Adams on Zaleucus

Jon Rowe has a very interesting post at "Positive Liberty" on Jefferson and Adams. But in the course of it he says:

John Adams too wrote a book that posited pagan Greco-Roman religion as “rational, intelligible, and eternal, for the real happiness of man in society, and throughout his duration.” If the orthodox carefully examined that book as they did Jefferson’s, it seems to me, Adams could have gotten in as much trouble as did Jefferson.

I'm not so sure, because Adams doesn't say that pagan Greco-Roman religion is "rational, intelligible, and eternal, for the real happiness of man in society, and throughout his duration"; he says that Zaleucus's preamble to his laws places religion, morals, and government on a philosophy which it serves as a basis that is "rational, intelligible, and eternal &c." But while the original context is pagan and Greco-Roman, it's unclear, in fact, that what Adams identifies as the content of Zaleucus's preamble would have been regarded by anyone as particularly pagan or Greco-Roman at all; the view argued for by Adams in the work from which the text comes, i.e., that government is subject to progressive improvement that successively uncovers the eternal principles of good government, is an extremely common one in the period. Read in that context it's fairly innocuous; one reads it naturally as simply saying that Zaleucus was one step closer to the ideal republic than his predecessors because he built his laws on eternally true principles, without, however, coming as close to that goal as his successors. (I think Rowe handles the passage better in a later post.)

Incidentally, Adams is simply adapting Cicero here. Tracing the influence of Cicero in this period is difficult, since something that sounds like it might have direct Ciceronian influence might actually just be second-hand. But Adams had a pretty hefty collection of Cicero in his library, and, equally importantly, Lord Kames actually gives us a text for Zaleucus's preamble, and Adams's summary fits it only very loosely (it fits Cicero's discussion very well). So either Adams had a text of Zaleucus other than that of Home's, or (much more probably) he misread Cicero's philosophical expansion of the preamble as Cicero's summary of it. A good example, one of many, of the importance of Cicero in early modern political and moral philosophy.

UPDATE: He has a very good post in response, and notes a letter from Adams to Jefferson in which Adams mentions Zaleucus again.

Dashed Off

It's been a while since I've done one of these 'dashed off' posts. I'm a very profligate note-taker; I'm constantly writing notes to myself in one form or another. Here is a small semi-random selection of some things I've noted down recently. Some may be wrong, some right, some are simply statements of positions I'm considering arguments for and against; some are passing thoughts I've had that I felt at the time I should note down for further thought or examination, some just idle thoughts while doing something else And yes, some of them are simply obscure.

--the impulse to good actions felt by the one who reads Scripture as a motive of credibility re its divine nature

photovoltaic farms with compressed air storage

Mathematicians don't just want theorems; they want natural, useful theorems.

The government doesn't have the right to stop you from doing some things because the responsibility for stopping yourself from doing those things lies wholly with you.

New evidence does not merely affect the likelihood of the hypothesis; it can affect the interpretation of the old evidence, too. (E.g., things once viewd as evidence for h can come to be seen as irrelevant to h.)

We do not conceive worlds with ease; indeed, we do not conceive worlds at all, but only fragments of worlds, supposing these worlds like our own (of which we have no adequate conception) except for fragmentary differences at which we vaguely gesture; thus we are in no position to evaluate these worlds overall except to the extent, and on the same basis, that we are able to do so for the actual world.

It is easier to distinguish wrong-ish and right-ish than wrong and right.

Nothing so practical as virtue.

When people affirm the importance of Reason, the danger is always that they are affirming that their reason, as it is, is more important than another's reason.

The Petrine authority is the authority to strengthen God's people and to exercise compassion on them by ecumenical council. (Abu Qurrah)

Much that is called love is not love but an egoism of two.

The transfigured receives glory by investment rather than by fusion.

To participate x is to be drawn into act by the act of x.

The joy of the Spirit manifests itself in the harmonious gestures of the children of God as they play and dance together. (cf. Jerome, Comm. in Zach. 2.8)

--on the character of non-sacramental commemoration of the Lord's Supper

God is such overwhelming good that no possible world in which He exists can be, on balance, evil; because no amount of evil can overbalance, on any reasonable standard of comparison, inexhaustible and superabundant good.

electromagnetic vs. electrodynamic suspension (EMS levs @ standstill, but requires a great deal of electronic monitroing; EDS less monitring, but need to build to 'take off' speed.)

Seeking some importuous heaven
the inane thought of an insane mind
eleme philosophies

In law we take up the cause of the human.

Only light can be a principle of union.

the word of truth "bearing fruit and growing" Col 1:6, 10, 19

The right to stable possession of property is rooted in the foresight of prudence.

If we take seriously the truth that every logical notation keeps track of 3 things (rule out, put in, unknown), then it seems that every system that allows contradiction explosion uses only infinite expressions (in abbreviated form, of course).
-> It's also the reason why it becomes difficult to diagram very complicated expressions, because the diagrams have to convey all 3 things for every term-combination, & it is difficult to find diagrammatical forms that both allow sufficient abbreviation and remain useful on a large scale.
-> The rules of addition & of weakening simply make explicit parts of the expression that were previously implicit in the unlimited domain.

"All these modes of the transfinite have existed from eternity as ideas in the Divine intellect." Cantor

Domains of discourse are not sets; there is no set of all sets, but we can have all sets in our domains (We are talking Cantorian sets here): for instance, i can say, "No set is the set of all sets," which quantifies over all sets.

the sublime experienced vs. the exaltation in the experience of the sublime

The testimony of the Spirit is a "light so irradiating the mind as to affect it gently, and display to it the inner relations of the truth that had hitherto been concealed" Kuyper (Enc. Sacr. Theo. 557).
-> this causes a struggle between our "deepest life-consciousness" and the consciousness of the world to which we formerly were subject; in this struggle we see ourselves and the world in [light of] Scripture. The veil is slowly pushed aside& we begin to recognize the imposing authority of Scripture, as a man born blind might slowly begin to see color, and to delight in it.

An opinion is probable to the extent that it can gain the assent of the prudent by intrinsic or extrinsic argument. (The most common & important case of extrinsic argument here is the authority of other prudent people.)

Probabilism makes an immense amount of sense when the following obtain:
(1) the less safe option is not certainly contrary to natural law or Church teaching
(2) the conscience of the doer is not violated by it
(3) if public it is not likely to create scandal and stumblingblocks to those with weaker consciences
(4) to the best one can determine one is motivated by love of God and neighbor.
It is primarily when these conditions fail or are uncertain that the matter becomes less clear, & probabilism more doubtful.

--Leibniz on barbarism in physics

We should not think of A E I O as kinds of proposition so much as formats. They are enunciations of the enunciable.

the sin of censoriousness: treating prudential counsels as dictates of natural law
(one of the problems of tutiorism is that it encourages censoriousnss as laxism encourages licentiousness)

Every icon is an icon of Christ, and therefore of the Trinity; icons of saints represent the fact that Christ is in His saints and the saints in Christ.

It is in the nature of poetry accidentally to say something profound in saying something obvious: the profound in the obvious.

these secularist-ridden, superstitious, dark times

The best thing to do with a formal system is to push it until it breaks. How else can one determine the specifications for its proper use?

ubi dubium libertas

logic as an aid to translation

Doubt is a debt to be settled.

poetic meditation: "emotion recollected in tranquillity" (Wordsworth)

history as an act of social bonding

"Philosophy is not produced by those who spend their efforts on verbal skirmishes and contests." St. Isidore of Pelusium Ep. 220

Each musical instrument has its own sophia or wisdom.

Distrust of prudent and the presumption of being prudent oneself are the two things that most distort our moral judgments.

A Post of Pirates

Just because.

* Oh, Better Far to Live and Die (from The Pirates of Penzance)

* George Harrison Singing the Pirate Song

* The VeggieTales Version of The Pirates Who Don't Do Anything

* The Relient K Version of The Pirates Who Don't Do Anything

* My favorite Jack London novel

* Stevenson's Treasure Island

* Sir Walter Scott's The Pirate

Analogy as an Equivalence Relation

Due to lack of sleep and tiring work, my brain has been officially MIA since about 1 o'clock this afternoon, so it's very risky to do a logic post, even a simple one. But since my brain has been lost somewhere since about 1 o'clock, my ability to assess risks is impaired. So here goes.

An equivalence relation is a relation that has the following characteristics:

It is reflexive (a is related to a).
It is symmetrical (if a is related to b, b is related to a).
It is transitive (if a is related to b, and b is related to c, a is related to c).

One might regard analogy, understood as a relation, as meeting each of these criteria.

A is analogous to A. This can be taken as a tautology, so we can add the analogy a : a to any inference at any time, for any a. So if you are reasoning analogically you can always take something as its own analogue.

If A is analogous to B, B is analogous to A. If there is something in or about A that is similar enough to something in or about B that we can say that A is analogous to B, for that very reason we can say that B is analogous to A.

So analogy in general is certainly reflexive and symmetrical.

If A is analogous to B, and B is analogous to C, A is analogous to C. Slightly trickier. Consider:

(1) A is analogous to B. (Premise)
(2) B is analogous to C. (Premise)
(3) C is analogous to B. (from 2 by Symmetry)

It is clear from (1) and (3) that A and C are analogous in at least one respect: namely, they both are analogous to B. Thus if we take 'is analogous to' to mean 'is analogous to in any way', analogy is always transitive. Sometimes when we are talking about analogy we restrict to the transitivity of analogy to what might be called relevant analogy, i.e., cases where the analogy of A to B and of B to C meet some special condition that allows us to say the two are relevant to each other. This is an entirely legitimate way to go, of course; but we set aside such approaches for now.

So analogy is an equivalence relation. On the basis of this you can build an axiom system using analogy as your only equivalence relation. (I'll simply write 'x is analogous to y' as 'xy'.)

We'll take the above properties and analogize them:

Reflexivity: (aa)
Symmetry: (ab)(ba) [i.e., 'a is analogous to b' is analogous to 'b is analogous to a']
Transitivity: (((ab)c)(a(bc)))

Some other axioms you might have:

Verisimilitude: T(aa)
Falselikeness: F(~T)
Double negation (~(~a))(a)
Analogical Distributivity of Disanalogy: (~(ab))((~a)b))
Analogical Distributivity of Disjunction: ((a v (b v c))((a v b) v (a v c))

And so forth. Because analogy's being taken as an equivalence relation we can substitute analogue for analogue. There's nothing distinctively interesting about this, since it's just an ordinary, humdrum sort of logic, with the only qualification being that it's all done with analogies. Actually, unless I'm mistaken, it's a straightforward equational logic in which all of the equations are analogies. Proofs are straightforward, e.g.:

(1) (~(F(~(aa)))) [premise to be refuted]
(2) (~(~(aa)F)))) [1, symmetry]
(3) (aa)F [2, double negation]
(4) T(aa) [axiom]
(5) F(~T) [axiom]
(6) (aa)(~T) [3,5 substitution]
(7) (T)(~T) [4,7 substitution]

(7) is the analogical version of a contradiction.

Links

* There's a new Secular Philosophy blog up; right now it doesn't have much, but it might eventually be interesting.

The First Carnival Against Pornography and Prostitution is up at "The Burning Times". (ht)

* Those who have an interest in MacIntyre's discussions of Tradition, Genealogy, and Encyclopaedia will also find Abraham Kuyper's Encyclopaedia of Sacred Theology (1898) interesting; the work opens with several chapters discussing the history and idea of Encyclopaedia as a field of inquiry. Fascinating material.

* Paul Redding, The Relation of Logic to Ontology in Hegel (PDF)

James K. A. Smith, Continental Philosophy of Religion: Recommended Practices for the Future of the Field (PDF)

P. Gaffney, Saint Louis Marie de Montfort and the Bérullian School at the Montfortians Spirituality pages

Rahman & Carniellie, The Dialogical Approach to Paraconsistency (PDF)

Delphine, Kolesnik, L’union de l’âme et du corps selon Malebranche

* glach at FQI on Robert Boyle's distinction between qualities.

* Historical examples of letters of marque. In the U.S. Congress has the constitutional authority to issue such letters, authorizing and commissioning privateers as agents of the U.S. government. (Most European states gave up authority to do so with the 1856 Declaration of Paris.)

* Jen of "Et tu?" has a post on how she became pro-life.

ADDED LATER

* Harriet Beecher Stowe, A Key to Uncle Tom's Cabin, Presenting the Original Facts and Documents upon which the Story is Founded, Together with Corroborative Statements Verifying the Truth of the Work.

Rough Jottings on Syncategorematic and Categorematic Infinites

And I do mean rough. It has been known since the Middle Ages that talk of infinites admits of two basic types of interpretation, the categorematic and the syncategorematic. Roughly, if I say "The numbers for counting are infinite," I can mean that for any number or magnitude to which one counts (which is always finite), there is a greater to which he counts (which is always finite). That's syncategorematic. Or I can mean that the counting numbers together constitute something greater than any number or magnitude to which one can count. They are not the same because they have different logical properties. If I take "An infinity of numbers will be counted" categorematically, I mean that all the numbers actually counted constitute a magnitude greater than any finite number; if I take it syncategorematically, I mean that any given finite number of numbers counted will be surpassed by some larger finite number of numbers counted. The former gives me an infinite magnitude; the latter gives me an unending series of finite magnitudes.

Most people assume that syncategorematic infinites are necessarily potential. This is not so clear: Leibniz, for instance, argues for an actual syncategorematic infinite. If a syncategorematic infinite is potential, it indicates a count or increase that is always finite but does not stop. The count is actually infinite (in the sense that it has no finite stopping point) but is not an actual infinite (because it is always finite). But not every syncategorematic infinite is obviously potential.

Here is a possible example. If every traversal requires a beginning and an end, and an infinite past has no beginning, this is a problem only if we already assume that traversal of an infinite past would require traversal of infinite days. But on the infinite past view, every day in the past is finitely distant from the present; it's just that for every finitely distant day there's a day that is more distant. Thus this is true: For every day in the past, traversal of the days from that day to today is traversal of a finite number of days. The fact that there are infinite such days doesn't change this. This is true just as much as it is true that the fact that every integer is a finite distant from zero is not made a problem by the fact that there are infinite numbers. This is, arguably, Aquinas's point in response to arguments that purport to demonstrate the impossibility of an infinite past, although he does not use the terminology. Such arguments cannot show that an actual syncategorematically infinite past is impossible; at most they show that an actual categorematically infinite past is impossible. We can think of it as a count (backwards in time): every day is counted, but the count never ceases to be finite, because every day is a finite distance from the day at which we begin. Just as every natural number is a finite distance from zero (and thus counting never gets you anything other than a finite number), so every day in the past is a finite period of time before today. What makes the infinite is not that there is ever any infinite distance actually covered, but that there is no finite limit to the finite distances covered.

On the other hand, the only thing that makes this an actual infinite is that we have asserted by fiat that the syncategorematically infinite count is completely actual --the days have already gone by. If someone insisted that every syncategorematic infinite is potential, there's very little grounds on which one could argue that they are wrong. Leibniz, for instance, argues that extension is an instance of actual syncategorematic infinity: every part of an extended body has an actual division into other parts of that body. If, indeed, the latter is true, the parts of the body are an actual syncategorematic infinite: no part would be infinitely small, since very part would be finitely small, but there is no limit to how finitely small you could get. But if someone simply denied this, holding instead that the division is always potential, there's no clear argument you could give otherwise; it's not as if you could say, "Here, look, see for yourself, these are all the infinite divisions of the extended body." Thus there doesn't seem to be any available (non-question-begging) argument that a syncategorematic infinite is actual; one either postulates it or not, and it would seem there's an end on it.

Re-Draft of a Poem

Septentrion

The whisper of a wind that curls beneath the stars
brushes my cheek; the rain of light is constant
while the galaxies, all rushing, their presence withdraw
as though, from some primeval atom, they burst,
soared into life, and never stopped.
Round and round the stars speed along a crease
some strange black thing has drawn,
a symphony of circles, well mingling with well.
And I, who know no star but home,
speed through the ceaseless black of night,
no light for my path save the singing suns,
and sail the dark Septentrion out to forever's end.

Kindle and Keep

The Ceremonies for Candlemas Day

by Robert Herrick

Kindle the Christmas brand, and then
Till sunset let it burn;
Which quench'd, then lay it up again,
Till Christmas next return.

Part must be kept, wherewith to teend
The Christmas log next year;
And where 'tis safely kept, the fiend
Can do no mischief there.

Arnauld's Summary of Malebranche's Epistemology

Arnauld suggests that Malebranche's epistemology can be summarized in three points:

The first is that our mind can see material things not through themselves, but only through representative beings which are distinct from our perceptions and must precede them, and to which he gave the name 'ideas,' though it was a misuse of the word.

The second is that our mind can find those ideas, or beings representative of material things, only in God.

The third is that what makes it possible for the mind to find them in God is that God contains in himself an infinite intelligible extension.

Antoine Arnauld, On True and False Ideas, Kremer, tr. Edwin Mellen (1990) p. 106. The summary is fairly decent, as one would expect of Arnauld, although one can quibble a bit with both the selection and the unqualified statements.

Subalternating Suppositions

I previously noted a supposition that allows subalternation without any bothering with existential import; discussing the matter with Tom, I said at one point that I didn't know if the particular supposition I noted was required. Having thought about the matter more, I can think of the following distinct suppositions that allow for subalternation.

(1) A and I as having existential import. Whatever it means to attribute existential import to propositions, it's generally taken for granted that attributing it to A and I allows subalternation. Similarly for E and O.

(2) Some S is S. Whether we take "Some S is S" as existential or not, it still makes supposition possible:

-S+P
+S+S
Therefore +S+P

-S-P
+S+S
Therefore +S-P

(3) A propositions as double propositions. Lewis Carroll allows subalternation in his system by making A propositions double propositions: "All S is P" simply means "Some S is P and No S is nonP." (He also accepts that A and I have existential import. But I don't see that this is strictly required by the move; Carroll accepts existential import for A and I for independent reasons.) Welton also has this view, and suggests the same for E propositions.

(4) Instantiation with generalization. We can add to term logic forms of instantiation and generalization:

Start with -S+P (All S is P, i.e., every instance of S is P)
instantiate to *S+P (a given instance of S is P)
generalize to +S+P (Some S is P).

Whether you think this fourth supposition is a case of 'existential import' depends, I think, on what you think something like universal instantiation is in the predicate calculus.

I'm sure there are others that could be put forward.

UPDATE: Doing a bit of reading, I find that Carveth Read claims that subalternation follows merely by the principle of identity; McCosh says it follows from the principle that "whatever is true of a class is true of any and of each of the members of the class." I think Read means same thing as McCosh; Veitch also claims subalternation rests on the principle of "Identity of whole and part". Morell likewise says that the correctness of subalternation "depends upon the relation which a logical whole bears to its parts." Parimal Kumar Ray gives two arguments for subalternation: (1) the particular simply repeats (part of) the information in the universal; and (2) what fails even in one case cannot be universally affirmed and what obtains even in one case cannot be universally denied. Francis Garden just says that it is "plain to the dullest capacity."

Expect Lighter Posting

If the past few days are any indication, February is going to be an insanely busy month for me. I'll still be posting, but the forecast is for a much slower rate.