Locations

1979 ◽  
Vol 9 (2) ◽  
pp. 323-333 ◽  
Author(s):  
William J. Edgar

Zeno's challenge to the usual mathematical characterization of extension is still with us. Butchvarov, considering the limits of ontological analysis, writes, “I shall not explore [the decision to accept the infinite regress in which the pursuit of the analytical ideal is involved], beyond noting that the infinite divisibility of space is the reductio ad absurdum of any attempt to understand space in terms of its ultimate, simple parts.” Grünbaum states this problem, commonly known as the Measure Paradox, concisely, “[How can one conceive] of an extended continuum as an aggregate of unextended elements ?”

1980 ◽  
Vol 17 (02) ◽  
pp. 574-576
Author(s):  
Manish C. Bhattacharjee

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.


1980 ◽  
Vol 17 (2) ◽  
pp. 574-576 ◽  
Author(s):  
Manish C. Bhattacharjee

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.


Dialogue ◽  
1970 ◽  
Vol 9 (3) ◽  
pp. 356-365 ◽  
Author(s):  
Eike-Henner W. Kluge

Consider the paradox of Achilles and the tortoise. Both Zeno and the philosophic tradition after him have accorded it the status of a legitimate problem. It is my aim to show, that both Zeno and the tradition have been mistaken; that the basis of the alleged paradox is a none too clear analysis of the nature of spatial relations; and that the appearance of the paradox itself rests on a confusion of two types of analysis: an ontological analysis on the one hand, and a qualitative one on the other. I shall therefore suggest a solution to the paradox that in effect amounts to a denial of its legitimacy.


Author(s):  
ANNA DOROTA KRYSTEK

Infinite divisibility for the free additive convolution was studied in Ref. 20. A complete characterization of [Formula: see text]-infinitely divisible distributions was given, and it was explained in Ref. 21 that this characterization is an analogue of the classical Lévy–Khintchine characterization. In fact, the analogue of the Gaussian distribution appeared even earlier, when the central limit theorem for free additive convolution was proven in Ref. 19. In this paper we define the notion of [Formula: see text]-infinitely divisibility and give the description of infinitely divisible compactly supported probability measures relative to the conditionally free convolution. We also show that the Lévy–Khintchine measures associated with a [Formula: see text]-infinitely divisible distribution μ can be calculated, as in the classical or free case, as a weak limit of measures related with the convolution semigroup generated by (μ, φ) for [Formula: see text]-infinitely divisible.


Philotheos ◽  
2019 ◽  
Vol 19 (1) ◽  
pp. 85-105
Author(s):  
Jeffrey Dirk Wilson ◽  

St. Thomas’s Third Way to prove the existence of God, “Of Possibility and Necessity” (ST 1, q.2, art. 3, response) is one of the most controverted passages in the entire Thomistic corpus. The central point of dispute is that if there were only possible beings, each at some time would cease to exist and, therefore, at some point in time nothing would exist, and because something cannot come from nothing, in such an eventuality, nothing would exist now—a reductio ad absurdum conclusion. Therefore, at least one necessary being must exist. Generations of critics and defenders have contended over St. Thomas’s proof. This article argues that the principle of pros hen analogy is implicit in the Third Way and that once identified explains the ontological dependency of possible beings, as secondary analogates, on the first necessary being, as primary analogate. Thus, without the necessary being as primary analogate, possible beings simply could not exist. The fact that they do exist is evidence for the existence of the necessary being. St. Thomas makes synthesizes the principle of pros hen analogy, as found in Aristotle’s Metaphysics, with the Neoplatonic principle of participation. Aristotle develops pros hen analogy in contradistinction to univocal and equivocal predication as well as to genus in Metaphysics 4.2, 11.3, 12.3-5. Since Scotus and re-enforced by modern analytic logic, philosophers have almost universally regarded any kind of analogical predication as a sub-category of equivocal predication and, thus, implicitly occlude the possibility of considering pros hen analogy in their readings of the Third Way. Distinction of per se and per accidens infinite regress and of radical and natural contingency are also central to understanding the Third Way. While resolving apparent problems in the Third Way, the article also seeks to rehabilitate the doctrine of pros hen analogy as a basic principle in Thomistic and, indeed, Aristotelian metaphysics.


Author(s):  
B. L. Soloff ◽  
T. A. Rado

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.


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