Saturday, December 02, 2017

Lewis Carroll and Euclid

Lewis Carroll, or Charles Dodgson, as he was known in professional life, was, of course, a mathematician. Most of his mathematical work published in his lifetime was in linear and matrix algebra (Dodgson condensation is named after him, for instance), although he was interested in a number of other fields, as well. In addition to work in mathematics itself, he also wrote on mathematical pedagogy, and, in particular was a vehement defender of continuing to use Euclid to teach geometry. This defense is primarily found in Euclid and His Modern Rivals (1879) and Supplement to Euclid and His Modern Rivals (1885).

He gives his purpose for the first book right at the beginning:

The object of this little book is to furnish evidence, first, that it is essential, for the purpose of teaching or examining in elementary Geometry, to employ one textbook only; secondly, that there are strong a priori reasons for retaining, in all its main features, and specially in its sequence and numbering of Propositions and in its treatment of Parallels, the Manual of Euclid; and thirdly, that no sufficient reasons have yet been shown for abandoning it in favour of any one of the modern Manuals which have been offered as substitutes.

It is written in the form of a satirical dialogue between Minos and Rhadamanthus, both of whom are examiners treating modern textbooks like examination papers, the Phantasm of Euclid, and Professor Niemand, the counsel for the modern would-be replacements. Minos's description is perfect: "His hair, from much running of fingers through it, radiates in all directions, and surrounds his head like a halo of glory, or like the second Corollary of Euclid I.32." The second Corollary of I.32 is "All the exterior angles of any rectilineal figure are together equal to four right angles", and in Todhunter the diagram for it is:

The Elements of Euclid for the Use of Schools and Colleges - 1872 page 36b

One of Carroll's consistent points throughout is that for a geometry textbook you are not actually presenting geometry itself; what you want is "a book that will exercise the learner in habits of clear definite conception, and enable him to test the logical value of a scientific argument", as Minos tells the Phantasm of Euclid. Thus it is irrelevant whether there are omissions; overloading the curriculum is a danger to be avoided, and, in any case, if it's just a matter of adding a few theorems that have turned out to be especially useful, adding such things to Euclid is something that geometry teachers have always done. In addition, you want a clear line of inferences. While there are many cases in which you could do something in a different order than Euclid does, for teaching beginners, this is not something you should be getting into, and Euclid, having been a standard reference for so long, provides the service of a universal reference, with a numbering system on which everyone can agree.

Carroll regards only two of the criticisms of Euclid to be of any significance: the criticism that Euclid does not distinguish problems from theorems (which had been proposed as a major criticism in Carroll's day), and the criticism of Euclid's treatment of parallels. The former Carroll seems to find easily answered (separating problems and theorems doesn't actually seem to provide any improvement for the teaching of beginners), and most of the book is concerned with the latter. Part of the complexity of the latter is perhaps due to the fact that Carroll thinks axioms have to be established as axioms -- as Euclid tells Minos in discussing Playfair's Axiom, "What is an Axiom at one stage of our knowledge is often anything but an Axiom at an earlier stage" -- so to determine what should count as axiom, you need to lay out what it is useful for proving within a system and determine how it meets the several requirements for what you are trying to do. And, of course, in teaching geometry, one of the requirements is that it be suitable for beginners, that is, that it be something that can be grasped and used without a developed sense of geometrical constructions or proof techniques; most modern treatments Carroll thinks get tempted off the right pedagogical road by pursuit of a standard of elegance or rigor that raises the difficulty, without increasing clarity, for people just starting out.

Carroll had no problem with doing things differently from Euclid, however, as long as you didn't try to overcomplicate beginner's work with it, and he himself devoted a considerable amount of thought to different ways of handling parallels. One way is found in his Curiosa Mathematica, Part I -- or, actually two ways, since in his original version he used a hexagon in his substitute for Euclid's parallel postulate, but decided instead to simplify it further in the third edition to a tetragon. Part of what Carroll wanted to do was come up with a substitute for Euclid's treatment of the parallels that did not, like almost all other proposed at the time, involve infinities or infinitesimals in one way or another, but just used basic ideas easily accessible to human reason. His proposed substitute is, "In any Circle, the inscribed Tetragon is greater than any one of the Segments that lie outside it."

A great many people wonder why Carroll, so creative, shows little interest in non-Euclidean geometries; but, of course, even today non-Euclidean geometries are not what you think about for teaching people just starting out, so one wouldn't expect it to arise in the context of his work on mathematical pedagogy. As for the geometrical work itself, though, Carroll quite clearly regards Euclidean geometry as true, and thus the primary issue as one of finding the best foundations for a Euclidean geometry. It's also worth recalling -- mathematicians in particular tend to forget it when thinking about the history of mathematics -- that mathematical results do not propagate instantaneously, and prior to the twentieth century, they propagated very slowly indeed across national lines. People kept up with international work, as they could, but people in different nations often didn't share the same notations, teach the same methods, or prefer the same approaches. Carroll, even if he had not simply thought it a bunch of clever paradoxes, could have been aware of the work on non-Euclidean geometry without having had the kind of access to it that would have made it possible for him to work on the subject without essentially starting from scratch himself or devoting several years of his life to researching it.

Music on My Mind

Clamavi De Profundis, "Christmas Medley".

Adam Smith on Music

An interesting passage from Adam Smith on music (Theory of Moral Sentiments I.II.26):

When music imitates the modulations of grief or joy, it either actually inspires us with those passions, or at least puts us in the mood which disposes us to conceive them. But when it imitates the notes of anger, it inspires us with fear. Joy, grief, love, admiration, devotion, are all of them passions which are naturally musical. Their natural tones are all soft, clear, and melodious; and they naturally express themselves in periods which are distinguished by regular pauses, and which upon that account are easily adapted to the regular returns of the correspondent airs of a tune. The voice of anger, on the contrary, and of all the passions which are akin to it, is harsh and discordant. Its periods too are all irregular, sometimes very long, and sometimes very short, and distinguished by no regular pauses. It is with difficulty, therefore, that music can imitate any of those passions; and the music which does imitate them is not the most agreeable. A whole entertainment may consist, without any impropriety, of the imitation of the social and agreeable passions. It would be a strange entertainment which consisted altogether of the imitations of hatred and resentment.

Friday, December 01, 2017

Dashed Off XXV

"beings do not wish to be governed badly" (Aristotle, Met 1076a)

Taking into account all possibilities is as teleological as taking into account a goal in the future,and for similar reasons.

What has proportion is by nature reason-like.

A society cannot be more free than it is temperate or courageous.

the industriousness of spiritual poverty

The fundamental wrong of hypocrisy is that it is a refusal to repent.

The spirit of repentance is the mean between hypocrisy and brazenness.

four senses of id quod non est (Victorinus)
(1) privation
(2) not another
(3) not yet
(4) above what is

does not please on being seen
displeases on being seen
pleases on not being seen

problems as signs of predicables

God can be first moving cause only by being first efficient cause.

memorable, intelligible, true
appetible, eligible, good
lovable, enjoyable, beautiful

As a man may sin with a hand or foot, so Adam sinned with the whole human race.

the inbreaking of the world

The visible part of the Church is but the tip of its iceberg.

True love unifies by signs.

coherence and our sense of the external world as thoroughly philosophical

No human being has intrinsic title to the service of another human being.
extrinsic titles by: just exchange (private good) or just law (common good)
Just exchange requires it be for equivalent service, or for appropriate wage, or in compensation for loss or risk.
Just law, of course, requires that it be genuinely consistent with and conducive to common good.

A government does not have intrinsic title to the property of its citizens. Extrinsic title may rise from requirements of common good, either positive (general taxation) or negative (seizure for purposes of punishment) or from specific benefits (exchange of goods and services).

It is a moral responsibility of every good citizen not to appeal to the coercive power of the state except where genuinely necessary for safety and justice.

Justice is a giving virtue.

The human mind is naturally aphoristic.

participation and reflection as the fundamental mode of human learning

Aristotle's De Caelo 292a3-6 describes a lunar occultation of Mars. Three possible dates for it (Savoce, Natali):
16 March 325
4 May 357
20 March 361

syscholazein kai symphilosophein

Rashi's commentary on Gen 1:2: "The Throne of glory was suspended in the air and hovering over the face of the water with the breath of the mouth of the Holy One, blessed be He, and with His word, like a dove, which hovers over the nest."

schismatics as brethren (Optatus)

Medieval etymologies make more sense when one recognizes that they are extrapolating from how many Latin words were in fact formed.

commercio formatarum in the unity of the Church (Optatus Adv Don Book 2.iii)

communicatio memoriis sanctorum

"L'attention est la seule faculté de l'âme qui donne accès à Dieu." Weil

"it is one contradistinction of genius from talent, that is predominant end is always comprised in the means; and this is one of the many points, which establish an analogy between genius and virtue" Coleridge

Problems must be investigated many times in many ways to be properly understood.

constancy and coherence as signs of substance
substance as ground of invariances

A real definition summarizes a real explanation.

the evening reflection and the morning reflection of the Church

"in respect of Christ's true body no order is above priesthood, whereas in respect of Christ's mystic body, the episcopate is above the priesthood" (ST Supp 29.6ad1)

unction is intrinsically petitionary

Sacramental form should (1) establish what sacrament is given (2) indicate the divine power working in the sacrament (3) identify the effect. (Matrimony, however, complicates these matters.)

"just as baptism is a spiritual regeneration and penance a spiritual resurrection, so extreme unction is a spiritual healing or cure" (ST Supp 30.1)

People often fail to do what they prefer simply from the difficulty, or from inertia; and it is mere equivocation to say that this is because they prefer nondifficulty or not exerting themselves. Not preferring to use the means is not the same as preferring not to use the means.

The right to punish must always be bestowed; seizing it is wrong in and of itself.

The authority to punish cannot be severed from the responsibility to punish.

The most basic form of retributivism is that one may only punish the deserving. No retributivist in practice also holds that all the deserving are to be punished, so the only question then is what additional principles are needed.

Hart's theory of punishment gets things exactly backwards. Retributivism is suited only to answering the general justifying aim, except in certain obvious cases; utility is only a suitable consideration for systems already restricting punishment to the guilty, and set up for precisely that purpose of punishing the guilty. Whom we actually punish must be tempered by concerns for general welfare, however.

eagerness to punish as a character flaw

Most arguments against the death penalty may be adapted to have force against life imprisonment.

One needs reasoning well before one gets to argument.

toledoth // apostolicity

Whether a story or account is useful is a purely causal question.

laws of nature // world-soul
(the analogy becomes more exact if we think of natural powers of the world-soul)

What makes geometry so powerful is the ability to make new definitions.

the twin themes of pity and hope in Middle-Earth

pity and counsels of healing

the conditions of good government (cp Polybius)
(1) The political order is voluntarily accepted by the people through reason rather than through force.
(2) Governance is by the most just and most wise.
(3) The community is structured by traditionary and customary respect (for gods, for parents, for elders, for laws) and the will of the majority prevails.

confirmation as the sacrament of many ends

centers as point-boundaries
circularity as directional indistinguishability

putting one idea in the guise of another to see how they interrelate

There is no single property of pleasantness common to all pleasures.

hierarchy, collegiality, conciliarity
subsidiarity, solidarity, x

stylization of thought as an instrument of thought

geography of possibilities, topography of reasons

aphorism as cellular communication

Human sexuality naturally tends to allegorize other things as sexual (this allegorization is a major part of what is called bawdiness).

Estel as the condition for the possibility of Amdir in matters of salvation (estel being trust that healing is possible, amdir being expectation of that very good)

Amdir: expectation OF good
Estel: expectation THAT Good will do good

the human person as demiurge

"Romance and poetry, like ivy, lichens, and wall-flowers, need Ruin to make them grow." Hawthorne

The problem with American Catholicism is not that it has no roots but that it does not put down any. Its roots are inherited and not encouraged to grow deeper into new soil.

The privation of sin does not expire with time.

accounts of qualia & accounts of figurative language

The promulgation of consent is governed by convention.

in dubio pro reo
in dubio mitius

Having been united by goodwill with the Word, the Church became inseparable from Him, having in all things one work with Him, in a supremely intimate union. The Word, indwelling the Church, unites with Himself all He receives, preparing the Church to enter into communion with all the dignity that He, the Son, indwelling the Church, makes common for them. He makes the Church one with Him by virtue of the unity to which He raises the Church, communicating to the Church all primacy and willing by good will to accomplish all manner of things with and in and through the Church.

To be united in marriage is to be such that some of one's operations are cooperations simply by virtue of the marriage itself.

(1) Marriage is a more basic society than civil society.
(2) Civil society has moral obligations to marriage.

Mt 6:13
Kingdom : Father :: power : Son :: glory : Spirit (Bulgakov)

An account of belief is defective if it does not allow for believing in common.

We can misapply 'I'. ('Am I the one doing that?')

"the whole world is man's potential and peripheral body" (Bulgakov)

deference-structures, loyalty-structures (membership), and exchange-structures in society

deference (authority), loyalty (common wisdom, communal values), and exchange (shared agreement) as colors of starting-points for arguments in rhetoric

The heavens filtered through human mind declare the glory of God; by human poetry day utters speech to day and by human lore night manifest knowledge to night.

Duradus claims diaconate is a sacramental; Victoria takes this to be probably true; Bellarmine takes it to be a sacrament. Starting with Paul VI there is clear attribution of indelible character.
Given the nature of the diaconate, one would expect to be able better to observe the major-sacramentality of the order in extraordinary rather than ordinary matters.
The deacon does not serve only by doing but by the witness of being.
Optatus on the diaconate as third priesthood (Contra Parmen 1.13); see also Leo I (Ep 12.5, 14.3f); Jerome (Ep 48,21)

All discussion of pure possibility seems to require something like Aristotle's argument by analogy for prime matter.

Much of scientific experimentation proceeds by making a series of bets that will ultimately result in a loss; the scientist is looking for a loss.

Betting against a necessary truth is a sure loss regardless of one's evidence for it.

necessity-like contingent truths (one's own existence, very general causes, practically-necessary truths with moral certainty)

Lack of evidence is only evidence to the contrary to the extent one's search is discernibly general.
There is a dog in the room -> A dog exists
~ (There is no dog in the room -> No dog exists)

Note that language in Genesis begins with God and comes down to man; man extends it to describe his world; the temptation comes by conversation, and the fall leads man to be afraid of God's voice; then man seeks to ascend to God and God confounds the language.

(1) Not all human judgment is belief, or of the same kind.
(2) Under the right conditions, probable reasoning can lead to certainty.
(3) How evidence affects the probability of a conclusion depends on the entire context, not solely on features of the evidence, and changing the evidence can sometimes require evaluation of all the other evidence.
(4) Evidence may overdetermine a conclusion.
(5) Evidence does not always affect the probability of a conclusion; it may change other features of evidence (e.g., availability or defeasibility).
(6) Absence of evidence is only evidence of absence if one has definite reason to think one must accept a negation as failure rule for one's conclusions.
(7) A reasonable person not only considers evidence for a position but ramifications of changing a position.
(8) There are no degrees of belief as such.
(9) Evidence and belief are distinct things not subject to the same measure.
(10) Logical inference captures more fundamental aspects of evidence evaluation than probability theory.
(11) Inquiry is more properly modeled as a search than as a probabilistic weighing.
(12) When people talk about probabilities in the context of inquiry, they do not mean only one kind of thing.
(13) New evidence can change what counts as evidence.
(14) The most important element for evaluation of evidence is why something is or is not evidence; any reasonable assessment of probabilities is downstream from this.

True humility has an intrinsic link with clarity of perspective.

People make themselves evident.

the dangers of soundbite ethics

schematic instrument // formalized argument

"Reflected beauty like reflected light has a special loveliness of its own -- or we shouldn't, I suppose, have been created." Tolkien

Gently and Roughly

Speak Gently
by David Bates

Speak gently! -- It is better far
To rule by love, than fear --
Speak gently -- let not harsh words mar
The good we might do here!

Speak gently! -- Love doth whisper low
The vows that true hearts bind;
And gently Friendship's accents flow;
Affection's voice is kind.

Speak gently to the little child!
Its love be sure to gain;
Teach it in accents soft and mild: --
It may not long remain.

Speak gently to the young, for they
Will have enough to bear --
Pass through this life as best they may,
'T is full of anxious care!

Speak gently to the aged one,
Grieve not the care-worn heart;
The sands of life are nearly run,
Let such in peace depart!

Speak gently, kindly, to the poor;
Let no harsh tone be heard;
They have enough they must endure,
Without an unkind word!

Speak gently to the erring -- know,
They may have toiled in vain;
Perchance unkindness made them so;
Oh, win them back again!

Speak gently! -- He who gave his life
To bend man's stubborn will,
When elements were in fierce strife,
Said to them, 'Peace, be still.'

Speak gently! -- 't is a little thing
Dropped in the heart's deep well;
The good, the joy, which it may bring,
Eternity shall tell.

Speak Roughly
by Lewis Carroll

Speak roughly to your little boy,
And beat him when he sneezes;
He only does it to annoy,
Because he knows it teases.

Wow! wow! wow!

I speak severely to my boy,
I beat him when he sneezes;
For he can thoroughly enjoy
The pepper when he pleases!

Wow! wow! wow!

Thursday, November 30, 2017

Sword in the Stone

People studying the provenance of various legends and myths usually trace back the idea of the sword in the stone (in Arthurian legend) to the hagiography of St. Galgano Guidotti, whose feast is today. St. Galgano was a twelfth-century saint. He was a knight, and said to be rather arrogant and ruthless, but one day his horse refused to be guided and ran up to the hill of Montesiepe, where he had a vision of the Archangel Michael. In response, he drove his sword into a rock, which, it is said, it went through as if it were butter, and fused with the stone. There he started a hermitage, the Rotonda at Montesiepe (which was later given to the Cistercians), and there you can see the sword even today.

San Galgano Spada nella roccia

Galgano lived during the period when the first formalized canonization process was being put into place, and thus, when he was canonized a few years after his death, he was one of the first to go through that process. For that reason we know more about his actual life than we probably would have otherwise known. (The earlier default process, by long local veneration, has many advantages, but, unlike the formal process often lets historical traces fade into the mists of legend.) When in the nineteenth century it became fashionable to be preemptively skeptical of legends like St. Galgano's -- i.e., not merely recognizing them as stories with accumulation and occasionally transformation, misunderstanding, and assimilation to other stories, but treating them as active fictions made up whole cloth unless it can be shown otherwise -- the sword was often assumed to be a modern forgery; but the sword is indeed medieval, and the basic story goes back almost to the life of St. Galgano himself. Were the sword to have vanished, people would doubtless now regard it as pure fiction; but, whatever one's explanation of how it got there, there actually is a sword in the stone.

Nonsense and Wonder

If, therefore, nonsense is really to be the literature of the future, it must have its own version of the Cosmos to offer; the world must not only be the tragic, romantic, and religious, it must be nonsensical also. And here we fancy that nonsense will, in a very unexpected way, come to the aid of the spiritual view of things. Religion has for centuries been trying to make men exult in the 'wonders' of creation, but it has forgotten that a thing cannot be completely wonderful so long as it remains sensible. So long as we regard a tree as an obvious thing, naturally and reasonably created for a giraffe to eat, we cannot properly wonder at it. It is when we consider it as a prodigious wave of the living soil sprawling up to the skies for no reason in particular that we take off our hats, to the astonishment of the park-keeper. Everything has in fact another side to it, like the moon, the patroness of nonsense. Viewed from that other side, a bird is a blossom broken loose from its chain of stalk, a man a quadruped begging on its hind legs, a house a gigantesque hat to cover a man from the sun, a chair an apparatus of four wooden legs for a cripple with only two.

G. K. Chesterton, "A Defence of Nonsense"

Wednesday, November 29, 2017

Optative Inference

If we can have imperative logic and erotetic logic, we can surely have a logic of optatives (or euctic logic, if you prefer the Greek).

Suppose, for instance, someone says, "God save the Queen!" From this I can infer, "There is a Queen." If I say, "If only we were rich!", from this you can infer, "We are not rich." If someone says, "May John get well soon!", you can directly infer that John is not well yet.

A very natural way to interpret optative inference would be to take optatives to be assertions about wishing or wanting. If I say, "If only it were so", this does seem to be very much like, "I wish it were so", and the two would at least often be equivalent. This, you will note, is essentially the Bolzano approach; Bolzano thought that questions worked this way, but it's even more plausible with optatives. It does raise a question, though. Bolzano's account of questions naturally has a number of problems, not least that which Husserl noted about its implausibility in dealing with silent wondering. Are there optative analogues to 'silent wondering'?

If optatives are not assertions like this, then truth values need to be answered, and presumably there would be some analogy to imperatives in this way.

Sluggard and Lobster

The Sluggard
by Isaac Watts

'Tis the voice of the sluggard; I heard him complain,
"You have waked me too soon, I must slumber again."
As the door on its hinges, so he on his bed,
Turns his sides and his shoulders and his heavy head.

"A little more sleep, and a little more slumber;"
Thus he wastes half his days, and his hours without number,
And when he gets up, he sits folding his hands,
Or walks about sauntering, or trifling he stands.

I pass'd by his garden, and saw the wild brier,
The thorn and the thistle grow broader and higher;
The clothes that hang on him are turning to rags;
And his money still wastes till he starves or he begs.

I made him a visit, still hoping to find
That he took better care for improving his mind:
He told me his dreams, talked of eating and drinking;
But scarce reads his Bible, and never loves thinking.

Said I then to my heart, "Here's a lesson for me,"
This man's but a picture of what I might be:
But thanks to my friends for their care in my breeding,
Who taught me betimes to love working and reading.

'Tis the Voice of the Lobster
by Lewis Carroll

'Tis the voice of the Lobster: I heard him declare
"You have baked me too brown, I must sugar my hair."
As a duck with its eyelids, so he with his nose
Trims his belt and his buttons, and turns out his toes.
When the sands are all dry, he is gay as a lark,
And will talk in contemptuous tones of the Shark;
But, when the tide rises and sharks are around,
His voice has a timid and tremulous sound.

I passed by his garden, and marked, with one eye,
How the Owl and the Panther were sharing a pie:
The Panther took pie-crust, and gravy, and meat,
While the Owl had the dish as its share of the treat.
When the pie was all finished, the Owl, as a boon,
Was kindly permitted to pocket the spoon;
While the Panther received knife and fork with a growl,
And concluded the banquet by ---

Monday, November 27, 2017

Evening Note for Monday, November 27

Thought for the Evening: The Hegelian Ontological Argument

Graham Oppy, in his article on ontological arguments for the SEP:

I provide no example of a ‘Hegelian’ ontological argument because I know of no formulation of such an argument. Many people assert that Hegel provided an ontological argument; but, when pressed for a list of the premises of the argument, Hegel’s friends fail to deliver.

I find this a little baffling, because while there are complications with interpreting Hegel in general, and while there are complications with interpreting Hegel on ontological arguments (because the best discussion, in Lectures on the Philosophy of Religion, is something of a mess due to not being in a finished form), there is no real mystery about this -- the basic outlines, at least, are clear enough, and there's no excuse for Oppy to be talking about it at all if he is incapable of doing the basic scholarship of actually picking up Hegel and working through it on his own. I thought I would say a few things about it; I am going to try to avoid the very technical and finicky (anything Hegelian gets both very quickly), in order to deal with the basic point.

The first and most important thing to understand about Hegel on the ontological argument -- about Hegel on anything, really -- is that Hegel thinks concepts, positions, and arguments are dynamic, not static. They are in motion. Arguments do not consist in a "list of the premises" (although single stages, snapshots, will have such a thing); they consist in the movement from premise to conclusion. And, what is more, arguments transform into arguments, positions into positions, concepts into concepts in rigorous fashion. This is the fundamental key to grasping the basics of Hegel's position on the ontological argument: Hegel's argument is not going to be just a single stage, but is going to be a result of an argument being faced with an objection which can be overcome by a rethinking of the original argument in light of the objection. That's Hegelian dialectic: the original argument is right (but not as originally interpreted), the objection to it is right (but it opens the possibility of an interpretation to which it does not apply). It's perfectly fine to call the last stage of this 'Hegel's ontological argument', but the whole point is that you cannot understand its 'list of premises' unless you understand how those premises grew.

Stage I. Hegel begins with Anselm's version of the argument; it is where he starts and in a sense where he will end up. He intends to give a version of Anselm's argument. It will, of course, not be Anselm as Anselm understood him, but Anselm Hegelianized, transformed. Things are complicated a bit, as well, by the fact that Hegel's Anselm, like Kant's on those few occasions where Kant acknowledges him, is a somewhat Cartesianized Anselm. That argument is, more or less (this is just the simplified form of an argument that can be explicated more fully):

(1) God is what is most perfect, beyond which nothing can be thought.
(2) If God is merely an idea, He is not what is most perfect.

In other words, we start with God 'subjectively', as idea, a possibility, distinct from being, and since God cannot be God and be merely 'subjective', God must also be 'objective', exist in reality. This is the transition involved in Anselm's argument.

Stage II. To this, Kant opposes the objection that being is not a real predicate, and so does not add anything to the concept. As Hegel notes, this assumes there is no difference between the case of God and finite, limited, contingent things. But the objection has some bite because Anselm's argument starts with the concept distinct from being and then transitions to being; this seems to be the sort of thing that can only be done with hypothetical necessity. The ontological argument assuming God's existence to get God's existence.

Thus we have Anselm's argument, which is not exactly refuted by Kant's objection (since Kant's objection assumes that the case of God is not different from the case of thalers), but which is problematized by it; and Kant's objection, which does not quite succeed as a refutation but raises a serious problem for Anselm. But there are no impasses in Hegel.

Stage III. The problem, Hegel thinks, is that both Anselm and Kant think that you can start with the concept rather than the existence. This is not quite right. Remember, Hegel thinks that concepts are in motion. Concepts do not just sit there; they express themselves. This is the reason for the famous comment Hegel makes on Kant's thalers: You can't imagine thalers into existence, but you can achieve them as a goal by working for them. We don't merely go around with the concept of money; our concept of money expresses itself into an actual system of economics in which money can be obtained. Working for money shows that concepts move into actual being. The concept obviously is generally not just the same as the being; but concept is related to being as (actualizing) potential to actual. The concept has existence potentially; but this is, again, not a mere passive potential, but is being worked out as the motion of the concept. The subjective concept is making itself objective. This is true of all concepts, although it is in the very nature of how Hegel thinks of this that the potential dynamism in each concept will often work itself out in very surprising ways. This is very important: Concepts are not static for Hegel; they are ongoing processes expressing a potential.

Thus another way to state the problem both with Anselm and with Kant, as Hegel thinks of it, is that they are both thinking of concepts or ideas as static, and thus missing part of what it is to be a concept in the first place. (Hegel would, of course, regard Oppy's demand for a list of premises as a sign that he, too, misses the point, not because you can't give such lists of premises, but because they are only samplings of the actual argument, identifying only one stage of it, and unable to be interpreted without a context. If Oppy gets a list of premises, what is he going to do with them? Merely assume that he understands them? Guess at their meaning? As we'll see this is not a mere quibble; it is the heart of the matter.) If, however, we interpret Anselm's argument not statically but dynamically, the argument avoids any problem raised by Kant's objection. The concept, in being a concept, is an activity of turning itself into reality. It is not merely subjective; it is becoming objective; it is a living movement. God is not assumed; being is not assumed as being in the concept, it is put forward as the goal, the result, of the task or process that the concept is.

Thus the premises are not a problem here; if you want premises, they are the same as Anselm's (in the Cartesianized forms of which the simplified version is given above). This doesn't help you any, however; you need to know the interpretation, which you can only have by establishing its place in the dialectic. Hegel's premises are rethinkings of Anselm's. A crude, rough way to get a sense of what Hegel means is that Anselm's starting-points need to be interpreted teleologically. Mind, conceptualizing the Absolute, works itself out to be the Absolute. This is why Hegel is so very sympathetic to the ontological argument: interpreted in Hegelian terms, it just is the basic outline of Hegel's system.

Various Links of Note

* Emanuel Rutten, Dissolving the Scandal of Propositional Logic?

* There's been some recent hubbub over the CFPB, a relatively new agency devoted to upholding financial protections for consumers; the Obama-appointed Director, Richard Cordray, is leaving. The Trump administration appointed an Acting Director -- and Cordray appointed a Deputy Director to become Acting Director. The latter would in most cases be insanely stupid, since the first principle of government ethics is that actions under color of authority must have an appropriate ground of authority, and most Directors would not have such an authority. But in this particular case, when Congress set up the CFPB, it gave the Director the authority to appoint a Deputy Director and the Deputy Director the power to be the Acting Director when there is need. The conflict has led to legal action. In reality, I don't think Cordray has a leg to stand on here, although he has received support from some significant people, like Senator Warren; yes, Cordray has the authority to appoint a Deputy Director, but the Federal Vacancies Reform Act gives the President practically unlimited power to appoint an Acting Director, as long as it is someone who has already been appointed with the consent of the Senate. The FVRA has not been repealed; the standing rule for legal interpretation is that laws cannot be repealed merely by implication, so courts must uphold both laws in as substantive a sense as possible. The most natural way to do that is to hold that the President can appoint an Acting Director in either way: by letting a Deputy Director serve as Acting Director without special appointment, or by specially appointing someone. And the other issue here is that in a matter of dispute over how the government itself works, one defers by default to the relevant Constitutional office; as Congress has not explicitly required the President to let the Deputy Director become Acting Director (a requirement that would certainly be challenged and could very well not be constitutional), as a matter of government ethics (and constitutional law), the President would typically be presumed to have the authority to act as he could in any other case. This is not a sure thing, because laws can add complications, but it seems to me the natural diagnosis. In any case, Adam White discusses the matter with the relevant legal quirks. It has also been argued previously, by Kent Barnett, that the legislation concerning the Deputy Director of the CFPB is itself constitutionally problematic.

* Pius XI, Quas Primas, on the Feast of Christ the King:

If princes and magistrates duly elected are filled with the persuasion that they rule, not by their own right, but by the mandate and in the place of the Divine King, they will exercise their authority piously and wisely, and they will make laws and administer them, having in view the common good and also the human dignity of their subjects. The result will be a stable peace and tranquillity, for there will be no longer any cause of discontent. Men will see in their king or in their rulers men like themselves, perhaps unworthy or open to criticism, but they will not on that account refuse obedience if they see reflected in them the authority of Christ God and Man. Peace and harmony, too, will result; for with the spread and the universal extent of the kingdom of Christ men will become more and more conscious of the link that binds them together, and thus many conflicts will be either prevented entirely or at least their bitterness will be diminished.

* Charles Dickens and Two Kinds of Punch

* The Babylon Bee, Liberal Christian Attempts to Debate Atheist but They Just Agree on Everything. Sometimes parody is practically truth.

Currently Reading

Lewis Carroll, Alice's Adventures in Wonderland and Through the Looking-glass
Adam Smith, Theory of Moral Sentiments
Cathy Cobb, Monty Fetterolf, and Harold Goldwhite, The Chemistry of Alchemy
Kenneth Laine Ketner, Elements of Logic: An Introduction to Peirce's Existential Graphs
David Makinson, Sets, Logic and Maths for Computing
Edith Stein, The Hidden Life
Tanith Lee, The Secret Books of Paradys, III & IV

Bee and Crocodile

Against Idleness and Mischief
by Isaac Watts

How doth the little busy bee
Improve each shining hour,
And gather honey all the day
From every opening flower!

How skilfully she builds her cell!
How neat she spreads the wax!
And labours hard to store it well
With the sweet food she makes.

In works of labour or of skill
I would be busy too:
For Satan finds some mischief still
For idle hands to do.

In books, or work, or healthful play
Let my first years be past,
That I may give for every day
Some good account at last.

How Doth the Little Crocodile
by Lewis Carroll

How doth the little crocodile
Improve his shining tail,
And pour the waters of the Nile
On every golden scale!

How cheerfully he seems to grin,
How neatly spreads his claws,
And welcomes little fishes in,
With gently smiling jaws!

Sunday, November 26, 2017

Fortnightly Book, November 26

Charles Lutwidge Dodgson got his pen name by taking his first two names, translating them into Latin (Carolus Ludovicus), switching them, and re-translating them into English a different way. He was not the one who actually chose it -- he submitted to his editor, Edmund Yates, as one candidate among several for a pen-name, the others being Edgar Cuthwellis, Edgar U. C. Westhill, and Louis Carroll. Yates chose Lewis Carroll, thus sparing us Alice in Wonderland by Edgar Cuthwellis. Dodgson studied to be an Anglican priest, but concluded in the end that it was not for him; he became a mathematician at Christ Church, a position he seems to have detested, perhaps because he found himself intellectually lonely there -- Dodgson, despite a certain shyness due to his stuttering, was an extremely sociable person, with a wide network of friends and an immense correspondence, and any kind of isolation seems to have caused problems for him. (It seems, for instance, to have hampered his work in logic that he had no one to discuss it with except John Cook Wilson, who not only did not fully understand what he was doing, but was a bit patronizing about it, as well.)

Alice's Adventures in Wonderland was published in 1865, in part on the recommendation of George MacDonald; Through the Looking-glass was published in 1871. I'll be doing both. Despite both being nonsense-tales, they are elaborately constructed out of any number of logical, mathematical, and recreational puzzles. For instance, here is Carroll's own description of Through the Looking-glass as a chess game:

Alice chess game

We'll see what we can pull out of the puzzle and riddle of the tales; it is not an accident that they are both structured on games, so let the game begin.