A new hypothesis on the basic features characterising the Foundations of Mathematics is suggested. By means of them the entire historical development of Mathematics before the 20th Century is summarised through a table. Also the several programs, launched around the year 1900, on the Foundations of Mathematics are characterised by a corresponding table. The major difficulty that these programs met was to recognize an alternative to the basic feature of the deductive organization of a theory - (...) more precisely, to Hilbert’s main tenet. Ironically, already half a century before the births of these programs the alternative organization has been substantially represented by Lobachevsky's theory on parallel lines. Moreover, although each program’s founder recognised the basic features in a partial way only, all together these programs represented just the four possible foundational approaches. (shrink)

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in (...) the evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert’s program due to Simpson [1988], and predicativism in the extended form due to Feferman and Schütte. -/- Shore [2010, 2013] proposes that equivalences in reverse mathematics be proved in the same way as inequivalences, namely by considering only omega-models of the systems in question. Shore refers to this approach as computational reverse mathematics. This paper shows that despite some attractive features, computational reverse mathematics is inappropriate for foundational analysis, for two major reasons. Firstly, the computable entailment relation employed in computational reverse mathematics does not preserve justification for the foundational programs above. Secondly, computable entailment is a Pi-1-1 complete relation, and hence employing it commits one to theoretical resources which outstrip those available within any foundational approach that is proof-theoretically weaker than Pi-1-1-CA0. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many (...) partial successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s (...) claim that his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

Operations research science is defined as the science that is concerned with applying scientific methods to complex problems in managing and directing large systems of people, including resources and tools in various fields, private and governmental work, peace and war, politics, administration, economics, planning and implementation in various domains. It uses scientific methods that take the language of mathematics as a basis for it and uses computer, without which it would not have been possible to achieve numerical solutions to the (...) raised problems, those that need correct solutions, when the solutions abound and the options are multiple, so we need a decision based on correct scientific foundations and takes into account all the circumstances and changes that you can encounter the decision-maker during the course of work, and nothing is left to chance or luck, but rather everything that enters into the account and plays its role in decision-making, and we get that when we use the concepts of neutrosophic science to reformulate what the science of operations research presented in terms of methods and methods to solve many practical problems, so we will present in this research a study aimed at shedding light on the most important methods used to solve nonlinear models, which is the Lagrangian multiplier method for nonlinear models constrained by equality and then reformulated using the concepts of neutrosophic science. (shrink)

The engineering knowledge research program is part of the larger effort to articulate a philosophy of engineering and an engineering worldview. Engineering knowledge requires a more comprehensive conceptual framework than scientific knowledge. Engineering is not ‘merely’ applied science. Kuhn and Popper established the limits of scientific knowledge. In parallel, the embrace of complementarity and uncertainty in the new physics undermined the scientific concept of observer-independent knowledge. The paradigm shift from the scientific framework to the broader participant engineering framework entails a (...) problem shift. The detached scientific spectator seeks the ‘facts’ of ‘objective’ reality – out there. The participant, embodied in reality, seeks ‘methods’, about how to work in the world. The engineering knowledge research program is recursively enabling. Advances in engineering knowledge are involved in the unfolding of the nature of reality. Newly understood, quantum uncertainty entails that the participant is a natural inquirer. ‘Practical reason’ is concerned with ‘how we should live’– the defining question of morality. The engineering knowledge research program is selective seeking ‘important truths’, ‘important knowledge’, ‘important methods’ that manifest value, and serve the engineering agenda of ‘the construction of the good.’ The importance of engineering knowledge research program is clear in the new STEM curriculum where educators have been challenged to rethink the relation between science and engineering. A 2015 higher education initiative to integrate engineering colleges into liberal arts and sciences colleges has stalled due to the confusion and conflict between the engineering and scientific representations of knowledge. (shrink)

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foundation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building blocks (...) for a theory of pregeometry. This work is largely a synthesis of ideas that serve as a precursor for conceptualizing the notion of space in physical theories. In particular, the approach we espouse is based on a constructivist philosophy, wherein ``structureless structures'' are syntactic types realizing formal proofs and programs. Spaces and algebras relevant to physical theories are modeled as type-theoretic routines constructed from compositional rules of a formal language. This offers the remarkable possibility of taxonomizing distinct notions of geometry using a common theoretical framework. In particular, this perspective addresses the crucial issue of how spatiality may be realized in models that link formal computation to physics, such as the Wolfram model. (shrink)

Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly shown (...) with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory. (shrink)

Harry Heft's Ecological Psychology in Context is an important book in many ways. For one thing, it adds considerably to our understanding of the historical background of J.J. Gibson's thought. But more than that, Heft aims to place ecological psychology not just historically, but philosophically. He says "This volume shows that radical empiricism stands at the heart of Gibson's ecological program, and it can usefully be employed as the conceptual centerpiece for ecological psychology more broadly construed" (p. xvi). While I (...) was impressed with Harry's argument to this effect, I'm not yet entirely persuaded. In these brief remarks I'll try to explain why. (shrink)

The curriculum design, faculty characteristics, and experience of implementing masters' level international research ethics training programs supported by the Fogarty International Center was investigated. Multiple pedagogical approaches were employed to adapt to the learning needs of the trainees. While no generally agreed set of core competencies exists for advanced research ethics training, more than 75% of the curricula examined included international issues in research ethics, responsible conduct of research, human rights, philosophical foundations of research ethics, and research regulation (...) and ethical review process. Common skills taught included critical thinking, research methodology and statistics, writing, and presentation proficiency. Curricula also addressed the cultural, social, and religious context of the trainees related to research ethics. Programs surveyed noted trainee interest in Western concepts of research ethics and the value of the transnational exchange of ideas. Similar faculty expertise profiles existed in all programs. Approximately 40% of faculty were female. Collaboration between faculty from low- and middleincome countries (LMICs) and high-income countries (HICs) occurred in most programs and at least 50% of HIC faculty had previous LMIC experience. This paper is part of a collection of papers analyzing the Fogarty International Research Ethics Education and Curriculum Development program. (shrink)

This essay considers what it means to understand natural language and whether a computer running an artificial-intelligence program designed to understand natural language does in fact do so. It is argued that a certain kind of semantics is needed to understand natural language, that this kind of semantics is mere symbol manipulation (i.e., syntax), and that, hence, it is available to AI systems. Recent arguments by Searle and Dretske to the effect that computers cannot understand natural language are discussed, and (...) a prototype natural-language-understanding system is presented as an illustration. (shrink)

This paper discusses the rationale for, and efforts to quantify the success of, philosophy outreach efforts at the University of North Carolina at Chapel Hill, with a focus on the National High School Ethics Bowl (NHSEB). We explore the program's democratic foundations and its potential to promote civic and intellectual virtues. After describing pioneering efforts to empirically access the impact of NHSEB, we offer recommendations to empower publicly and empirically-engaged philosophers to conduct further studies in the future.

I offer a critical review of several different conceptions of the activity of foundational research, from the time of Gauss to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of a priori structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist alternative, (...) guiding Riemann, Poincaré, Weyl and others, that seeks to perfect available conceptual systems with the aim to avoid conceptual limitations and expand the range of theoretical options. I shall contend that, at times, assumptions about the foundational enterprise emerge from certain dogmas that are frequently inherited from previous, outdated images. To round the discussion, I mention some traits of an alternative program that investigates the epistemology of mathematical knowledge. (shrink)

This essay takes a critical look at aesthetics as the basis for nature preservation, presenting three reasons why we should not rely on aesthetic foundations to justify the environmentalist program. First, a comparison to other kinds of aesthetic value shows that the aesthetic value of nature can provide weak reasons foraction atbest. Second, not everything environmentalists want to protect has positive aesthetic qualities. Attempts have been made to get around this problem by developing a reformist attitude towards natural aesthetics. (...) I argue that these approaches fail. Third, development can be as aesthetically positive as nature. If it is simply beauty we are looking for, why can't the beauty of a wellconstructed dam or a magnificent skyscraper suffice? (shrink)

Holism in interwar Germany provides an excellent example for social and political in- fluences on scientific developments. Deeply impressed by the ubiquitous invocation of a cultural crisis, biologists, physicians, and psychologists presented holistic accounts as an alternative to the “mechanistic worldview” of the nineteenth century. Although the ideological background of these accounts is often blatantly obvious, many holistic scientists did not content themselves with a general opposition to a mechanistic worldview but aimed at a rational foundation of their holistic projects. (...) This article will discuss the work of Kurt Goldstein, who is known for both his groundbreaking contributions to neuropsychology and his holistic philosophy of human nature. By focusing on Goldstein’s neurolinguistic research, I want to reconstruct the empirical foundations of his holistic program without ignoring its cultural background. In this sense, Goldstein’s work provides a case study for the formation of a scientific theory through the complex interplay between specific empirical evidences and the general cultural developments of the Weimar Republic. (shrink)

his article will focus on the mechanistic origins of the computer metaphor, which forms the conceptual framework for the methodology of the cognitive sciences, some areas of artificial intelligence and the philosophy of mind. The connection between the history of computing technology, epistemology and the philosophy of mind is expressed through the metaphorical dictionaries of the philosophical discourse of a particular era. The conceptual clarification of this connection and the substantiation of the mechanistic components of the computer metaphor is the (...) main goal of this article. The statement is substantiated that the invention of mechanical computing devices, having a long history in the European engineering tradition, formed the prerequisites for the emergence of machine functionalism in the modern philosophy of mind. The idea of multiple implementation stems from the principle that a formal symbol system prescribes rules for the use of rational abstractions through the physical architecture of a computational engine. The article considers the reasons for the conceptual shift and reveals the semantic foundations for the metaphorical transfer of the properties of abstract objects from the theory of automata to the field of modern philosophy of mind. The criticism and ways of protecting the philosophical program of machine functionalism are analyzed by changing the content of the metaphor “Mind as machine”. The reasons for the stability of the information-computer approach in cognitive sciences are also disclosed and explained. (shrink)

Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper (...) investigates both conditions and philosophical background necessary for that modification. The main conclusion is that the concept of infinity as underlying contemporary mathematics cannot be reduced to a single Peano arithmetic, but to at least two ones independent of each other. Intuitionism, quantum mechanics, and Gentzen’s approaches to completeness an even Hilbert’s finitism can be unified from that viewpoint. Mathematics may found itself by a way of finitism complemented by choice. The concept of information as the quantity of choices underlies that viewpoint. Quantum mechanics interpretable in terms of information and quantum information is inseparable from mathematics and its foundation. (shrink)

The boundless nature of the natural numbers imposes paradoxically a high formal bound to the use of standard artificial computer programs for solving conceptually challenged problems in number theory. In the context of the new cognitive foundations for mathematics' and physics' program immersed in the setting of artificial mathematical intelligence, we proposed a refined numerical system, called the physical numbers, preserving most of the essential intuitions of the natural numbers. Even more, this new numerical structure additionally possesses the (...) property of being a bounded object allowing us to work with quite similar axioms like the classic Peano axioms, but in a finite environment and with an enriched physical dimension. Finally, we present several enlightening examples and we conclude that the physical numbers provide a natural formal setting for approaching classic problems in number theory from a more hybrid perspective, i.e. with a potential participation in the generation of solutions, not only of working mathematicians but also of more sophisticated artificial interactive (mathematical) intelligent agents (within the context of cognitive-computational metamathematics or artificial mathematical intelligence) and more controlled by physically-inspired principles. Finally, this paper addresses a highly new, bottom-up and paradigm-shifting approach to the foundations of physics: One should refine and improve the conceptual formal setting of the language that we use for understanding physical phenomena (e.g. the mathematical grounding concepts and theories) for being able to understand better more subtle and complex physical phenomena. (shrink)

The main objective of this dissertation is to philosophically assess how the use of informational concepts in the field of classical thermostatistical physics has historically evolved from the late 1940s to the present day. I will first analyze in depth the main notions that form the conceptual basis on which 'informational physics' historically unfolded, encompassing (i) different entropy, probability and information notions, (ii) their multiple interpretative variations, and (iii) the formal, numerical and semantic-interpretative relationships among them. In the following, I (...) will assess the history of informational thermophysics during the second half of the twentieth century. Firstly, I analyse the intellectual factors that gave rise to this current in the late forties (i.e., popularization of Shannon's theory, interest in a naturalized epistemology of science, etc.), then study its consolidation in the Brillouinian and Jaynesian programs, and finally claim how Carnap (1977) and his disciples tried to criticize this tendency within the scientific community. Then, I evaluate how informational physics became a predominant intellectual current in the scientific community in the nineties, made possible by the convergence of Jaynesianism and Brillouinism in proposals such as that of Tribus and McIrvine (1971) or Bekenstein (1973) and the application of algorithmic information theory into the thermophysical domain. As a sign of its radicality at this historical stage, I explore the main proposals to include information as part of our physical reality, such as Wheeler’s (1990), Stonier’s (1990) or Landauer’s (1991), detailing the main philosophical arguments (e.g., Timpson, 2013; Lombardi et al. 2016a) against those inflationary attitudes towards information. Following this historical assessment, I systematically analyze whether the descriptive exploitation of informational concepts has historically contributed to providing us with knowledge of thermophysical reality via (i) explaining thermal processes such as equilibrium approximation, (ii) advantageously predicting thermal phenomena, or (iii) enabling understanding of thermal property such as thermodynamic entropy. I argue that these epistemic shortcomings would make it impossible to draw ontological conclusions in a justified way about the physical nature of information. In conclusion, I will argue that the historical exploitation of informational concepts has not contributed significantly to the epistemic progress of thermophysics. This would lead to characterize informational proposals as 'degenerate science' (à la Lakatos 1978a) regarding classical thermostatistical physics or as theoretically underdeveloped regarding the study of the cognitive dynamics of scientists in this physical domain. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

The paper argues that unlike Ramsey, Frege and Russell lacked the idea of an arbitrary function and this had important consequences for their foundational programs.

Surveillance programs supporting the management of One Health issues such as antibiotic resistance are complex systems in themselves. Designing ethical surveillance systems is thus a complex task (retroactive and iterative), yet one that is also complicated to implement and evaluate (e.g., sharing, collaboration, and governance). The governance of health surveillance requires attention to ethical concerns about data and knowledge (e.g., performance, trust, accountability, and transparency) and empowerment ethics, also referred to as a form of responsible self-governance. Ethics in reflexive (...) governance operates as a systematic critical-thinking procedure that aims to define its value: What are the “right” criteria to justify how to govern “good” actions for a “better” future? The objective is to lay the foundations for a methodological framework in empirical bioethics, the rudiments of which have been applied to a case study to building reflexive governance in One Health. This ongoing critical thinking process involves “mapping, framing, and shaping” the dynamics of interests and perspectives that could jeopardize a “better” future. This paper proposes to hybridize methods to combine insights from collective deliberation and expert evaluation through a reflexive governance functioning as a community-based action-ethics methodology. The intention is to empower individuals and associations in a dialogue with society, which operation is carried out using a case study approach on data sharing systems. We based our reasoning on a feasibility study conducted in Québec, Canada (2018–2021), envisioning an antibiotic use surveillance program in animal health for 2023. Using the adaptive cycle and governance techniques and perspectives, we synthesize an alternative governance model rooted in the value of empowerment. The framework, depicted as a new “research and design (R&D)” practice, is linking operation and innovation by bridging the gap between Reflexive, Evaluative, and Deliberative reasonings and by intellectualizing the management of democratizing critical thinking locally (collective ethics) by recognizing its context (social ethics). Drawing on the literature in One Health and sustainable development studies, this article describes how a communitarian and pragmatic approach can broaden the vision of feasibility studies to ease collaboration through public-private-academic partnerships. The result is a process that “reassembles” the One Health paradigm under the perspective of global bioethics to create bridges between the person and the ecosystem through pragmatic ethics. (shrink)

Local reports from different international societies have considered the achievement of the successful Glocalized architecture model in line with the 2030 UN Sustainable Development Goals (SDGs). The Aga Khan Cultural Foundation’s International Program for Islamic Architecture has also prioritized the understanding of the success drivers in architectural projects. This study aimed to detect the potentials of the common global indicators to access qualitative design assessment through analyzing the Aga Khan Award’s reports. The selected methodology in the present study is a (...) quantitative approach using the systematic content analysis and coding techniques for qualitative data obtained from the technical. The physical, non-physical, modern, and traditional factors that have contributed to the success of the works as well as their combinations were extracted and analyzed using Sensible and Abstract international, national, and local indications. There is a relative superiority for Sensible indications (A combination of modern and physical factors). The hybrid data distribution provides the ground to assess the works, and this can be used to manage the globalization challenges in the contemporary architecture of Muslim societies. (shrink)

Developments in the realm of formal sciences and math foundations during the twentieth century were marked by important methodological advances. Such new approaches partialy owe their appearance to the abandonment of the previous paradigm. To identify how this transition occured, in this essay we observe some aspects regarding the works of Gödel and Tarski, who, under a certain interpretations, restructure epistemological bases of math's formalisms. It'll be argued that the theoretical variabilities produced in abstract sciences upon weakening previous viewpoints (...) forced to abandon some of the components of hegemonic programs. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

The critique of philosophical foundations of neoclassical economics is significant, because of its hegemony on economic education and research programs in Iran and worldwide academies. Due to an epistemological fallacy, methodological individualism plays a prominent role in the philosophy of economic; since the ontological aspects of economy are reduced to methodological considerations. Accordingly, critique of methodological individualism is regarded as the main entry for philosophical analysis of neoclassical economics. This article aims to analyze and appraise the methodological individualism (...) from critical realism’s point of view. Critical realism is taken as a stand for criticizing methodological individualism, because critical realism and neoclassical economics as a positive approach to economics, both share a realistic worldview. The critical realism’ critique of methodological individualism is bases on analyzing the concepts of formalism, syllogism, social atomism, isolation and reduction. From critical realism’ point of view because of unrealistic postulations of methodological individualism, neoclassical economics is turned to an abstract and deductive science such as mathematics with a low potentiality of explanation. (shrink)

Organismal death is foundational to the evolution of life, and many biological concepts such as natural selection and life history strategy are so fashioned only because individuals are mortal. Organisms, irrespective of their organization, are composed of basic functional units—cells—and it is our understanding of cell death that lies at the heart of most general explanatory frameworks for organismal mortality. Cell death can be exogenous, arising from transmissible diseases, predation, or other misfortunes, but there are also endogenous forms of death (...) that are sometimes the result of adaptive evolution. These endogenous forms of death—often labeled programmed cell death, PCD—originated in the earliest cells and are maintained across the tree of life. Here, we consider two problematic issues related to PCD (and cell mortality generally). First, we trace the original discoveries of cell death from the nineteenth century and place current conceptions of PCD in their historical context. Revisions of our understanding of PCD demand a reassessment of its origin. Our second aim is thus to structure the proposed origin explanations of PCD into coherent arguments. In our analysis we argue for the evolutionary concept of PCD and the viral defense-immunity hypothesis for the origin of PCD. We suggest that this framework offers a plausible account of PCD early in the history of life, and also provides an epistemic basis for the future development of a general evolutionary account of mortality. (shrink)

Despite of the fact that Reichenbach clearly acknowledged his indebtedness to Hilbert, the influence of this leading mathematician of the time on him is grossly neglected. The present paper demonstrates that the decisive years of the development of Reichenbach as a philosopher of science coincide with, and also partly followed the “philosophical” turn of Hilbert’s mathematics after 1917 that was fixed in the so called “Hilbert’s program”. The paper specifically addresses the fact that after 1917, Hilbert saw the axiomatic method (...) as an instrument for providing the foundations not only of mathematics but also of other sciences. In particular, Hilbert’s axiomatic program was closely connected with the theoretical physics and arguably helped Einstein to discover the general theory of relativity. In this context, one can see Reichenbach’s project to axiomatize Einstein’s theory of relativity as a continuation of this project. Under Russell’s influence, after 1914 Hilbert also developed an interest in mathematical logic. Reichenbach experienced similar transition from axiomatics to logic which went together with turn of his interest from Hilbert to Russell. Reichenbach’s rapprochement to Russell also supported the transition of his interests from epistemology to ontology. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Wilhelm Ostwald’s program of a physical energetics is the attempt at a comprehensive description of nature on the basis of the concept of energy. In his book Energetische Grundlagen der Kulturwissenschaft, first published in 1909, Ostwald applies this conception to the area of culture. His central assumption is that cultural phenomena should be described by the energetic notion of “efficiency relation” (Güteverhältnis). His systematic thesis is that science, when organized according to the Machian “principle of economy,” proves as the highest (...) form of cultural expression, since it instantiates the notion of quality relation most efficiently, that is, “with the lowest energy expenditure.” This view echoes August Comte’s “law of the three stages” and is intended to supply it with a scientific, i.e., energetic foundation. Max Weber regarded Ostwald’s energetic theory of culture as a misguided attempt at an absolutization of the methods of concept formation within the natural sciences. As he wrote in his devastating review essay “’Energetische’ Kulturtheorien” (1909), Ostwald transformed a certain world view (Weltbild) into a scientifically frivolous ideology (Weltanschauung). In particular, Ostwald’s adherence to the Comtean law of three stages and the associated hierarchy of the sciences were criticized by Weber as outdated and completely beside the point. According to Weber, the concepts of the cultural sciences are not at all dependent on natural scientific concepts such as ‘energy.’ In his view, culture cannot be reduced to nature. But exactly this seemed to be the principal aim of Ostwald’s program. In this paper, I will critically investigate Weber’s critique of that program. I shall argue that Ostwald’s assumption of a natural basis of culture can be ‘rescued’ as a methodological device, but that Ostwald’s – thoroughly substantialist – view of energy should be discarded as a metaphysical relict of ancient ‘stuff ontology.’ . (shrink)

From mitochondria to meerkats, the natural world is full of spectacular examples of social behaviour. In the early 1960s W. D. Hamilton changed the way we think about how such behaviour evolves. He introduced three key innovations - now known as Hamilton's rule, kin selection, and inclusive fitness - and his pioneering work kick-started a research program now known as social evolution theory. This is a book about the philosophical foundations and future prospects of that program. [Note: only the (...) Introduction is available to download.]. (shrink)

This dissertation lays the foundation for a new theory of non-relational intentionality. The thesis is divided into an introduction and three main chapters, each of which serves as an essential part of an overarching argument. The argument yields, as its conclusion, a new account of how language and thought can exhibit intentionality intrinsically, so that representation can occur in the absence of some thing that is represented. The overarching argument has two components: first, that intentionality can be profi tably studied (...) through examination of the semantics of intensional transitive verbs (ITVs), and second, that providing intensional transitive verbs with a nonrelational semantics will serve to provide us with (at least the beginnings of) a non-relational theory of intentionality. This approach is a generalization of Anscombe's views on perception. Anscombe held that perceptual verbs such as "see" and "perceive" were ITVs, and that understanding the semantics of their object positions could help us to solve the problems of hallucination and illusion, and provide a theory of perception more generally. I propose to apply this strategy to intentional states and the puzzles of intentionality more generally, and so Anscombe's influence will be felt all through the dissertation. -/- In the first chapter, titled "Semantic Verbs are Intensional Transitives", I argue that semantic verbs such as "refers to", "applies to", and "is true of" have all of the features of intensional transitive verbs, and discuss the consequences of this claim for semantic theory and the philosophy of language. One theoretically enriching consequence of this view is that it allows us to perspicuously express, and partially reconcile two opposing views on the nature and subject-matter of semantics: the Chomskian view, on which semantics is an internalistic enterprise concerning speakers' psychologies, and the Lewisian view, on which semantics is a fully externalistic enterprise issuing in theorems about how the world must look for our natural language sentences to be true. Intensional Transitive Verbs have two readings: a de dicto reading and a de re reading; the de dicto reading of ITVs is plausibly a nonrelational reading, and the intensional features peculiar to this reading make it suitable for expressing a Chomskian, internalist semantic program. On the other hand, the de re reading is fully relational, and make it suitable for expressing the kinds of word-world relations essential to the Lewisian conception of semantics. And since the de dicto and de re readings are plausibly related as two distinct scopal readings of the very same semantic postulates, we can see these two conceptions of semantics as related by two scopal readings of the very same semantic postulates. -/- In chapter two, titled "Hallucination and the New Problem of Empty Names", I argue that the problem of hallucination and the problem of empty names are, at bottom, the same problem. I argue for this by reconstructing the problem of empty names in way that is novel, but implicit in much of the discussion on empty names. I then show how, once recast in this light, the two problems are structurally identical down to an extremely fine level of granularity, and also substantially overlap in terms of their content. If the problems are identical in the way I propose, then we should expect that their spaces of solutions are also identical, and there is signi cant support for this conclusion. However, there are some proposed solutions to the problem of hallucination that have been overlooked as potential solutions to the problem of empty names, and this realization opens new non-relational approaches to the problem of empty names, and to the nature of meaning more generally. -/- In chapter three, titled "Intensionality is Additional Phrasal Unity", I argue for a novel approach to the semantics of intensional contexts. At the heart of my proposal is the Quinean view that intensional contexts should, from the perspective of the semantics, be treated as units, with the material in them contributing to the formation of a single predicate. However, this proposal is subject to a number of objections, including the criticism that taken at face value, this would render intensional contexts, which seem to be fully productive, non-compositional. I begin by discussing the concept of the unity of the phrase, and pointing to various ways that phrases can gain additional unity. I then proposes that the intensionality of intensional transitive verbs is best construed as a form of semantic incorporation; ITVs, on their intensional readings, meet all of the criteria for qualifying as incorporating the nominals in their object positions. I then give a semantics for ITVs that builds on existing views of the semantics of incorporation structures, and gesture at how this can be extended to intensional clausal verbs, including the so-called propositional attitude verbs. (shrink)

Philosophy for Children' program that Mathew Lipman and his colleagues have developed is now known in our society and has led to thinking and research in this regard. Thus, to consider the challenges that are in front of this program can lead to the richness of these researches. Three challenges are in front of this program: philosophical, psychological, and educational. The philosophical challenge is due to the point that philosophy is mainly dependent on the history of philosophy and thoughts of (...) preceding philosophers. This dependence should of course be along with critique, but this dependence cannot be denied anyway. Hence, philosophizing cannot be reduced to the methods of thinking. Psychological challenge is rooted in the approaches of developmental psychology that emphasize on phases in human thinking. Accordingly, abstract methods of philosophizing cannot be used in the period of childhood. Educational challenge is related to basic cultural values that might be shaken in the process of philosophical interrogations. The philosophical challenge requires that teaching philosophy to children emphasize on an amalgamation of method and content. The psychological challenge makes us cautious as to looking for more investigations on the periodical characteristic of thinking. And finally, the educational challenge requires that criticizing cultural values, being necessary in active education, is not started from foundational issues of culture. The period of childhood can only be fitted to interrogation of low level cultural issues and values and leave the foundational cultural issues to philosophizing in higher ages. (shrink)

Variation, adaptation, heredity and fitness, constraints and affordances, speciation, and extinction form the building blocks of the (Neo-)Darwinian research program, and several of these have been called “Darwinian principles.” Here, we suggest that caution should be taken in calling these principles Darwinian because of the important role played by reticulate evolutionary mechanisms and processes in also bringing about these phenomena. Reticulate mechanisms and processes include symbiosis, symbiogenesis, lateral gene transfer, infective heredity mediated by genetic and organismal mobility, and hybridization. Because (...) the “Darwinian principles” are brought about by both vertical and reticulate evolutionary mechanisms and processes, they should be understood as foundational for a more pluralistic theory of evolution, one that surpasses the classic scope of the Modern and the Neo-Darwinian Synthesis. Reticulate evolution moreover demonstrates that what conventional (Neo-)Darwinian theories treat as intra-species features of evolution frequently involve reticulate interactions between organisms from very different taxonomic categories. Variation, adaptation, heredity and fitness, constraints and affordances, speciation, and extinction therefore cannot be understood as “traits” or “properties” of genes, organisms, species, or ecosystems because the phenomena are irreducible to specific units and levels of an evolutionary hierarchy. Instead, these general principles of evolution need to be understood as common goods that come about through interactions between different units and levels of evolutionary hierarchies, and they are exherent rather than inherent properties of individuals. (shrink)

Observations of animals engaging in apparently moral behavior have led academics and the public alike to ask whether morality is shared between humans and other animals. Some philosophers explicitly argue that morality is unique to humans, because moral agency requires capacities that are only demonstrated in our species. Other philosophers argue that some animals can participate in morality because they possess these capacities in a rudimentary form. Scientists have also joined the discussion, and their views are just as varied as (...) the philosophers’. Some research programs examine whether animals countenance specific human norms, such as fairness. Other research programs investigate the cognitive and affective capacities thought to be necessary for morality. There are two sets of concerns that can be raised by these debates. They sometimes suffer from there being no agreed upon theory of morality and no clear account of whether there is a demarcation between moral and social behavior; that is, they lack a proper philosophical foundation. They also sometimes suffer from there being disagreement about the psychological capacities evident in animals. Of these two sets of concerns—the nature of the moral and the scope of psychological capacities—we aim to take on only the second. In this chapter we defend the claim that animals have three sets of capacities that, on some views, are taken as necessary and foundational for moral judgment and action. These are capacities of care, capacities of autonomy, and normative capacities. Care, we argue, is widely found among social animals. Autonomy and normativity are more recent topics of empirical investigation, so while there is less evidence of these capacities at this point in our developing scientific knowledge, the current data is strongly suggestive. (shrink)

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of (...) available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

Abstract - The aim of the study is to identify the degree of administrative transparency in the Palestinian higher educational institutions in the Gaza Strip. In the study, the researchers adopted a descriptive and analytical method. The research population consisted of administrative staff, whether academic or administrative, except for those in senior management or the university council. The study population reached 392 employees. A random sample was selected (197). The number of questionnaires recovered was (160) with a recovery rate of (...) (81.2%). The researchers used a questionnaire for the data collection and were treated using SPSS to obtain the results. The results show that there is no significant difference between male responses and female responses due to gender variable. The results also confirm that there is no significant difference between respondents' responses due to the age variable. The results also showed a significant difference between respondents' responses attributed to the university variable. There is a fundamental difference between respondents' responses attributed to the scientifically qualified variable. The results also confirmed a significant difference between respondents' responses attributed to the management level variable. The results also confirmed a significant difference between respondents' responses due to variable years of service. The research reached a number of recommendations, the most important of which is: The necessity of Palestinian universities to adhere to the application of transparency standards in all university activities. The need to benefit from regional and international experience in the application of transparency systems within universities and to examine the possibility of applying these systems in our universities. As well as the need to engage in the program of teaching transparency in universities, as it is confirmed that only five universities participated in this experiment. The importance of raising awareness among the employees of Palestinian universities to clarify the foundations of building transparency and its dimensions to represent the active supporter through workshops and seminars. (shrink)

Yoshimi has attempted to defuse my argument concerning the identification of network abstraction with empiricist abstraction - thus entailing psychologism - by claiming that the argument does not generalize from the example of simple feed-forward networks. I show that the particular details of networks are logically irrelevant to the nature of the abstractive process they employ. This is ultimately because deep artificial neural networks (ANNs) and dynamical systems theory applied to the mind (DST) are both associationisms - that is, empiricist (...) theories that derive the principles of thought from the causal history of the organism/system. On this basis, I put forward a new aspect of the old argument by noting that ANNs & DST are the causal bases of the phenomena of passive synthesis, whereas the language of thought hypothesis (LOT) and the symbolic computational theory of mind (CTM) are the causal bases of the phenomena of active synthesis. If the phenomena of active synthesis are not distinct in kind from and are thus reducible to those of passive synthesis, psychologism results. Yoshimi’s program, insofar as it denies this fundamental phenomenological distinction, is revealed to be the true anti-pluralist program, by essentially denying the causal efficacy of the mechanistic foundations of active synthesis by referring phenomenology exclusively to associationism for its causal foundation. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

Is PDP Connectionism compatible with Cognitive Linguistics? It is unfortunate that this question has not received the attention it deserves, since at stake is the very possibility of a unified "West Coast Cognitive Science" approach to language. Part I of this paper argues that a systematic approach to the question of compatibility must involve an enumeration and analysis of the general principles used by each research program in their linguistic explanations. This approach is carried out in Parts II and III, (...) and the conclusion is that the explanatory principles of PDP Connectionism are fundamentally data-driven, whereas those of Cognitive Linguistics rely essentially on structure that the mind contributes to language use. Part IV presents several computational models of metaphor and analogy as case studies of the practical difficulties involved in reconciling these two frameworks. Finally, Part V examines the philosophical foundations of their respective explanatory strategies in order to get a clearer view of the theoretical obstacles to a unified account. (shrink)

This theme issue has the founding ambition of landscaping Data Ethics as a new branch of ethics that studies and evaluates moral problems related to data (including generation, recording, curation, processing, dissemination, sharing, and use), algorithms (including AI, artificial agents, machine learning, and robots), and corresponding practices (including responsible innovation, programming, hacking, and professional codes), in order to formulate and support morally good solutions (e.g. right conducts or right values). Data Ethics builds on the foundation provided by Computer and Information (...) Ethics but, at the same time, it refines the approach endorsed so far in this research field, by shifting the Level of Abstraction of ethical enquiries, from being information-centric to being data-centric. This shift brings into focus the different moral dimensions of all kinds of data, even the data that never translate directly into information but can be used to support actions or generate behaviours, for example. It highlights the need for ethical analyses to concentrate on the content and nature of computational operations — the interactions among hardware, software, and data — rather than on the variety of digital technologies that enables them. And it emphasises the complexity of the ethical challenges posed by Data Science. Because of such complexity, Data Ethics should be developed from the start as a macroethics, that is, as an overall framework that avoids narrow, ad hoc approaches and addresses the ethical impact and implications of Data Science and its applications within a consistent, holistic, and inclusive framework. Only as a macroethics Data Ethics will provide the solutions that can maximise the value of Data Science for our societies, for all of us, and for our environments. (shrink)

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation (...) to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality. (shrink)

Within the current mainstream research in the foundations of physics, much attention has been turned to the program of Axiomatic Reconstruction of Quantum Theory in terms of Information-Theoretic principles (ARQIT). ARQIT aims at finding a few general information-theoretic principles from which, once translated into mathematical terms, one can formally derive the structure of quantum theory. This chapter explores the role of mechanistic explanations and mathematical explanations (in particular, structural explanations) within ARQIT. With such considerations as a point of departure, (...) we investigate how ARQIT contributes to the explanation of quantum phenomena, and the possible prospects for explanations provided by mechanical interpretations of quantum theory. (shrink)

In this paper, I compare the methodology of the Austrian school to two alternative methodologies from the economic mainstream: the ‘orthodox’ and revealed preference methodologies. I argue that Austrian school theorists should stop describing themselves as ‘extreme apriorists’ (or writing suggestively to that effect), and should start giving greater acknowledgement to the importance of empirical work within their research program. The motivation for this dialectical shift is threefold: the approach is more faithful to their actual practices, it better illustrates the (...) underlying similarities between the mainstream and Austrian research paradigms, and it provides a philosophical foundation that is much more plausible in itself. (shrink)

Concerns have been raised by both researchers and authorities regarding conspiracy theorists rejecting experts. To address the validity of these concerns, we need to delve into two key inquiries regarding who qualifies as an expert on conspiracy theories, and what constitutes an epistemically rational response (from a conspiracy theorist) when faced with expert testimony. The first inquiry presents a challenge when considering a reputationalist versus a realist account of experts. On the reputationalist account rejecting experts may be viewed as little (...) more than rejecting those whom society has collectively deemed as experts. Alternatively, adopting a realist account raises the challenge of determining who the genuine experts are. I argue that the realist account is the more compelling option for pursuing the first question. Moreover, I explore two prevalent accounts from existing literature that prescribe how epistemic agents should respond to expert testimony: the Preemptive View and the Community View. Through an examination using the simulation program Laputa, I demonstrate that both accounts are insufficient. Consequently, I argue that without a clear identification of experts in the broader context of conspiracy theories, the initial concern lacks a solid foundation, and the sense of urgency may be unwarranted. (shrink)

For millennia, knowledge has eluded a precise definition. The industrialization of knowledge (IoK) and the associated proliferation of the so-called knowledge communities in the last few decades caused this state of affairs to deteriorate, namely by creating a trio composed of data, knowledge, and information (DIK) that is not unlike the aporia of the trinity in philosophy. This calls for a general theory of knowledge (ToK) that can work as a foundation for a science of knowledge (SoK) and additionally distinguishes (...) knowledge from both data and information. In this paper, I attempt to sketch this generality via the establishing of both knowledge structures and knowledge systems that can then be adopted/adapted by the diverse communities for the respective knowledge technologies and practices. This is achieved by means of a formal–indeed, mathematical–approach to epistemological matters a.k.a. formal epistemology. The corresponding application focus is on knowledge systems implementable as computer programs. (shrink)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

Many philosophers working on the branches of philosophy that deal with the normative questions have adopted a " Reasons First" program. This paper criticizes the foundational assumptions of this program. In fact, there are many different concepts that can be expressed by the term 'reason' in English, none of which are any more fundamental than any others. Indeed, most of these concepts are not particularly fundamental in any interesting sense.

The philosophical study of mind in the twentieth century was dominated by a research program that used a priori methods to address foundational questions. Since that time, however, the philosophical study of mind has undergone a dramatic shift. To provide a more accurate picture of contemporary philosophical work, I compared a sample of highly cited philosophy papers from the past five years with a sample of highly cited philosophy papers from the twentieth century. In the twentieth century sample, the majority (...) of papers used purely a priori methods, while only a minority cited results from empirical studies. In the sample from the past five years, the methodology is radically different. The majority of papers cite results from empirical studies, a sizable proportion report original experimental results, and only a small minority are purely a priori. Overall, the results of the review suggest that the philosophical study of mind has become considerably more integrated into the broader interdisciplinary field of cognitive science. (shrink)