegetical difficulty can perhaps be overcome.

Here is one way. Accept a relationist B-theory of time, and then say that something is determinate insofar as we can delineate the times of its beginning and end. But on a relationist B-theory, sub specie aeternitatis, we just have a doubly infinite sequence without time-as-a-container, and no non-relative, non-arbitrary way of identifying times like "November 15, 2011". Of course, we can stipulate names for beginning and end times of some events, and then with this stipulative delineation in hand, we can delineate temporally when other events will happen. Thus, if a match struck just before noon, it will come on fire just after noon. Thus, to derive facts about when events happen we need facts about when other events happen. We cannot derive when-facts from eternal laws. Spinoza is clear on his view that times are the product of human beings divisions of duration.

If all there was to being a determinate mode was having a beginning and end time, I think that would be a satisfactory answer. But I think temporally determinate modes may be prior on his view to times. Perhaps, though, his thought is this. What we can derive from L is the whole sequence of things, but considered as an undivided sequence, and all divisions and delineations in the sequence are due to us. And from a delineated cause—say, a match's being struck, which is delineated from what comes before (the movement of the match) and what comes after (the fire)—there can be derived a delineated effect. Again, on this reading, the division in the modes is arbitrary.

Actually, I am not sure that Spinoza's mode-to-haver relationship is reductive. But I think it gives an illuminating reading.

A general form of philosophical argument

This is a bit cynical, but while reading Spinoza I was really struck by the prevalence of the following implicit line of philosophical argument, not just in Spinoza:

1. My theory cannot handle Xs.
2. So, there are no Xs.

It seemed obvious to me that the thing for Spinoza to do was not to conclude that there is no contingency, but to conclude that his theory was inadequate to handle contingency.

I use this form of argument myself.  Perhaps too much.  It takes wisdom to know when the thing to say is that the theory is inadequate to handle Xs and when to conclude that there are no Xs.

Metaphysically Aristotelian quantification

There is a sense in Aristotelian metaphysics that "there are only substances". They are all there is a focal sense. Yet if we can talk about and quantify over accidents or modes, surely there are accidents or modes.

Here, then, is a simple quantified logic that preserves the Aristotelian intuition. This logic is developed only in the case of modes (or tropes) that are non-relational—that subsist in a single substance. The logic has the standard resources of first order sentential logic, together with the standard universal quantifier symbols ∀x and ∃x which quantify over substances x. But additionally there are two new quantifier symbols: ∀_ax and ∃_ax which quantify over a's modes x. Thus, "Some table has an accident" becomes:

1. ∃x(Table(x) and ∃_xy(Accident(y,x))).

Then we can say that only the substances exist simpliciter—only they are quantified over by the standard quantifiers Ax and Ex. Modes "exist" only relative to the substance of which they are modes—they are grounded in that substance, as is indicated in the language by the subscripted quantifiers.

We can say that the mode-quantifier ∃_ax yields existential quantification in an analogical sense. And we can spell out the analogy at least to some degree by giving rules of inference that are structurally analogous to those for the focal-sense quantifier ∃x.

Here's another application of the notion of relative existence. We might, for instance, hesitate to say that characters in novels really exist, but we might think (I am hesitant about that, too) that novels really exist. We might then think that for any novel N, there is a pair of quantifiers ∃_Nx and ∃_Nx over the entities-in-N. If S is some Star Trek novel, then when we say that ∃_Sx(Klingon(x)), we are not really saying that there really are Klingons. We are saying that virtually, in-the-novel, relative-to-the-novel there are Klingons. This is not a fact about Klingons but about the novel, and our primary ontological commitment is to the novel. Of course then our logic then needs to be suitably designed so that we cannot infer from ∃_Sx(Klingon(x)) that ∃x(Klingon(x)). This can all be done, and what I shall do below for modes can be done for characters in novels. Again, quantification over characters is quantification in an analogical sense.

The rest of this post is almost entirely technical and can be skipped.

We leave the truth-functional rules unchanged. We modify the quantificational rules as follows:

Universal elimination: From ∀xF(x) and Substance(a), you get to infer F(a). From ∀_axF(x) and Mode(d,a) you get to infer F(d).

Universal introduction: If you have a subproof assuming Substance(c) and concluding with F(c), and the subproof cites nothing involving c from outside of itself, then you get to infer ∀xF(x). If you have a subproof assuming Mode(c,a) and concluding with F(c), and the subproof cites nothing involving c from outside of itself, then you get to infer ∀_axF(x).

Existential elimination: If you have ∃xF(x) and a subproof from (F(c) and Substance(c)) to S, where the subproof cites nothing involving c from outside of itself and c does not appear in S, then you get to infer S. If you have ∃_axF(x) and a subproof from (F(c) and Mode(c,a)) to S, where the subproof cites nothing involving c from outside of itself and c does not appear in S, then you get to infer S.

Existential introduction: From Substance(a) and F(a), you get to infer ∃xF(x), and from Mode(c,a) and F(c), you get to infer ∃_axF(x).

And we add an additional equality introduction rule: If you have Mode(c,a) and Mode(c,b), then you get to infer a=b.

Models contain a substantial domain S and a function m that assigns to each member of S a set of objects, with the property m(x) and m(y) have no elements in common if x and y are distinct. We can define interpretations and satisfaction in a straightforward way, restricting the interpretations of the Substance and Mode predicates in such a way that I(Substance) is always equal to S and I(Mode) is the set of all pairs (x,y) such that x is in S and y is a member of m(x). (We don't put this rule in in the case of existence-in-a-novel.)

I haven't checked it, but I expect that we have soundness and completeness.

If, like Spinoza and unlike Aristotle, we want to allow for nested modes, this can be done, too.

Progress report: naturalism and persons

This is just a progress report, a promissory note without much argument. I've been thinking a lot about naturalism and persons. Specifically, I've been thinking whether there is room for persons in a naturalistic ontology. One lemma that I've become convinced of is that if necessarily all persons are substances, so that if x is a person, then for x to exist is not a matter of something beyond x having some property or standing in some relation, then naturalism is false. In an earlier post, I gave an argument for this conclusion based on speculative physics, but now I am convinced that the conclusion holds independently of the speculative physics. Basically, the idea is that if naturalism holds, strong AI is true (it would be too weird if naturalism were true but minds had to be tied to a biology like ours), but if strong AI is true, then I suspect it is possible for a token computer program to be a person, and token computer programs are not substances (their existence is a matter of a computer having a particular state).

Moreover, it is plausible that finite persons are ontologically homogeneous: if one finite person is a substance, they all necessarily are. If this is correct, then if we are substances, naturalism is false.

Are persons substances? Are we substances? If we adopt an Aristotelian ontology, there are three alternatives to a person being a substance: she might be accident-like (e.g., a trope or a token relation), she might be the essence of a substance, or she might not exist. I take it that persons exist. The same kinds of thoughts that suggest that if naturalism holds, persons need not be substances, also suggest that if naturalism holds, then persons need not be essences of substances. So, on this kind of ontology, the question comes down to: Can persons be accident-like?

But consider the following thoughts: (a) if naturalism is true, then the best theory of personal identity will be a memory-based theory, (b) programs can seamlessly move between processors and even between computers, and (c) accident-like entities cannot move between substances. To me, these thoughts suggest that if naturalism holds, persons can't be accident-like, unless appearances are deceiving and moving from one body to another, or one computer to another, wouldn't involve a movement between substances. But the only way this could be is if the persons are accidents of some grand global substances, like the Cosmos, or Spacetime, or the Fields of a unified field theory.

Thus, assuming an ontology that has only substances and accident-like entities, the conclusion I draw is that if naturalism holds of persons, we are all modes (to use Spinozostic terminology) of one or more global substances. I doubt that on a sparse theory of properties and relations there will be enough modes to do the job. So the ontology will have to be one on which there are one or more global substances, of which everything else is a mode, and the modes are abundant. Moreover, since we have properties, this ontology will have to be one on which accident-like entities can be nested. I suspect that abundance will cause Unger-like problems with identifying who exactly we are, but I would like to have a better argument against such a Spinozistic ontology.

So this is where I am at right now in the argument: either some non-naturalistic account of persons is true, or a Spinozistic naturalistic ontology of one or more global substances, with nestable modes, probably abundant, holds. Of course I am convinced that the Spinozistic account is false (if only for ethical reasons: it doesn't do justice to the ethical importance of the body), but it would be nice to have a good ontological arguemnt here. With some modal imagination we might make progress: for instance we might think that even if in fact such an ontology holds, surely it would be possible to have persons apart from such an ontology, and this is enough to sink the naturalistic account. But I would rather not rely on modal imagination.

There is a lot of detail here that can be questioned. But the basic idea is, I think, sound: further progress on the question of whether the existence of persons is compatible with naturalism is going to be a matter not just of metaphysica specialis but of metaphysica generalis (i.e., of ontology).

Can conscience command something immoral?

Consider the following claim:
(*) It is never immoral to do what conscience commands.
It would be nice if (*) were true. For instance, it would allow us to defend the duty to obey conscience against the objection that sometimes it is immoral to follow conscience. (Another way to defend the duty to obey conscience is to allow, with Mark Murphy, that sometimes one can both have a duty to do something and a duty to refrain from doing it.) It seems on the face of it that there are only two plausible views on which (*) comes out true. The first is (individual) relativism on which morality is defined by the dictates of one's conscience, which is thus infallible. The second is a version of disjunctivism according to which some beliefs about what one ought to do come from conscience and others come from merely apparent conscience, which are two distinct sources of moral belief (the second may actually be a mess of different sub-sources), with conscience being infallible. Unless the disjunctivism comes along with an infallible criterion for distinguishing the two sources, it's not going to be very useful in practice, since one then won't be able to tell if a given moral belief is a dictate of conscience or only seems to be so.

However, even if one rejects relativism and disjunctivism, (*) is not quite as absurd as it may seem. The main reason to reject (*) is due to counterexamples, but I am actually not able to come up with clear counterexamples against (*) once one takes into account Thomistic/Kantian insights about the importance of maxims to the individuation of action types. The maxim of an action is a description of the action which includes the end, means and reasons for the action; it is something from which it is clear why the action is done. Let's now try two apparent counterexamples to (*):

• Hauptsturmfuehrer Mueller believes he is obliged to kill Jews. But what is Mueller's actual maxim--what is the description under which the actions are seen as obligatory, and which explains why the action is being done by him? Mueller does not wish to kill Jews because the word "Juden" has five letters or because Jews are descendants of Abraham. He wishes to kill Jews because, let's say, he believes Jews are diabolical subhumans. If so, then the action he believes himself to be obliged to do is something like: kill Jews who are diabolical subhumans in order to improve the world. But now that we have attended to the maxim conscience commands Mueller to act under, we see that what he is commanded by conscience to do is impossible, but not actually immoral. If, per impossibile, there were a diabolical subhuman Jew killing whom would improve the world, to kill him would be permissible, indeed laudatory. But it is logically impossible for there to be such (since no subhuman can be Jewish, as only humans can be Jewish). Suppose, then, Mueller moved by his maxim kills a Jewish neighbor. Then, Mueller has indeed done something immoral. But he has not done what his conscience commanded. For his conscience commanded him to kill someone who is a diabolical subhuman, and in killing his neighbor he did no such thing, though he thought he did.
• Dr. Smith believes she should do non-consensual dangerous medical experiments on George for the greater good of humankind. The difference between the case of Smith and that of Mueller is that the hauptsturmfuehrer was acting from the basically correct moral principle that dangerous subhumans should be killed, a principle we affirm when we kill a tiger leaping at us, but was misapplying the principle. The ruthless doctor, however, is a utilitarian, and while her principle that the welfare of one may be sacrificed for the greater good of many is mistaken, her application of it is correct. However, I think a variant of the move made in the preceding case can be made here. Dr. Smith recognizes the fact that George loses out in the transaction. (If she doesn't, the case becomes very similar to that of Mueller.) Now she is acting in conscience. Thus she is not merely acting in a way that harms George because she doesn't care about George, the way an akratic agent might. Rather, she recognizes that she is harming George, but believes that the harm is justified by the greater benefit to humankind. If so, then the maxim is really something like this: do medical experiments on George whose danger to George is morally outweighed by the greater good of humankind. But once again, were the danger indeed morally outweighed by the greater good of humankind, Dr. Smith's actions would be right. But in fact the danger is not outweighed, because serious bodily harms to one person are not morally outweighed in the relevant sense by benefits to another (in the way in which an inconvenience might be morally outweighed by benefits to others; it would be perfectly fine for Dr. Smith to inconvenience George, say by making him wait for an appointment, while trying to find a cure for cancer), and so what Dr. Smith does in fact once again does not fall under her own maxim, even though she thinks she does. What conscience commands her to do is not immoral, though under the circumstances it may be impossible, and what she does is immoral, but is not what conscience commanded her.
  Objection: The maxim does not say that the danger to George is morally outweighed, but simply that it is outweighed in the utilitarian sense, in that the expected disutility to George is less than the expected utility to others.
  Response: Maybe. But if so, then Smith's real maxim will include the truth of utilitarianism--it will be something like: do medical experiments on George whose expected disutility to George is outweighed by the expected utility to others and thereby partially fulfill the duty to maximize total utility. And this maxim, once again, does not command something immoral, but something impossible, since it is impossible to partially fulfill the duty to maximize total utility since there is no such duty. Once again, what Smith does is immoral, but does not accord with her maxim.

It's also worth noting that the objection that this is not how Mueller and Smith explicitly formulate their maxim to themselves is beside the point. For as we can learn from Kant or Freud (or maybe Leibniz or Spinoza as well), we frequently do not know which motives we act on.

Now one might say that the above interpretations are somewhat strained. Maybe. But there is a good argument for thinking something like them is true. The argument goes as follows: if (*) is true, and both relativism and disjunctivism are false, then some such interpretation must be right. One might ask why we should believe (*). But there is very good reason to believe (*), namely the plausibility of the following argument:

1. It is always immoral to refrain from obeying conscience.
2. It is never immoral to refrain from doing something immoral.
3. Therefore, to obey conscience is never something immoral.

That said, I still need to bite the bullet in one respect if I accept this argument. The interpretations of maxims that I gave imply that sometimes conscience requires me to do something impossible, and hence that ought does not imply can. And there I do need to bite the bullet, after having softened it slightly by noting that although one can be obliged to do something impossible, one cannot be culpable for failing.

Let me end with a last objection. Can't we likewise say that it is a duty to try to follow conscience, and that Mueller and Smith are doing something obligatory which they succeed at, namely they really do try to follow conscience? But this generates a problem. For is not their trying to follow conscience the same action as their murder or medical experiments, so that the same action is obligatory and yet wrong? No! The action of trying to follow conscience starts before they start the immoral actions, since trying to follow conscience includes an attempt to discern which of the options before one is in accord with conscience, an attempt that fails.

Note 1: I am not claiming (*) is true, just that it is not as absurd it may seem.

Note 2: I think my suggestion is rather in the spirit of Spinoza's account in the Treatise on the Emendation of the Intellect of how all that we call error is just confusion. I am certainly not claiming that Spinoza is right about that, but that, too, is not quite as absurd as it seems.