We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

What are the constraints, cues, and mechanisms that help learners create successful word-meaning mappings? This study takes up linguistic disjunction and looks at cues and mechanisms that can help children learn the meaning of or. We first used a large corpus of parent-child interactions to collect statistics on or uses. Children started producing or between 18-30 months and by 42 months, their rate of production reached a plateau. Second, we annotated for the interpretation of disjunction in child-directed speech. Parents used or mostly as exclusive disjunction, typically accompanied by rise-fall intonation and logically inconsistent disjuncts. But when these two cues were absent, disjunction was generally not exclusive. Our computational modeling suggests that an ideal learner could successfully interpret an English disjunction (as exclusive or not) by mapping forms to meanings after partitioning the input according to the intonational and logical cues available in child-directed speech.

This article introduces and clarifies a neglected sense of the word ἤ (‘or’) employed by Aristotle and other authors. In this sense, called ‘indifferent’, ἤ signifies ‘one or the other, regardless of which’. It is shown how attention to this use makes it possible to explain the source of the ambiguity of certain sentences, most obviously, though not exclusively, sentences that make a necessity claim about an embedded disjunction, for example ‘It is necessary that A or B’. Why this sense cannot be explained, as some scholars have suggested, by the distinction between exclusive and inclusive ἤ is also discussed. Finally, it is shown how awareness of this sense might rescue Aristotle from a gross inconsistency.

The use of the symbol $\mathbin {\boldsymbol {\vee }}$ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol $\mathbin {\boldsymbol {\vee }}$ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol $\mathbin {\boldsymbol {\vee }}$ for disjunction can be traced to Whitehead and Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of $\mathbin {\boldsymbol {\vee }}$ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed.

Using an ITS mutation rate as calibration reference, a three-locus timetree was generated for the genus Lobaria and its most important clades. The timetree resolved most clades with strong support and gave an estimate of the diversification time for Lobaria during the early Oligocene. A fossil impression from a 12–24 million-year-old Miocene deposit is hypothesized here to belong to an ancestral Lobaria species. Additionally, the age estimate indicates that the paleoclimate and the closing or opening of the Bering Strait played a major role in shaping the current distribution of most Lobaria species. It is hypothesized that the Bering land bridge acted as a major highway during warm-temperate climate periods, but as a barrier during Arctic climate times.

This article compares the Apocalypse of Weeks with Galatians to examine whether the motif of creatio e contrario is apocalyptic. While reviewing the themes of revelation, salvation and eschatology in each text, it argues that creatio e contrario is absent from and theologically foreign to the Apocalypse; by contrast, this motif permeates Galatians, not because Paul retrieves it from the apocalypses but because for him the divine economy is shaped by the disjunctive, e contrario history of the crucified and risen Christ. Thus, creatio e contrario should be classified not as apocalyptic but as christomorphic.

This article presents a case study of the influence of Muslim and Christian logicians on medieval Jewish law. The case in question is why it is a punishable offense for Jews to eat mammals that do not have either sign of purity—that is, neither have split hooves nor chew their cud—and the article examines the answers given by three medieval Jewish sages: Rashi, Maimonides, and Naḥmanides. The Written Law of the Torah explicitly allows the consumption of mammals, such as cattle, with both signs of purity. It also explicitly prohibits the eating of mammals, such as camels or pigs, with one sign but not the other. It does not, however, appear to explicitly prohibit the consumption of mammals, such as horses, with neither sign. Using a fortiori logic, Rashi derives a punishable prohibition against eating horses from the prohibition against eating camels and pigs. Maimonides ascribes this prohibition to the Oral Law of the Talmud. Naḥmanides, by contrast, attributes it directly to the Written Law without relying on either a fortiori logic or the Oral Law. This article argues that this solution was available to Naḥmanides because he adopted inclusive disjunction from Christian logicians, but it was not available to Maimonides because he adopted exclusive disjunction from Muslim logicians. The choice between inclusive and exclusive disjunction is shown to continue to be of importance in modern American law.

Two new species of Convolvulus (Convolvulaceae), C. excelsus R.R.Mill and C. infantispinosus R.R.Mill, are described from Saudi Arabia. Convolvulus excelsus, an exceptionally tall species, has affinities with C. erinaceus Ledeb. but is phytogeographically disjunct from that and other allied species. Two new subspecies are also described: Convolvulus hystrix Vahl subsp. dhofarica R.R.Mill, from Oman, and C. oxyphyllus Boiss. subsp. sheilae R.R.Mill, from Saudi Arabia. Each novelty is given a provisional IUCN conservation assessment.

Adelocaryum Brand (Boraginaceae – Cynoglosseae) is shown to be the correct name for Paracaryopsis (H.Riedl) R.R.Mill, and the new combination Adelocaryum lambertianum (C.B.Clarke) R.R.Mill is made. The new species Adelocaryum nebulicola R.R.Mill is described from Oman and its affinities with the Indian species A. coelestinum (Lindl.) R.R.Mill are discussed. A synopsis of and revised key to the entire genus is provided as well as a revised description of Adelocaryum coelestinum. As circumscribed here Adelocaryum is restricted to tall mesophytic herbs lacking long glochidiate spinules on the wing-like margin of the nutlets. The desert annual or biennial Brandella erythraea is here excluded from Adelocaryum. The new combination Brandella erythraea forma subexalata (H.Riedl) R.R.Mill is made. Lindelofia spectabilis Lehm., for which the current correct name is L. longiflora (Benth.) Baill., is designated lectotype of the genus Lindelofia Lehm.

The genus Campylanthus (Scrophulariaceae) is revised and 15 species are recognized. The genus shows a markedly disjunct pattern of distribution, with two species in Macaronesia, 12 in northeastern Africa and Arabia, and one in western Pakistan. With few exceptions all have very restricted distributions. The position of the genus within the Scrophulariaceae is discussed, and it is concluded that Campylanthus is best placed as incertae sedis. Morphological aspects of the genus are discussed and a cladistic analysis including all species is presented. The analysis indicates a basal split between western and eastern species in the genus. A key, descriptions and distribution maps for all species are provided, and some lectotypes and neotypes are selected.