… ETIAM PER PRAEPOSTEROS HOMINES …: A NOTE ON AUGUSTINE, CONFESSIONES 9.18

In Book 9 of his Confessions, Augustine recounts that his mother Monica told him how ‘a weakness for wine gradually got grip upon her’ as a little girl. After some time, so the story goes, God healed her from her bad habit. In this context, Augustine observes: ‘When father and mother and nurses are not there, you are present. You have created us, you call us, you use human authorities set over us to do something for the health of our souls.’ Even though at first sight this passage does not seem to pose any problems, one wonders about the exact meaning of the last part: etiam per praepositos homines boni aliquid agis ad animarum salutem. First, it is to be noted that Henry Chadwick's translation cited here leaves etiam untranslated. Moreover, it is not certain at all that Augustine really wants to say that God heals human souls ‘even by those human beings who are set over us’. As the subsequent lines of this paragraph make clear, God freed Monica from her sin through her servant, who scoffingly called her young mistress ‘a little boozer’ (meribibulam). This renders the phrase etiam per praepositos homines problematic, on the one hand, because the meaning of etiam (which often implies a kind of gradation) is unclear and, on the other, because it is difficult to regard Monica's servant as one of the ‘human authorities’. Nothing in the text compels us to identify this servant with the old famula of Monica's parents who, according to the preceding paragraph (9.17), was ‘vehement with a holy severity in administering correction and soberly prudent in her teaching’. At any rate, the ancilla mentioned here (9.18) is depicted not as an authoritative person but rather as someone who quarrels with her young domina (that is, with Monica), not in order to heal or educate her but merely to irritate her.

Announcement: First Edition of IASA-TC 06 Online

Archives hold original video recordings in a range of types, from media-dependent, carrier-based analogue videotapes to computer-file-based digital recordings. The appropriate preservation treatments for this array reflect the variation in the source recordings. For analogue videotapes, for example, digitisation is called for. Meanwhile, examples of digital file-based recording may require rewrapping into a fresh file "wrapper" or a combination of digital transcoding and rewrapping. When complete, IASA-TC 06 will cover the full range of topics in the preceding paragraph, as well as providing advice on shooting ethnographic, documentary, and oral history video footage in a manner that maximizes its "preserve-ability".

Ch.4 Interpretation, Art.4.2

This commentary focuses on Article 4.2 of the UNIDROIT Principles of International Commercial Contracts (PICC) concerning interpretation of unilateral statements and other conduct of a party. Under Art 4.2, the statements and other conduct of a party shall be interpreted according to that party's intention if the other party knew or could not have been unaware of that intention. If the preceding paragraph is not applicable, such statements and other conduct shall be interpreted according to the meaning that a reasonable person of the same kind as the other party would give to it in the same circumstances. This commentary discusses interpretation according to the intention of the party making the statement or engaging in the conduct, interpretation according to the understanding of reasonable persons, the relationship between Art 4.2(1) and (2), and burden of proof for parties wishing to invoke Art 4.2(1) or Art 4.2(2).

The New Story in Biology: Parts and Wholes in the Web of Life

In July of 1969 the Apollo 11 spacecraft emerged from the dark side of the moon and the on-board camera panned through the vast emptiness of outer space. Against the backdrop of interstellar night hung the great ball of earth, with the intense blue of its oceans and the delicate ochres of its landmasses shimmering beneath the vibrant and translucent layer of its atmosphere. In the shock of this visual moment, distances between us contracted; boundaries and borders ceased to exist. But the impression that sent the adrenaline flowing through my veins was that the teeming billions of organisms writhing about under the protective layer of the atmosphere were not separate—they were interdependent, fluid, and interactive aspects of the one organic dance of the planet’s life. The preceding paragraph, an entry form my diary written a few days after images of the whole earth first appeared on television, cannot be classed as scientific analysis. But it is entirely consistent with what the new story of science has revealed about the relationship between human and environmental systems in biological reality. The large problem here is that the political and economic narratives that now serve as the basis for coordinating global human activities are premised on scientifically outmoded assumptions about this relationship in the old story of classical physics. And this problem is further complicated by the fact that the view of this relationship that is still widely viewed as scientific in Darwin’s theory of evolution is also premised on these scientifically outmoded assumptions. Darwin went public with his theory for the first time in a paper presented to the Linnean Society in 1848. This paper begins with the following sentence: “All nature is at war, one organism with another, or with external nature.” In The Origins of Species , Darwin is more specific about the character of this war: “There must be in every case a struggle for existence, either one individual with another of the same species, or with the individuals of distinct species, or with the physical conditions of life.”

Expansions of dense linear orders with the intermediate value property

Let ℜ be an expansion of a dense linear order (R, <) without endpoints having the intermediate value property, that is, for all a, b ∈ R, every continuous (parametrically) definable function f: [a, b] → R takes on all values in R between f(a) and f(b). Every expansion of the real line (ℝ, <), as well as every o-minimal expansion of (R, <), has the intermediate value property. Conversely, some nice properties, often associated with expansions of (ℝ, <) or with o-minimal structures, hold for sets and functions definable in ℜ. For example, images of closed bounded definable sets under continuous definable maps are closed and bounded (Proposition 1.10).Of particular interest is the case that ℜ expands an ordered group, that is, ℜ defines a binary operation * such that (R, <, *) is an ordered group. Then (R, *) is abelian and divisible (Proposition 2.2). Continuous nontrivial definable endo-morphisms of (R, *) are surjective and strictly monotone, and monotone nontrivial definable endomorphisms of (R, *) are strictly monotone, continuous and surjective (Proposition 2.4). There is a generalization of the familiar result that every proper noncyclic subgroup of (ℝ, +) is dense and codense in ℝ: If G is a proper nontrivial subgroup of (R, *) definable in ℜ, then either G is dense and codense in R, or G contains an element u such that (R, <, *, e, u, G) is elementarily equivalent to (ℚ, <, +, 0, 1, ℤ), where e denotes the identity element of (R, *) (Theorem 2.3).Here is an outline of this paper. First, we deal with some basic topological results. We then assume that ℜ expands an ordered group and establish the results mentioned in the preceding paragraph. Some examples are then given, followed by a brief discussion of analytic results and possible limitations. In an appendix, an explicit axiomatization (used in the proof of Theorem 2.3) is given for the complete theory of the structure (ℚ, <, +, 0, 1, ℤ).

The Ambivalent Triumph of Optimism

To increase—even to live—human populations require exploitable resources. Concern for the future of our children makes us wonder how long resources will last. Attitudes toward conservation depend largely on information furnished by the press, radio, and television. How good is this information? Mostly it is not very good. We don't have to probe the shoddier representatives of the press to illustrate the fine art of warping attitudes. A single example from a quality source will do. How much petroleum is there in the world? This is not a simple question. Do we want to know the total amount of petroleum resources, both discovered and undiscovered? This is obviously debatable. A more useful base on which to lay plans for the near future is what is called proved reserves, which is defined as the supply "that can be economically produced with current technology at today's prices." Before proceeding further it would be well to call attention to the confusibility of the terms resources and reserves. A creative writer who turned out a novel in which the two principal characters were named Jean Robinson and Jan Robertson would be criticized for causing needless confusion. Unfortunately the analysts of the real world frequently burden the public with terms that, though definitively different, scarcely differ to the eye and ear. Such are resources and reserves. These terms have been used for so long that they can hardly be jettisoned now. When a feeling of imminent confusion sweeps over the reader, he is urged to review the definitions in the preceding paragraph. Even for reserves there is no precise and stable figure. A new technology may lower the cost of taking oil out of the ground. A rise in price will cause the ledger entry for some underground oil to be moved from the category of economically unrecoverable to that of economically recoverable. The scarcity that causes the price to rise "brings oil out of the ground," in the words of optimistic economists. Scarcity, in the mind of some economists, creates more oil. (Geologists know better.) The price of oil is very sensitive to proved reserves, but decidedly insensitive to estimates of ultimate resources.

Dynamic decision problems in an insurance company

1.1. — In this paper we shall consider some of the decisions which have to be made in the normal course of business in an insurance company. We shall see that the “right” decisions can be found only when the problems are analysed in their proper dynamic context.As examples of the decision problems which we shall study, we can mention the following:(i) What premium rates should be quoted on the insurance contracts, which the company offers to the public?(ii) How much should the company spend to promote the sale of its policies?(iii) When should the company refuse to underwrite a proposed insurance contract?(iv) How shall the company reinsure its portfolio of insurance contracts?(v) What reserve funds should an insurance company keep?(vi) How shall the company's funds be invested?Any actuary will be familiar with such problems, and he will probably feel that these problems cannot be satisfactorily solved with the methods offered by the classical actuarial theory.1.2. — In some earlier papers [I] and [2] it has been argued that such problems can best be solved in the frame work of utility theory. As an illustration we shall take Problem (iii) in the preceding paragraph, and consider an insurance company in the following situation:(i) The company has a capital S.(ii) The company holds a portfolio of insurance contracts which will lead to a total payment of x to settle claims. F1(x) is the distribution of the variate x.

Investigations in the Field of Rubber Vulcanization. IV. Phenomenon of Vulcanization Optimum in Mixtures with a Large Proportion of Constructive Agent

1. In mixtures with a large content of constructive (vulcanizing) agent, the vulcanization-optimum phenomenon is connected with the formation of dense space-lattices in the structure of the vulcanizate, which inhibit the formation of crystalline or highly oriented segments during elongation. 2. In contrast to mixtures with a small content of vulcanization agent, the vulcanization optimum of which is explained by superimposition of oppositely directed constructive and destructive processes, the case noted in the preceding paragraph shows a maximum only on the kinetic curve representing the change in strength. The kinetic curves representing relative elongation, swelling, and solubility are monotonic in character. 3. The maximum on the kinetic curve representing the change in strength in mixtures with a large content of constructive agent occurs before complete combination of the latter with the rubber. 4. In consequence of the absence of oppositely directed actions on the part of sulfur and oxygen, the vulcanization of sodium-butadiene rubber mixtures shows a maximum only on the kinetic curves representing the change in strength. 5. The position of the strength maximum in mixtures with a large content of constructive agent depends on the rate of deformation. As the rate of deformation is decreased, the maximum appears after more prolonged vulcanization periods of the mixtures. 6. The strength of natural rubber vulcanizates at the vulcanization optimum is a linear function of the quantity of crystalline phase formed during elongation.

A note on the Entscheidungsproblem

In a recent paper the author has proposed a definition of the commonly used term “effectively calculable” and has shown on the basis of this definition that the general case of the Entscheidungsproblem is unsolvable in any system of symbolic logic which is adequate to a certain portion of arithmetic and is ω-consistent. The purpose of the present note is to outline an extension of this result to the engere Funktionenkalkul of Hilbert and Ackermann.In the author's cited paper it is pointed out that there can be associated recursively with every well-formed formula a recursive enumeration of the formulas into which it is convertible. This means the existence of a recursively defined function a of two positive integers such that, if y is the Gödel representation of a well-formed formula Y then a(x, y) is the Gödel representation of the xth formula in the enumeration of the formulas into which Y is convertible.Consider the system L of symbolic logic which arises from the engere Funktionenkalkül by adding to it: as additional undefined symbols, a symbol 1 for the number 1 (regarded as an individual), a symbol = for the propositional function = (equality of individuals), a symbol s for the arithmetic function x+1, a symbol a for the arithmetic function a described in the preceding paragraph, and symbols b1, b2, …, bk for the auxiliary arithmetic functions which are employed in the recursive definition of a; and as additional axioms, the recursion equations for the functions a, b1, b2, …, bk (expressed with free individual variables, the class of individuals being taken as identical with the class of positive integers), and two axioms of equality, x = x, and x = y →[F(x)→F(y)].

THE RÓLE OF STREPTOCOCCI IN EXPERIMENTAL POLIOMYELITIS OF THE MONKEY

It is the opinion of Bull, that the streptococci recovered from poliomyelitic tissues, while having no etiological or pathological relationship to the virus of poliomyelitis, occur as secondary invaders in the disease. Smillie and Amoss indicated that the bacteria may be agonal invaders. The results of the experiments reported in this paper point to another source of the streptococci. They occur as contaminants which are introduced into the cultures during the process of grinding tissues. The source of the streptococcus may therefore be the air of the place in which the cultures are made. We have come to this conclusion because first, the tissues of which cultures yielded streptococci were derived from a number of monkeys with experimental poliomyelitis still in a vigorous state. Secondly, when the tissues were ground bacteria were noted much more frequently in their cultures than in those in which fragments of the same brains were used. Thirdly, microorganisms occurred more often in cultures made in the routine laboratory than in a special room where asepsis was carried to the extreme of a major surgical operation on man. Fourthly, streptococci were obtained from the air of the places where cultures were made. Finally, there is no correlation between the cultures of two portions of the same brain. The streptococci occurred in some cultures in pure growth and in others admixed with other ordinary species of bacteria. The latter were often found, in turn, in pure culture and what applies to streptococci, as mentioned in the preceding paragraph, applies equally to the staphylococci, diphtheroids, spore-bearing rods, and other miscellaneous, familiar microorganisms. We could not determine that there exists any etiological relation of the streptococci to poliomyelitis. The fermentation reactions of the microorganisms obtained from the air, from non-poliomyelitic and poliomyelitic monkey brains indicate that bacteria from any of these sources are markedly different. So also with the serological reactions of agglutination and precipitation. Furthermore no agglutination was observed when the serum of monkeys convalescent from experimental poliomyelitis was mixed with any of the streptococci recovered or those received directly or indirectly from Rosenow. Moreover, the intracerebral injection with cultures, irrespective of their source, induced in rabbits a purulent type of meningoencephalitis, often associated with streptococcic septicemia. This result is at marked variance with any known effects of the true filtrable virus of poliomyelitis in man and in the monkey.