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)

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.

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)

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)

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)

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)

On scientific and moral revolutions -- Using the dead for the living: the benthamite moral revolution -- Immoralizing and criminalizing abortion: the doctors revolution -- Irredentism and counter-revolutions in geology and abortion -- The american bioethics revolution -- The structure of moral revolutions.

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)

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)

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)

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)

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.

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.

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)

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)

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)

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)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

What is a language? What do scientific grammars tell us about the structure of individual languages and human language in general? What kind of science is linguistics? These and other questions are the subject of Ryan M. Nefdt's Language, Science, and Structure. -/- Linguistics presents a unique and challenging subject matter for the philosophy of science. As a special science, its formalisation and naturalisation inspired what many consider to be a scientific revolution in the study of mind and language. Yet (...) radical internal theory change, multiple competing frameworks, and issues of modelling and realism have largely gone unaddressed in the field. Nefdt develops a structural realist perspective on the philosophy of linguistics which aims to confront the aforementioned topics in new ways while expanding the outlook toward new scientific connections and novel philosophical insights. On this view, languages are real patterns which emerge from complex biological systems. Nefdt's exploration of this novel view will be especially valuable to those working in formal and computational linguistics, cognitive science, and the philosophies of science, mathematics, and language. (shrink)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition (PUC), which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential (...) to Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)

According to the standard story of action, a story that can be traced back at least to David Hume , actions are those bodily movements that are caused and rationalized by a pair of mental states: a desire for some end, where ends can be thought of as ways the world could be, and a belief that something the agent can just do, namely, move her body in the way to be explained, has some suitable chance of making the world (...) the relevant way. Bodily movements that occur otherwise aren't actions, they are mere happenings. (shrink)

The normativity of so-called “coherence” or “structural” requirements of rationality has been hotly debated in recent years. However, relatively little has been said about the nature of structural rationality, or what makes a set of attitudes structurally irrational, if structural rationality is not ultimately a matter of responding correctly to reasons. This paper develops a novel account of incoherence (or structural irrationality), critically examining Alex Worsnip’s recent account. It first argues that Worsnip’s account both over-generates and under-generates incoherent patterns of (...) attitudes, and then proposes an alternative that both avoids these problems and captures a crucial insight behind Worsnip’s account. According to this account, a set of attitudes is incoherent just in case having all of the attitudes in that set is incompatible with reacting to a question in a way that one is, in virtue of having the attitudes, committed to. (shrink)

Although the idiom “genesis and structure” is usually associated with the rise of structuralism in the late 1950s and early 1960s, the two notions are arguably among the most persistent methods in the history of modern philosophy. This article outlines the emergence of “genetic epistemology” in the seventeenth century, when the seemingly antithetical character of the conceptual pair was reworked into a productive epistemological theory, especially in Descartes, Hobbes, Spinoza, and Leibniz, who increasingly used diachronic (genetic) narratives to explain the (...) synchronic (structural) features in their theories. Against Cassirer, I argue that it was Descartes rather than Hobbes who first presented structural issues genetically. In Descartes’ natural philosophy, his frequent claims that showing how a thing is produced reveals its true nature foreshadow precisely what Hobbes and Isaac Barrow later describe as causal definitions of geometric figures, in which the process of ideal generation by motion is what constitutes the very essence of a figure. I link this method to the historicizing discourse on origins in the Enlightenment and conclude by suggesting that there is a trace of Platonic idealism in genetic epistemology. (shrink)

The bridges of Königsberg case has been widely cited in recent philosophical discussions on scientific explanation as a potential example of a structural explanation of a physical phenomenon. However, when discussing this case, different authors have focused on two different versions, depending on what they take the explanandum to be. In one version, the explanandum is the _failure_ of a given individual in performing an Eulerian walk over the bridge system. In the other version, the explanandum is the _impossibility_ of (...) performing an Eulerian walk over the bridges. The goal of this paper is to show that only the latter version amounts to a real case of a structural explanation. I will also suggest how to fix the first version, and show how my remarks apply to other purported cases of structural explanations. (shrink)

This volume addresses the problem of how language expresses conceptual information on event structures and how such information can be reconstructed in the interpretation process. The papers present important new insights into recent semantic and syntactic research on the topic. The volume deals with the following problems in detail: event structure and syntactic construction, event structure and modification, event structure and plurality, event structure and temporal relation, event structure and situation aspect, and event structure and language ontology. Importantly, the (...) topic is discussed not only on the basis of English and German but on the basis of other languages including Mandarin, Japanese, Korean, Indonesian, and Igbo as well. This volume thus provides solid evidence towards clarifying the empirical use of event based analyses. (shrink)

The history of biology is mottled with disputes between two distinct approaches to the organic world: structuralism and functionalism. Their persistence across radical theory change makes them difficult to characterize: the characterization must be abstract enough to capture biologists with diverse theoretical commitments, yet not so abstract as to be vacuous. This Element develops a novel account of structuralism and functionalism in terms of explanatory strategies (Section 2). This reveals the possibility of integrating the two strategies; the explanatory successes of (...) evolutionary-developmental biology essentially depend on such integration (Section 3). Neither explanatory strategy is universally subordinate to the other, though subordination with respect to particular explanatory tasks is possible (Section 4). Beyond structuralism and functionalism, philosophical analysis that centers explanatory strategies can illuminate conflicts within evolutionary theory more generally (Section 5). (shrink)

This chapter contains sections titled: Poetry (Briefly) The Aesthetics of Fiction (Again) A Non‐Aesthetic Art? Fiction as Non‐Aesthetic.

It has been argued that organizational structures (the way tasks are defined, allocated, and coordinated) can influence moral agency in organizations. In particular, low values on different structural parameters (functional concentration, specialization, separation, and formalization) are said to foster an organizational context (allowing for relating to the goals and output of the organization, moral deliberation, and social connectedness) that is conducive to moral agency. In this paper, we investigate the relation between the organizational structure and moral agency in the (...) case of a.s.r. (a large Dutch insurance company). While our empirical results fit the thesis that low values on structural parameters positively relate to moral agency, they also refine our understanding of the influence of structural parameters. In particular, our data suggest that the influence of functional concentration not only depends on whether it is low, but also on the type of criterion used for identifying business units; they suggest that the specific organizational context may put a limit to lowering design parameters and points at several non-structural factors that have an influence on the relation between structure and moral agency. In all, the paper contributes to a more detailed understanding of the conditions conducive to moral agency in organizations. (shrink)

The topic of this dissertation is what thought must be like in order for the laws and generalizations of psychology to be true. I address a number of contemporary problems in the philosophy of mind concerning the nature and structure of concepts and the ontological status of mental content. Drawing on empirical work in psychology, I develop a number of new conceptual tools for theorizing about concepts, including a counterpart model of concepts' role in linguistic communication, and a deflationary theory (...) of concepts' formal features. I also suggest some new answers to old problems, arguing, for example, that content realism is not hostage to a naturalized semantics. This dissertation can, as a whole, be read as a sympathetic re-evaluation of the language of thought hypothesis (LOT). LOT claims that thoughts are sentences in a mental language of computation, and are composed of meaningful, atomic symbols—concepts—which are individuated entirely by their formal features. Each chapter either defends various components of LOT from recent criticism, or fills in gaps in the theory. I begin the dissertation by introducing the language of thought project, and motivating and explaining each of its central components. In chapter 2, I discuss a recent competitor to atomism—neo-empiricism—and argue that it fails to meet several key desiderata on theories of concepts, and defend atomism from similar charges. In chapter 3, I argue against a view common to both philosophy and psychology: that concepts must be shareable. If true, atomism is in jeopardy. I find shareability to be unmotivated, and suggest an alternative counterpart model of concepts that does a better job of explaining the things shareability was supposed to explain. Chapter 4 takes up the question of what formal features are and how mental symbols are individuated. I develop a reductive account, arguing that formal features are certain sorts of physical properties and symbol types are sets of these properties. I turn to the topic of content in chapter 5, and defend a very strong version of content realism against recent criticism. (shrink)

The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

Several promising approaches have been developed to represent conscious experience in terms of mathematical spaces and structures. What is missing, however, is an explicit definition of what a ‘mathematical structure of conscious experience’ is. Here, we propose such a definition. This definition provides a link between the abstract formal entities of mathematics and the concreta of conscious experience; it complements recent approaches that study quality spaces, qualia spaces, or phenomenal spaces; and it provides a general method to identify and (...) investigate structures of conscious experience. We hope that ultimately this work provides a basis for developing a common formal language to study consciousness. (shrink)

In this book Daly attempts to forge a new ethical approach to issues of social structures, an area of thought deficient in traditional Catholic ethics. Daly argues that the concept of the structures of virtue and vice provide the best ethical lens with which to scrutinize the effects of social structures on personal character and the well-being of the community. His argument relies on two premises: First, he considers the nexus between structures and individual moral agency (...) - arguing that Catholic ethics has failed to account for these realities adequately. The second premise concerns virtue theory, once again emphasizing the importance of accounting for the individual when approaching societal ethics. With the establishment of these premises, Daly furthers the book's ultimate goal: the development of ethical concepts capable of scrutinizing social structures regarding how they shape personal moral character, as well as how they causally impact the well-being of people and groups. Drawing on the works of Thomas Aquinas as well as social theories such as critical realism, Daly fills a lacuna in Catholic ethics that addresses the structure-agency problem that has plagued this field of study. (shrink)

Dedicated to exploring the crossroads where complex sentences and information management - more specifically information structure and reference tracking - come together.

Part I: The representation of life -- Can life be given a real definition? -- The representation of the living individual -- The representation of the life-form itself -- Part II: Naive action theory -- Types of practical explanation -- Naive explanation of action -- Action and time -- Part III: Practical generality -- Two tendencies in practical philosophy -- Practices and dispositions as sources of the goodness of individual actions -- Practice and disposition as sources of individual action.

Well-Structured Mathematical Logic does for logic what Structured Programming did for computation: make large-scale work possible. From the work of George Boole onward, traditional logic was made to look like a form of symbolic algebra. In this work, the logic undergirding conventional mathematics resembles well-structured computer programs. A very important feature of the new system is that it structures the expression of mathematics in much the same way that people already do informally. In this way, the new system is (...) simultaneously machine-parsable and user-friendly, just as Structured Programming is for algorithms. Unlike traditional logic, the new system works with you, not against you, as you use it to structure--and understand--the mathematics you work with on a daily basis. The book provides a complete guide to its subject matter. It presents the major results and theorems one needs to know in order to use the new system effectively. Two chapters provide tutorials for the reader in the new way that symbols move when logical calculations are performed in the well-structured system. Numerous examples and discussions are provided to illustrate the system's many results and features. Well-Structured Mathematical Logic is accessible to anyone who has at least some knowledge of traditional logic to serve as a foundation, and is of interest to all who need a system of pliant, user-friendly mathematical logic to use in their work in mathematics and computer science. (shrink)

There are realist and antirealist interpretations of the free energy principle (FEP). This paper aims to chart out a structural realist interpretation of FEP. To do so, it draws on Worrall’s (Dialectica 43(1–2): 99–124, 1989) proposal. The general insight of Worrall’s paper is that there is progress at the level of the structure of theories rather than their content. To enact Worrall’s strategy in the context of FEP, this paper will focus on characterising the formal continuity between fundamental equations of (...) thermodynamics—such as Boltzmann’s equation and Gibbs’s equation—on the one hand, and Friston’s characterisation of FEP on the other. Lack of a universal consensus on the physical character of entities that feature in thermodynamics, information theory and FEP notwithstanding, I argue that there is structural continuity and unity at the level of mathematical equations that regiment entropy, information and free energy. The existence of such structural continuity and unity provides grounds for structural realism about FEP. (shrink)

We show that it is relatively consistent with ZFC to have PCF structures of heightδ, for all ordinalsδ<ω3.