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.

Treatment versus enhancement

I don't think you have much hope of having a distinction between treatment and enhancement unless you have the notion of the normal state or proper function of the human body. I previously thought we want a distinction between treatment and enhancement for such purposes as figuring out what the task of the physician as such is and what requests from the patient the physician has a right to turn down flat. For instance, a physician who receives a request to remove a cancer, and who judges that removal of the cancer is feasible, safe and ethically permissible, has a medical duty to either remove the cancer or refer to someone else. On the other hand, a physician who receives a request to pierce a patient's ears for earrings, even though she no doubt judges this to be feasible and ethically permissible, has no medical duty to perform the procedure or refer to someone else, since it is not a medical treatment.

But a new kind of case seems to me to make the distinction even more pressing, and this is cases where it is not possible to ask the patient's consent. Suppose that in the middle of heart surgery, the surgeon notices an old bullet lodged near the heart. The bullet does not impair the heart's functioning, so the patient's consent to the heart operation does not extend to the bullet. But it is intrinsically morally permissible for the surgeon to remove the bullet if she reasonably judges that doing so is good for the patient (of course, there may be laws and regulations that prohibit this, in which case it will be extrinsically impermissible). On the other hand, if a brain surgeon removing a cancer from someone's brain reasonably judges, on the basis of the latest research, that moving a few neurons around will make the subject super-fast at arithmetic with large numbers, that is unacceptable. Likewise, if in the course of a Caesarian the physician notes that the tubes could be tied and judges that the patient would be better off not getting pregnant, that too is unacceptable, whether or not consensual sterilization is permissible (this is, alas, not a hypothetical case).

One can try to handle this with "presumed consent", but that's kludgy, and probably doesn't work. Presumed consent from an unconscious suicidal patient for emergency treatment following the attempted suicide is going to involve dubious counterfactuals, like asking what the patient would want if the patient were fully sane (there might be no fact of the matter about this), and, besides, you probably can't make sense of "sane" without the concept of normalcy. Moreover, we can imagine cases where one can presume that the patient would consent if asked, but the action is still wrong. For instance, one may well know of many patients that they would agree to have a gift of diamonds worth millions sewed into them as a part of surgery, if they were going to be later notified and could have the diamonds safely removed through another surgery and if there was no other way for them to be given the diamonds. But to sew in the diamonds as part of heart surgery, without having sought the patient's consent, is morally impermissible--or at least it's bad medicine.

As in heaven so on earth

Here are some thoughts on St Matthew's version of the Lord's Prayer, many taken from or loosely inspired by things people said at our Department Bible study yesterday (though what I say should not be taken as representing anything like a consensus). First, my translation:

⁹Our father, who art in heaven:
    Thy name be sanctified,
    ¹⁰thy kingdom come,
    thy will come to pass,
        as in heaven so on earth.
    ¹¹Give us daily our supersubstantial [epiousion] bread.
    ¹²And forgive us our debts
        as we forgive our debtors.
    ¹³Do not bring us to a trial,
        but instead deliver us from the evil one [tou ponerou]. (Matthew 6:9-13)

The overall theme is that of the earthly and the heavenly, with the earthly being brought in conformity with the heavenly, by our own activity and that of our father. "As in heaven so on earth", I take it, applies to each: "thy name be sanctified", "thy kingdom come" and "thy will come to pass." Each of these three is simultaneously a request and a personal commitment to the indicated task, and in each case the act of praying is already partly constitutive of the prayed-for result: by praying these we sanctify our Father's name, make his kingdom present and do his will.

Implicit behind all three requests is an image of the majesty of God enthroned above the heavenly hosts who sanctify his name and bring his will to pass--and yet this King of the Universe is also our father.

The prayer is enveloped between the "father" (the first word in the Greek--while in Aramaic and Hebrew, "our father" would be one word) and "the evil one" at the end. This involves reading tou ponerou as "the evil one" (masculine) rather than as generically "evil" (neuter). This is supported the neatness of the resulting envelope structure, the central focus in the prayer on the beyond-earthly significance of our actions, as well as the implicit imagery of the angels of the heavenly host.

The central request is for our epiousios bread. We really don't know how to translate the word. A leading view is that it is the bread for the day to come. But it could also be the bread needed for our existence or ousia, the bread for the life to come, or, following St Jerome's Latin calque, the supersubstantial bread. In any case, the Church has traditionally taken a Eucharistic reading of the text, and such a reading makes the tendency of the earthly towards the heavens come to a head here: we sanctify his name and do his will just as the angels do, and here we boldly ask for the bread of angels, the new manna, the earthly bread made into the body of him who became flesh for us, the bread that is literally the Logos of God on which man lives (cf. Jesus' struggles with the evil one two chapters back in Matthew). At the same time, this reading should not rule out--and indeed the heavenly-earthly parallelism structure is very friendly to it--that this is also a request for what we need for our earthly lives from our heavenly royal father.

In verse 12, we have a switch from the positive to the negative aspects of transforming the earthly into the heavenly. The debt of our sin to God imposes on us an obligation we cannot pay and yet paying which is essential to the coming of his kingdom on earth. We boldly ask that it be forgiven, because (seemingly a non sequitur, but yet God in love for our children makes it follow) of our forgiving the debts of our debtors. It is neither good to be debtor nor creditor, and here by ceasing to be creditors we cease to be debtors. The forgiveness here is in the first instance a loosing or a release. The essential effect is normative, that the debtor is quit of the debt. Of course, when we forgive another, the essential effect is not all that we are called to: we are called to an affective component--we should feel as if the person who sinned against us is no longer in debt to us--and sometimes to a concrete reaching out to heal the relationship. Likewise, God's forgiveness heals us, and gives us the grace to avoid incurring further indebtedness, as indicated by the next verse.

The trials of verse 13 may well include ordinary temptations, but it is also plausible that the text is specifically talking of the trials of persecution and torture. We pray that our father not bring us there, and at the same time we should not deliberately take ourselves there either (there is the scary story in Eusebius about the early Christian who from bravado turned himself in to the Romans--and then broke down and apostasized). Finally, we are reminded that we do not struggle against mere flesh and blood, but that persecutions and temptations are the work of infernal intelligence, like the devil that Jesus fought two chapters back.

48 arguments against naturalism

Consider this argument:

1. A desire to be morally perfect is morally required for humans.
2. If naturalism is correct, a desire to be morally perfect cannot be fulfilled for humans.
3. If a desire cannot be fulfilled for humans, it is not morally required for humans.
4. Therefore, naturalism is not correct.

This argument provides a schema for a family of arguments. One obtains different members of the family by replacing or disambiguating the underlined terms in different ways.

If one disambiguates "naturalism" as physicalism (reductive or not), one gets an argument against physicalism (reductive or not). If one disambiguates "naturalism" in the Plantinga way as the claim that there is no God or anybody like God, one gets an argument for theism or something like it. Below I will assume the first disambiguation, though I think some versions of the schema will have significant plausibility on the Plantingan disambiguation.

One can replace "morally required" by such terms as "normal", "non-abnormal" or "required for moral perfection".

One can replace "to be morally perfect" by "for a perfect friendship", "to be perfectly happy" or "to know with certainty the basic truths about the nature of reality" or "to know with certainty the basic truths about ethics" or "to have virtue that cannot be lost". While (1) as it stands is quite plausible, with some of these replacements the requiredness versions of (1) become less plausible, but the "non-abnormal" version is still plausible.

Probably the hardest decision is how to understand the "cannot". The weaker the sense of "cannot", the easier it is for (2) to hold but the harder it is for (3) to hold. Thus, if we take "cannot" to indicate logical impossibility, (2) becomes fairly implausible, but (3) is very plausible as above.

I would recommend two options. The first is that the "cannot" indicate causal impossibility. In this case, (3) is very plausible. And (2) has some plausibility for "moral perfection" and all its replacements. For instance, it is plausible that if naturalism is true, certain knowledge of the basic truths about the nature of reality or about ethics is just not causally available. If, further, moral perfection requires certainty about the basic truths of ethics (we might read these as at the normative level for this argument), then moral perfection is something we cannot have. And if we cannot have moral perfection, plausibly we cannot have perfect friendship either. Likewise, if naturalism is true, virtue can always be lost due to some quantum blip in the brain, and if moral perfection requires virtue that cannot be lost, then moral perfection is also unattainable. And perfect happiness requires certain knowledge of its not being such as can be lost. Maybe, though, one could try to argue that moral perfection is compatible with the possibility of losing virtue as long as the loss itself is not originated from within one's character. But in fact if naturalism is true, it is always causally possible to have the loss of virtue originate from within one's character, say because misleading evidence could come up that convinces one that torture is beneficial to people, which then leads to one conscientiously striving to become cruel.

The second option is that the "cannot" is a loosey-goosey "not really possible", weaker than causal impossibility by not counting as possible things that are so extraordinarily unlikely that we wouldn't expect them to happen over the history of humankind. Thus, in this sense, I "cannot" sprout wings, though it seems to be causally possible for my wavefunction to collapse into a state that contains wings. Premise (2) is now even more plausible, including for all the substituents, while premise (3) still has some plausibility, especially where we stick to the "morally required" or "required for moral perfection", and make the desire be a desire for moral perfection.

If I am counting correctly, if we keep "naturalism" of the non-Plantingan sort, but allow all the other variations in the argument, we get 48 arguments against naturalism, though not all independent. Or we can disjoin the conjunctions of the premises, and get an argument with one premise that is a disjunction of 48 conjunctions of three premises. :-)

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.

Attitudes to risk and the law of large numbers

People do things that seem to be irrational in respect of maximizing expected utilities. For instance, art collectors buy insurance, even though it seems that the expected payoff of buying insurance is negative—or else the insurance company wouldn't be selling it (some cases of insurance can be handled by distinguishing utilities from dollar amounts, as I do here, but I am inclined to think luxury items like art are not a case like that). Likewise, people buy lottery tickets, and choose the "wrong" option in the Allais Paradox.

Now, there are all sorts of clever decision-theoretic ways of modeling these phenomena and coming up with variations on utility-maximization that handle them. But rather than doing that I want to say something else about these cases.

Why is it good to maximize expected utilities in our choices (and let's bracket all deontic constraints here—let's suppose that none of the choices are deontically significant)? Well, a standard and plausible justification involves the Law of Large Numbers [LLN] (I actually wonder if we shouldn't be using the Central Limit Theorem instead—that might even strengthen the point I am going to make). Suppose you choose between option A and option B in a large number of independent trials. Then, on moderate assumptions on A and B, the LLN applies and says that if the number of trials N is large, probably the payoff for choosing A each time will be relatively close to NE[A] and the payoff for choosing B each time will be relatively close to NE[B], where E[A] and E[B] are the expected utilities of A and B, respectively. And so if E[A]>E[B], you will probably do better in the long run by choosing A rather than by choosing B, and you can (on moderate assumptions on A and B, again) make the probability that you will do better by choosing A as high as you like by making the number of trials large.

But here's the thing. My earthly life is finite (and I have no idea how decision theory is going to apply in the next life). I am not going to have an infinite number of trials. So how well this LLN-based argument works depends on how fast the convergence of observed average payoff to the statistically expected payoff in the LLN is. If the convergence is too slow relative to the expected number of A/B-type choices in my life, the argument is irrelevant. But now here's the kicker. The rate of convergence in the LLN depends on the shape of the distributions of A and B, and does so in such a way that the lop-sided distributions involved in the problems mentioned in the first paragraph of the paper are going to give particularly slow convergence. In other words, the standard LLN-based argument for expected utility maximization applies poorly precisely to the sorts of cases where people don't go for expected utility maximization.

That said, I don't actually think this cuts it as a justification of people's attitudes towards things like lotteries and insurance. Here is why. Take the case of lotteries. With a small number of repetitions, the observed average payoff of playing the lottery will likely be rather smaller than the expected value of the payoff, because the expected value of the payoff depends on winning, and probably you won't win with a small number of repetitions. So taking into account the deviation from the LLN actually disfavors playing the lottery. The same goes for insurance and Allais: taking into account the deviation from the LLN should, if anything, tell against insuring and choosing the "wrong" gamble in Allais.

Maybe there is a more complex explanation--but not justification--here. Maybe people sense (consciously or not—there might be some evolutionary mechanism here) that these cases don't play nice with the LLN, and so they don't do expected utility maximization, but do something heuristic, and the heuristic fails.

The human battery: Fun experiments to do with kids

Here's a fun set of experiments to do with kids. You need two pennies, two nickels and a voltmeter that can show voltages of the order of 10-50 millivolts. I used this cheap one. Probes with alligator clips make the experiments easier (I bought some alligator clips in Walmart's automotive section and soldered them on probes from an old multimeter), but you can do it with straight probes, too (in that case, replace "attach the probes" should be replaced with "touch the probes").

Experiment 1: Attach the probes to a penny and a nickel, respectively. Set the voltmeter to a scale that will show things of the order 10-50 mV (I used a 2000 mV scale). Have a volunteer hold the penny in one hand and nickel in the other. Measure the voltage. Ideally, the probes should be touching the coins, not the hands. I was getting about 15-35 mV, depending on which kid was holding the coins. If you're not getting much, maybe moisten the volunteers' hands. Then vary the coin combinations.

Experiment 2: Attach the probes to a penny and a nickel, respectively. Get two volunteers, and have each hold one of the coins. Make sure the volunteers aren't touching. Measure the voltage. Should be zero or very low (if the floor is conducting a bit). Now have them hold hands. There should be a very gratifying jump in voltage from this hand-holding switch! Note the voltage (it may take a while for it to stabilize).

Experiment 3: Set it up like for Experiment 2, but instead of having the volunteers hold hands, have the volunteer who is holding the penny hold out the other hand, palm up and outstretched. Put a nickel and a penny on that palm, with the nickel above, in such a way that the penny doesn't touch the skin (so don't put them in the middle of the palm, but maybe more on the heel; or maybe use a quarter instead of the nickel). Then instead of having the volunteers hold hands, have the second volunteer--the one holding the nickel--press a thumb from the free hand onto the penny that is on top of the nickel, being careful to make sure the penny doesn't make contact with the first volunteer's skin. Compare the voltage to that in Experiments 1 and 2. You've now got a two-cell human battery!

There are lots of fun variables to vary. Change the size of the volunteers. Wet or dry hands. See if drinking a lot makes a difference. See if temperature makes a difference (indoor vs. outdoor, say).

You can also do this, which I haven't tried, but it should work. What I did try, though, was this (though I used lime juice), which very gratifyingly powered an LED. When it went out, adding more lime juice turned it back on.

The genre of the universe

You get a book, with the title page and covers missing, and you start to read. After a while, you realize it's a book of fiction. Some time later, you realize it's a book of science fiction. Then you realize it's a book of hard science fiction. The more you learn about the genre of the book, the better you can make predictions about what is to come in the book. Prior to learning it's a book of science fiction, you thought you could make inferences based on the present limits of technology, but after you learned that it was science fiction, these inferences became bad. And once you've learned that it's hard science fiction, you become able to make inferences on the basis of most if not all of the laws of nature that we know of.

The physical universe is God's book. It took us a while—namely, until around the late middle ages—to figure out the genre, namely that the genre is deeply mathematical. Once we figured out the genre, it became very easy to make fast progress understanding the book and making predictions.

A good work of art tends to have a deep unity of genre in it (which is compatible with all sorts of complexity). There is, thus, good reason to suppose that once we've identified the genre of the parts of the work we have seen, something generically similar will follow.

Modern science, thus, grasped an important aspect of God's artistic plan for the universe, as in Galileo's remark about the book of nature being written in the language of mathematics. It is a difficult question whether the practice of science can rationally stand without such theistic underpinnings.

Stupidity, triteness and immorality

I suspect that many philosophers would rather have their work be criticized as being morally perverse than as being stupid or merely tritely repeating unoriginal claims from the literature. At least, I find myself with feelings like that. Does this preference expose a deep vice in me?

I am not sure. It may simply be that I trust other philosophers' judgment as to what is stupid or in the literature more than I trust their moral judgment. At least, if the moral perversity criticism came from one of the philosophers whose moral judgment I really trusted, the judgment would worry me a lot more. But I am not sure it would still worry me as much as a judgment of stupidity or unoriginality from someone of comparable epistemic authority.

Universal love

Love contains three aspects: appreciation, benevolence and a striving for union. Suppose that we are supposed to love all human beings. In a secular context, each of the three aspects of love threatens to make the love in many cases rather anemic. It is only in a context like that of Judaeo-Christian theology that one can have a love that is both rich and universal. For let's consider the aspects severally.

Appreciation: Unless we have some picture of the human being as in the image and likeness of God, it is difficult to see that much to appreciate in a Mengele. This can perhaps be overcome if one has a robust enough notion of human nature, though perhaps that is just bringing in the image and likeness of God in a hidden way.

Benevolence: It is possible to will the good to all, as this involves a merely dispositional property. But a merely dispositional beneficence is an anemic sort of benevolence. In a religious context, however, the benevolence can act as a genuine beneficence through prayer and something like the communion of the saints.

Unitiveness: While appreciation and benevolence by themselves imply a kind of union, love's striving for union goes beyond these. But in a secular context one can't really go much beyond these in many cases. First, there is the problem of those who appear completely morally corrupt, with whom a further union would be morally problematic. In a religious context, however, the striving for union connects with eschatology. Every individual human on earth is someone with whom we can strive for eternal union in heaven (even if we believe that we won't achieve this union in every case). Second, and even more seriously, there is the problem of the billions of people with whom we simply cannot have a deeper union, because life is too short and their lives do not intersect our lives enough (for a more radical case, one might cite people in the distant past or distant future!) Again, this is overcome in a religious context, often by a potential for liturgical union—in liturgy, we are importantly united with people all over the world participating in the same liturgy—and always by a striving for a union in heaven that is prefigured by the liturgical union.

An interesting question is how the unitiveness will be realized in heaven between those who are in heaven and those who are in hell. I think here there is a kind of liturgical union, in that both those who are in heaven and those who are in hell are united in praise of God: those in heaven deliberately and explicitly so, while those in hell praise God by the value of their existence and the divine justice they exemplify. This is probably a hard saying.

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If the above is right, then the duty of universal love can only fully come into its own in a religious context.

Leibniz, bodies and phenomena

Leibniz tells us that bodies are phenomena. He also tells us that phenomena are modes of monads. Now, the modes of monads are appetites and perceptions. But appetites and perceptions are identity-dependent on the monad that they are appetites and perceptions of. Your appetite or perception may be very much like mine, but it is numerically distinct from mine. But this seems to imply that the moon you see and the moon I see are numerically distinct. For the moon you see is a mode of you, and hence identity-dependent on you, while the moon I see is a mode of me, and hence not numerically distinct with the moon that is identity-dependent on you.

Something must go. The identity dependence of modes on the monad is central to Leibniz's argument against inter-modal causation: he insists that the same mode cannot have a leg in each of two monads. My suggestion is that what Leibniz should say, and maybe what he really thinks, is that real phenomena, like the moon, aren't modes of monads in the narrow sense that implies identity dependence, but are grounded in monads, and in that sense are modes of monads in the broad sense. Consider "the committee's opinion." This is grounded in the committee members' minds, but it is not identity-dependent on any one committee member: individual committee members can change their view while the committee is still "of the same mind."

Here is one way to make this go. The moon is a phenomenon and it has a two-fold ground. One part of the ground are monads having "lunar perceivings", like the one I had last night when looking through the telescope, and like the one I am now, according to Leibniz, unconsciously having. But the moon isn't just a lunar perceivings, because your lunar perceiving is distinct from my lunar perceiving. The other part of the ground is what unifies the lunar perceivings in different monads, and that is the monads that are elements (in Robert Adams' phraseology) of the moon. Your lunar perceiving represents the same lunar monads as my lunar perceiving does.

For Leibniz, as for Aristotle, being and unity are interchangeable. To have being, bodies need a source of unity. On this reading, there are two sources of unity in the moon: first, the perception of a monad, say you or me, unifies the many lunar monads that are being perceived; second, the lunar monads unify the perceptions of the many monads. There is no vicious circularity here.

This significantly qualifies Leibniz's alleged idealism. It sounds idealist to say that bodies are phenomena. But they aren't just any phenomena, they are "well founded" phenomena (to use Leibniz's phrase), and a part of what constitutes them into the self-identical phenomena that they are is the monads that are appearing in the appearance.

The above brings together ideas I got from at least two of our graduate students. Another move suggested by one of them is to take the unification of the lunar perceivings to happen through the complete individual concept of the moon which is confusedly found in all of the lunar perceivings. I think this, too, is a possible reading of Leibniz, but I think it makes for poorer philosophy, since I don't think there is any complete individual concept of the moon found in all lunar perceivings, except in the way that the concepts of causes are, by essentiality of origins, found in the effects.

When should you adopt an expert's opinion over your own?

Consider two different methods for what to do with the opinion of someone more expert than yourself, on a matter where both you and the expert have an opinion.

Adopt: When the expert's opinion differs from yours, adopt the expert's opinion.

Caution: When the expert's opinion differs from yours, suspend judgment.

To model the situation, we need to assign some epistemic utilities.  The following are reasonable given that the disvalue of a false opinion is significantly worse than the value of a true belief, at least by a factor of ~2.346 in the case of confidence level 0.95, according to the hate-love ratio inequality.

• Utility of having a true opinion: +1
• Utility of having a false opinion: approximately -2.346
• Utility of suspending judgment: 0

Given these epistemic utilities, we can do some quick calculations.  Suppose for simplicity that you're perfect at identifying the expert as an expert (surprisingly, replacing this by a 0.95 confidence level makes almost no difference).  Suppose the expert's level of expertise is 0.95, i.e., the expert has probability 0.95 of getting the right answer.  Then it turns out that Adopt is the better method when your level of expertise is below 0.89, while Caution is the better method when your level of expertise is above 0.89.  Approximately speaking, Adopt is the better method when you're more than about twice as likely to be wrong as the expert; otherwise, Caution is the better method.

In general, Adopt is the better method when your level of expertise is less than e/(D-e(D-1)), where e is the expert's level of expertise and D is the disutility of having a false opinion (which should be at least 2.346 for opinions at confidence level 0.95).  If your level of expertise is higher than that, Caution is the better method.

Here is a graph (from Wolfram Alpha) of the level of expertise you need to have (y-axis), versus the expert's level of expertise (x-axis), in order for adopting Caution rather than Adopt to be epistemic-decision-theory rational, where D=2.346.

Here is a further interesting result. If you set the utility of a false opinion to -1, which makes things more symmetric but leads to an improper scoring rule (with undesirable results like here), then it turns out that Adopt is better than Caution whenever your level of expertise is lower than the expert's. But for any utility of false opinion that's smaller than -1, it will be better to adopt Caution when the gap in level of expertise is sufficiently small.
If you want to play with this stuff, I have a Derive worksheet with this. But I suspect that there aren't many Derive users any more.