This is the first, out of two papers, devoted to Andrzej Grzegorczyk’s point-free system of topology from Grzegorczyk :228–235, 1960. https://doi.org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation. Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze separation structures (...) and Grzegorczyk structures, and establish their properties which will be useful in the sequel. We prove that in the class of Urysohn spaces with countable chain condition, to every topologically interpreted representative of a point in the sense of Grzegorczyk’s corresponds exactly one point of a space. We also demonstrate that Tychonoff first-countable spaces give rise to complete Grzegorczyk structures. The results established below will be used in the second part devoted to points and topological spaces. (shrink)

A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of (...) the difficulties arising from the known definitions of verisimilitude. (shrink)

We face with the question of a suitable measure theory in Euclidean point-free geometry and we sketch out some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the notion of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.

This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means (...) of mereology and Whitehead-like connection structures. We list and briefly analyze axioms for mereological structures, as well as those for connection structures. We argue that mereology is a good tool to model so called spatial relations. We also try to justify our choice of axioms for connection relation. Finally, we briefly discuss two theories: Grzegorczyk’s point-free topology and Tarski’s geometry of solids. (shrink)

In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we (...) show that Grzegorczyk points are maximal contracting filters in the sense of De Vries, but the converse inclusion is not necessarily true. We also compare the notions of a Grzegorczyk point and an ultrafilter, and establish several properties of topological spaces based on Grzegorczyk structures. The main results of the paper are representation and completion theorems for G-structures. We prove both set-theoretical and topological representation theorems for various classes of G-structures. We also present topological object duality theorem for the class of complete G-structures and the class of concentric spaces, both restricted to structures which satisfy countable chain condition. We conclude the paper with proving equivalence of the original Grzegorczyk axiom with the one accepted by us as axiom. (shrink)

We address the fundamental question why we should use PageRank and similar link-based algorithms in search engines, if at all. In a legendary article from 1998, the Google founders gave an intriguing wisdom-of-crowds justification for PageRank according to which the latter tracks quality online. This striking suggestion stands in contrast to the view that PageRank merely tracks what is popular. However, Masterton and Olsson showed that web-ecologies generated by Google-like assumptions essentially fail to reflect the scale-free structure of the (...) web. They pointed to attraction to popularity or a rich-get-richer effect being the likely main cause of scalefreeness. In this article, we explore dual models of linking behavior, i.e. models that combine attraction to importance with attraction to popularity. Our results, obtained through computer simulation, indicate that there exist dual models that give rise both to a wisdom-of-crowds effect for PageRank and to scale-free web-graphs, thus giving a partial vindication of the wisdom-of-crowds thesis for the real web. Future work should explore larger web-graphs as well as other aspects pertaining to the empirical plausibility of dual linking models. (shrink)

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations (...) on fronts, generalizing the Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby (...) demonstrating the independence of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)

In this book I investigate the necessary structure of the aether the stuff that fills the whole universe. Some of my conclusions are. 1. There is an enormous variety of structures that the aether might, for all we know, have. 2. Probably the aether is point-free. 3. In that case, it should be distinguished from Space-time, which is either a fiction or a construct. 4. Even if the aether has points, we should reject the orthodoxy that all (...) regions are grounded in points by summation. 5. If the aether is point-free but not continuous, its most likely structure has extended atoms that are not simples. 6. Space-time is symmetric if and only if the aether is continuous. 7. If the aether is continuous, we should reject the standard interpretation of General Relativity, in which geometry determines gravity. 8. Contemporary physics undermines an objection to discrete aether based on scale invariance, but does not offer much positive support.". (shrink)

Predictive processing theories are increasingly popular in philosophy of mind; such process theories often gain support from the Free Energy Principle —a normative principle for adaptive self-organized systems. Yet there is a current and much discussed debate about conflicting philosophical interpretations of FEP, e.g., representational versus non-representational. Here we argue that these different interpretations depend on implicit assumptions about what qualifies as representational. We deploy the Free Energy Principle instrumentally to distinguish four main notions of representation, which focus (...) on organizational, structural, content-related and functional aspects, respectively. The various ways that these different aspects matter in arriving at representational or non-representational interpretations of the Free Energy Principle are discussed. We also discuss how the Free Energy Principle may be seen as a unified view where terms that traditionally belong to different ontologies—e.g., notions of model and expectation versus notions of autopoiesis and synchronization—can be harmonized. However, rather than attempting to settle the representationalist versus non-representationalist debate and reveal something about what representations are simpliciter, this paper demonstrates how the Free Energy Principle may be used to reveal something about those partaking in the debate; namely, what our hidden assumptions about what representations are—assumptions that act as sometimes antithetical starting points in this persistent philosophical debate. (shrink)

We study some connections between two kinds of emph{overlap} relations: that of point-free geometries in the sense of Grzegorczyk, Whitehead and Clarke, and that recently introduced by Sambin within his constructive approach to topology. The main thesis of this paper is that the overlap relation in the latter sense is a necessary tool for a constructive and intuitionistic development of point-free geometry.

Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from the (...) class='Hi'>point of view of finite combinatorics.The main results of the present work are as follows. In Theorem 2.6 we characterize the existence of tuples of weakly generic automorphisms with the aid of the profinite topology of free groups. In Corollary 2.12 we will show that if has finite topological rank r (and satisfies a further, mild technical condition) then the existence of a weakly generic tuple in implies the existence of weakly generic tuples in for all natural number. Finally, in Theorem 3.2 we show that if is a countable model of an ℵ0‐categorical, simple theory in which all types over the empty set are stationary and has a pair of weakly generic automorphisms then it has tuples of weakly generic automorphisms of arbitrary finite length.At the technical level we will combine elementary investigations about the profinite topology of free groups with the results of [11] about topological ranks of the automorphism groups of some structures. (shrink)

Over the next few issues, you will notice some changes to the Journal of Medical Ethics. Box 1 summarises the new structure for the journal. ### Box 1. Summary of the new structure of the journal Regular sections Editorial Guest Editorial Current Controversies (free web access) Leading Article (free web access) Peer reviewed original contributions New special sections •Teaching and Learning Ethics •Clinical Ethics •Research Ethics •Global Medical Ethics •Law, Ethics and Medicine •Review Essay Ethics Briefings Book Reviews (...) Letters and eLetters News and notes Occasional sections Brief Reports Debate Point of view Medical Student Essay Glossary Current Controversies will briefly describe a current issue of public interest. Informal comment will be invited from a number of commentators from a variety of disciplines. The goal of this section is to provide a publicly accessible resource to promote informed general debate. There will be free web access to the Current Controversies. The Leading Article …. (shrink)

In this Spinozist defence of the educational promotion of students’ autonomy I argue for a deterministic position where freedom of will is deemed unrealistic in the metaphysical sense, but important in the sense that it is an undeniable psychological fact. The paper is structured in three parts. The first part investigates the concept of autonomy from different philosophical points of view, looking especially at how education and autonomy intersect. The second part focuses on explicating the philosophical position of causal determinism (...) and it seeks to open up a way to conceive of education for autonomy without relying on the notion of free will in a metaphysical sense. The concluding part attempts to outline a Spinozistic understanding of education for autonomy where autonomy is grounded in the student's acceptance and understanding of the necessary constraints of natural causation rather than processes of self-causation. (shrink)

This article deals with the methodologies commonly used in the framework of the structural approach to social representations. It concerns free and hierarchical evocations, the characterization questionnaire, the similarity analysis, the basic cognitive schemes model, the attribute-challenge technique and the test of context independence. More than a simple review of these methodologies, it offers a critical approach concerning the problems encountered and related to: thresholds or “cutoff points” used to diagnose the structure and the accuracy of the structural diagnosis, (...) grouping methods employed to reduce the corpus of verbal associations, the dilemma between reliability and feasibility, especially in field research, the adequacy and number of modalities of response in the framework of the structural diagnosis. Following this evaluation, this article suggests potential solutions to overcome these methodological limitations. Moreover, as methodological issues are closely related to theoretical questions, the link between social representation theory and identity approaches is discussed. (shrink)

Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. (...) It considers often neglected issues, such as the need for a more general account of thede dicto-de re distinction, and quasi-indicators. Extended deductive capacities require a subdivision of Konolige''s notion of belief into two distinct technical notions,potential anddispositional belief. The former has to do with what an artificial agent could in principle come to actively believe, given enough time and its specific logical competence; the latter with what an agent can be assumed to believe with respect to a specific goal to be fulfilled. (shrink)

This article is devoted to the analysis of arguments from empirical science against free will. Its main purpose is to reveal their deep anti-naturalism. This anti-naturalism lies in the use of a concept of free will that cannot be the subject of naturalistic consideration, as well as in the various explanatory and ontological paradoxes that arguments from empirical science lead in case when someone is trying to generalize the explanatory principles underlying them. At the beginning of the article, (...) the author gives a general notion of the free will problem, a working definition of naturalism and the place of arguments from empirical science in discussions about free will. To achieve the main goal of the article, the author suggests a classification of arguments from empirical science, which includes five types: from prediction, from manipulation, from the brain, from illusion, from the substitution of concepts. In accordance with this classification, the structure of the article is defined, where each of the presented types is sequentially considered. The logic of considering each type of argument is approximately the same: explication of the essence of the argument of a particular type, its analysis, identification of basic principles and their generalization, demonstration of the negative consequences that it leads to, and answers to possible objections. In the course of the consideration, the author formulates an ontologically neutral concept of free will as a set of abilities associated with the agent’s control over his actions. At the end of the article, the main points is summed up, the idea of naturalistic compatibilism is proposed, the role of arguments from empirical science in discussions about free will is clarified, as is the problem of free will itself, the question of the sources of “chimerization” of naturalism is briefly highlighted, and the problem of completeness of the proposed reasoning is touched upon. (shrink)

In this paper we make a simple theoretical point using a practical issue as an example. The simple theoretical point is that robustness is not 'all or nothing': in asking whether a system is robust one has to ask 'robust with respect to what property?' and 'robust over what set of changes in the system?' The practical issue used to illustrate the point is an examination of degrees of linkage between sub-networks and a pointed contrast in robustness (...) and fragility between the dynamics of (1) contact infection and (2) information transfer or belief change. Time to infection across linked sub-networks, it turns out, is fairly robust with regard to the degree of linkage between them. Time to infection is fragile and sensitive, however, with regard to the type of sub-network involved: total, ring, small world, random, or scale-free. Aspects of robustness and fragility are reversed where it is belief updating with reinforcement rather than infection that is at issue. In information dynamics, the pattern of time to consensus is robust across changes in network type but remarkably fragile with respect to degree of linkage between sub-networks. These results have important implications for public health interventions in realistic social networks, particularly with an eye to ethnic and socio-economic sub-communities, and in social networks with sub-communities changing in structure or linkage. (shrink)

The standard presentation of topological spaces relies heavily on (naïve) set theory: a topology consists of a set of subsets of a set (of points). And many of the high-level tools of set theory are required to achieve just the basic results about topological spaces. Concentrating on the mathematical structures, category theory offers the possibility to look synthetically at the structure of continuous transformations between topological spaces addressing specifically how the fundamental notions of point and open come about. (...) As a byproduct of this, one may look at the different approaches to topology from an external perspective and compare them in a unified way. Technically, the category of sober topological spaces can be seen as consisting of (co)algebraic structures in the exact completion of the elementary category of sets and relations. Moreover, the same abstract construction of taking the exact completion, when applied to the category of topological spaces and continuous functions produces an extension of it which is cartesian closed. In other words, there is one general mathematical construction that, when applied to a very elementary category, generates the category of topological spaces and continuous functions, and when applied to that category produces a very suitable category where to deal with all sorts functions spaces. Yet, via such free constructions it is possible to give a new meaning to Marshall Stone’s dictum: “always topologize” as the category of sets and relations is the most natural way to give structure to logic and the category of topological spaces and continuous functions is obtained from it by a good mix of free – i.e. syntactic – constructions. (shrink)

This paper argues for the hypothesis of direct compositionality (as in, e.g., Montague 1974), according to which the combinatory syntactic rules specify a set of well-formed expressions while the semantic combinatory rules work in tandem to directly supply a model-theoretic interpretation to each expression as it is "built" in the syntax. (This thus obviates the need for any level like LF and, concomitantly, for any rules mapping surface structures to such a level.) I focus here on one related group (...) of phenomena: the interaction of "paycheck" pronouns with Weak Crossover effects and i-within-i effects. These interactions were studied in Jacobson (1977) as they show up in Back-Peters sentences. There I argued that these interactions show that paycheck pronouns have a complex representation at LF; here I show that all of the observations in this earlier work are compatible with the hypothesis of direct compositionality. The key tool is the adoption of a variation-free semantics (a semantics which makes no use of variables as part of the semantic machinery). In addition to the general consequences for the syntax/semantics interface, there are two other main results. First, I provide new arguments for a variable-free semantics. For example, it will be shown that under this view the paycheck reading of a pronoun comes for free; most other theories posit additional mechanisms and/or an additional lexical meaning for pronouns, and thus paycheck and regular pronouns are only accidentally homophonous. Second, I reiterate one of the central points in Jacobson (1977): this is that the first pronoun in a Bach-Peters sentence is indeed a paycheck pronoun, and hence nothing special needs to be said about these sentences nor does any new machinery need to be invoked for them. (shrink)

De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also established.

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the (...) similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. (shrink)

The present report is a, somewhat lengthy, addendum to "A new deconstructive logic: linear logic," where the elimination of cuts from derivations in sequent calculus for classical logic was studied ‘from the point of view of linear logic’. To that purpose a formulation of classical logic was used, that - as in linear logic - distinguishes between multiplicative and additive versions of the binary connectives.The main novelty here is the observation that this type-distinction is not essential: we can allow (...) classical sequent derivations to use any combination of additive and multiplicative introduction rules for each of the connectives, and still have strong normalization and confluence of tq-reductions.We give a detailed description of the simulation of tq-reductions by means of reductions of the interpre- tation of any given classical proof as a proof net of PN2 (the system of second order proof nets for linear logic), in which moreover all connectives can be taken to be of one type, e.g., multiplicative.We finally observe that dynamically the different logical cuts, as determined by the four possible combinations of introduction rules, are independent: it is not possible to simulate them internally, i.e., by only one specific combination, and structural rules. (shrink)

First published in 1848, Frederick Grimke's book, in the words of the editor, "deserves comparison with Tocqueville's justly famous work, Democracy in America, and is in certain ways superior. It is the single best book written by an American in the nineteenth century on the meaning of our political way of life." A second edition of Grimke's work was published in 1856, and a third edition appeared posthumously in 1871, but since then this classic in American thought has been almost (...) completely lost to sight. Grimke was born in South Carolina in 1791, and later moved to Ohio where he became a judge. He remained a bachelor, led a rich and cosmopolitan intellectual life, and accumulated an excellent library. His sisters Angelina (wife of the abolitionist Theodore Weld) and Sarah were both famous for deserting their South Carolina heritage and becoming active in the abolition and woman suffrage movements. In 1842 Grimke retired from the bench to devote the remainder of his life to study and writing, setting himself the task of educating his contemporaries in the nature of their society. His major achievement was The Nature and Tendency of Free Institutions. Grimke's range of topics includes the right of the majority, the character and operation of elective governments, the function of political parties, the American contrasted with the English and French constitutions, and the separation of powers in the American political systems. He sees governmental institutions as the expression of the general structure of society which calls them into being. In his Introduction, Mr. Ward points to Grimke's thesis "that the separation of powers in the frame of the American constitution works not because power is distributed within the government but because all branches of the government are, directly or indirectly, responsible to the will of the majority of the people outside the doors of government." As a result of the party system, Grimke wrote, "we may vary the paraphernalia of government as much as we please, but it still obstinately persists in every one of its departments to be a government based upon the popular will." Mr. Ward calls attention to Grimke's passionate belief that "freedom is its own justification" and that its ultimate value is that "it created the kind of character which made freedom possible." He held that "the only way to make a man fit for freedom is to give him freedom." Yet, unlike his sisters, he shared a view of race that was pervasive in his time and was unable to imagine the extension of freedom to the slave. In contradiction to his views of government and freedom, he upheld Negro slavery even to the extent of sanctioning secession to protect it. To him, "the open affirmation of the right of secession would serve to maintain the Union, not destroy it.". (shrink)

We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We (...) also show how extracted programs can be translated into Haskell. As an application we extract a program converting the signed digit representation of real numbers to infinite Gray code from a proof of inclusion of the corresponding coinductive predicates. (shrink)

This book focuses on the phenomena of inertia and gravitation, one objective being to shed some new light on the basic laws of gravitational interaction and the fundamental nature and structures of spacetime. Chapter 1 is devoted to an extensive, partly new analysis of the law of inertia. The underlying mathematical and geometrical structure of Newtonian spacetime is presented from a four-dimensional point of view, and some historical difficulties and controversies - in particular the concepts of free (...) particles and straight lines - are critically analyzed, while connections to projective geometry are also explored. The relativistic extensions of the law of gravitation and its intriguing consequences are studied in Chapter 2. This is achieved, following the works of Weyl, Ehlers, Pirani and Schild, by adopting a point of view of the combined conformal and projective structure of spacetime. Specifically, Mach's fundamental critique of Newton's concepts of 'absolute space' and 'absolute time' was a decisive motivation for Einstein's development of general relativity, and his equivalence principle provided a new perspective on inertia. In Chapter 3 the very special mathematical structure of Einstein's field equations is analyzed, and some of their remarkable physical predictions are presented. By analyzing different types of dragging phenomena, Chapter 4 reviews to what extent the equivalence principle is realized in general relativity - a question intimately connected to the 'new force' of gravitomagnetism, which was theoretically predicted by Einstein and Thirring but which was only recently experimentally confirmed and is thus of current interest. (shrink)

This article is a contribution to the existing debate about the marketization of higher education and offers a detailed study of the way the practices of marketization manifest themselves at the level of discourse in higher education. Taking its point of departure in Critical Discourse Analysis and using a text-driven procedure for genre analysis, the article describes and analyses the international student prospectus as an instance of a highly promotional genre which clearly reflects the values and forces of the (...) free market. The article contains two analyses. The first analysis compares four instances of the international student prospectus genre from Finland, Scotland, Australia and Japan and tries to establish genre membership and genre characteristics by considering the overall text structure, and by looking for similarities in content and `rhetorical moves'. The second analysis is an in-depth analysis of the language use in the international student prospectus from the University of Stirling, Scotland. This analysis pays particular attention to the way the rhetorical moves and visual and lexico-grammatical features in the text are used to represent the two main participants in the text: the university and its students. Both analyses show that the student prospectus is trying to construct an image of the University of Stirling and its students which goes hand in hand with the new trend in higher education — namely that of offering innovative products to `demanding' clients on the look-out for the best possible `university experience'. (shrink)

Summary By introducing the concept of “invariants”, Koffka endowed perceptual psychology with a flexible theoretical tool, which is suitable for representing vision situations in which a definite part of the stimulus pattern is relevant but not sufficient to determine a corresponding part of the perceived scene. He characterised his “invariance principle” as a principle conclusively breaking free from the “old constancy hypothesis”, which rigidly surmised point-to-point relations between stimulus and perceptual properties. In this paper, we explain the (...) basic terms and assumptions implicit in Koffka’s concept, by representing them in a set-theoretic framework. Then, we highlight various aspects and implications of the concept in terms of answers to six separate questions: forms of invariants, heuristic paths to them, what is invariant in an invariant, roots of conditional indeterminacy, variability vs. indeterminacy, and overcoming of the indeterminacy. Lastly, we illustrate the lasting value and theoretical power of the concept, by showing that Koffka’s insights relating to it do occur in modern perceptual psychology and by highlighting its role in a model of perceptual transparency. (shrink)

The Russian financial crisis of August 1998, which occurred between the Asian recession and the devaluation of the Brazilian real in January 1999, put a question-mark over many certainties. It demonstrated that the most destructive speculative activities of financial players can only have free rein when there is a collapse of the state. The crisis proved that the markets need a state and cannot replace it. It was also the moment when people became aware of the dynamics of a (...) globalized financial economy (Stiglitz, 1999a; 1999b), leading to a critical rereading of the policies recommended in the 1990s and a direct questioning of the IMF and its actions. In Russia it caused a paradigm shift that could turn out to be salutary. In this regard the August 1998 crisis looks like the endpoint on the route followed since 1992 by the transition in Russia (Sapir, 1999a). We can see in the crisis both elements directly linked to the financial liberalization of 1985-95 and structural elements peculiar to the consequences of the transition and the policies adopted. This is why it suggests a reinterpretation of the entire development of the transition in Russia starting from 1992. (shrink)

We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘point-free’ definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.

This paper concerns the structure of any spatially extended things, including regions of space or spacetime. I shall use intuitions about the quantity of extended things to argue for a dichotomy: either a given finite extended thing is point-free gunk, that is, it has no points as parts, or it is made of grit, that is there are only finitely many points.

We consider certain linear orders with a function on them, and discuss for which types of functions the resulting structure is or is not computably categorical. Particularly, we consider computable copies of the rationals with a fixed-point free automorphism, and also ω with a non-decreasing function.

Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one (...) free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

Free-will incompatibilism has become a motte-and-bailey doctrine (Shackel 2014), and is currently being maintained by standard motte-and-bailey strategies. In this paper, I explain why incompatibilism has a motte-and-bailey structure and why philosophers who do not aim to dismantle it are complicit in both the maintenance of this problematic doctrine and the normalization of a host of bad practices engaged in by those who actively exploit it. To solidify the diagnosis, I provide a paradigmatic motte-and-baileying case that has been ongoing (...) for over a decade. Specifically, I discuss how motte-and-baileying has generated widespread confusion surrounding the logical structure and conclusion of manipulation arguments. Even more specifically, I look at Mele's so-called "Zygote Argument for incompatibilism". I point out that Mele currently conflates under two distinct arguments with different logical forms and substantively different conclusions under that heading, and explain how this has needlessly impeded progress in the free-will debate. The original variant of the Zygote Argument was invalid because it aimed to establish that determinism precludes (destroys, undermines, is antagonistic to) free will, but its supported a far weaker non-explanatory conclusion. In direct response to this invalidity objection, Mele took his critic's suggestion to change the conclusion of his argument to the thesis that free will and determinism are perhaps spuriously associated -- but he also covertly changed his preferred definition of 'incompatibilism' to pick out the non-explanatory conclusion of the new variant of the Zygote Argument which allowed him to continue speaking AS IF his argument was still an argument for incompatibilism according to his original definition of 'incompatibilism'. It is not simply that Mele made these changes or that he failed to mention in print that he made them (despite having over a decade to do so), but that he has actively attempted to discredit his critics by insisting--contrary to fact--that those who do not use his negative definition of 'incompatibilism' are using the term in a nonstandard and nontraditional way that he has "never had any use for" and there is some kind of connection (which he does describe) between the invalidity objection to his original argument that the definition of 'incompatibilism' one prefers. Oddly, Mele has mentioned only one "invalidity objection" in print, but this objection is direct at the revised Zygote Argument--even though no one had ever pressed an invalidity objection to his new argument (the form of which is patently valid). As a direct result of Mele's evasive behaviors (covertly redefining jargon to cover changes to the form/conclusion of his argument), many people--including Mele's own former graduate students--have published articles in which they fail to recognize that Mele changed his argument and redefined terms, thereby perpetuating the false narrative that the new Zygote Argument has the same "incompatibilist" conclusion as the original (which, notably, had the same conclusion as its predecessor, Pereboom's Four-Case Argument). Moreover, Mele has not even ONCE corrected those who "misdescribe" his revised argument as concluding that determinism is antagonstic to (precludes, undermines, rules out, etc.) free will. For example, Mele never corrects those who mistakenly claim that the revised Zygote Argument has the same "incompatibilist" conclusion as Pereboom's, nor has Mele ever mentioned that he now defines the term 'incompatibilism' differently than Pereboom--since Pereboom since uses this term to refer to the explanatory conclusion of the original Zygote Argument, which had the same explanatory conclusion of his Four-Case Argument. To further throttle his critics, Mele has obliquely suggested that the invalidity objection to his original Zygote Argument works only if one accepts his critic's idiosyncratic definition of 'incompatibilism' -- a patently false charge (since the term 'incompatibilism' doesn't even appear in his arguments) and one that has needlessly confused his audience. Indeed, other philosophers have now made this false and quite indefensible accusation explicitly in print, thereby helping Mele and others to continue motte-and-baileying with impunity. I close by preemptively responding to strategies commonly used by motte-and-bailey apologists to suppress legitimate criticisms of their equivocation and well-poisoning strategies (e.g. "Philosophers are allowed to define their technical terms however they like" and "the motte/bailey divide is a distinction without a difference") which have hitherto kept their philosophical audience from participating in a legitimate discussion about why tracking the distinction between the the "motte" thesis (a negative, arguably spurious association claim) and the "bailey" thesis (a positive explanatory claim) is not trivial, but is instead one that is absolutely essential to making progress in the free-will debate. Of course, a single critic cannot (almost by definition) undermine a motte-and-bailey doctrine once it has been established. As such, even if every diagnosis in this essay is accurate, it will not change the discourse. The motte-and-baileying will continue, and the debate will remain in needless deadlock, until a critical threshold of OBSERVERS learn about the motte/bailey distinction and ask apologists for motte-and-bailey incompatibilism to stop their motte-and-baileying. -/- Manuscript available upon request, plz gmail me: kristin.mickelson.42@. (shrink)

In this paper we develop a point-free approach to the study of topological spaces and functions on them, establish platforms for both and present some findings on recursive points. In the first sections of the paper, we obtain conditions under which our approach leads to the generation of ideal objects with which mathematicians work. Next, we apply the effective version of our approach to the real numbers, and make exact connections to the classical approach to recursive reals. In (...) the succeeding sections of the paper, we introduce machinery to produce functions on topological spaces and find succinct conditions which will be effectivized in our sequel. (shrink)

This is a selection of essays on moral responsibility that represent the major components of John Martin Fischer's overall approach to freedom of the will and moral responsibility. The collection exhibits the overall structure of Fischer's view and shows how the various elements fit together to form a comprehensive framework for analyzing free will and moral responsibility. The topics include deliberation and practical reasoning, freedom of the will, freedom of action, various notions of control, and moral accountability. The essays (...) seek to provide a foundation for our practices of holding each other (and ourselves) morally and legally accountable for our behavior. A crucial move is the distinction between two kinds of control. According to Fischer, "regulative control" involves freedom to choose and do otherwise ("alternative possibilities"), whereas "guidance control" does not. Fischer contends that guidance control is all the freedom we need to be morally responsible agents. Further, he contends that such control is fully compatible with causal determinism. Additionally, Fischer argues that we do not need genuine access to alternative possibilities in order for there to be a legitimate point to practical reasoning. Fischer's overall framework contains an argument for the contention that guidance control, and not regulative control, is associated with moral responsibility, a sketch of a comprehensive theory of moral responsibility (that ties together responsibility for actions, omissions, consequences, and character), and an account of the value of moral responsibility. On this account, the value of exhibiting freedom (of the relevant sort) and thus being morally responsible for one's behavior is a species of the value of artistic self-expression. (shrink)

In the first section we briefly describe methodological assumptions of point-free geometry and topology. We also outline history of geometrical theories based on the notion of emph{region}. The second section is devoted to concise presentation of the content of the LLP special issue on point-free theories of space.

Structural realists contend that the properties and relations in the world are more fundamental than the individuals. However, the standard model theory used to analyse the structure of logical theories can make it difficult to see how such an idea could be coherent or workable: for in that theory, properties and relations are constructed as sets of individuals. In this paper, I look at three ways in which structuralists might hope for an alternative: by appealing to predicate-functor logic, Tractarian geometry, (...) or cylindric algebras. I argue that the first two are problematic, but that the third is promising. (shrink)

This paper is based on the comments I gave to Alfred Mele regarding his original Zygote Argument during my presentation at a small workshop on manipulation arguments in Budapest back in 2012. After those comments, Mele changed the conclusion of his original Zygote Argument (OZA) from a positive, explanatory conclusion to a negative, non-explanatory conclusion--and, correspondingly, redefined 'incompatibilism' so that it would no longer refer in his work to the view that determinism precludes (undermines, eliminates, destroys, etc.) free will, (...) but refers narrowly to the perhaps spurious association claim that appears in the conclusion of the revised Zygote Argument (Mele 2013+). Yet, over the last decade, Mele has made no comment in print about the changes he made, the invalidity objection that led to them, nor to the fact that his revised Zygote Argument was originally presented by me as a (non-optimal) reaction to my invalidity objection to his original Zygote Argument. To my knowledge, Mele has only mentioned this 2015 paper once, at it was not in the context of understanding manipulation arguments; it was, rather, in the context of defending his revised, non-explanatory definition of 'incompatibilism' at the opening of Aspects of Agency (p. 6, n. 4). There, Mele singles out *just this 2015 paper* as a place where they'll find what Mele degrades as a type of nonstandard/nontraditional definition of 'incompatibilism' that he rejects. This is notable because Mele provides no empirical evidence that his preferred definition is standard, and most (including Lehrer, who coined the term) reject the negative, non-explanatory, association-based definition that Mele came to endorse in the aftermath of my invalidity objection to OZA. So, if Mele had a genuine concern about philosophers who use the term 'incompatibilism', then Mele could have--and should have--named almost any leading figure in free will for this purpose (since most--including Pereboom, Vihvelin, Haji, etc.) reject the non-explanatory definition that Mele-2013+ now endorses. Yet, for untold reasons, Mele isolated the working definition of 'incompatibilism' used in one paper by one unemployed junior researcher to use as his example--even though Neil Levy had used this same definition in previously published work (eg. Levy 2011). Moreover, if Mele were genuinely interested in helping his readers understand the ambiguity of terms like 'compatibilism' and 'incompatibilism' it is a mystery that he referenced a paper in which nothing of substance hung on the definitions given to these terms -- especially considering that he might have instead pointed them to my OTHER 2015 paper, "A Critique of Vihvelin's Three-Fold Classification" in which the MAIN AIM of the paper is to expose the difficulties facing anyone who wants to define the terms 'compatibilism' and 'incompatibilism' in a way that everyone will accept (including a critique of the negative, non-explanatory "incompossibilist" definition that Mele adopted after my objection to OZA). By all appearances, Mele's main aim in citing specifically THIS paper and none of my other work was to give readers the false impression that my working definition of 'incompatibilism' played some role in my charge that his argument is invalid (which it doesn't, given that the term doesn't appear in either the premises or conclusion of that argument). Mele adds to this unseemly rhetorical campaign in his book *Manipulation Agents* where he mentions an invalidity objection in the intro (p. 84) and then discusses that objection in the final lines of Chapter 5 of the book (p. 120-121). The invalidity objection discussed here is completely pedantic, has never been seriously raised in the primary literature (and was previously addressed in multiple places my multiple philosophers, including me), and has nothing whatever to do with my invalidity objection. In other words, Mele was content to discuss an invalidity objection that no one has ever had to an argument that is clearly valid while completely ignoring the ONLY substantive invalidity objection to his argument in print. This is unfortunate, because it has led to serious confusion --including the patently false description of my invalidity objection to OZA as an objection to the revised version of the Zygote Argument that Mele adopted in *response* my objection (e.g., Capes mistakenly claims "Mickelson (2015) contends that arguments like this [i.e. like the revised Zygote Argument] are invalid. But that’s because she defines “incompatibilism” differently than I’ve defined it here" in his "Manipulation Arguments and Direct Arguments" chapter in the 2023 Wiley-Blackwell Companion to Free Will; I did not say this, and the definition of 'incompatibilism' is irrelevant to my objection). In "The Zygote Argument Is Invalid--Now What?", I simply use the invalidity of the simple 2-premise Zygote Argument as a foil to make a series of more philosophically significant points (e.g. regarding the dialectical structure of the free-will debate, the role of best-explanation reasoning, and to develop the first-ever "master manipulation argument"). Mele has yet to address my reasons for calling attention to the non-trivial invalidity of his OZA or to any of my answers to the "Now What?" question in this paper, even though this question and my proposed answers to this question are the paper's main point. For those interested in a more recent discussion of how the logical and metaphilosophical observations made in this "Now What?" paper have helped to move the free-will debate forward, I suggest looking at the discussions of the "paradigm shift" in the free-will debate that helps to explain why the free-will debate has become mired in stalemates and empty verbal disputes that are found, for example, in my contributions to the Wiley-Blackwell Companion to Free Will (Intro and Chapter 4, 2023) and my paper "Free Will, Self-Creation, and the Paradox of Moral Luck" (2019). (shrink)

The paper presents the main idea of point-free theories of space based on Tarski's system of point-free geometry. First, the general idea of the so-called point-free ontology was discussed, as well as the epistemological and methodological reasons for its adoption. Next, Whitehead's method of extensive abstraction, which is the methodological basis for the construction of point-free theories of space, is presented, and the fundamental concepts of mereology are discussed. The main part of (...) the paper is a discussion of Tarski’s geometry of solids, its postulates and metatheoretical properties. The paper ends with a short description of the contribution of Polish researchers to the development of research on point-free theories of space. (shrink)

At this point I should say something about one of the frequent criticisms addressed to me, and to which I have always wanted to respond, that in the process of characterizing the production of Europe’s inferior Others, my work is only negative polemic which does not advance a new epistemological approach or method, and expresses only desperation at the possibility of ever dealing seriously with other cultures. These criticisms are related to the matters I’ve been discussing so far, and (...) while I have no desire to unleash a point-by-point refutation of my critics, I do want to respond in a way that is intellectually pertinent to the topic at hand.What I took myself to be undertaking in Orientalism was an adversarial critique not only of the field’s perspective and political economy, but also of the sociocultural situation that makes its discourse both so possible and so sustainable. Epistemologies, discourses, and methods like Orientalism are scarcely worth the name if they are reductively characterized as objects like shoes, patched when worn out, discarded and replaced with new objects when old and unfixable. The archival dignity, institutional authority, and patriarchal longevity of Orientalism should be taken seriously because in the aggregate these traits function as a worldview with considerable political force not easily brushed away as so much epistemology. Thus Orientalism in my view is a structure erected in the thick of an imperial contest whose dominant wing it represented and elaborated not only as scholarship but as a partisan ideology. Yet Orientalism hid the contest beneath its scholarly and aesthetic idioms. These things are what I was trying to show, in addition to arguing that there is no discipline, no structure of knowledge, no institution or epistemology that can or has ever stood free of the various sociocultural, historical, and political formations that give epochs their peculiar individuality. Edward W. Said is Parr Professor of English and Comparative Literature at Columbia University. His most recent contribution to Critical Inquiry is “An Ideology of Difference”. (shrink)

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms (...) of Russell's second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. (shrink)

The fungal cell wall is a dynamic structure that protects the cell from changes in osmotic pressure and other environmental stresses, while allowing the fungal cell to interact with its environment. The structure and biosynthesis of a fungal cell wall is unique to the fungi, and is therefore an excellent target for the development of anti‐fungal drugs. The structure of the fungal cell wall and the drugs that target its biosynthesis are reviewed. Based on studies in a number of fungi, (...) the cell wall has been shown to be primarily composed of chitin, glucans, mannans and glycoproteins. The biosynthesis of the various components of the fungal cell wall and the importance of the components in the formation of a functional cell wall, as revealed through mutational analyses, are discussed. There is strong evidence that the chitin, glucans and glycoproteins are covalently cross‐linked together and that the cross‐linking is a dynamic process that occurs extracellularly. BioEssays 28: 799–808, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

The article develops a general theory of the goals of free moral commitment. The theoretical hook is the discussion of the strict efficiency striving as demanded by the movement and theory of effective altruism. A detailed example shows prima facie counterintuitive consequences of this efficiency striving, the analysis of which reveals various problems such as: merely point-like but not structural commitment; radical universalism; violation of established moral standards and institutions. The article takes these problems as an occasion to (...) develop a general theory of moral investment with moral guidelines and planning instruments of its implementation such as: efficiency; preservation of existing moral standards and obligations, especially also towards those close to one; rooted universalism with adequate consideration of all beneficiaries of one's moral concern through allocation of separate budgets; real efficiency also through inclusion of strategic and organic investments. (shrink)

In this note a T1 formal space is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of a formal space, and prove that the class of points of a weakly set-presentable formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties for constructive topological spaces , strengthening separation properties discussed elsewhere. Finally we relate (...) the properties for ct-spaces with corresponding properties of formal spaces. (shrink)

This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide in presence of axiom stipulating non-existence of (...) atoms. (shrink)