"What can we expect from the study of Chinese philosophy? « In the philosophical systems of the Hindoos and the Chinese there are still hidden treasures, in which the anticipation of scientific discoveries, the results of thousands of years of occidental research, is most striking. Such are the words of Edward von Hartmann, the most famous living German philosopher1. Much labour has been spent in Europe on the Indian Vedanta philosophy, which had such a marked influence on Arthur Schopenhauer. « (...) The Upanishads, says the author of the Parerga and Paralipomena, are the outcome of the highest human wisdom.... They afford the most remunerative and sublime reading possible in this world, which has been the consolation of my life, as it will be that of my death 2. I do not see why the many germs scattered over the vast field of Chinese philosophy should not have a similar fertilizing influence on some philosophical European mind also. The deep impression caused by the Tao-tê-king will support my view. But much work remains to be done before Chinese philosophy will take its proper place in the history of philosophy. The burden of this task lies with us who are living in China and studying her language and literature, for, while great care is bestowed on all her sister languages in Europe and America, Chinese, the oldest of all, but the youngest in the curriculum of our high-schools, is treated as a step-child by public opinion. This paper is meant as a move in the direction just indicated.". (shrink)

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pt. 1. Philosophical essays -- pt. 2. Miscellaneous essays.

We argue against some of Reichenbach's claims about causal forks are incorrect. We do not see why the Second Law of Thermodynamics rules out the existence of conjunctive forks open to the past. In addition, we argue that a common effect rarely forms a conjunctive fork with its joint causes, but it sometimes does. Nevertheless, we think there is something to be said for Reichenbach's idea that forks of various kinds are relevant to explaining why we know more about the (...) past than about the future. And entropy turns out to play a role in the explanation, though not the determining role that Reichenbach envisions. (shrink)

Inspired by the hugely popular sitcom The Good Place, which uses a comic format to examine moral dilemmas and schools of ethical thought, this is a brief tour of the main issues that face humans when we try to "do the right thing." Using traditional and modern thought experiments, as well as 21st century dilemmas from the etiquette of texting to the narcissism of "selfie" culture, here is everything you need to know about reaching a good place in life.

We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that dependence is equivalent to bounded non-forking assuming NTP 2.

For n≥3, define Tn to be the theory of the generic Kn-free graph, where Kn is the complete graph on n vertices. We prove a graph-theoretic characterization of dividing in Tn and use it to show that forking and dividing are the same for complete types. We then give an example of a forking and nondividing formula. Altogether, Tn provides a counterexample to a question of Chernikov and Kaplan.

The stability theory of first order theories was initiated by Saharon Shelah in 1969. The classification of abstract elementary classes was initiated by Shelah, too. In several papers, he introduced non-forking relations. Later, Shelah [17, II] introduced the good non-forking frame, an axiomatization of the non-forking notion.We improve results of Shelah on good non-forking frames, mainly by weakening the stability hypothesis in several important theorems, replacing it by the almost λ-stability hypothesis: The number of types over (...) a model of cardinality λ is at most λ+.We present conditions on Kλ, that imply the existence of a model in Kλ+n for all n. We do this by providing sufficiently strong conditions on Kλ, that they are inherited by a properly chosen subclass of Kλ+. What are these conditions? We assume that there is a ‘non-forking’ relation which satisfies the properties of the non-forking relation on superstable first order theories. Note that here we deal with models of a fixed cardinality, λ.While in Shelah [17, II] we assume stability in λ, so we can use brimmed models, here we assume almost stability only, but we add an assumption: The conjugation property.In the context of elementary classes, the superstability assumption gives the existence of types with well-defined dimension and the ω-stability assumption gives the existence and uniqueness of models prime over sets. In our context, the local character assumption is an analog to superstability and the density of the class of uniqueness triples with respect to the relation ≼bs is the analog to ω-stability. (shrink)

We discuss the role of weakly normal formulas in the theory of thorn forking, as part of a commentary on the paper [5]. We also give a counterexample to Corollary 4.2 from that paper, and in the process discuss “theories with selectors.”.

We prove that a theory T has stable forking if and only if Teq has stable forking.

We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\mathrm {ACFG}$. This theory was introduced in [16] as a new example of $\mathrm {NSOP}_{1}$ nonsimple theory. In this paper we describe more features of $\mathrm {ACFG}$, such as imaginaries. We also study various independence relations in $\mathrm {ACFG}$, such as Kim-independence or forking independence, and describe interactions between them.

We consider existentially closed fields with several orderings, valuations, and [Formula: see text]-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Moreover, forking agrees with dividing, and forking can be characterized in terms of forking in ACVF, RCF, and [Formula: see text]CF.

Let Δ be a set of formulas. In this paper we study the following question: under what assumptions on Δ, the concept “a complete Δ-type p over B does not fork over A ⊆ B” behaves well. We apply the results to the structure theory of ω1-saturated models.

We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M, generalizing a result of Dolich on o-minimal theories in [4].

We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for discrete first-order real rosy theories.

A ternary relation [Formula: see text] between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth studying. The main application is a better understanding of thorn-forking, which turns out (...) to be closely related to modular pairs in the lattice of algebraically closed sets. (shrink)

T is stable. We define the notion of meager regular type and prove that a meager regular type is locally modular. Assuming I < 2o and G is a definable abelian group with locally modular regular generics, we prove a counterpart of Saffe's conjecture. Using these results, for superstable T we prove the conjecture of vanishing multiplicities. Also, as a further application, in some additional cases we prove a conjecture regarding topological stability of pseudo-types over Q.

We introduce the notion of a w-good \-frame which is a weakening of Shelah’s notion of a good \-frame. Existence of a w-good \-frame implies existence of a model of size \. Tameness and amalgamation imply extension of a w-good \-frame to larger models. As an application we show:Theorem 0.1. Suppose\. If \ = \mathbb {I} = 1 \le \mathbb {I} < 2^{\lambda ^{++}}\)and\is\\)-tame, then\.The proof presented clarifies some of the details of the main theorem of Shelah and avoids using (...) the heavy set-theoretic machinery of Shelah by replacing it with tameness. (shrink)

We give a characterisation of forking in the context of simple theories in terms of the fundamental order.

We consider existentially closed fields with several orderings, valuations, and p-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Mo...

During replication, the topology of DNA changes continuously in response to well‐known activities of DNA helicases, polymerases, and topoisomerases. However, replisomes do not always progress at a constant speed and can slow‐down and even stall at precise sites. The way these changes in the rate of replisome progression affect DNA topology is not yet well understood. The interplay of DNA topology and replication in several cases where progression of replication forks reacts differently to changes in DNA topology ahead is discussed (...) here. It is proposed, there are at least two types of replication fork barriers: those that behave also as topological barriers and those that do not. Two‐Dimensional (2D) agarose gel electrophoresis is the method of choice to distinguish between these two different types of replication fork barriers. (shrink)

We study properties of forking in the classes of all finite models of a complete theory in a finite variable logic. We also study model constructions under the assumption that forking is trivial.

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...) correspondence language, so both can express the same input–output behavior of processes. (shrink)