The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the 20th century. More precisely, it is argued that the accounts of Helmholtz and Hertz may be taken as prototypes of representational accounts in which structure preservation plays an essential role. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date (...) version of a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach’s early theory of a relativized constitutive but non-apodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept of representation that conceived of a particular representation as only one phase in a continuous process determined by pragmatic considerations. Pragmatic aspects of representations are further elaborated in the classical account of C.I. Lewis and the more modern of Hasok Chang. (shrink)

The aim of this paper is to characterize the various structuralist reduction concepts as structure-preserving maps in a succinct and unifying way. To begin with, some important intuitive adequacy conditions are discussed that a good (structuralist) reduction concept should satisfy. Having reconstructed these intuitive conditions in the structuralist framework, it turns out that they divide into two mutually incompatible sets of requirements. Accordingly there exist (at least) two essentially different types of structuralist reduction concepts: the first type stresses the (...) existence of a deductive or inferential link between the reducing and the reduced theory; the second type emphasizes the greater explanatory power the reducing theory should have in comparison with the reduced theory. The problem of the incompatibility of equally plausible reduction concepts is treated in the last section and a proposal is made for its solution consisting in the definition of a multiple synthetizing reduction relation. (shrink)

The article approaches cut elimination from a new angle. On the basis of an arbitrary inference relation among logically atomic formulae, an inference relation on a language possessing logical operators is defined by means of inductive clauses similar to the operator-introducing rules of a cut-free intuitionistic sequent calculus. The logical terminology of the richer language is not uniquely specified, but assumed to satisfy certain conditions of a general nature, allowing for, but not requiring, the existence of infinite conjunctions and disjunctions. (...) We investigate to what extent structural properties of the given atomic relation are preserved through the extension to the full language. While closure under the Cut rule narrowly construed is not in general thus preserved, two properties jointly amounting to closure under the ordinary structural rules, including Cut, are. -/- Attention is then narrowed down to the special case of a standard first-order language, where a similar result is obtained also for closure under substitution of terms for individual parameters. Taken together, the three preservation results imply the familiar cut-elimination theorem for pure first-order intuitionistic sequent calculus. -/- In the interest of conceptual economy, all deducibility relations are specified purely inductively, rather than in terms of the existence of formal proofs of any kind. (shrink)

In this paper Gillman Payette looks at various structural properties of the underlying logic X, and ascertains if these properties will hold of the forcing relation based on X. The structural properties are those that do not deal with particular connectives directly. These properties include the structural rules of inference, compactness, and compositionality among others. The presentation of the logic X is carried out in the style of algebraic logic; thus, a description of the resulting ‘forcing algebras’ is given. The (...) paper concludes with a discussion of first-order classical forcing as a particular instance of these properties. (shrink)

We characterize the model companions of universal Horn classes generated by a two-element algebra (or ordered two-element algebra). We begin by proving that given two mutually model consistent classes M and N of L (respectively L') structures, with $\mathscr{L} \subseteq \mathscr{L}'$ , M ec = N ec ∣ L , provided that an L-definability condition for the function and relation symbols of L' holds. We use this, together with Post's characterization of ISP(A), where A is a two-element algebra, to show (...) that the model companions of these classes essentially lie in the classes of posets and semilattices, or characteristic two groups and relatively complemented distributive lattices. (shrink)

Peter Spirtes and Clark Glymour. Casual Structure Among Measured Variables Preserved with Unmeasured Variables.

This paper concerns product constructions within the continuous-logic framework of Ben Yaacov, Berenstein, Henson, and Usvyatsov. Continuous-logic analogues are presented for the direct product, direct sum, and almost everywhere direct product analyzed in the work of Feferman and Vaught. These constructions are shown to possess a number of preservation properties analogous to those enjoyed by their classical counterparts in ordinary first-order logic: for example, each product preserves elementary equivalence in an appropriate sense; and if for \(i\in \mathbb {N}\) \(\mathcal {M}_i\) (...) is a metric structure and the sentence \(\theta \) is true in \(\prod _{i=0}^k\mathcal {M}_i\) for every \(k\in \mathbb {N}\), then \(\theta \) is true in \(\prod _{i\in \mathbb {N}}\mathcal {M}_i\). (shrink)

This article compares the elucidation of the semantic structure and fixity of a number of key terms and concepts of the Qur'an by two contemporary scholars, Toshihiko Izutsu (1914-1993) and Syed Muhammad Naquib al-Attas (1931--), with that of al-Raghib al-Isfahani (d. ca 443/1060), the author of the celebrated Kitab al-mufradat fi gharib al-Qur'an. By 'key terms and concepts' are meant those words used by the Qur'an which play a decisive role in making up the basic conceptual structure of (...) the Qur'anic worldview. The article shows how the Qur'an profoundly changed and subsequently fixed the meaning of Arabic terms, particularly those key terms relating to religion and ethics, and it highlights the fact that the contemporary semantic analysis of the Qur'anic vocabulary has its precedent in the fifth/eleventh century. (shrink)

It is hypothesized that iron from biological tissues, liberated during decay, may have played a role in inhibiting loss of anatomical information during fossilization of extinct organisms. Most tissues in the animal kingdom contain iron in different forms. A widely distributed iron‐bearing molecule is ferritin, a globular protein that contains iron crystallites in the form of ferrihydrite minerals. Iron concentrations in ferritin are high and ferrihydrites are extremely reactive. When ancient animals are decaying on the sea floor under anoxic environmental (...) conditions, ferrihydrites may initialize the selective replication of some tissues in pyrite FeS2. This model explains why some labile tissues are preserved, while other more resistant structures decay and are absent in many fossils. A major implication of this hypothesis is that structures described as brains in Cambrian arthropods are not fossilization artifacts, but are instead a source of information on anatomical evolution at the dawn of complex animal life. (shrink)

This paper presents a proposal for how British structural-functionalist anthropology can cope with some change. It may not seem a very sensible proposal, but I think it needs to be registered. I use a structure of universities in a country to illustrate the proposal.

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriately understood. In addition, we briefly rehearse (...) some reasons for restricting structural contraction. (shrink)

We prove the preservation theorems for NATP; many of them extend the previously established preservation results for other model-theoretic tree properties. Using them, we also furnish proper examples of NATP theories which are simultaneously TP2 and SOP. First, we show that NATP is preserved by the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, the preservation of NATP for two kinds of dense/co-dense expansions, i.e. the theories of lovely pairs and of (...) [Formula: see text]-structures for geometric theories, and dense/co-dense expansion on vector spaces is proved. Next, we prove the preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also the preservation of NTP1 and NTP2 is considered. Finally, we present some proper examples of NATP theories using the results proved in this paper, including the parametrization of DLO and the expansion of an algebraically closed field by adding a generic linear order. In particular, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP. (shrink)

The study of law and information technology comes with an inherent contradiction in that while technology develops rapidly and embraces notions such as internationalization and globalization, traditional law, for the most part, can be slow to react to technological developments and is also predominantly confined to national borders. However, the notion of the rule of law defies the phenomenon of law being bound to national borders and enjoys global recognition. However, a serious threat to the rule of law is looming (...) in the form of an assault by technological developments within artificial intelligence (AI). As large strides are made in the academic discipline of AI, this technology is starting to make its way into digital decision-making systems and is in effect replacing human decision-makers. A prime example of this development is the use of AI to assist judges in making judicial decisions. However, in many circumstances this technology is a ‘black box’ due mainly to its complexity but also because it is protected by law. This lack of transparency and the diminished ability to understand the operation of these systems increasingly being used by the structures of governance is challenging traditional notions underpinning the rule of law. This is especially so in relation to concepts especially associated with the rule of law, such as transparency, fairness and explainability. This article examines the technology of AI in relation to the rule of law, highlighting the rule of law as a mechanism for human flourishing. It investigates the extent to which the rule of law is being diminished as AI is becoming entrenched within society and questions the extent to which it can survive in the technocratic society. (shrink)

In this paper, we aim at explaining the relevance of thought experiments in philosophy and the history of science by describing them as particular instances of two categories of creative thinking: metaphorical reasoning and abductive cognition. As a result of this definition, we will claim that TEs hold an ignorance-preserving trait that is evidenced in both TEs inferential structure and in the process of scenario creation they presuppose. Elaborating this thesis will allow us to explain the wonder that philosophers (...) of science have consistently shown for TEs, as well as the high functionality of TEs in the creative aspects of scientific and philosophical praxis. (shrink)

Semantics in the Montagovian tradition combines two basic tenets. One tenet is that the semantic value of a sentence is an intension, a function from points of evaluations into truth-values. The other tenet is that the semantic value of a composite expression is the result of applying the function denoted by one component to arguments denoted by the other components. Many philosophers object to intensional semantics on the grounds that intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. (...) They propose instead that the semantic values of sentences must be structured propositions. In rejecting intensional semantics, philosophers who endorse structured propositions also usually reject functional compositionality, undermining both tenets of the Montagovian programme. I defend a semantic theory that incorporates both structured propositions and functional compositionality. I argue that this semantic theory can preserve many explanatory benefits of Montague semantics. Finally, I show how treating composition functional application can resolve core problems internal to a theory of structured propositions. (shrink)

The last decade has seen impressive and intriguing advances in the exploration of vestiges of consciousness in patients with disorders of consciousness . Consciousness is an extremely complex area of research so it is difficult to provide unequivocal interpretations of these new findings from DOC-studies. This review therefore provides a conceptual analysis of a series of key studies in this area of research. The main upshot is that different studies of preserved consciousness in DOC are best seen as targeting different (...) aspects of consciousness rather than a unitary property of being conscious. These different aspects of consciousness thus seem to dissociate and fractionate in DOC. This provides a deeper understanding of the nature and structure of consciousness in general, and it provides suggestions for future research in DOC and the science of consciousness. Further methodological, conceptual, and ethical issues are discussed. (shrink)

Retention of structure across theory change has been invoked in support of a ‘structural’ alternative to more traditional entity-based scientific realism. In that context the transition from Newtonian mechanics to the Special Theory of Relativity is often regarded as a very significant instance of structural preservation, or retention, associated with correspondence-based recovery. The joint derivation, from a small set of elementary and ontologically neutral assumptions, of both the Galilei and the Lorentz transformation exemplifies the virtues of structural approaches to (...) the foundations of physical theories. The common origination of the resulting two relativistic frameworks sheds light on both the successes and the limitations of correspondence claims. However, the cognitive-operational character of the basic assumptions lends no support to the structural realist’s ‘inference to the best explanation’. (shrink)

The increasing availability of personal data of a sequential nature, such as time-stamped transaction or location data, enables increasingly sophisticated sequential pattern mining techniques. However, privacy is at risk if it is possible to reconstruct the identity of individuals from sequential data. Therefore, it is important to develop privacy-preserving techniques that support publishing of really anonymous data, without altering the analysis results significantly. In this paper we propose to apply the Privacy-by-design paradigm for designing a technological framework to counter the (...) threats of undesirable, unlawful effects of privacy violation on sequence data, without obstructing the knowledge discovery opportunities of data mining technologies. First, we introduce a k-anonymity framework for sequence data, by defining the sequence linking attack model and its associated countermeasure, a k-anonymity notion for sequence datasets, which provides a formal protection against the attack. Second, we instantiate this framework and provide a specific method for constructing the k-anonymous version of a sequence dataset, which preserves the results of sequential pattern mining, together with several basic statistics and other analytical properties of the original data, including the clustering structure. A comprehensive experimental study on realistic datasets of process-logs, web-logs and GPS tracks is carried out, which empirically shows how, in our proposed method, the protection of privacy meets analytical utility. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to (...) be so used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

Especially nice models of intuitionistic set theories are realizability models $V$, where $\mathcal A$ is an applicative structure or partial combinatory algebra. This paper is concerned with the preservation of various choice principles in $V$ if assumed in the underlying universe $V$, adopting Constructive Zermelo–Fraenkel as background theory for all of these investigations. Examples of choice principles are the axiom schemes of countable choice, dependent choice, relativized dependent choice and the presentation axiom. It is shown that any of these (...) axioms holds in $V$ for every applicative structure $\mathcal A$ if it holds in the background universe.1 It is also shown that a weak form of the countable axiom of choice, $\textbf{AC}^{\boldsymbol{\omega, \omega }}$, is rendered true in any $V$ regardless of whether it holds in the background universe. The paper extends work by McCarty and Rathjen. (shrink)

In the lengthy debate over the question of scientific realism one of the least discussed positions is structural realism. However, this position ought to attract critical attention because it purports to preserve the central insights of the best arguments for both realism and anti-realism. John Worrall has in fact described it as being ‘the best of both worlds’ that recognizes the discontinuous nature of scientific change as well as the ‘no-miracles’ argument for scientific realism. However, the validity of this claim (...) has been called into question by Stathis Psillos. He questions its ability to correctly account for the examples of scientific change that its supporters, like Worrall, claim ought to be understood in a structural realist light. (shrink)

We prove the NTP1 property of a geometric theory T is inherited by theories of lovely pairs and H‐structures associated to T. We also provide a class of examples of nonsimple geometric NTP1 theories.

Classrooms are unlevel knowing fields, contested terrains where knowledge and ignorance are produced and circulate with equal vigor, and where members of dominant groups are accustomed to having an epistemic home-terrain advantage. My project focuses on one form of resistance that regularly surfaces in discussions with social-justice content. Privilege-preserving epistemic pushback is a variety of willful ignorance that many members of dominant groups engage in when asked to consider both the lived and structural injustices that members of marginalized groups experience (...) daily. I argue that this dominant form of resistance is neither an expression of skepticism nor a critical-thinking practice. I suggest that standard philosophical engagements with these expressions of resistance are incapable of tracking the harms of privilege-preserving epistemic pushback. I recommend treating this pushback as a “shadow text,” that is, as a text that runs alongside the readings in ways that offer no epistemic friction. I offer this as one critical philosophical practice for making students mindful of the ways they contribute to the circulation of ignorance and epistemic violence during the course of their discussions. (shrink)

The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite (...) quantum systems. 6. (shrink)

We prove a number of consistency results complementary to the ZFC results from our paper [J. Cummings, M. Foreman, M. Magidor, Canonical structure in the universe of set theory: part one, Annals of Pure and Applied Logic 129 211–243]. We produce examples of non-tightly stationary mutually stationary sequences, sequences of cardinals on which every sequence of sets is mutually stationary, and mutually stationary sequences not concentrating on a fixed cofinality. We also give an alternative proof for the consistency of (...) the existence of stationarily many non-good points, show that diagonal Prikry forcing preserves certain stationary reflection properties, and study the relationship between some simultaneous reflection principles. Finally we show that the least cardinal where square fails can be the least inaccessible, and show that weak square is incompatible in a strong sense with generic supercompactness. (shrink)

Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, (...) and hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic that can be determined by a finite number of matrices. Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic. (shrink)

This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares of (...) opposition respectively. We clarify the differences between these two cubes, and discuss their gradual extensions, as well as the one of the hexagon when vertices are no longer two-valued. The second part of the paper is dedicated to the use of these structures of opposition for discussing the comparison of two items. Comparing two items usually involves a set of relevant attributes whose values are compared, and may be expressed in terms of different modalities such as identity, similarity, difference, opposition, analogy. Recently, J.-Y. Béziau has proposed an “analogical hexagon” that organizes the relations linking these modalities. Elementary comparisons may be a matter of degree, attributes may not have the same importance. The paper studies in which ways the structure of the hexagon may be preserved in such gradual extensions. As another illustration of the graded hexagon, we start with the hexagon of equality and inequality due to R. Blanché and extend it with fuzzy equality and fuzzy inequality. Besides, the cube induced by a tetra-partition can account for the comparison of two items in terms of preference, reversed preference, indifference and non-comparability even if these notions are a matter of degree. The other cube, which organizes the relations between the different weighted qualitative aggregation modes, is more relevant for the attribute-based comparison of items in terms of similarity. (shrink)

Hubert Dreyfus once noted that it would be difficult to ascertain whether Edmund Husserl had a computational theory of mind. I provide evidence that he had one. Both Steven Pinker and Steven Horst think that the computational theory of mind must have two components: a representational-symbolic component and a causal component. Bearing this in mind, we proceed to a close-reading of the sections of “On the Logic of Signs” wherein Husserl presents, if I’m correct, his computational theory of mind embedded (...) in a language of thought. My argument goes like this: the computational theory of mind is the idea, following Haugeland, that the mind comes prepackaged as, or is endogenously constrained to be, an automatic formal system; this explains, according to Husserl, why automatic trains of thought without logical intent resemble arguments exhibiting deductive structure with logical intent. In general, an automatic formal system yields true results provided that the syntactic symbols with which they compute are univocal and are semantically evaluable, and the mechanized inferences they perform are valid and preserve truth. These two conditions describe a computational cognitive process: the first condition connects representations to syntax, and the second condition uses the syntax, in inauthentic judging, to arrive at true conclusions through blind causality. Now, in point of textual fact, these are the conditions which Husserl attributes to our “natural psychological mechanism of symbolic inference” which typically yields true results. Since a formal system attributed to the “internal structure” of the mind, and guided by blind causality, just is the computational theory of mind, it follows, I think, that Husserl had a computational theory of mind. This computational theory is, moreover, embedded in a language of thought, since Husserl attributes a language-like form to our thoughts so that they may be mechanically processed. I conclude with a discussion of my results. (shrink)

This paper presents how the classical architectural forms – Greek-roman forms – are preserved in early Christian churches built in the Palestinian area between the fourth and the sixth centuries AD. We follow the concept that architecture defines a non-verbal communication form, a language possible to be decoded. Will be discussed questions regarding long-term preservation or change of this buildings in a historical structure evaluating their formal and ideological aspects.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Classrooms are unlevel knowing fields, contested terrains where knowledge and ignorance are produced and circulate with equal vigor, and where members of dominant groups are accustomed to having an epistemic home-terrain advantage. My project focuses on one form of resistance that regularly surfaces in discussions with social-justice content. Privilege-protective epistemic pushback is a variety of willful ignorance that many members of dominant groups engage in when asked to consider both the lived and structural injustices that members of marginalized groups experience (...) daily. I argue that this dominant form of resistance is neither an expression of skepticism nor a critical-thinking practice. I suggest that standard philosophical engagements with these expressions of resistance are incapable of tracking the harms of privilege-protecting epistemic pushback. I recommend treating this pushback as a “shadow text,” that is, as a text that runs alongside the readings in ways that offer no epistemic friction. I offer this as one critical philosophical practice for making students mindful of the ways they contribute to the circulation of ignorance and epistemic violence during the course of their discussions. (shrink)

Consider a general class of structural inference rules such as exchange, weakening, contraction and their generalizations. Among them, some are harmless but others do harm to cut elimination. Hence it is natural to ask under which condition cut elimination is preserved when a set of structural rules is added to a structure-free logic. The aim of this work is to give such a condition by using algebraic semantics. We consider full Lambek calculus (FL), i.e., intuitionistic logic without any structural (...) rules, as our basic framework. Residuated lattices are the algebraic structures corresponding to FL. In this setting, we introduce a criterion, called the propagation property, that can be stated both in syntactic and algebraic terminologies. We then show that, for any set R of structural rules, the cut elimination theorem holds for FL enriched with R if and only if R satisfies the propagation property. As an application, we show that any set R of structural rules can be "completed" into another set R*, so that the cut elimination theorem holds for FL enriched with R*, while the provability remains the same. (shrink)

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...) problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. (shrink)

In a bipartite quantum system, quantum states are classified as classically correlated and quantum correlated states, the later are important resources of quantum information and computation protocols. Since correlations of quantum states may vary under a quantum channel, it is necessary to explore the influence of quantum channels on correlations of quantum states. In this paper, we discuss CC-preserving, QC-breaking and strongly CC-preserving local quantum channels of the form \ and obtain the structures of these three types of local quantum (...) channels. Moreover, we obtain a necessary and sufficient condition for a quantum state to be transformed into a CC state by a specific local channel \ in terms of the structure of the input quantum state. Lastly, as applications of the obtained results, we present a classification of local quantum channels \ and describe the quantum states which are transformed as CC ones by the corresponding local quantum channel. (shrink)

Biodiversity is a key concept in the biological sciences. While it has its origin in conservation biology, it has become useful across multiple biological disciplines as a means to describe biological variation. It remains, however, unclear what particular biological units the concept refers to. There are currently multiple accounts of which biological features constitute biodiversity and how these are to be measured. In this paper, I draw from the species concept debate to argue for a set of desiderata for the (...) concept of “biodiversity” that is both principled and coheres with the concept’s use. Given these desiderata, this concept should be understood as referring to difference quantified in terms of the phylogenetic structure of lineages, also known as the ‘tree of life’. (shrink)

Structural realism has various diverse manifestations. One of the things that structural realists of all stripes have in common is their endorsement of what I call 'the structural continuity claim'. Roughly, this is the idea that the structure of successful scientific theories survives theory change because it has latched on to the structure of the world. In this talk I elaborate, elucidate and modify the structural continuity claim and its associated argument. I do so without presupposing a particular (...) conception of structure that favours this or that kind of structural realism but instead by concentrating on neutrally formulated historical facts. The result, I hope, throws light on what a structural realist must do to evidentially benefit from the historical record of science. The implicit argument underwriting the structural continuity claim can be reconstructed as follows: Premise (1) Only structural elements of predictively and explanatorily successful scientific theories have been (and will be) preserved through theory change. Premise (2): Preservation of an element implies or at least is good evidence for its (approximate) truth. Premise (3): Non-preservation of an element implies or at least is good evidence for its falsity. Conclusion: It is probably the case that only structural elements are (approximately) true. In this summary I restrict my comments to the first premise. Several points can be raised with respect to it. First, not all structures are created equal. Some play no active role in the predictive and explanatory success of a theory because they do not correspond to any structure in the world. Their non-preservation would therefore not encumber the structural realist. Traditional scientific realists have long employed a distinction between essential and idle posits to weed out those elements of theories that played no substantial role in their predictive and explanatory success.. (shrink)

The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we present a new approach to conditionals, capturing particularly well their dynamic part as revision policies. We thoroughly axiomatize a principle of conditional preservation as an indifference property with respect to conditional structures of worlds. This principle is developed in a semi-quantitative setting, so as to reveal (...) its fundamental meaning for belief revision in quantitative as well as in qualitative frameworks. In fact, it is shown to cover other proposed approaches to conditional preservation. (shrink)

The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional (or, more generally, factual) beliefs and need specific treatment. In this paper, we present a new approach to conditionals, capturing particularly well their dynamic part as revision policies. We thoroughly axiomatize a principle of conditional preservation as an indifference property with respect to conditional structures of worlds. This principle is developed in a semi-quantitative setting, (...) so as to reveal its fundamental meaning for belief revision in quantitative as well as in qualitative frameworks. In fact, it is shown to cover other proposed approaches to conditional preservation. (shrink)

We show that any structure of finite Morley Rank having the definable multiplicity property has a rank and multiplicity preserving interpretation in a strongly minimal set. In particular, every totally categorical theory admits such an interpretation. We also show that a slightly weaker version of the DMP is necessary for a structure of finite rank to have a strongly minimal expansion. We conclude by constructing an almost strongly minimal set which does not have the DMP in any rank (...) preserving expansion, and ask whether this structure is interpretable in a strongly minimal set. (shrink)

Exceptionally preserved fossils are the product of complex interplays of biological and geological processes including burial, autolysis and microbial decay, authigenic mineralization, diagenesis, metamorphism, and finally weathering and exhumation. Determining which tissues are preserved and how biases affect their preservation pathways is important for interpreting fossils in phylogenetic, ecological, and evolutionary frameworks. Although laboratory decay experiments reveal important aspects of fossilization, applying the results directly to the interpretation of exceptionally preserved fossils may overlook the impact of other key processes that (...) remove or preserve morphological information. Investigations of fossils preserving non-biomineralized tissues suggest that certain structures that are decay resistant are rarely preserved, and decay-prone structures can fossilize, albeit rarely. As we review here, decay resistance is an imperfect indicator of fossilization potential, and a suite of biological and geological processes account for the features preserved in exceptional fossils. Organisms decayed experimentally in seawater have been used as direct analogs for soft-bodied fossil taxa, with fossils representing a snapshot of a particular stage of decay. We argue that numerous geological and biological processes account for fossilization and that all of these should be considered when reconstructing extinct organisms. (shrink)