We investigate profinite structures in the sense of Newelski interpretable in fields. We show that profinite structures interpretable in separably closed fields are the same as profinite structures weakly interpretable in . We also find a strong connection with the inverse Galois problem. We give field theoretic constructions of profinite structures weakly interpretable in and satisfying some model theoretic properties, like smallness, m-normality, non-triviality, being -rank 1. For example we interpret in this way the profinite (...) structure consisting of the profinite group together with a distinguished Sylow p-subgroup of its standard structural group. (shrink)

We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms and satisfying the existence of m-independent extensions (we call them compact e-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of m-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to (...) compact e-structures. In particular, we notice that a variant of the group configuration theorem holds in this context. A general construction of compact structures is described. Using it, a class of examples of compact e-structures which are not small is constructed. It is also noticed that in an m-stable compact e-structure every orbit is equidominant with a product of m-regular orbits. (shrink)

We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the “Weak Independence Theorem” for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property [Formula: see text]. Fourth, we describe Kim-dividing (...) in these PAC substructures and show several results related to the SOPnhierarchy. Fifth, we characterize the algebraic closure in PAC structures. (shrink)

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 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)

We study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite group (...) can be realized as the stabilizer of a point in a strongly minimal structure of bounded valency. (shrink)

We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures, extending Zheng’s work for the profinite graph to the setting of Fraïssé classes of finite ordered binary relational structures with the Ramsey property. This work is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. Based on these topological Ramsey spaces and the work of Huber-Geschke-Kojman on inverse limits of finite ordered graphs, we prove that for each (...) such Fraïssé class, its universal inverse limit structure has finite big Ramsey degrees under finite Baire-measurable colorings. For such Fraïssé classes satisfying free amalgamation as well as finite ordered tournaments and finite partial orders with a linear extension, we characterize the exact big Ramsey degrees. (shrink)

It is well-known that feature structures can be fruitfully viewed as forming a Scott domain. Once a linguistically motivated notion of set value in feature structures is countenanced, however, this is no longer possible inasmuch as unification of set values in general fails to yield a unique result. In Pollard and Moshier 1990 it was shown that, while falling short of forming a Scott domain, the set of feature structures possibly containing set values satisfies the weaker condition of forming a (...) 2/3 SFP domain when equipped with an appropriate notion of subsumption: that is, for any finite setS of feature structures, there is a finite setM of minimal upper bounds ofS such that any upper bound ofS is approximated by a member ofM. Unfortunately, the 2/3 SFP domains are not as pleasant to work with as Scott domains since they are not closed under all the familiar domain constructions; and the question has remained open whether the feature structure domain satisfies the added condition of profiniteness. In this paper we resolve this question in the affirmative. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

We study relationships between certain algebraic properties of groups and rings definable in a first order structure or *-closed in a compact G-space. As a consequence, we obtain a few structural results about ω-categorical rings as well as about small, nm-stable compact G-rings, and we also obtain surprising relationships between some conjectures concerning small profinite groups.

Let $$\textbf{K}$$ and $$\textbf{M}$$ be locally finite quasivarieties of finite type such that $$\textbf{K}\subset \textbf{M}$$. If $$\textbf{K}$$ is profinite then the filter $$[\textbf{K},\textbf{M}]$$ in the quasivariety lattice $$\textrm{Lq}(\textbf{M})$$ is an atomic lattice and $$\textbf{K}$$ has an independent quasi-equational basis relative to $$\textbf{M}$$. Applications of these results for lattices, unary algebras, groups, unary algebras, and distributive algebras are presented which concern some well-known problems on standard topological quasivarieties and other problems.

We introduce the Profinite Hull functor of special groups, showing that it gives rise to a new local - global principle, the subform reflection property. We also indicate applications of this principle to the abstract algebraic theory of quadratic forms.

We propose a model-theoretic framework for investigating profinite groups. Within this framework we define and investigate small profinite groups. We consider the question if any small profinite group has an open abelian subgroup.

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

Profinite groups are Galois groups. The effective study of infinite Galois groups was initiated by Metakides and Nerode [8] and further developed by LaRoche [5]. In this paper we study profinite groups without considering Galois extensions of fields. The Artin method of representing a finite group as a Galois group has been generalized by Waterhouse [14] to profinite groups. Thus, there is no loss of relevance in our approach.The fundamental notions of a co-r.e. profinite group, recursively (...) profinite group, and the degree of a co-r.e. profinite group are defined in §1. In this section we prove that every co-r.e. profinite group can be effectively represented as an inverse limit of finite groups. The degree invariant is shown to behave very well with respect to open subgroups and quotients. The work done in this section is basic to the rest of the paper.The commutator subgroup, the Frattini subgroup, thep-Sylow subgroups, and the center of a profinite group are essential in the study of profinite groups. It is only natural to ask if these subgroups are effective. The following question exemplifies our approach to this problem: Is the center a co-r.e. profinite group? Theorem 2 provides a general method for answering this type of question negatively. Examples 3,4 and 5 are all applications of this theorem. (shrink)

Dans cet ouvrage publié en 1942, complété en 1945 par la Phénoménologie de la perception, « s’affirme pour la première fois une philosophie existentielle où le mode d’être ultime du pour-soi ne s’avère pas être, en dépit des intentions et des descriptions contraires, celui d’une conscience-témoin » (A. de Waelhens, préface). La structure du comportement se place au niveau de l’expérience non pas naturelle mais scientifique et s’efforce de prouver que cette expérience, c’est-à-dire l’ensemble des faits qui constituent le (...) comportement, n’est pas compréhensible dans les perspectives ontologiques que la science adopte spontanément. (shrink)

This collection of papers (including three completely new ones) by one of the foremost philosophers in epistemology transcends two of the most widely misunderstood positions in philosophy--foundationalism and coherentism. Audi proposes a distinctively moderate, internalist foundationalism that incorporates some of the virtues of both coherentism and reliabilism. He develops important distinctions between positive and negative epistemic dependence, substantively and conceptually naturalistic theories, dispositional beliefs and dispositions to believe, episodically and structurally inferential beliefs, first and second order internalism, and rebutting as (...) opposed to refuting skepticism. These contrasts are applied not only to rational belief, but to rational action and the rationality of desires and intentions. The overall position is a pluralist, moderately rationalistic, internalist theory of justification and a partly externalist conception of knowledge. However, by virtue of offering a theory of rationality as well as an account of knowledge and justified belief, it will interest philosophers of ethics, science, and the social sciences and teachers and students of epistemology. (shrink)

A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure‐mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be (...) distinguished cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons.Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher‐order relations. (shrink)

There is good reason to believe that scientific realism requires a commitment to the objective modal structure of the physical world. Causality, equilibrium, laws of nature, and probability all feature prominently in scientific theory and explanation, and each one is a modal notion. If we are committed to the content of our best scientific theories, we must accept the modal nature of the physical world. But what does the scientific realist’s commitment to physical modality require? We consider whether scientific (...) realism is compatible with Humeanism about the laws of nature, and we conclude that it is not. We specifically identify three major problems for the best-systems account of lawhood: its central concept of strength cannot be formulated non-circularly, it cannot offer a satisfactory account of the laws of the special sciences, and it can offer no explanation of the success of inductive inference. In addition, Humeanism fails to be naturalistically motivated. For these reasons, we conclude that the scientific realist must embrace natural necessity. (shrink)

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman (...) also suggests how The Structure of Appearance introduces issues which Goodman later continues in his essays and in the Languages of Art. There remains the task of understanding Good man's project as a whole; to see the deep continuities of his thought, as it ranges from logic to epistemology, to science and art; to see it therefore as a complex yet coherent theory of human cognition and practice. What we can only hope to suggest, in this note, is the b. road Significance of Goodman's apparently technical work for philosophers, scientists and humanists. One may say of Nelson Goodman that his bite is worse than his bark. Behind what appears as a cool and methodical analysis of the conditions of the construction of systems, there lurks a radical and disturbing thesis: that the world is, in itself, no more one way than another, nor are we. It depends on the ways in which we take it, and on what we do. (shrink)

What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. Numerical taxonomists sought (...) to establish a mathematical method for classification that was universal to every type of organism, and I argue this intrinsically implicated them in a qualitative re-organization of the work of all systematists. I also discuss how Numerical Taxonomy’s re-organization of practice became entrenched across systematic biology even as opposing schools produced their own competing mathematical methods. In this way, the structure of the work process became more fundamental than the methodological theories that motivated it. (shrink)

Epistemic defeat is standardly understood in either evidentialist or responsibilist terms. The seminal treatment of defeat is an evidentialist one, due to John Pollock, who famously distinguishes between undercutting and rebutting defeaters. More recently, an orthogonal distinction due to Jennifer Lackey has become widely endorsed, between so-called doxastic (or psychological) and normative defeaters. We think that neither doxastic nor normative defeaters, as Lackey understands them, exist. Both of Lackey’s categories of defeat derive from implausible assumptions about epistemic responsibility. Although Pollock’s (...) evidentialist view is superior, the evidentialism per se can be purged from it, leaving a general structure of defeat that can be incorporated in a reliabilist theory that is neither evidentialist nor responsibilist in any way. (shrink)

An approach to argument macrostructure -- The dialectical nature of argument -- Toulmin's problematic notion of warrant -- The linked-convergent distinction, a first approximation -- Argument structure and disciplinary perspective : the linked-convergent versus multiple-co-ordinatively compound distinctions -- The linked-convergent distinction, refining the criterion -- Argument structure and enthymemes -- From analysis to evaluation.

Structural realism has been suggested as the best compromise in the debate on scientific realism. It proposes that we should be realist about the relational structure of the world, not its nature. However, it faces an important objection, first raised by Newman against Russell: if relations are not qualified, then the position is either trivial or collapses into empiricism, but if relations are too strongly qualified, then it is no longer SR. A way to overcome this difficulty is to (...) talk about modal, or nomological relations instead of purely extensional relations. I argue that this is insufficient, for then, SR collapses into modal empiricism. I suggest, however, that ME could be the best position in the debate on scientific realism. 1Introduction2Objections to Structural Realism3How to Escape Newman’s Objection4Which Modal Relations Are Retained in Theory Change?5Are Modal Relations Real?6Relativity and Fundamentality7Is Modal Empiricism Really Empiricism?8Could Modal Empiricism Be the Best of Both Worlds? (shrink)

We study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for profinite groups. We show that any sorted profinite group has a universal SEP-cover. Our proof gives an alternative proof for the existence of a universal embedding cover of a profinite group. Also our proof works for any full subcategory of the sorted profinite groups, which is closed under (...) taking finite quotients, fibre products, and inverse limits. We also show that any sorted profinite group having SEP has a sorted complete system whose theory is $\omega $ -categorical and $\omega $ -stable under the assumption that the set of sorts is countable. (shrink)

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC (...) property is first order. (shrink)

Metaphor has a double life. It can be described as a directional process in which a stable, familiar base domain provides inferential structure to a less clearly specified target. But metaphor is also described as a process of finding commonalities, an inherently symmetric process. In this second view, both concepts may be altered by the metaphorical comparison. Whereas most theories of metaphor capture one of these aspects, we offer a model based on structure-mapping that captures both sides of (...) metaphor processing. This predicts (a) an initial processing stage of symmetric alignment; and (b) a later directional phase in which inferences are projected to the target. To test these claims, we collected comprehensibility judgments for forward (e.g., “A rumor is a virus”) and reversed (“A virus is a rumor”) metaphors at early and late stages of processing, using a deadline procedure. We found an advantage for the forward direction late in processing, but no directional preference early in processing. Implications for metaphor theory are discussed. (shrink)

An increasing number of epistemologists defend the notion that some perceptual experiences can immediately justify some beliefs and do so in virtue of (some of) their phenomenal properties. But this view, which we may call phenomenal dogmatism, is also the target of various objections. Here I want to consider an objection that may be put as follows: what is so special about perceptual phenomenology that only it can immediately justify beliefs, while other kinds of phenomenology—including quite similar ones—remain ‘epistemically inert’? (...) I will argue that, to overcome this objection, the phenomenal dogmatist should incorporate into her view a general principle—I call it the ‘experiential attitude/doxastic content link’ principle—that essentially extends the view from the perceptual case to other phenomenal states. (shrink)

The given is the state of a mind in its primary engagement with the world. A satisfactory epistemology—one, it turns out, that is foundationalist and includes a naïve realist view of perception—requires a certain account of the given. Moreover, knowledge based on the given requires both a particular view of the world itself and a heterodox account of judgment. These admittedly controversial claims are supported by basic ontological considerations. I begin, then, with two contradictory views of the world per se (...) and the structure one experiences. I draw out the consequences of these two views for what intentionality is. The two views yield incompatible accounts of the given. The definitive spontaneity of the one account, and passivity of the other, can be understood in terms of the structure (or lack thereof) in the given. In defense of the claim that a structured given is not an apt epistemic basis, I examine an attempt to found an epistemology on such an account in light of the so-called myth of the given. I maintain that the given, if it is to provide some justification for taking the world to be a particular way, must be unstructured. To support this, I first discuss a significant problem with traditional foundationalism. I then argue that a satisfactory (foundationalist) epistemology requires the rejection of the orthodox propositional view of judgment in favor of a non-propositional, reistic view. (shrink)

This book identifies the Romantic notion of the whole as the fundamental epistemological source of the notion of structure in the thinking of the Prague Linguistic Circle, primarily its Russian representatives, and studies what amounted to the slow.

In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.

We construct a collection of new topological Ramsey spaces of trees. It is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. We give an example of its application by proving a partition theorem for profinite graphs.

In this book, the author shows that it is necessary to enrich the conceptual frame of the theory of rational choice beyond consequentialism. He argues that consequentialism as a general theory of rational action fails and that this does not force us into the dichotomy teleology vs deontology. The unity of practical reason can be saved without consequentialism. In the process, he presents insightful criticism of standard models of action and rational choice. This will help readers discover a new perspective (...) on the theory of rationality. The approach is radical: It transcends the reductive narrowness of instrumental rationality without denying its practical impact. Actions do exist that are outlined in accordance to utility maximizing or even self-interest maximizing. Yet, not all actions are to be understood in these terms. Actions oriented around social roles, for example, cannot count as irrational only because there is no known underlying maximizing heuristic. The concept of bounded rationality tries to embed instrumental rationality into a form of life to highlight limits of our cognitive capabilities and selective perceptions. However, the agent is still left within the realm of cost-benefit-reasoning. The idea of social preferences or meta-preferences cannot encompass the plurality of human actions. According to the author they ignore the plurality of reasons that drive agency. Hence, they coerce agency in fitting into a theory that undermines humanity. His theory of structural rationality acknowledges lifeworld patterns of interaction and meaning. (shrink)

Structural requirements of rationality prohibit various things, like having inconsistent combinations of attitudes, having means-end incoherent combinations of attitudes, and so on. But what is the distinctive feature of structural requirements of rationality? And do we fall under an obligation to be structurally rational? These issues have been at the heart of significant debates over the past fifteen years. Some philosophers have recently argued that we can unify the structural requirements of rationality by analyzing what is constitutive of our attitudes (...) (Lee, 2020; Worsnip, 2018a). It has also been suggested that, in the course of good first-personal deliberation, agents should treat structurally irrational combinations of attitudes as off-limits (Worsnip, 2021). In this paper, I raise a worry for these two theses concerning structural rationality. Roughly, I argue that some imperfect epistemic agents (like us) can be disposed to have structurally irrational combinations of attitudes. Also, when these imperfect agents deliberate, they should not treat structurally irrational combinations of attitudes as off-limits. Given our imperfections, being structurally irrational can very well be the best option we have. More generally, these observations reveal that structural rationality should not always be theorized independently from more “substantive” norms, like responsiveness to reasons or expected value optimization. (shrink)

Many theories of kind representation suggest that people posit internal, essence-like factors that underlie kind membership and explain properties of category members. Across three studies (N = 281), we document the characteristics of an alternative form of construal according to which the properties of social kinds are seen as products of structural factors: stable, external constraints that obtain due to the kind’s social position. Internalist and structural construals are similar in that both support formal explanations (i.e., “category member has property (...) P due to category membership C”), generic claims (“Cs have P”), and the generalization of category properties to individual category members when kind membership and social position are confounded. Our findings thus challenge these phenomena as signatures of internalist thinking. However, once category membership and structural position are unconfounded, different patterns of generalization emerge across internalist and structural construals, as do different judgments concerning category definitions and the dispensability of properties for category membership. We discuss the broader implications of these findings for accounts of formal explanation, generic language, and kind representation. (shrink)

In this paper, I present a class of ‘structural’ abstraction principles, and describe how they are suggested by some features of Cantor's and Dedekind's approach to abstraction. Structural abstraction is a promising source of mathematically tractable new axioms for the neo-logicist. I illustrate this by showing, first, how a theorem of Shelah gives a sufficient condition for consistency in the structural setting, solving what neo-logicists call the ‘bad company’ problem for structural abstraction. Second, I show how, in the structural setting, (...) we can measure the logical strength of abstraction principles using categories of interpretations between theories. (shrink)

Open-mindedness enjoys widespread recognition as an intellectual virtue. This is evident, among other ways, in its appearance on nearly every list of intellectual virtues in the virtue epistemology literature. Despite its popularity, however, it is far from clear what exactly openmindedness amounts to: that is, what sort of intellectual orientation or activity is essential to it. In fact, there are ways of thinking about open-mindedness that cast serious doubt on its status as an intellectual virtue.Consider the following description, from Robert (...) Roberts and Jay Wood (2007), of a ‘bright college freshman, taking an introductory course in philosophy.’. (shrink)