Does chemistry reduce to physics? If this means ‘Can we derive the laws of chemistry from the laws of physics?’, recent discussions suggest that the answer is ‘no’. But sup posing that kind of reduction—‘epistemological reduction’—to be impossible, the thesis of ontological reduction may still be true: that chemical properties are determined by more fundamental properties. However, even this thesis is threatened by some objections to the physicalist programme in the philosophy of mind, objections that generalize to the (...) chemical case. Two objections are discussed: that physicalism is vacuous, and that nothing grounds the asymmetry of dependence which reductionism requires. Although it might seem rather surprising that the philosophy of chemistry is affected by shock waves from debates in the philosophy of mind, these objections show that there is an argumentative gap between, on the one hand, the theoretical connection linking chemical properties with properties at the sub-atomic level, and, on the other, the philosophical thesis of ontological reduction. The aim of this paper is to identify the missing premises (among them a theory of physical possibility) that would bridge this gap. Introduction: missing elements and the mystery of discreteness The refutation of physicalism A combinatorial theory of physical possibilia Combinatorialism and the Bohr model Objections The missing premises and a disanalogy with mind. (shrink)

Albert Lewis's article analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra.Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:i. Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical (...) education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein.ii. Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways.iii. Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a ‘chemical conjunction‘, which was developed largely dialectically by Hermann. (shrink)

Two articles on the reduction of chemistry are examined. The first, by McLaughlin (1992), claims that chemistry is reduced to physics and that there is no evidence for emergence or for downward causation between the chemical and the physical level. In a more recent article, Le Poidevin (2005) maintains that his combinatorial approach provides grounding for the ontological reduction of chemistry, which also circumvents some limitations in the physicalist program. †To contact the author, please write to: (...) Department of Chemistry and Biochemistry, UCLA, 607 Charles E. Young Drive East, Box 951569, Los Angeles, CA 90095-1569; e-mail: [email protected]. (shrink)

Classical atoms—“part-less, ontologically irreducible simples” as the conference flyer puts it—are not the atoms of modern chemistry and analogies with the latter can be construed in various ways. They have figured in the historical development of concepts of chemical affinity but without, as Alan Chalmers and I have independently argued, making any significant contribution to empirically justified theories. A purely combinatorial conception of the formation of compounds by juxtaposing atoms is associated with Daltonian atomism. I review the merits (...) of this idea as a solution to problems posed by developments in early nineteenth century chemistry and go on to suggest that subsequent developments in chemistry are as much in agreement with ideas associated with Aristotle as with the ancient atomists, if not more so. The basic issues can be understood without getting involved in detailed chemistry and I hope what I have to say will be of interest to philosophers concerned with the metaphysics of matter but with no special knowledge of chemistry. (shrink)

For the last twenty years Luis Prieto, in his published work in French, has reiterated that the systematic study of the codes (other than natural languages) which were invented by men for communication purposes is in and of itself an undertaking essential for an understanding of both the laws of communication in general and of the mechanisms of these systems of communication—the totality of which would make up the (Saussurian) semiology of communication (Prieto 1966, 1968, 1975). Among these systems the (...) symbols of chemistry—referred to as such for a long time— and their combinatory rules constitute a very ancient code or series of codes (Crosland, 1962). Up to now this code has not been subjected to a genuine semiological study, except for the essay by Dagognet (1969, see Mounin 1970) which is more literary or poetical and metaphysical than scientific. (shrink)

In the last years there has been a great improvement in the development of computational methods for combinatorial chemistry applied to drug discovery. This approach to drug discovery is sometimes called a “rational way” to manage a well known phenomenon in chemistry: serendipity discoveries. Traditionally, serendipity discoveries are understood as accidental findings made when the discoverer is in quest for something else. This ‘traditional’ pattern of serendipity appears to be a good characterization of discoveries where “luck” plays (...) a key role. In this sense, some initial failures in combinatorial chemistry are frequently attributed to a naïf appropriation of a “serendipity model” for discovery (a “serendipity mistake”). In this paper we try to evaluate this statement by criticizing its foundations. It will be suggested that the notion of serendipity has different aspects and that the criticism to the first attempts could be understood as a “serendipity mistake.” We will suggest that “serendipity” strategies, a kind of blind search, can be seen sometimes as a “genuine part” of scientific practice. A discussion will ensue about how this characterization can give us a better understanding of some aspects of serendipity discoveries. (shrink)

Chemistry, genetics, physics, and linguistics all present instances of reuse. I use the example of how behavioral constraints may have contributed to the emergence of phonemic reuse. Arising from specific facts about speech production, perception, and learning, such constraints suggest that combinatorial reuse is domain-specific. This implies that it would be more prudent to view instances of neural reuse not as reflecting a but as a fortuitous set of converging phenomena.

The interrelation between two theories, theory of complexity and theory of systems, is analyzed by using the chemical graph-theoretical concept. The idea of complexity is systemized through three components: diachronic, synchronic, and combinatorial complexity. The relationships between entropy and complexity, as well as the problem of function are also discussed.

Drawing on the work of Bernadette Bensaude-Vincent and Isabelle Stengers on the history of chemistry, this article develops the idea that drug molecules can be understood as ‘informed materials’. This study argues that molecules should not be viewed as discrete objects, but as constituted in their relations to complex informational and material environments. Through a case study of commercial pharmaceutical R&D, the article examines the role of combinatorial and computational chemistry in enriching the informational and material environment (...) of potential drug molecules. Within the contemporary pharmaceutical laboratory, experiments on molecules can be conducted not just in vitro and in vivo but also, according to researchers, in silico. Molecules come to exist not just as physical reagents but also as elements of arrays, libraries and databases of other molecules, and in a virtual form in computer simulations and virtual libraries. Molecules are also understood by researchers to exist in a ‘chemical space’ of other different molecules, where the notion of chemical space is used both to refer to differences in molecular structure and to territories owned or occupied by particular firms. The article argues that pharmaceutical companies do not merely discover molecular structures that potentially could exist, but also invent novel forms of chemical entity. (shrink)

Human language, hominin tool production modes, and multimodal communications systems of primates and other animals are currently well-studied for how they display compositionality or combinatoriality. In all cases, the former is defined as a kind of hierarchical nesting and the latter as a lack thereof. In this article, I extend research on combinatoriality and compositionality further to investigations of everyday primate skills. Daily locomotion modes as well as behaviors associated with subsistence practices, hygiene, or body modification rely on the hierarchical (...) nesting of different behavioral and cognitive actions into complex skills. I introduce a scheme which uses hierarchical organization to differentiate combinatorial from compositional skills. Combinatorial skills are defined either as aggregational or linearly hierarchical depending on whether the skill occurs momentarily in space or unfolds sequentially over time. Compositional skills are defined either as nested or interactionally hierarchical depending on whether the skill results in new constructs or in new interactions between existing constructs. The methodology I propose combines epistemological hierarchy theory with data from primatological field research and experimental and comparative psychological research and provides a means to integrate current constructionist and extended views on cognition and action with older research on behavioral logics in psychology and operational chain thinking in anthropology. The approach furthermore synchronizes with ongoing research on teleonomy, intentionality, and creativity. -/- . (shrink)

Combinatorial behavior involves combining different elements into larger aggregates with meaning. It is generally contrasted with compositionality, which involves the combining of meaningful elements into larger constituents whose meaning is derived from its component parts. Combinatoriality is commonly considered a capacity found in primates and other animals, whereas compositionality often is considered uniquely human. Questioning the validity of this claim, this multidisciplinary special issue of the International Journal of Primatology unites papers that each study aspects of combinatoriality and compositionality (...) found in primate and bird communication systems, tool use, skills, and human language. The majority of authors conclude that compositionality is evolutionarily preceded by combinatoriality and that neither are uniquely human. This introduction briefly introduces readers to the major findings and issues raised by the contributors. -/- . (shrink)

The ArgumentJohann von Justi, the foremost literary cameralist of his generation, served as chief police commissioner in Göttingen between 1755 and 1757. While in Göttingen, Justi offered lectures at the university on the “œconomic, police and cameral sciences.” He also arrested vagrants, wrote on chemistry, disciplined unruly students, conducted chemical experiments, supervised the pricing of Göttingen's staple goods, engaged in a public controversy with a prominent Berlin chemist, edited and published a bi-weekly periodical (Göttingische Policey-Amts Nachrichien), and worked with (...) the university's curator to refashion the academic structure of the sciences. Taken together, these various activities reflected his broad vision for social and academic change, a vision with important implications for the form and content of the sciences. Drawing on archival material in Göttingen, on articles from thePolicey-Amts Nachrichten, and on Justi's other cameralist and chemical writings, I use his everyday experiences as a local police official to explore the meaning of his chemical work. I argue that Justi's chemistry was suffused with the cameralist dreams and ambitions of a small-town police commissioner. It is what I call police chemistry. (shrink)

CHAPTER Addenda to Pure Combinatory Logic This chapter will treat various additions to, and modifications of, the subject matter of Chapters-7. ...

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 to (...) create a coherent mathematical view of these foundations. The result of this collaborative work is presented here in the hope that it does justice to the individual contributor and that the reader has a chance of judging the work as a whole. E. Engeler ETH Zurich, April 1994 lCollected in Chapter III, An Algebraization of Algorithmics, in Algorithmic Properties of Structures, Selected Papers of Erwin Engeler, World Scientific PubJ. Co. , Singapore, 1993, pp. 183-257. I Historical and Philosophical Background Erwin Engeler In the fall of 1928 a young American turned up at the Mathematical Institute of Gottingen, a mecca of mathematicians at the time; he was a young man with a dream and his name was H. B. Curry. He felt that he had the tools in hand with which to solve the problem of foundations of mathematics mice and for all. His was an approach that came to be called "formalist" and embodied that later became known as Combinatory Logic. (shrink)

We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, (...) λ □κ, κ□κ*. We prove that if holds in V. As an application, we show that ZFC + PFA Con. We also obtain one Woodin cardinal as a lower bound on the consistency strength of stationary reflection at κ+ for a singular, countably closed limit cardinal κ such that # exists; likewise for the failure of □κ* at such a κ. (shrink)

Reader-friendly without compromising the precision of exposition, the book includes many new research results not found in the available literature.

Chemistry and physics are two sciences that are hard to connect. Yet there is significant overlap in their aims, methods, and theoretical approaches. In this book, the reduction of chemistry to physics is defended from the viewpoint of a naturalised Nagelian reduction, which is based on a close reading of Nagel's original text. This naturalised notion of reduction is capable of characterising the inter-theory relationships between theories of chemistry and theories of physics. The reconsideration of reduction also (...) leads to a new characterisation of chemical theories. This book is primarily aimed at philosophers of chemistry and chemists with an interest in philosophy, but is also of interest to the general philosopher of science. (shrink)

The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the coupling constants of the fundamental fields which? via high energy scattering? are the bridge from the combinatorial world into dynamics. The untenable distinction between what is?observed?, or measured, and what is not, upon which current quantum theory is based, is not needed. (...) If we are to speak of mind, this has to be present? albeit in primitive form? at the most basic level, and not to be dragged in at one arbitrary point to avoid the difficulties about quantum observation. There is a growing literature on information-theoretic models for physics, but hitherto the two disciplines have gone in parallel. In this book they interact vitally. (shrink)

It is proved that $\Pi^1_1$ -indescribability in $P_{\kappa}\lambda$ can be characterized by combinatorial properties without taking care of cofinality of $\lambda$ . We extend Carr's theorem proving that the hypothesis $\kappa$ is $2^{\lambda^{<\kappa}}$ -Shelah is rather stronger than $\kappa$ is $\lambda$ -supercompact.

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount (...) of revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent. (shrink)

Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: assuming ωV1 = ωL1, there is no real in V[d] which is eventually different from the reals in L[ d], where d is Hechler over V; adding one Hechler real makes the invariants on the left-hand side of Cichoń's diagram equal ω1 and those on the right-hand side equal 2ω (...) and produces a maximal almost disjoint family of subsets of ω of size ω1; there is no perfect set of random reals over V in V[ r][ d], where r is random over V and d Hechler over V[r], thus answering a question of the first and second authors. (shrink)

. Computational chemistry grew in a new era of “desktop modeling,” which coincided with a growing demand for modeling software, especially from the pharmaceutical industry. Parameterization of models in computational chemistry is an arduous enterprise, and we argue that this activity leads, in this specific context, to tensions among scientists regarding the epistemic opacity transparency of parameterized methods and the software implementing them. We relate one flame war from the Computational Chemistry mailing List in order to assess (...) in detail the relationships between modeling methods, parameterization, software and the various forms of their enclosure or disclosure. Our claim is that parameterization issues are an important and often neglected source of epistemic opacity and that this opacity is entangled in methods and software alike. Models and software must be addressed together to understand the epistemological tensions at stake. (shrink)

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of a square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied.

Recent investigations surprisingly indicate that single RNA "stem-loops" operate solely by chemical laws that act without selective forces, and in contrast, self-ligated consortia of RNA stem-loops operate by biological selection. To understand consortial RNA selection, the concept of single quasi-species and its mutant spectra as drivers of RNA variation and evolution is rethought here. Instead, we evaluate the current RNA world scenario in which consortia of cooperating RNA stem-loops are the basic players. We thus redefine quasispecies as RNA quasispecies consortia (...) and argue that it has essential behavioral motifs that are relevant to the inherent variation, evolution and diversity in biology. We propose that qs-c is an especially innovative force. We apply qs-c thinking to RNA stem-loops and evaluate how it yields altered bulges and loops in the stem-loop regions, not as errors, but as a natural capability to generate diversity. This basic competence-not error-opens a variety of combinatorial possibilities which may alter and create new biological interactions, identities and newly emerged self identity functions. Thus RNA stem-loops typically operate as cooperative modules, like members of social groups. From such qs-c of stem-loop groups we can trace a variety of RNA secondary structures such as ribozymes, viroids, viruses, mobile genetic elements as abundant infection derived agents that provide the stem-loop societies of small and long non-coding RNAs. (shrink)

Are there practical reasons for and against belief? For example, do the practical benefits to oneself or others of holding a certain belief count in favor of that belief? I argue "No." My argument involves considering how practical reasons for belief, if there were such things, would combine with other reasons for belief in order to determine all-things-considered verdicts, especially in cases involving equally balanced reasons of either a practical or an epistemic sort.

Understanding whether the long and elaborate songs of male gibbons have syntax and hierarchical structures is an interesting question in the evolution of language, because gibbons are near humans in the phylogenetic tree and a hierarchically organized syntax is considered to be a basic component of human language. We conducted field research at Danum Valley Conservation Area in northern Borneo to test the hypothesis that gibbon songs have syntax and chunks. We followed one Mueller’s gibbon group for 1 week in (...) the dry and rainy seasons every year from 2001 to 2009, collecting vocal and behavioral data. Results show that songs emitted by the studied male gibbon were governed by combinatory rules. Some context-dependent songs had different combinatory rules, although they overlapped with the songs whose contexts were uncertain. The male Mueller’s songs had characteristics that suggest existence of chunk structure. These results provided an important perspective in the study of language origin. (shrink)

Chemistry and dynamics are closely related in G.W. Leibniz's thinking, from the corpuscularism of his youth to the theory of conspiracy movements that he proposes in his later years. Despite the importance of chemistry and chemical thought in Leibniz's philosophy, interpreters have not paid enough attention to this subject, especially in the recent decades. This work aims to contribute to filling this gap in Leibnizian studies. In this first part of the work I will expose the theory of (...) matter that the young Leibniz conceives under the influence of chemical corpuscularism. Leibniz uses R. Boyle's interpretation of the Aristotelian idea of form in order to give an explanation of the unity and cohesion of bodies. As opposed to the Cartesians, Leibniz puts forth the idea of a dependence between the variables of extension, movement and figure, without losing analytical clarity and with the aim of extending the explanatory power of physics to natural phenomena difficult to approach by Cartesian mechanics. (shrink)

We introduce, in a general setting, an ‘‘analytic’’ version of standard equational calculi of combinatory logic. Analyticity lies on the one side in the fact that these calculi are characterized by the presence of combinatory introduction rules in place of combinatory axioms, and on the other side in that the transitivity rule proves to be eliminable. Apart from consistency, which follows immediately, we discuss other almost direct consequences of analyticity and the main transitivity elimination theorem; in particular the Church−Rosser and (...) the leftmostreduction theorems for the associated notions of reduction. The last two sections deal with analytic combinatory calculi with the extensionality rule added. Here, as far as the elimination of transitivity is concerned, we have only partial results, which unfortunately do not cover, at present, full CL + Ext. Yet, they are sufficient to prove the decidability of weaker combinatory calculi with extensionality, including e.g. BCK + Ext. (shrink)

This is an attempt to take a look at chemistry from the point of view of practical realism. Besides its social–historical and normative aspects, the latter involves a direct reference to experimental research. According to Edward Caldin chemistry depends on our being able to isolate pure substances with reproducible properties. Thus, the very basis of chemistry is practical. Even the laws of chemistry are not stable but are subject to correction. At the same time, these statements (...) do not necessarily make Edward Caldin a predecessor of practical realism. The latter has other predecessors, like Rom Harré’s policy realism or Sami Pihlström’s pragmatic realism. Chemistry is an experimental science. The experiment is a purposeful and critically theory-guided constructive, manipulative, material interference with nature according to Rein Vihalemm, the founder of practical realism. Chemistry is physics-like science but just partly so. This is an important point in the context of the current paper. (shrink)

Department of Economics, George Mason University, MSN 1D3, Carow Hall, Fairfax VA 22030, USA E-mail: [email protected] (http://hanson.gmu.edu).

Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning (...) bitstrings to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before. (shrink)

The purpose of this paper is to review and critique Wessel Reijers and Bert Gordijn’s paper Moving from value sensitive design to virtuous practice design. In doing so, it draws on recent literature on developing value sensitive design (VSD) to show how the authors’ virtuous practice design (VPD), at minimum, is not mutually exclusive to VSD. This paper argues that virtuous practice is not exclusive to the basic methodological underpinnings of VSD. This can therefore strengthen, rather than exclude the VSD (...) approach. Likewise, this paper presents not only a critique of what was offered as a “potentially fruitful alternative to VSD” but further clarifies and contributes to the VSD scholarship in extending its potential methodological practices and scope. It is concluded that VPD does not appear to offer any original contribution that more recent instantiations of VSD have not already proposed and implemented. (shrink)

We prove that the theory IΔ0, extended by a weak version of the Δ0-Pigeonhole Principle, proves that every integer is the sum of four squares (Lagrange's theorem). Since the required weak version is derivable from the theory IΔ0 + ∀x (xlog(x) exists), our results give a positive answer to a question of Macintyre (1986). In the rest of the paper we consider the number-theoretical consequences of a new combinatorial principle, the ‘Δ0-Equipartition Principle’ (Δ0EQ). In particular we give a new (...) proof, which can be formalized in IΔ0 + Δ0EQ, of the fact that every prime of the form 4n + 1 is the sum of two squares. (shrink)

In his long and illuminating paper [1] Joe Barback defined and showed to be non-vacuous a class of infinite regressive isols he has termed “complete y torre” isols. These particular isols a enjoy a property that Barback has since labelled combinatoriality. In [2], he provides a list of properties characterizing the combinatoria isols. In Section 2 of our paper, we extend this list of characterizations to include the fact that an infinite regressive isol X is combinatorial if and only (...) if its associated Dekker semiring D satisfies all those Π2 sentences of the anguage LN for isol theory that are true in the set ω of natural numbers. of the various function and relation symbols of LN via the “lifting ” to D of their Σ1 definitions in ω coincide with their interpretations via isolic extension.) We also note in Section 2 that Π2-correctness, for semirings D, cannot be improved to Π 3-correctness, no matter how many additional properties we succeed in attaching to a combinatoria isol; there is a fixed equation image sentence that blocks such extension. In Section 3, we provide a proof of the existence of combinatorial isols that does not involve verification of the extremely strong properties that characterize Barback's CT isols. (shrink)

Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the Hurewicz 1927 problem is positive, it is shown here that semifilter trichotomy implies a negative answer to a slightly stronger form (...) of this problem. (shrink)

We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for (...) pairs (RT₂²) splits into a stable version (SRT₂²) and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for RT₂² and SRT₂²). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL₀, DNR, and BΣ₂. We show, for instance, that WKL₀ is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is Π₁¹-conservative over the base system RCA₀. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch, Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply SRT₂² (and so does not imply RT₂²). This answers a question of Cholak, Jockusch, and Slaman. Our proofs suggest that the essential distinction between ADS and CAC on the one hand and RT₂² on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions. (shrink)

We give an overview of a research line concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered on some other perhaps not so large cardinal. While this is of great interest to set theorists, one of the main motivations behind this line of research is in its applicability to other areas of mathematics. We give some details about this and we expose some possible directions for further (...) research. (shrink)

This book reflects on the significant and highly original scientific contributions of Hans Primas. A professor of chemistry at ETH Zurich from 1962 to 1995, Primas continued his research activities until his death in 2014. Over these 50 years and more, he worked on the foundations of nuclear magnetic resonance spectroscopy, contributed to a number of significant issues in theoretical chemistry, helped to clarify central topics in quantum theory and the philosophy of physics, suggested innovative ways of addressing (...) interlevel relations in the philosophy of science, and introduced cutting-edge approaches in the flourishing young field of scientific studies of consciousness. His work in these areas of research and its continuing impact is described by noted experts, colleagues, and collaborators of Primas. All authors contextualize their contributions to facilitate the mutual dialog between these fields. (shrink)

We employ the notions of "sequential function" and "interrogation" (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using Longley's preorder-enriched category of partial combinatory algebras and decidable applicative structures. We also investigate total combinatory algebras of partial functions. One of the results is that every realizability topos is a geometric quotient of a realizability topos on a total combinatory algebra.

Recently, philosophers have come forth with approaches to chemistry based on its actual practice, imparting to it a proper aim and character of its own. These approaches add to the currently growing movement of pluralist philosophies of science. We draw on recent pluralist accounts from chemistry and analyse three notions from modern chemical practice and theory in terms of these accounts, in order to complement the so far more general pluralist approaches with specific evidence. Our survey reveals that (...) the concept of element indicates conceptual pluralisms in chemistry. that electronegativity illustrates methodological pluralism in determining one and the same concept, and that acidity is an instance of plurality hidden behind ‘one notion’. (shrink)

This is an attempt to take a look at chemistry from the point of view of practical realism. Besides its social–historical and normative aspects, the latter involves a direct reference to experimental research. According to Edward Caldin chemistry depends on our being able to isolate pure substances with reproducible properties. Thus, the very basis of chemistry is practical. Even the laws of chemistry are not stable but are subject to correction. At the same time, these statements (...) do not necessarily make Edward Caldin a predecessor of practical realism. The latter has other predecessors, like Rom Harré’s policy realism or Sami Pihlström’s pragmatic realism. Chemistry is an experimental science. The experiment is a purposeful and critically theory-guided constructive, manipulative, material interference with nature according to Rein Vihalemm, the founder of practical realism. Chemistry is physics-like science but just partly so. This is an important point in the context of the current paper. (shrink)

The regulation of glucose dehydrogenase (GLD) in Drosophila illustrates the combinatorial aspects of gene regulation in development. Furthermore, the findings serve to point up a general question about cukaryotic structural gene control: is regulation of expression always optimal?

The results of this paper extend some of the intimate relations that are known to obtain between combinatory logic and certain substructural logics to establish a general characterization theorem that applies to a very broad family of such logics. In particular, I demonstrate that, for every combinator X, if LX is the logic that results by adding the set of types assigned to X (in an appropriate type assignment system, TAS) as axioms to the basic positive relevant logic B∘T, then (...) LX is sound and complete with respect to the class of frames in the Routley-Meyer relational semantics for relevant and substructural logics that meet a first-order condition that corresponds in a very direct way to the structure of the combinator X itself. (shrink)