An important lesson that philosophy can learn from the Turing Test and computer science more generally concerns the careful use of the method of Levels of Abstraction (LoA). In this paper, the method is first briefly summarised. The constituents of the method are “observables”, collected together and moderated by predicates restraining their “behaviour”. The resulting collection of sets of observables is called a “gradient of abstractions” and it formalises the minimum consistency conditions that the chosen abstractions must satisfy. (...) Two useful kinds of gradient of abstraction – disjoint and nested – are identified. It is then argued that in any discrete (as distinct from analogue) domain of discourse, a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus, the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering. The result formalises an approach that is rather common in computer science but has hitherto found little application in philosophy. So the philosophical value of the method is demonstrated by showing how making the LoA of discourse explicit can be fruitful for phenomenological and conceptual analysis. To this end, the method is applied to the Turing Test, the concept of agenthood, the definition of emergence, the notion of artificial life, quantum observation and decidable observation. It is hoped that this treatment will promote the use of the method in certain areas of the humanities and especially in philosophy. (shrink)

The international debate on the ethics and legality of autonomous weapon systems (AWS), along with the call for a ban, primarily focus on the nebulous concept of fully autonomous AWS. These are AWS capable of target selection and engagement absent human supervision or control. This paper argues that such a conception of autonomy is divorced from both military planning and decision-making operations; it also ignores the design requirements that govern AWS engineering and the subsequent tracking and tracing of moral responsibility. (...) To show how military operations can be coupled with design ethics, this paper marries two different kinds of meaningful human control (MHC) termed levels of abstraction. Under this two-tiered understanding of MHC, the contentious notion of ‘full’ autonomy becomes unproblematic. (shrink)

The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method ofion”, (...) the philosophical fruitfulness of the new method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)

I diagnose the current debate between epistemological and ontological emergentism as a Kantian antinomy, which has reasonable but irreconcilable thesis and antithesis. Kantian antinomies have recently returned to contemporary philosophy in part through the work of Luciano Floridi, and the method of levels of abstraction. I use a thought experiment concerning a computer simulation to show how to resolve the epistemological/ontological antinomy about emergence. I also use emergentism and simulations in artificial life to illuminate both levels of (...) abstraction and theoretical challenge for building intelligent agents. (shrink)

Although many simulations draw upon only one level of abstraction, the process for generating rich simulations requires a dynamic interplay between abstract and concrete knowledge. A complete model of simulation must account for a mind and brain that can bridge the perceptual with the conceptual, the episodic with the semantic, and the concrete with the abstract.

This paper deploys elements of the philosophy of information in order to explore ideas of dialogical governance. Dialogue in the governance of contentious issues is at least partly a response to the recognition of pluralism among perspectives on various issues. This recognition is prevalent in the context of European governance. However, it is a first step to a better understanding of diverging opinion, rather than an end point. This paper argues that the PoI offers a fruitful path to follow up (...) this first step. Specifically, PoI provides epistemological tools that can be used to clarify the meanings of terms and relevance of perspectives at issue in dialogical scenarios. Importantly, this approach revises the enlightenment view of the individual, offering a more nuanced and ultimately more accurate view of the self as internally complex. This represents a step beyond the status quo wherein these things are taken as unproblematic. This paper argues that PoI’s resources ought to feature as a methodological background to a reinvigorated dialogical governance paradigm. This method and these resources can inform an improved view of dialogical governance in Europe and, in their generality, beyond. (shrink)

From the advent of general purpose, Turing-complete machines, the relation between operators, programmers and users with computers can be observed as interconnected informational organisms (inforgs), henceforth analysed with the method of levels of abstraction (LoAs), risen within the philosophy of information (PI). In this paper, the epistemological levellism proposed by L. Floridi in the PI to deal with LoAs will be formalised in constructive terms using category theory, so that information itself is treated as structure-preserving functions instead of (...) Cartesian products. The milestones in the history of modern computing are then analysed through constructive levellism to show how the growth of system complexity lead to more and more information hiding. (shrink)

Peirce’s beta graphs are roughly equivalent to our first-order predicate logic. However, Bellucci and Pietarinen have recently argued that the beta graphs are not well-equipped to handle asymmetric relative terms. I survey four proposed solutions to the problem and find them all wanting. I offer a fifth solution according to which Peirce’s beta graphs function at three different levels of abstractness from natural language. I diagnose the problem of asymmetric relative terms as arising when we transition from the first (...) to the second level of abstractness. Making grammatical information encoded in natural language explicit at the first level of abstractness and interpreting graphs at the second level of abstractness as shorn of grammatical information resolves the problem. The solution is both well-motivated by Peirce’s own commitments and increases the expressiveness of the beta graphs. (shrink)

ion is arguably one of the most important methods in modern science in analysing and understanding complex phenomena. In his book The Philosophy of Information, Floridi (The philosophy of information. Oxford University Press, Oxford, 2011) presents the method of levels of abstraction as the main method of the Philosophy of Information. His discussion of abstraction as a method seems inspired by the formal methods and frameworks of computer science, in which abstraction is operationalised extensively in programming (...) languages and design methodologies. Is it really clear what we should understand by levels of abstraction? How should they be specified? We will argue that levels of abstraction should be augmented with annotations, in order to express semantic information for them and reconcile the method of level of abstraction (LoA’s) with other approaches. We discuss the extended method when applied e.g. to the analysis of abstract machines. This will lead to an example in which the number of LoA’s is unbounded. (shrink)

1. "The map of logic." Comparatively recently, Kant's words to the effect that in the two thousand years since Aristotle logic had made "not a single step forward and, all things considered, it seems to be a fully finished and completed discipline" used to be quoted widely and not unsympathetically. Today, however, there are works about logic in which the listing of logical disciplines runs into the dozens. In this regard the attempt by the American logician N. Rescher to compile (...) a diagram or "map of logic," in which the list of the branches of logic takes up several pages, is noteworthy. Also characteristic is the following statement by one of the major modern representatives of mathematical logic, S. Kleene: "Since the discovery of non-Euclidean geometries by Lobachevsky and Bolyai , it has become clear that different systems of geometries are conceptually equally possible…. Identically, there are different logics.". (shrink)

In this paper, following the claims made by various mathematicians, I try to construct a theory of levels of abstraction. I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction. In the final section, I briefly explore some of main philosophical consequences of the theory.

Language comprehension of action verbs recruits embodied representations in the brain that are assumed to invoke a mental simulation. This extends to abstract concepts, as well. We, therefore, argue that mental simulation works across levels of abstractness and involves higher-level schematic structures that subsume a generic structure of actions and events.

The use of "levels of abstraction" in philosophical analysis (levellism) has recently come under attack. In this paper, we argue that a refined version of epistemological levellism should be retained as a fundamental method, which we call the method of abstraction. After a brief introduction, in section two we make clear the nature and applicability of the (epistemological) method of levels of abstraction. In section three, we show the fruitfulness of the new method by applying (...) it to five case studies: the concept of agenthood, the Turing test, the definition of emergence, quantum observation and decidable observation. In section four, we further characterise and support the method by distinguishing it from three other forms of "levellism": (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In this context, we also briefly address the problems of relativism and antirealism. In the conclusion, we indicate some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)

There are no clear criteria regarding what kind of beliefs should count as folk-economic beliefs, or any way to make an exhaustive list that could be filtered through such criteria. This allows the target article authors, Boyer & Petersen, to cherry-pick FEBs, which results in the omission of some well-established FEBs. The authors do not sufficiently address a strong relationship between ideology and FEBs.

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. (...) I will consider comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences. (shrink)

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. (...) I will consider comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences. (shrink)

Levels of organization are structures in nature, usually defined by part-whole relationships, with things at higher levels being composed of things at the next lower level. Typical levels of organization that one finds in the literature include the atomic, molecular, cellular, tissue, organ, organismal, group, population, community, ecosystem, landscape, and biosphere levels. References to levels of organization and related hierarchical depictions of nature are prominent in the life sciences and their philosophical study, and appear not (...) only in introductory textbooks and lectures, but also in cutting-edge research articles and reviews. In philosophy, perennial debates such as reduction, emergence, mechanistic explanation, interdisciplinary relations, natural selection, and many other topics, also rely substantially on the notion. -/- Yet, in spite of the ubiquity of the notion, levels of organization have received little explicit attention in biology or its philosophy. Usually they appear in the background as an implicit conceptual framework that is associated with vague intuitions. Attempts at providing general and broadly applicable definitions of levels of organization have not met wide acceptance. In recent years, several authors have put forward localized and minimalistic accounts of levels, and others have raised doubts about the usefulness of the notion as a whole. -/- There are many kinds of ‘levels’ that one may find in philosophy, science, and everyday life—the term is notoriously ambiguous. Besides levels of organization, there are levels of abstraction, realization, being, analysis, processing, theory, science, complexity, and many others. In this article, the focus will be on levels of organization and debates associated with them, and other kinds of levels will only be discussed when they are relevant to this main topic. (shrink)

This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This (...) book is most successful in a small, seminar style class. Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers For all readers interested in abstract mathematics. (shrink)

Psychopathy is a personality disorder frequently associated with immoral behaviors. Previous behavioral studies on the influence of psychopathy on moral decision have yielded contradictory results, possibly because they focused either on judgment (abstract evaluation) or on choice of hypothetical action, two processes that may rely on different mechanisms. In this study, we explored the influence of the level of psychopathic traits on judgment and choice of hypothetical action during moral dilemma evaluation. A population of 102 students completed a questionnaire with (...) ten moral dilemmas and nine non-moral dilemmas. The task included questions targeting both judgment (“Is it acceptable to … in order to …?”) and choice of hypothetical action (“Would you … in order to …?”). The level of psychopathic traits of each participant was evaluated with the Levenson Self-Report Psychopathy (LSRP) scale. Logistic regression fitted with the generalized estimating equations method analyses were conducted using responses to the judgment and choice tasks as the dependent variables and psychopathy scores as predictor. Results show that a high level of psychopathic traits, and more specifically those related to affective deficit, predicted a greater proportion of utilitarian responses for the choice but not for the judgment question. There was no first-order interaction between the level of psychopathic traits and other potential predictors. The relation between a high level of psychopathic traits and increased utilitarianism in choice of action but not in moral judgment may explain the contradictory results of previous studies where these two processes were not contrasted. It also gives further support to the hypothesis that choice of action endorsement and abstract judgment during moral dilemma evaluation are partially distinct neural and psychological processes. We propose that this distinction should be better taken into account in the evaluation of psychopathic behaviors. (shrink)

Experimental philosophers have disagreed about whether "the folk" are intuitively incompatibilists or compatibilists, and they have disagreed about the role of abstraction in generating such intuitions. New experimental evidence using Construal Level Theory is presented. The experiments support the views that the folk are intuitively both incompatibilists and compatibilists, and that abstract mental representations do shift intuitions, but not in a univocal way.

Mapping from acoustic signals to lexical representations is a complex process mediated by a number of different levels of representation. This paper reviews properties of the phonetic and phonological levels, and hypotheses about how category structure is represented at each of these levels, and evaluates these hypotheses in light of relevant electrophysiological studies of phonetics and phonology. The paper examines evidence for two alternative views of how infant phonetic representations develop into adult representations, a structure-changing view and (...) a structure-adding view, and suggests that each may be better suited to different kinds of phonetic categories. Electrophysiological results are beginning to provide information about phonological representations, but less is known about how the more abstract representations at this level could be coded in the brain. (shrink)

If we are to find the criteria for critical analyses of social arrangements and processes not in some abstract, universalist framework, but from the guiding ‘self-interpretations’ of the societies in question, as contemporary contextualist and ‘communitarian’ approaches to social philosophy suggest, the vexing question arises as to where these self-interpretations can be found and how they are identified. The paper presents a model according to which there are four interdependent as well as partially autonomous spheres or ‘levels’ of socially (...) relevant self-interpretation that have to be taken into account equally in order to provide a sound basis for social and political criticism. Thus, it is from the tensions and incoherences between (A) social ideas and doctrines, (B) social institutions and practices, (C) individual beliefs and convictions, and (D) body-practices and habits that social pathologies can be identified and possible solutions can be envisaged. (shrink)

Apart from a few notable exceptions, the current retreat from Grand Theory has been accompanied by a reluctance to think about how we might theorize different forms of social formation. The present study began as an attempt to understand one such community form, the nation. However, in delineating an analytical method that allowed the theoretical space for exploring the ontological contradictions endemic to living as part of a national community, it became necessary to work comparatively across history and across different (...) social forms. In doing so, the article argues for a method that conceives of the various kinds of human community as formed in the changing and contradictory intersections of (diacritically distinguishable) levels of integration—from the most embodied ties of face-to-face reciprocity to the most abstract relations of strangers-in-association such as exemplified in the electronic communications of "information capitalism.". (shrink)

Scientific data are often subjected to two contradictory over-simplifications. People who have no personal experience in science often say that a certain idea has been scientifically established and feel that the question is therewith settled. They do not distinguish among methods, or generalizations in different fields. This implies that all science is infallible. The other oversimplification comes from the specialist; he may dismiss the work of men who study the problems approaching his own but who use methods different from his. (...) This view implies that only one type of scientific investigation is really sound. Both groups are wrong, for science is neither infallible nor wholly untrustworthy. In fact, science as an abstract whole is nothing; it is the name given collectively to all methods which men have used to explore natural processes and the results obtained by the use of such methods. Some problems are sufficiently simple and accessible to be explored in detail while others can be treated only after a set of postulates have been set as a starting point. A mechanism must be established within which it is possible to deal with the problems at hand. In other words, there are levels of scientific research which may be arranged in a series based on increasing assumptions. The more complex levels are formed by assuming the data and methods of those simpler and adding to them a new set of assumptions with the aid of which it is possible to treat the phenomena to be studied. Material cannot be carried directly from one level to another unless attention is given to the premises on which the conclusions have been drawn. Since such attention is not always given, entire fields of research have sometimes been brought into suspicion on the part of those working in what they themselves style “a more fundamental field.” Yet there may be data available at a different level which, when properly used, would be of value in their own work. (shrink)

I have based my psychological hypotheses on studies in perception and in personality. Research in these two areas began independently, but by the late forties the supposedly unconnected processes came to be seen as different aspects of one process. For instance, a low tolerance for perceptual ambiguity and cognitive dissonance was found to be significantly correlated with lack of emotional responsiveness, dogmatism, and authoritarianism; conversely, a high tolerance for perceptual ambiguity and cognitive dissonance was found to be significantly correlated with (...) tolerance of emotional ambivalence, openness to new experience, and a liberal world view.1 Later studies, primarily those conducted in the sixties, then established strong correlations between these findings and information-processing styles. Information processing involves three stages: first, stimuli are selected from the environment ; these stimuli are then arranged into "dimensions"; finally, if two or more dimensions result, they are compared and/or combined according to certain rules. H. M. Schroder and his colleagues have established correlations between personality styles and styles of information processing.2 For example, an intolerant personality—that is, one with a low integration index—"identifies and organizes stimuli in a fixed way, and the rules derived from existing schemata are explicit in defining this one way" . What psychologists call an "abstract personality" and identify in terms of "flexibility" or "tolerance of ambiguity"—what in literary studies is most conveniently called "negative capability"—is not necessarily characterized as lacking rules but rather as possessing a greater number of conflicting rules on a lower level which may be accommodated by rules on a higher level. · 1. See Jerome S. Bruner and David Krech, eds., Perception and Personality, 2nd ed. and Robert R. Blake and Glenn V. Ramsey, eds., Perception: An Approach to Personality . Although, as Else Frenkel-Brunswick says, "rigidity in one respect may go with flexibility in another," she also adds: "There is some indication that in the case of distinct intolerance of emotional ambivalence one may as a rule be able to locate at least some aspects of intolerance of cognitive ambiguity although these may often be more apparent on a higher level than that of perception proper" The present essay, since it is one section of a projected larger study, deals with the issues inherent in this approach in only a limited fashion. One could, for instance, quote whole essays in this branch of psychology dealing with ambiguity and point to their relevance for some aspects of literary study and the teaching of literature. Ambiguity, of course, is also a central term in New Criticism. See William Empson, Seven Types of Ambiguity and Ernst Kris and Abraham Kaplan, "Aesthetic Ambiguity," in Psychoanalytic Explorations in Art, ed. Kris , pp. 243-64.· 2. H. M. Schroder, M. J. Driver, and S. Streufert, "Levels of Information Processing," in Thought and Personality, ed. Peter B. Warr , pp. 174-91. All citations to this work will appear in the text. Reuven Tsur, senior lecturer in Hebrew literature at Tel-Aviv University, is the author of several books in Hebrew on medieval and modern Hebrew poetry and, in English, A Perception-Oriented Theory of Metre. (shrink)

Digital organizations form part of the new wave of blockchain technologies, following Bitcoin and related cryptocurrencies. “Utopia ofion” offers an analysis of the utopian promise of digital organizations through a reading of one such project, Colony. We provide a critique of the ideology of Colony's white paper, supplemented by readings of pages from its website, as a member of a genre of texts that promote their products through seemingly neutral, technical descriptions. Colony's texts suggest an abstract, contextless and scaleless organizational (...) solution—powered by smart contracts on a blockchain—that, according to its proponents, might be applied to any social situation, from small firm to state-level governance. For its users, this organization combines a promise of sovereignty removed from that of the state, as well as implied financial returns. Our reading of Colony echoes the critiques of scholars arguing that cyberlibertarianism is a dominant politic of blockchain technologies. Furthermore, drawing on critiques of code as law and the elision of the social in smart contracts, we argue that Colony's vision presents a model of technical organization that substitutes for the state in the context of waning popular sovereignty. We ultimately suggest an understanding of digital organizations reminiscent of the settler colonial situation: the assumption of an empty social space to be filled, and the promise of sovereignty and riches for those occupying it. Analysis of these logics is relevant as hype increases around non-fungible tokens, Web3, and the corporate metaverse as well as data practices more widely. (shrink)

This paper is concerned with the interaction between formal semantics and the foundations of mathematics. We introduce a formal theory of truth, TLR, which extends the classical first order theory of pure combinators with a primitive truth predicate and a family of truth approximations, indexed by a directed partial ordering. TLR naturally works as a theory of partial classifications, in which type-free comprehension coexists with functional abstraction. TLR provides an inner model for a well known subsystem of second order (...) arithmetic; indeed, TLR is proof-theoretically equivalent to Predicative Analysis. (shrink)

Some explanations in social science, psychology and biology belong to a higher level than other explanations. And higher explanations possess the virtue of abstracting away from the details of lower explanations, many philosophers argue. As a result, these higher explanations are irreplaceable. And this suggests that there are genuine higher laws or patterns involving social, psychological and biological states. I show that this ‘abstractness argument’ is really an argument schema, not a single argument. This is because the argument uses the (...) ‘is lower than’ relation, and this relation admits of different readings. I then suggest four rigorous definitions of the ‘is lower than’ relation, and show that the abstractness argument’s prospects are much brighter for some of these definitions than for others. To show this, I evaluate the so-called ‘disjunctive threat’ to the abstractness argument. (shrink)

Marr's levels of analysis—computational, algorithmic, and implementation—have served cognitive science well over the last 30 years. But the recent increase in the popularity of the computational level raises a new challenge: How do we begin to relate models at different levels of analysis? We propose that it is possible to define levels of analysis that lie between the computational and the algorithmic, providing a way to build a bridge between computational- and algorithmic-level models. The key idea is (...) to push the notion of rationality, often used in defining computational-level models, deeper toward the algorithmic level. We offer a simple recipe for reverse-engineering the mind's cognitive strategies by deriving optimal algorithms for a series of increasingly more realistic abstract computational architectures, which we call “resource-rational analysis.”. (shrink)

Four experiments investigated the extent to which abstract quantitative information can be conveyed by basic visual features. This was done by asking observers to estimate and discriminate Pearson correlation in graphical representations where the first data dimension of each element was encoded by its horizontal position, and the second by the value of one of its visual features; perceiving correlation then requires combining the information in the two encodings via a common abstract representation. Four visual features were examined: luminance, color, (...) orientation, and size. All were able to support the perception of correlation. Indeed, despite the strikingly different appearances of the associated stimuli, all gave rise to performance that was much the same: just noticeable difference was a linear function of distance from complete correlation, and estimated correlation a logarithmic function of this distance. Performance differed only in regards to the level of noise in the feature, with these values compatible with estimates of channel capacity encountered in classic experiments on absolute perceptual magnitudes. These results suggest that quantitative information can be conveyed by visual features that are abstracted at relatively low levels of visual processing, with little representation of the original sensory property. It is proposed that this is achieved via an abstract parameter space in which the values in each perceptual dimension are normalized to have the same means and variances, with perceived correlation based on the shape of the joint probability density function of the resultant elements. (shrink)

I analyze in this article the different ways in which Descartes uses abstraction in the Regulæ, discussing his project of a mathematical physics, the role of the imagination, and the status of numbers. I also try to show that the doctrine of simple natures cannot be well accommodated with the theory of abstraction developed in Rule 14, having instead a greater affinity with Descartes’ later theory of abstraction and exclusion, in which imagination plays no role and everything (...) happens at a strictly intellectual level. This interpretation is supported by the recent discovery of the Cambridge manuscript, which almost certainly records an early stage of composition and in which the doctrine of simple natures is absent, thus being very probably a later development. (shrink)

Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short MF, (...) completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \, where mTT can be easily interpreted. Then to show the consistency of \ with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \ by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \ we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \ correctly. In particular the universe of \ is modelled by means of \-fixpoints following a technique due first to Aczel and used by Feferman and Beeson. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:russell: the Journal of Bertrand Russell Studies n.s. 33 (winter 2013–14): 173–90 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\kenneth\documents\type3302\rj 33,2 114 red.docx 2014-01-31 8:29 PM oeviews MODES AND LEVELS OF PERPLEXITY I. Grattan-Guinness Middlesex U. Business School Hendon, London nw4 4bt, uk [email protected] John Ongley and Rosalind Carey. Russell: a Guide for the Perplexed. London: Bloomsbury, 2013. Pp. ix, 212. isbn: 978-0-8264-9753-6. £45 (...) (hb), £14.99 (pb); us$80 (hb), us$24.95 (pb). i his book is the 41st in a series of guides to the work of various philosophers and philosopher groups, written at a level of readability for students. The authors survey the course of Bertrand Russell’s philosophical career, starting out with his work on logic and mathematics. The main philosophical tools are presented: in logic, they are term, proposition, proposition function, relation, paradox, and first- vis-à-vis higher-order logic. Then, moving on to epistemology, the principal philosophical notions are presented, such as sense-data, facts related to language, Russell’s overriding preference for positivistic philosophies and suspicions of metaphysics, knowledge by acquaintance and by description, theories of truth, logical atomism, percept, events, meaning, and inference in the context of scientific theories. It is nice to have many of the principal components of Russell’s philosophy exhibited together, including the later works An Inquiry into Meaning and Truth and Human Knowledge. The perplexed reader would like to be given precise references for Russell’s assertions on various points, especially when he was so prolific. A cited short item does not need more precision; but the two main chapters that cover the logic and epistemology story often seem to invoke The Principles of Mathematics or Principia Mathematica and yet contain only one precise citation of a longer text in their 64 pages (p. 85). The other chapters of the book are somewhat better in this respect. The index is excellent, though W. V. Quine was missed at pp. 29–30. The table of contents would have benefited from including the titles of the sections. q= 174 Reviews c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 ii Much ground is covered; however, the account is mitigated by the failure to provide a biographical factual survey that should have constituted the opening chapter. Little or no description or explanation is given of, among others, Cambridge University, its mathematical tripos, Russell’s research fellowship in 1895, the philosophical journals Mind and The Monist, Russell’s conversion from neo-Hegelian to positivistic philosophy following G. E. Moore around 1899, the start of personal contacts with Giuseppe Peano in 1900, the gradual involvement of A. N. Whitehead from around 1902, the financial rescue of Principia Mathematica by the grant from the Royal Society in 1909, the serious mistake in Volume 2 detected by Whitehead in 1911 while it was in press, the initial contact with Ludwig Wittgenstein from 1911, Russell’s switch from logic to epistemology in the early 1910s, Whitehead’s intentions for the fourth volume of Principia that was abandoned in 1918, the circumstances of the second edition published in the mid-1920s, Russell’s partial return to serious philosophical writings from the mid-1930s onwards, or the Trinity fellowship from 1944. Presumably the authors have made most of these omissions intentionally ; but the target audience is the loser. The opening “introduction” does mention some of these events and publications ; but its purpose is to provide a preliminary look at some of the main features of Russell’s logic, including the comprehension axiom “that every predicate defines a class” (p. 3), type theory, definite descriptions, “the noclass theory of classes” (p. 10), and the status and role of “analysis”. Why do these features need prologues when the others do not? When they are re-discussed in the later chapters on logic and epistemology, several near-repetitions occur. Furthermore, quantification does not receive sufficient consideration in the book; and the logical connectives and rules of inference none at... (shrink)

In _ Plato's Camera_, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories to (...) which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures. (shrink)

In _ Plato's Camera_, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories to (...) which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures. (shrink)

ABSTRACT Recently, many authors have argued that claims about determinism and free will are situated on different levels of description and that determinism on one level does not rule out free will on another. This paper focuses on Christian List’s version of this basic idea. It will be argued for the negative thesis that List’s account does not rule out the most plausible version of incompatibilism about free will and determinism and, more constructively, that a level-based approach to free (...) will has better chances to meet skeptical challenges if it is guided by reasoning at the moral level – a level that has not been seriously considered so far by proponents of this approach. (shrink)

Abstract:In this article we first review the development of the concept of global business citizenship and show how the libertarian political philosophy of free-market capitalism must give way to a communitarian view in order for the voluntaristic, local notion of “corporate citizenship” to take root. We then distinguish the concept of global business citizenship from “corporate citizenship” by showing how the former concept requires a transition from communitarian thinking to a position of universal human rights. In addition, we link global (...) business citizenship to global business strategy and to three analytical levels of ethical norms. Finally, we trace a process whereby global businesses can implement fundamental norms and learn to accommodate to legitimate cultural differences. (shrink)

Abstract:In this article we first review the development of the concept of global business citizenship and show how the libertarian political philosophy of free-market capitalism must give way to a communitarian view in order for the voluntaristic, local notion of “corporate citizenship” to take root. We then distinguish the concept of global business citizenship from “corporate citizenship” by showing how the former concept requires a transition from communitarian thinking to a position of universal human rights. In addition, we link global (...) business citizenship to global business strategy and to three analytical levels of ethical norms. Finally, we trace a process whereby global businesses can implement fundamental norms and learn to accommodate to legitimate cultural differences. (shrink)

Abstract:In this article we first review the development of the concept of global business citizenship and show how the libertarian political philosophy of free-market capitalism must give way to a communitarian view in order for the voluntaristic, local notion of “corporate citizenship” to take root. We then distinguish the concept of global business citizenship from “corporate citizenship” by showing how the former concept requires a transition from communitarian thinking to a position of universal human rights. In addition, we link global (...) business citizenship to global business strategy and to three analytical levels of ethical norms. Finally, we trace a process whereby global businesses can implement fundamental norms and learn to accommodate to legitimate cultural differences. (shrink)

The process of abstraction and concretisation is a label used for an explicative theory of scientific model-construction. In scientific theorising this process enters at various levels. We could identify two principal levels of abstraction that are useful to our understanding of theory-application. The first level is that of selecting a small number of variables and parameters abstracted from the universe of discourse and used to characterise the general laws of a theory. In classical mechanics, for example, (...) we select position and momentum and establish a relation amongst the two variables, which we call Newton’s 2nd law. The specification of the unspecified elements of scientific laws, e.g. the force function in Newton’s 2nd law, is what would establish the link between the assertions of the theory and physical systems. In order to unravel how and with what conceptual resources scientific models are constructed, how they function and how they relate to theory, we need a view of theory-application that can accommodate our constructions of representation models. For this we need to expand our understanding of the process of abstraction to also explicate the process of specifying force functions etc. This is the second principal level at which abstraction enters in our theorising and in which I focus. In this paper, I attempt to elaborate a general analysis of the process of abstraction and concretisation involved in scientific- model construction, and argue why it provides an explication of the construction of models of the nuclear structure. (shrink)

From flea bites to galaxies, from love affairs to shadows, Paul Feyerabend reveled in the sensory and intellectual abundance that surrounds us. He found it equally striking that human senses and human intelligence are able to take in only a fraction of these riches. "This a blessing, not a drawback," he writes. "A superconscious organism would not be superwise, it would be paralyzed." This human reduction of experience to a manageable level is the heart of Conquest of Abundance, the book (...) on which Feyerabend was at work when he died in 1994. Prepared from drafts of the manuscript left at his death, working notes, and lectures and articles Feyerabend wrote while the larger work was in progress, Conquest of Abundance offers up rich exploration and startling insights with the charm, lucidity, and sense of mischief that are his hallmarks. Feyerabend is fascinated by how we attempt to explain and predict the mysteries of the natural world, and he looks at the ways in which we abstract experience, explain anomalies, and reduce wonder to formulas and equations. Through his exploration of the positive and negative consequences of these efforts, Feyerabend reveals the "conquest of abundance" as an integral part of the history and character of Western civilization. "Paul Feyerabend . . . was the Norman Mailer of philosophy. . . . brilliant, brave, adventurous, original and quirky."—Richard Rorty, New Republic "As much a smudged icon as a philosophical position holder, [Feyerabend] was alluring and erotic, a torch singer for philosophical anarchy."—Nancy Maull, New York Times Book Review "[A] kind of final testament of Feyerabend's thought . . . Conquest of Abundance is as much the product of a brilliant, scintillating style as of an immense erudition and culture. . . . This book is as abundant and rich as the world it envisions."—Arkady Plotnitsky, Chicago Tribune. (shrink)

From flea bites to galaxies, from love affairs to shadows, Paul Feyerabend reveled in the sensory and intellectual abundance that surrounds us. He found it equally striking that human senses and human intelligence are able to take in only a fraction of these riches. "This a blessing, not a drawback," he writes. "A superconscious organism would not be superwise, it would be paralyzed." This human reduction of experience to a manageable level is the heart of _Conquest of Abundance_, the book (...) on which Feyerabend was at work when he died in 1994. Prepared from drafts of the manuscript left at his death, working notes, and lectures and articles Feyerabend wrote while the larger work was in progress, _Conquest of Abundance_ offers up rich exploration and startling insights with the charm, lucidity, and sense of mischief that are his hallmarks. Feyerabend is fascinated by how we attempt to explain and predict the mysteries of the natural world, and he looks at the ways in which we abstract experience, explain anomalies, and reduce wonder to formulas and equations. Through his exploration of the positive and negative consequences of these efforts, Feyerabend reveals the "conquest of abundance" as an integral part of the history and character of Western civilization. "Paul Feyerabend... was the Norman Mailer of philosophy.... brilliant, brave, adventurous, original and quirky."—Richard Rorty, _New Republic_ "As much a smudged icon as a philosophical position holder, [Feyerabend] was alluring and erotic, a torch singer for philosophical anarchy."—Nancy Maull, _New York Times Book Review_ "[A] kind of final testament of Feyerabend's thought... Conquest of Abundance is as much the product of a brilliant, scintillating style as of an immense erudition and culture.... This book is as abundant and rich as the world it envisions."—Arkady Plotnitsky, _Chicago Tribune_. (shrink)

Cognitive Science, Volume 46, Issue 2, February 2022.

The type-level abstraction is a formal way to represent molecular structures in biological practice. Graphical representations of molecular structures of biological objects are also used to identify functional processes of things. This paper will reveal that category theory is a formal mathematical language not only to visualize molecular structures of biological objects as type-level abstraction formally but also to understand how to infer biological functions from the molecular structures of biological objects. Category theory is a toolkit to understand (...) biological knowledge at the type-level formally, not individual token-level, as well as typical heuristic strategies in molecular biology. (shrink)