On the Tower of Babel


And they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth.

And the Lord came down to see the city and the tower, which the children of men builded.

And the Lord said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do.

Gen. 11

“To reach for heaven” adopts the Jewish custom of replacing “heaven” for the name “God”. Since these people are coming off the memory of the great flood their motive is to use technology to escape the consequences of divine judgment. As we’d put it, they’ll science themselves out of their (moral and religious) problems.

“Let us make a name for ourselves” plays on the scriptural idiom of “making a name” which is a properly divine act (cf. Genesis 12: 2, 2. Samuel,  1 Chronicles 17: 21, Zephaniah 3: 20). The sense is therefore that we will constitute ourselves as a people and set our own destiny apart from, and even in opposition to a divine action.

Both of these are only means to avoid being scattered over all the earth, which is an admirable goal that is even recognized as a divine act.  The ur-thought motivating this whole tower episode is the builders seeing that the unity of the whole world is a divine act. To achieve it by themselves, the builders know they must appropriate divine power for themselves.

God’s response to the project is two-sided. On the one hand, as many commentators point out, God has to “come down” in order to see the tower, IOW, any attempt to build to the heavens falls laughably short. On the other hand, God describes the danger in the unity of all persons as their unlimited growth in power, and so even if all human self-appropriations of divine power fall infinitely short of the genuine article they can nevertheless extend without limit.

As the myth describes, human power extends without limit through the hands, the imagination, and above all in speech. Our skill in building and making things suggests infinite power to the imagination,  and we proceed to make ourselves divine beings within the world created by speech. Some things really do exist within speech, above all political order and its possibility of extending indefinitely. If everyone imagines and says you are king, it does not follow that you are an imaginary king existing only in speech. This is the sense of the unity in speech, together with some technological skill* as giving rise to as sense that humanity can achieve the divine act of unifying all nations.

Nevertheless, human words can’t speak things into existence, and even if real political power arises from opinion, opinion as such need not rest on anything, and the attempt to make a name for ourselves is just this sort of substanceless opinion.

*In Genesis 11, this consists in advanced brick-making and building materials technology referenced in v. 3 


Will in knowledge

Part of extending knowledge beyond a certain point requires getting the will involved in the object of knowing. In things below us, our appropriate stance is of domination and control of the object, and so the dialectical extension of knowledge of what is beneath us uses operational definitions, experiments, imaginative models, etc. In things that are not beneath us the appropriate stance can never be domination but is an act of love.

Remedies for oppression

Say  that Eighth grade class B is underperforming and failing to get into High School, and everyone knows that a big part of the problem is that High School admissions boards have irrational prejudices against the letter B. You could do a lot of things, but you choose the following two-prong approach:

1.) You increase high school access to all members of class B.

2.) To combat the irrational prejudice against class B, you include lots of pictures of persons from that class in your High School promotional literature, proving that members from that group can succeed and making it clear to everyone that you strongly reject the irrational prejudice against them.

Assume the upsides of your approach are evident. What are the dangers?

The main danger is that by increasing access you will not do anything to help class B as a class but only increase the representation by the outliers of the group. The oppression of class B is a statistical cluster, and merely picking off the outliers from the group is carries at least three dangers:

1.) None of the systemic problems of the group are being addressed. Picking off outliers from a group not only leaves the statistical cluster unaffected, it will intensify it.

2.) The outliers of the group will tend to be the most talented, industrious, charismatic, attractive, etc. In other words, they are exactly the sort of persons that could be of greatest service to the group were they to stay within it. By separating them from the group we predict a brain drain and an absence of those who could have led the group to better itself if our policy pursued real empowerment.

3.)   We delude ourselves into thinking we are making real change when in fact we are strengthening dominant culture with the window-dressing of oppressed culture. The efforts we think are extending equality are in fact exaggerating divisions between groups.





Notes. 3.14.

-Image and likeness. If you can point to a map and say “This is Russia” you can point to a soul and say “This is God”.

-Before the Sixteenth Century we would not have expected anyone to relate to a text as their own. Texts took up to a year to copy and cost as much as a farm, and so could only be corporately owned. We’d no more expect a privately owned text than we would now expect a privately owned aircraft carrier or cell phone network. So of course the Bible was owned by a corporation and not an individual, and therefore at the disposal of a corporate body and its high-level agents and not any unaffiliated individual believer.

If some technology made cell phone networks much cheaper then I suppose future historians could look back at our time as the dark ages when a small corporate board controlled everyone’s ability to talk to each other and “kept the network to themselves”, or as the time before we had separated corporation and communication, but it doesn’t seem like a particularly illuminating way to describe life as I experience it.

The moral problem is unanswered. Say technology makes X able to be owned by anyone. Whether this is a wise move will depend on the X – Is it health care? Networks? Race cars? Atomic weapons?

-The Reformation and its Catholic response is therefore also a technological problem. Like all such problems it tends to be treated as self-justifying or at least inevitable. Why is technological power greeted with a sense of moral powerlessness?


“Like us in all things except sin”

The phrase isn’t understood until we hear it almost as a joke.

Nothing counts as a sin unless it is an abuse of human life and a squandering of properly human talents. Sin is to being human what sabotaging cars is to mechanical skill or torturing people is to surgical skill. So if ten men went to medical school and nine of them used their knowledge of the nervous system to cause maximal amounts of pain while extracting confessions while the other went on to work in a hospital, the last guy would be a surgeon like the others in all things but torture, just as Christ is a man like all others in all things but sin.


Short form of the Second Way

The short form of the Second Way is even briefer than the First Way:

1.) Some agent causes do not have agent causes.

2.) All agent causes that do not have agent causes are divine.

The proof is identical to the last two steps of the First Way, with “mover” replaced by its synonym “agent cause”.

1.) If this is false, then all agent causes have agent causes, and so to appeal to agent causality would not explain anything. A causal explanation would not be an explanation.

Notice that the argument does not depend on the principle of sufficient reason, but simply to the principle of contradiction. The claim is not that “there must always be an explanation” but that giving causes does give an explanation, and explanations must explain.

2.) An agent cause is any extrinsic cause of activity which is not a goal. This is, again, a vast and variegated group: the hand throws a ball, the shortening day causes the leaves to turn, the Moon causes the tides, the Theia impact caused the Moon, etc.

But then why can’t causes like this be both explanatory and infinite? The Moon causes tides, the Theia impact causes the Moon, some cluster of unnamed causes causes the Theia impact, etc… It looks like there is no end to a series of agent causes that explain.

Not quite: Look closer at the series tides, Moon, impact. Either the series is meant to explain tides or not. If so, then you’re positing the impact as the cause of the tides, i.e. you’re seeing the rise and fall of the tides, along with the orbit of the Moon, as ways in which the impact continues to happen.  In other words, you’re treating the Impact-tides sequence as being as much of a whole as the airburst-mushroom cloud sequence of an atom bomb exploding. If you’re not explaining the tides this way, then the impact is irrelevant to your explanation. Still, the explanation from the impact remains a possibility, and cutting the explanation off at the Moon is simply a practical matter. We acknowledge that the Moon has an agent cause, but ignore it in our explanation.

One can expand on agent causes indefinitely, but not infinitely. Agent causes are indefinite so far as there is no intrinsic limit on how far removed in time we might go in giving an agent cause for any given action, but when we say the causes are infinite we deny the existence of the one that serves as the explanation of the event. In a similar way, we might make a line segment indefinitely longer, but to make it infinitely longer makes it no longer a line segment.

When we say the causes are indefinite, we mean that there is no a priori way to tell how many subordinate agent causes the primary agent cause used to achieve any given effect, or how long it took these secondary causes to act. This still allows that these secondary causes might have acted over an infinite time, since the secondary causes are not finite with respect to each other but with respect to the primary cause.

The primary cause cannot be the universe, not because it’s obvious that the universe had an extrinsic cause but because the parts of the universe are always extrinsic causes to other parts. We can view physical systems either as moved (the First Way) or as movers (Second Way)

The primary cause is therefore a partless mover acting neither specially or temporally. This applies in some way to the human soul, and, as said above, STA has no problem seeing the soul as somehow divine. But divinity properly speaking would have to account for the unified action of the universe as such, and this all call deus. 

First Way in least terms

Put in simplest form, the First Way is four claims:

1.) All potentials are moved (or actualized) by a mover

2.) All things in motion are potential.

Thus, all things in motion are moved by a mover.

3.) Not all movers have movers.

4.) All movers without movers are divine.

1.) “The mover” is a portmanteau term for things that trigger motion, assemble something that moves, push a thing along, give objects a position with potential energy, create some nature that moves in some way by nature, etc. Potentials as such are reservoirs that various movers can draw upon, not agencies that initiate or continue activities. The claim is more or less just a recognition of what “potential” means, whether used in common speech or physics.

2.) All things in motion are able to be so. They are a lot of other things too, but they are at least this.

3.) This claim is based on a conceptual incoherence. STA tends to express this as a denial of an infinite regress, but shifts in our notion of infinity have made the old formulation more a liability than a source of insight. Even if one had infinite movers responsible for an action, not all movers could be such.

It’s this incoherence that demands transcendence of the sensible order. It demands that no matter how much activity or motion is explained by causal interaction, there is at least one cause that does not act in this way.

To give movers to all movers is to fall into the contradiction of positing something as an explanation which in incapable of explaining anything. If we explain the stability of the earth by resting it on a turtle we venture an explanation that cannot explain, and “the infinite regress of turtles” that arises from this is only way of pointing to the inherent contradiction of positing things that cannot explain as explanations.

4.) “Divine” means an immaterial and therefore non-interactive source of natural motions. On this account, even a human intellectual soul would count as in some sense divine, and STA has no problem with this. But if nature is in any way a unified system then there is a single divinity for its activity, and our sense that the incompatibility of Relativity and QM means that both are incomplete arises from just this sense of nature as a unified system.


Logic of the Five Ways

Most presentations of the Five Ways explain them in the same order STA presents them in his text, but this order is different from the logical order of his thought. We know this since STA is more explicit than most about what his logical order looks like. Four features are relevant:

1.) All argumentation for some claim seeks to give a middle term. STA recognizes two kinds of truth. Self-evident truths are those where the predicate is immediately belongs to the subject, all other truths are known mediately and therefore require some relation to a middle term. There is no single definition of “middle term” but there is an account of “middle” for any universal affirmative claim, namely a term that is more universal than the subject and less universal than the predicate.  Because of this, the middle term proving a universal affirmative proposition will be said of its subject while the predicate is said of it. IOW, we will prove the claim by a Barbara syllogism.

2.) More general terms are more knowable. This is why the the term that mediately proves some claim has to have a generality midway between the subject and predicate of the conclusion, thereby forming a Barbara syllogism. This is, in fact, exactly why those in the Aristotelian tradition call it a middle term, i.e. it has a generality midway between the major term (major = greatest in universality) and the minor term (minor = least in universality)

General terms are more knowable in the intellectual order since intelligence first knows ens commune, i.e. being as so general that it includes both the real and the fictional, the factual and the illusory. Logic starts with this crash of confusion and uses argumentation to winnow it down, first to exclude some object from the all-but-infinite things it is not and then establish, at least generally, what the object is.

3.) In proofs that X exists, the middle term is what the word X means. Language refers not immediately to things but to things through thought, and our thought comes to us first only as significant, not as specifying objects that are clearly seen as real as opposed to fictional or factual as opposed to illusory. Proving that something is only takes one step beyond this initial confusion, it doesn’t go all the way to placing something in a genus. In fact, in any of the Five Ways it is impossible to place the object in a genus.

Mysteria Saeculorum

The Mysteries of the Ages or the Primeval Mysteries are those marked by the person of Jesus Christ outside of the age described in the Gospels.

1.) The procession of the Logos from the Father.

2.) The creation and conservation of the universe.

3.) The prefigurement of Christ in the Old Covenant.

4.) The private and general judgment of creation.

5.) Christ the Lord of the new heaven and new earth.

No Algebra till Junior year

The number one failure of classical education is teaching mathematics, and since I’m convinced that all non-vocational pre-college education should be classical, it follows that everyone is failing to teach math. I was reminded of this while re-reading an explanation that Brandon gave in 2016 of Whewell’s reasons for basing mathematics instruction on geometrical proofs rather than analytic mathematics (i.e. algebra and geometry).

[Whewell] is not claiming that analytical mathematics — algebra and calculus — are inferior mathematics, or that they are ill-suited to discovery of mathematical truths; in fact, he thinks the opposite is true. He is also not saying that they should not be part of education at all. His argument is rather that they are not good as foundations — education, insofar as it is mathematical, should build up to them, not take them as basic. It’s the perfection of analytical mathematics, its capacity for extremely abstract representation, that makes it poorly suited for getting people used to thinking mathematically and rationally. And this is because in analytical mathematics, as such, you don’t actually think about problems — you think about formulas and abstract relations that can be interpreted in many different ways for many different kinds of problems. If people get started too early on this, it is easy for them to start using these x’s and y’s and formulas concerning them as nothing but a crutch.

Read the whole thing, along with Rob’s development in the comments section. We’ve clearly fallen into exactly the fault that Whewell wanted to avoid, and have dumped the geometrical approach almost entirely while dedicating years to teaching analytic methods.

The fundamental pedagogical mistake is in this approach is that it teaches abstractions before teaching what they are abstracted from. The mistake borders on insanity – it is literally the same thing as teaching kids formal logic without telling them the word equivalents of the symbols they are using. We could certainly run a logic class like this, and treat the process of training the kids to use logical symbols as the same sort of thing as programing computers to manipulate the same symbols. The problem is that the sort of kid who succeeds in such a Kafka-esque curriculum will be more harmed by his education than enlightened by it, since he will be succeed only by suppressing his natural desire to understand what he is doingMath that doesn’t start with the concrete is therefore a sort of anti-education that teaches kids they can never know what they are doing or why what they are doing is true.

As Brandon points out, formal systems are far more powerful, rigorous, and simple than any geometry could hope to be. We’ve known for a hundred years how many things Euclid leaves out or relies on his pictures to prove, i.e. how many things he cannot reduce to an axiom or definition. But we’ve confused the necessity of getting past Euclid with the mistaken idea that we could teach math without him. The power and rigor of the abstraction belongs to it precisely as abstraction, and unless we teach the foundation we will be left with a madhouse game of translating coded-messages into different message codes forever. Most kids won’t get math, we shouldn’t expect them to, and they might well learn more from rejecting the pedagogy than accepting it.


« Older entries