Cheapo Kerfing Plane

I might have to resaw some wood (cut it in half along the widest part) for a project this summer, and a useful tool for preparing a board for resawing is a kerfing plane (a.k.a. kerfing saw, a.k.a. rabbet saw, a.k.a. rebate saw…), which cuts ridges in the wood that guide the actual sawing. I don’t have a kerfing plane, or the money to spend on one or even the parts for one (or on an actual tool for resawing). What I do have is an old dovetail saw I got from my in-laws’ basement, some scrap wood I found on the side of the road, and a C-clamp. So I made this cheapo version, which to my untrained eye seems to do the job OK.

There are two pieces of wood, which are glued together (in this case were already glued together when I found them). The outer piece is the fence, which presses on the edge of the workpiece and keeps the saw cutting a straight line, just like a fence for any electric saw. The inner piece is the spacer; the width of the spacer determines how far the cut is from the edge of the workpiece, and the placement of the saw in relation to the spacer determines how deep the cut can go. Everything is held together by a C-clamp. It’s a bit of a juggling act to set up, but it does the job. I set it to cut a 1/8inch deep cut across a salvaged 2×4 and that’s exactly what it did. Bear in mind I’ve never done this before, so I could be completely wrong about the whole thing.

(There’s a hole in the fence because there was a hole in the fence when I found it.)



God, the Intelligible Sphere

The famous but enigmatic definition of God as “an infinite sphere whose center is everywhere and circumference nowhere” comes from the Book of Twenty-Four Philosophers, attested in the 12th century. You can find the text and explanation here (“Rule II”), though the explanation doesn’t shed as much light as you might like on what the definition means.

Alan of Lille, another 12th-century author, gives this explanation of the definition (with one change in wording), which I translate here in case anyone on the Internet would find it helpful (this is from his Theologicae Regulae, Rule VII, text from Migne, p. 627).

God is an intelligible sphere, whose center is everywhere and circumference nowhere. The rule above (“Only the Monad is Alpha and Omega”) proves this. For insofar as God lacks a beginning and end, he is referred to as a sphere; for it is a property of the spherical shape that it lack a beginning and end.

But he is not a bodily sphere, but an intelligible sphere. For when we call God a sphere, we ought not go down the path of imagination, so as to imagine him as a sphere in the likeness of physical bodies. But, led by the intelligence, by that definition we understand God himself to be a sphere because he is eternal. Thus, according to Martianus Capella, a crown [diadema] refers to possessing eternity, since it signifies the lack of a beginning or end. Thus the lack of a beginning and end is called a crown [diadema]- a “double-lack” [duo demens], as it were.

Then we have: …whose center is everywhere and circumference nowhere. O great difference between bodily and intelligible spheres! The center of a bodily sphere can hardly be said to be anywhere at all, it’s so miniscule, while its circumference is understood to occupy several points. But the center of the Intelligible Sohere is everywhere, and its circumference nowhere. “Center” refers to creation, for just as Time is considered but a moment in comparison with Eternity, so the creature compared to the immensity of God is but a point or center[1]. Therefore God’s immensity is referred to as his circumference, since by ordering all things, he in a certain sense surrounds all things, and everything is embraced under his immensity.

There’s also this other difference between the bodily and intelligible spheres: bodily spheres have an immobile center and mobile circumference[2]. But it’s the opposite for the intelligible sphere: God, remaining stable, gives motion to everything else.

[1] cf. Bonaventure, Itinerarium 6.2.

[2] As in the heavenly spheres, the orbits of the planets.

Deus est spaera intelligibilis, cujus centrum ubique, circumferentia nusquam. Hanc probat illa regula, qua dictum est, solam monadem esse alpha et omega: ex eo enim quod principio caret, et fine Deus, spaera dicitur: proprium enim spaericae formae est principio et fine carere.

Sed non est spaera corporalis, imo intelligibilis. Cum enim Deum spaeram esse dicimus, non oportet nos deduci ad imaginationes, ut imaginemur eum esse spaeram ad similitudinem corporum; sed, duce intelligentia, ea ratione intelligamus ipsum Deum esse spaeram quia aeternus est. Unde apud Martianum diadema dicitur aeternitas habere, quia principio et fine carere significatur. Unde carentia principii et finis diadema, quasi duo demens, id est principium et finem, apellatur.

Sequitur: cujus centrum ubique, circumferentia nusquam. O magna inter spaeram corporalem, et intelligibilem differentia! In spaera corporali centrum propter sui parvitatem vix alicubi esse perpenditur, circumferentia vero in pluribus locis esse comprehenditur. In intelligibili vero spaera centrum ubique, circumferentia nusquam. Centrum dicitur craetura, quia sicut tempus collatum aeternitati reputatur momentum, sic creatura immensitati Dei comparata, punctum, vel centrum. Immensitas ergo Dei circumferentia dicitur, quia omnia disponendo quodam modo omnipus circumfertur, et omnia infra suam immensitatem complectitur.

Haec etiam alia differentia inter spaeram corporalem, et intelligibilem, quia spaerae corporales centrum immobile, circumferentia mobilis; in spaera intelligibili contra, quia Deus stabiles manens dat cuncta moveri.



William on Ransom Theory

Another concise argument from William, this time theological, criticizing the ransom theory of atonement while preserving the truth in it:

Dominus redemit nos a diabolo; ergo per pretium datum diabolo, et dedit se pretium; ergo dedit se diabolo.

[The ‘Ransom’ argument.] “God redeemed us from the Devil. Therefore, [He redeemed us] at a cost paid to the Devil. And He gave Himself as the cost. Therefore, He gave Himself to the Devil.”

Hec argumentatio non valet: ‘Dominus redemit nos per pretium datum diabolo; ergo dedit pretium diabolo’. Et est ibi fallacia secundum consequens, quia fit ibi processus a superiori ad inferius affirmando, quia redimere pretio dato superius est ad dare pretium diabolo, quoniam diabolus detinuit homines in carcere tanquam custos. Custodi autem carceris non solvitur pretium, sed domino carceris. Deus enim est dominus inferni; et ita pretium illud erat dandum et reddendum Deo Patri.

[William’s reply.] “This argument is invalid…It commits the fallacy of [affirming] the consequent, since it proceeds by affirmation from the higher to the lower [i.e., from the general to the specific]. For redeeming at a given cost is higher [i.e. more general] than giving the price to the Devil, since the Devil detained men in prison as a jailkeeper. But you don’t pay bail to the jailkeeper, but to the master of the prison. For God is Master of Hell, and so the price was to be given and repaid to God the Father.”

First, William disputes the validity of the argument. I think the fallacy William is identifying is assuming that “redeemed from the Devil” must mean “redeemed by paying the Devil,” when that’s only one possible interpretation. So “affirmation from the higher to the lower” means “inferring a specific claim from a more general claim,” which is fallacious. He calls it an instance of  “the fallacy of the consequent,” and I think he has in mind reasoning like this:

  1. If God redeemed us by paying the Devil (specific claim), He redeemed us from the Devil (general claim).
  2. God redeemed us from the Devil.
  3. Therefore, God redeemed us by paying the Devil.

Which is obviously fallacious. So given that God redeemed humanity from the Devil, it doesn’t follow that God ransomed humanity from the Devil.

(I don’t think the part of the argument William quotes commits this fallacy, though. Maybe he just put it there as a placeholder.)

Second, William gives us a reason to doubt that the “ransom” interpretation is the correct one: we’re only under the devil’s power because God put us there as a punishment for our sins. Christ did redeem us from the Devil; but He did so by paying God, not the Devil. We really did give ourselves over to the Devil, but as our jailkeeper, not our owner. The fact that Christ’s death redeemed us from the Devil is not sufficient reason to think that Christ’s death was an atonement paid to the Devil, and not to God. On the other hand, the fact that the atonement was a debt paid to God doesn’t mean that Christ’s death didn’t free us from the dominion of the Devil.


Liar, Lunatic… Philosopher?

C.S. Lewis’ “Trilemma” (or “Liar, Lunatic, Lord” argument) is a familiar argument in Christian apologetics. Lewis didn’t actually originate it, but here’s how he puts it:

“A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic — on the level with the man who says he is a poached egg — or else he would be the Devil of Hell. You must make your choice.” (Mere Christianity)

The argument is basically this:

1. Jesus claimed to be God.
2. Someone who claimed to be God is either a liar, insane, or actually God.
3. If Jesus is a liar or insane, he can’t be a great moral teacher.
4. If Jesus is God, he is not merely a great moral teacher.
5. Therefore, either Jesus is God, or he is not a great moral teacher.

Sometimes this gets expanded into an outright argument for Christ’s divinity (I think G.K. Chesterton made this argument in The Everlasting Man):

6. Jesus displays profound moral integrity, so he’s not a liar.
7. Jesus seems to be mentally stable, so he’s not insane.
8. Therefore, Jesus is God.

It’s not a decisive argument, but it’s a pretty good one. But what interests me today is that a similar argument could be applied to Scorates’ claim to have a daimonion (not a demon, but a benevolent spirit) that spoke to him whenever he was about to do something he shouldn’t do:

1. Socrates claimed that a spirit regularly spoke to him.
2. Someone who claims that a spirit regularly speaks to him is either a liar, insane, or telling the truth.
3. Socrates displays profound moral integrity, so he’s not a liar.
4. Socrates seems to be mentally stable, so he’s not insane.
5. Therefore, Socrates was telling the truth about a spirit speaking to him.

Like Jesus, Socrates was certainly a very odd person- but he doesn’t seem mentally ill. And like Jesus, he wasn’t above using figurative language when he felt people were intellectually beneath him or not willing to follow his argument. But also like Jesus, it’s usually very clear when he’s using metaphors and when he’s being gravely serious, and what he says about the daimonion appears to fall into the latter category (especially since, unlike Jesus’ claim to divinity, his claim to have a guardian spirit probably wasn’t too unbelievable in his time). On the other hand, an isolated delusion of a spirit speaking to you in an otherwise stable personality is a little more believable than an isolated delusion that you’re, you know, the Lord God, in an otherwise stable personality. So I think our best conclusion is either that Socrates had a very specific, recurring delusion but was otherwise fine (seems unlikely to me, but possible), or that he actually had some kind of contact with a spirit.

You could make a further argument for the latter conclusion based on the fact that the daimonion seems to have actually guided him pretty well (until the very end… and there’s your counterargument).

How to process this as a Christian, I don’t know. The daimon could have been a demon, sweet-talking Socrates until it found a way to lead him to his death. Or it could have been an angel (who knows what an angel was doing in ancient Greece, but it’s not impossible). Or maybe there are other kinds of spirits. I don’t know! I’m just following the argument where it leads.


Against Extreme Divine Command Theory

William of Auxerre gives this brief but effective argument against the theory that actions are evil merely because God prohibits them:

Cum prohibitio sit ipse Deus prohibens, Deus ipse esset causa malitie in actione; quod absit.

“Since God’s prohibition [of an action] is just God himself prohibiting [the action], God Himself would be the cause of the evil in an action; which can’t be allowed.”

(Summa Aurea Book 2, Treatise 11, Chapter 3, Question 3)


A Set of Impossible Worlds?

Is it true to say (A) “Aragorn was at one point king of Gondor and Arnor” and false to say (-A) “Aragorn was at no point king of Gondor and Arnor?” My instinct is to say Yes, but if these are statements about the real world, the opposite is true, since Aragorn never existed.

We could say: For a culturally competent English speaker, the question assumes that we’re asking about some definite possible world w. In w, A is true and -A is false, while in the actual world -A is true and A is false.

But is there some possible world in which Aragorn is king of Gondor and Arnor? My first instinct is to say Yes, the world portrayed in the Lord of the Rings. Call it Middle-Earth.

But is Middle Earth a single world? Tolkien is famous for his many, many versions of Middle-Earth, in many of which Aragorn becomes King of Gondor and Arnor. So maybe Middle-Earth is a set of possible worlds.

But are those possible worlds even possible? For one thing, some (or all?) versions of Tolkien’s mythology have internal inconsistencies, so they are not possible worlds. And even the ones that don’t (if any) might be impossible for some logical or metaphysical reason that we don’t now understand: they might only appear possible to us.

Let’s bite the bullet and say that none of the possible worlds in the set “Middle Earth” could ever have existed- they’re just not logically possible. Suppose further that any possible world in which A is true, if there is one, would be contained in the set “Middle Earth.” It follows that there are no possible worlds in which A is true.

And yet…

-The statement “Aragorn was at one point king of Gondor and Arnor” is still true, but it’s true of an impossible world.

-When I say, “Aragorn was at one point king of Gondor and Arnor,” I’m not just saying that it’s possible for someone named Aragorn to be king of two kingdoms called Gondor and Arnor. That’s either true but boring or false for reasons I can’t understand. I’m successfully referring to an impossible individual (and when I say, “Frodo was never king of Gondor and Arnor,” I’m referring to another impossible individual and distinguishing him from the first).

-The set “Middle Earth” seems to be a set of impossible worlds, but not therefore an empty set of worlds, because I can state true facts about those worlds (“Aragorn was at one point king of Gondor and Arnor”), and I can distinguish between them (for example, I can distinguish the possible world in which the Ringbearer is named Frodo and the one in which he is named Bingo).

-All of this only works if the principle of explosion is false.


Star Trek and Religion

I realized recently that out of the five Star Trek series, the majority have religious first officers.

Original Series – Spock doesn’t talk about religion and probably wasn’t meant to have a religion at the time of writing. But later on Vulcans are definitely portrayed as religious, albeit in a very un-Judeo-Christian way (e.g., Tuvok). Seeing as Spock is pretty keen on being as Vulcan as possible, we can safely assume that he was religious.

Next Generation – To my knowledge Will Riker had no religion, but I could be wrong.

Deep Space Nine – Entire episodes revolve around Kira Nerys’ religious beliefs.

Voyager – Chakotay’s generic but genuine Native American spirituality is sympathetically portrayed, though the writers seem to have completely forgotten about it halfway through the show.

Enterprise – T’Pol is Vulcan, and is portrayed as engaging in spiritual practices to a greater degree than Spock.

So that’s four out of five, or three out of five if we don’t count Spock; in any case a majority. If we do count Spock, Riker is the lone secular exception. If we cheat and count Spock twice because of the Animated Series, that’s five out of six.

There’s also an interesting mix of beliefs- polytheism, ancestor veneration, nontheistic philosophical mysticism. The lack of monotheism is notable, though Bajoran religion is obviously imitative of the Abrahamic faiths.

Of course, other than Ben Sisko (sort of), we have zero religious captains. Kirk expresses belief in God, but he might have been rhetorical or sarcastic.