Understanding natural phenomena is an important aim of science. Since the turn of the millennium the notion of scientific understanding has been a hot topic of debate in the philosophy of science. A bone of contention in this debate is the role of truth and representational accuracy in scientific understanding. So-called factivists and non-factivists disagree about the extent to which the theories and models that are used to achieve understanding must be true or accurate. In this paper we address this (...) issue by examining a case from the practice of synthetic chemistry. We investigate how understanding is obtained in this field by means of an in-depth analysis of the famous synthesis of periplanone B by W. Clark Still. It turns out that highly idealized models—that are representationally inaccurate and sometimes even inconsistent—and qualitative concepts are essential for understanding the synthetic pathway and accordingly for achieving the synthesis. We compare the results of our case study to various factivist and non-factivist accounts of how idealizations may contribute to scientific understanding and conclude that non-factivism offers a more plausible interpretation of the practice of synthetic chemistry. Moreover, our case study supports a central thesis of the non-factivist theory of scientific understanding developed by De Regt, namely that scientific understanding requires intelligibility rather than representational accuracy, and that idealization is one way to enhance intelligibility. (shrink)

A maximal almost disjoint (mad) family $\mathscr{A} \subseteq [\omega]^\omega$ is Cohen-stable if and only if it remains maximal in any Cohen generic extension. Otherwise it is Cohen-unstable. It is shown that a mad family, A, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the sets G[A], A ∈A are nowhere dense. An ℵ 0 -mad family, A, is a mad family with the property that given any countable family $\mathscr{B} \subset (...) [\omega]^\omega$ such that each element of B meets infinitely many elements of A in an infinite set there is an element of A meeting each element of B in an infinite set. It is shown that Cohen-stable mad families exist if and only if there exist ℵ 0 -mad families. Either of the conditions b = c or $\mathfrak{a} ) implies that there exist Cohen-stable mad families. Similar results are obtained for splitting families. For example, a splitting family, S, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the boundaries of the sets G[S], S ∈S are nowhere dense. Also, Cohen-stable splitting families of cardinality ≤ κ exist if and only if ℵ 0 -splitting families of cardinality ≤ κ exist. (shrink)

The game Gls(κ) is played on a complete Boolean algebra B, by two players. White and Black, in κ-many moves (where κ is an infinite cardinal). At the beginning White chooses a non-zero element p ∈ B. In the α-th move White chooses pα ∈ (0.p)p and Black responds choosing iα ∈ {0.1}. White wins the play iff $\bigwedge _{\beta \in \kappa}\bigvee _{\alpha \geq \beta }p_{\alpha}^{i\alpha}=0$ , where $p_{\alpha}^{0}=p_{\alpha}$ and $p_{\alpha}^{1}=p\ p_{\alpha}$ . The corresponding game theoretic properties of c.B.a.'s are (...) investigated. So. Black has a winning strategy (w.s) if κ ≥ π(B) or if B contains a κ -closed dense subset. On the other hand, if White has a w.s., then κ ∈ [h₂(B). π(B)). The existence of w.s. is characterized in a combinatorial way and in terms of forcing. In particular, if 2κ = κ ∈ Reg and forcing by B preserves the regularity of κ, then White has a w.s. iff the power 2κ is collapsed to κ in some extension. It is shown that, under the GCH, for each set S ⊆ Reg there is a c.B.a. B such that White (respectively. Black) has a w.s. for each infinite cardinal κ ∈ S (resp. κ ∉ S). Also it is shown consistent that for each κ ∈ Reg there is a c.B.a. on which the game Gls(κ) is undetermined. (shrink)

A set of axioms implicitly defining the standard, though not instant-based but interval-based, time topology is used as a basis to build a temporal modal logic of events. The whole apparatus contains neither past, present, and future operators nor indexicals, but only B-series relations and modal operators interpreted in the standard way. Determinism and indeterminism are then introduced into the logic of events via corresponding axioms. It is shown that, if determinism and indeterminism are understood in accordance with their core (...) meaning, the way in which they are formally introduced here represents the only right way to do this, given that we restrict ourselves to one real world and make no use of the many real worlds assumption. But then the result is that the very truth conditions for sentences about indeterministic events imply the existence of tensed truths, in spite of the fact that these conditions are formulated (in the indeterministic axiom) in terms of tenseless language. The tenseless theory of time implies determinism, while indeterminism requires the flow of time assumption. (shrink)

A sequence x=xn:nω of elements of a complete Boolean algebra converges to a priori if lim infx=lim supx=b. The sequential topology τs on is the maximal topology on such that x→b implies x→τsb, where →τs denotes the convergence in the space — the a posteriori convergence. These two forms of convergence, as well as the properties of the sequential topology related to forcing, are investigated. So, the a posteriori convergence is described in terms of killing of tall ideals on ω, (...) and it is shown that the a posteriori convergence is equivalent to the a priori convergence iff forcing by does not produce new reals. A property of c.B.a.’s, satisfying -cc -cc and providing an explicit definition of the a posteriori convergence, is isolated. Finally, it is shown that, for an arbitrary c.B.a. , the space is sequentially compact iff the algebra has the property and does not produce independent reals by forcing, and that implies P is the unique sequentially compact c.B.a. in the class of Suslin forcing notions. (shrink)

A complete Boolean algebra ${\mathbb{B}}$ satisfies property ${(\hbar)}$ iff each sequence x in ${\mathbb{B}}$ has a subsequence y such that the equality lim sup z n = lim sup y n holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori convergence in complete Boolean algebras with the sequential topology and a characterization of sequential compactness of such spaces, is closely related to the cellularity of Boolean algebras. Here we determine the position of (...) property ${(\hbar)}$ with respect to the hierarchy of conditions of the form κ-cc. So, answering a question from Kurilić and Pavlović (Ann Pure Appl Logic 148(1–3):49–62, 2007), we show that ${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}$ is not a theorem of ZFC and that there is no cardinal ${\mathfrak{k}}$ , definable in ZFC, such that ${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}$ is a theorem of ZFC. Also, we show that the set ${\{ \kappa : {\rm each}\, \kappa{\rm -cc\, c.B.a.\, has}\, (\hbar ) \}}$ is equal to ${[0, \mathfrak{h})}$ or ${[0, {\mathfrak h}]}$ and that both values are consistent, which, with the known equality ${{\{\kappa : {\rm each\, c.B.a.\, having }\, (\hbar )\, {\rm has\, the}\, \kappa {\rm -cc } \} =[{\mathfrak s}, \infty )}}$ completes the picture. (shrink)

If κ is an infinite cardinal, a complete Boolean algebra B is called κ-supported if for each sequence 〈bβ : β αbβ = equation imagemath imageequation imageβ∈Abβ holds. Combinatorial and forcing equivalents of this property are given and compared with the other forcing related properties of Boolean algebras . The set of regular cardinals κ for which B is not κ-supported is investigated.

If κω is a cardinal, a complete Boolean algebra is called κ-dependent if for each sequence bβ: β<κ of elements of there exists a partition of the unity, P, such that each pP extends bβ or bβ′, for κ-many βκ. The connection of this property with cardinal functions, distributivity laws, forcing and collapsing of cardinals is considered.

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...) B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

Before daybreak on 23 November 57 B.C., about 11 weeks after his return from exile, Cicero wrote to Atticus and recorded for him, in diary form, events at Rome between 3 November and the date of writing. Clodius and his gangs were still causing trouble on the streets, interfering with the rebuilding of Cicero's house on the Palatine, and even molesting Cicero himself. Clodius was a candidate for the curule aedileship; if he were elected, he would succeed in evading the (...) accusation for vis which had been brought against him by Milo; he therefore made full use of his gangs to intimidate Rome and thus accelerate the elections. He was supported in this manœuvre by the consul Q. Caecilius Metellus Nepos, who planned to hold the comitia by surprise; this plan, however, was being thwarted by the tribune Milo, who was ready to use his power of obnuntiatio to prevent the elections being held. (shrink)

Au total 1367 documents avec une inscription en linéaire A sur les 1427 connus peuvent être datés selon le système d'Evans. Ils permettent d'établir avec certitude que cette écriture a été en usage en Crète du MM II au MR I B, avec peut-être un prolongement au MR II. En dehors de Crète, elle est attestée dans les Cyclades, à Kéa au MM III et au MR I B, à Milos au MR I et à Théra au MR I A (...) ; elle est connue à Cythère au MM IIΙ Β-MR I Aet elle a même gagné la Laconie sans qu'on puisse dire à quelle époque. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:American Journal of Philology 121.4 (2000) 655-658 [Access article in PDF] RONALD MELLOR. The Roman Historians. London and New York: Routledge, 1999. x + 212 pp. Paper, $21.99. This is a textbook, the purpose of which is to provide "an introduction to the masterpieces of Roman historical and biographical writing" (ix). Although the question of the usefulness of these writings to the modern historian is not overlooked, the principal (...) concern is "to take Roman historical writing on its own terms" (196). Very little background is assumed, and no Latin (by "Roman" the title refers to works composed in Latin, regardless of subject matter: hence Nepos' Pelopidas is in, but Polybius, Diodorus, and Dio are out, except [End Page 655] as background or comparanda). The author is a distinguished Tacitean scholar, and his style is at once clear and attractive. His survey begins with the origins of Roman historiography, with special attention given to what can be known of the early annalists, to the contribution of the elder Cato, and especially to Cicero's verdict on the efforts of them all. Fine chapters on Sallust and Livy follow, and, naturally in view of the author's predilections, a long and adoring chapter on Tacitus. Ammianus Marcellinus also gets his due, in a chapter that is actually longer than Sallust's. A single chapter is devoted to Roman biography (Nepos, Tacitus once more, Suetonius and the Historia Augusta), another to autobiography (Caesar, Augustus' Res Gestae). An appraisal of the Roman achievement, and its influence, concludes the book. The strengths of Mellor's treatment of every author and every subject are many. He is keenly attentive to ancient expectations and the particular context of the central authors whose works he examines; he is especially good at fitting the purposes of a historian's writings to the historian's actual circumstances. He constantly reminds the reader of the differences between Roman and modern conceptions of historical writing. He appreciates the importance of style in appraising and understanding ancient historiography. And he makes frequent acute observations that will save instructors who use this book a good deal of time and explanation, as when he remarks of Tacitean characterization that, "since he could not easily explain ambiguities, they are expressed as contradictions" (104). In sum, then, the volume is intelligent, congenial, and will be very serviceable in courses dealing with Roman history or with historiography.It is inevitable, when anyone reviews a work of such scope, that there will be quibbles. Let me record a few of mine. Students are likely to be misled by the use of "plebeian" on p. 20. To say that, in 52 B.C., Clodius Pulcher was "Caesar's man," in contrast to Milo who by implication was Pompey's (31), is to get it wrong (cf. W. Jeffrey Tatum, The Patrician Tribune [Chapel Hill 1999] 214-15, 234-35). Since Caesar reached the senior magistracies at the earliest possible age, it is not clear to me that "his early career progressed slowly" (171). The view of Roman marriage represented on p. 69 is somewhat old-fashioned, and, along those lines, it is anachronistic to speak of "the bigamous marriage celebration of the empress Messalina" (90: Tacitus' Narcissus is accurate when at Ann. 11.30 he asks Claudius: an discidium... tuum nosti?). One does not often hear, these days, of the "clinical objectivity of Thucydides" (44). In discussing Sallust's attraction to Thucydides (43-45), it might have been helpful to discuss the (admittedly not uncomplicated) issue of Atticism in late-first-century Rome. I am less convinced than Mellor is that the speech of Sallust's Caesar constitutes the historian's "plea for common sense" (38) in the midst of the triumviral proscriptions; after all, Sallust wrote Cato's speech as well. It can hardly be true, if only in view of Pliny's keen interest in his friend's literary productivity, that Suetonius' Lives "is a book written by and for the equestrian" (152), nor do I think the description of the imperial equestrian order that is given on [End Page 656] that page... (shrink)

Atque illo die certe Aricia rediens devertit Clodius ad se in Albanum: quod ut sciret Milo ilium Ariciae fuisse, suspicari tamen debuit eum, etiam si Romam illo die reverti vellet, ad villam suam, quae viam tangeret, deversurum.THIS passage is interesting in that its argument runs counter to the main picture which Cicero had earlier presented of the movements of Milo and Clodius before they met on the Appian Way in January 52 B.C. In an earlier passage Cicero says: ‘Interim cum (...) sciret Clodius–neque enim difficile erat id scire–xiter sollemne, legitimum, necessarium ante diem XIII Kalendas Februarias Miloni esse Lanuvium ad flaminem prodendum, quod erat dictator Lanuvii Milo, Roma subito ipse profectus pridie est, ut ante suum fundum, quod re intellectum est, Miloni insidias conlocaret.’ Cicero remains true to this latter version in all the relevant arguments concerning the motives and movements of Clodius and Milo. Milo had legitimate business at Lanuvium, and hence a legitimate reason for being on the road at the time of the affray; Clodius′ presence is explained by Cicero as due solely to the desire to place an ambush for his enemy at a convenient spot, i.e. in front of his farm, and for this reason he had set out from Rome a day before Milo, when his presence was really required in Rome. (shrink)

This essay reflects on 25 years since Christian Bioethics began publication and, in somewhat autobiographical fashion, engages two core concerns. First, although “non-ecumenism” may often appear a pretext for contention and division, I suggest that a respectful non-ecumenism may provide the opportunity for dialogue and the occasion for employing certain tools from religious studies. Second, although many are skeptical about the possibilities of identifying a “common morality,” a defense of that notion provides a plausible explanation for the development of limited (...) consensus on some issues in bioethics. (shrink)

Before daybreak on 23 November 57 B.C., about 11 weeks after his return from exile, Cicero wrote to Atticus and recorded for him, in diary form, events at Rome between 3 November and the date of writing. Clodius and his gangs were still causing trouble on the streets, interfering with the rebuilding of Cicero's house on the Palatine , and even molesting Cicero himself . Clodius was a candidate for the curule aedileship; if he were elected, he would succeed in (...) evading the accusation for vis which had been brought against him by Milo; he therefore made full use of his gangs to intimidate Rome and thus accelerate the elections. He was supported in this manœuvre by the consul Q. Caecilius Metellus Nepos, who planned to hold the comitia by surprise; this plan, however, was being thwarted by the tribune Milo, who was ready to use his power of obnuntiatio to prevent the elections being held. (shrink)

This paper examines the standard conceptualizations of the notion of hallucination in light of various non-ordinary phenomenological patterns associated with altered states of consciousness induced by psychoactive agents. It is argued that in general, the conceptualizations encountered in the literature do not do justice to the richness and complexity that the psychological phenomenology actually exhibits. A close inspection of this phenomenology reveals some pertinent distinctions which are usually not made in the scientific literature. On the one hand, the discussion is (...) based on first-hand experiences and, on the other hand, it is grounded in empirical and theoretical cognitive investigations of the phenomenology of human consciousness. Theoretically, the discussion is grounded in an approach highlighting the centrality of experience, meaning and action in cognition. (shrink)

What is human reason, how did it arise, how is it connected to animal reason? In The Enigma of Reason (ER) Hugo Mercier and Dan Sperber (2017) suggest that reason evolved driven by the need to support communication and coordination in small human groups. They contrast this to the idea that the function of reason is to enable humans to make better decisions and develop more accurate beliefs. After a summation of the ER argument, the theory is critiqued and two (...) of their assumptions -- that human cognition is based on massive modularity and that reason co-evolved with and is dependent upon language -- are challenged. Alternatives to these assumptions are presented from the perspective of pattern matching processes in neural dynamical systems, which it is asserted provides a more realistic approach to the functioning of the brain and mind. (shrink)

Modern science developed in the interflow of culture between west and east. Combing of pratice technology with philosophic thoughts formed experimental method. Holistic views contacting atomism produced system theory. System thoughts are applicated in the science and engineering of biosystems, and the cencepts of system biomedicine (Kamada T.1992), systems biology (Zieglgansberger W, Tolle TR.1993), system bioengineering and system genetics (Zeng BJ. 1994) were established. From positive to synthetic thoughts, philosophy have been developed ontology, cosmology, organism theories. Structurity is structure logic (...) system founded on entity, develop, exist axioms, tolerance, adaptation, fluctuate, interweave, transform theorems and integrate, adaptation, construct laws. Structurity be discussed on the cosmos, life, culture system, creation, hologram theories of structure ontology, construct mutation, simi-structure organism and entity emergence, symbol implication. From the relation of structure, function and development, the structurity put forward the cycle, spiral, triangle structure stability patterns of self-organization in structure complement each other and stratification, functional couple and interflow bounds growth, coordinativetransformation and holographic symmetry. (shrink)