The work provides comprehensively definitive, unconditional proofs of Riemann's hypothesis, Goldbach's conjecture, the 'twin primes' conjecture, the Collatz conjecture, the Newcomb-Benford theorem, and the Quine-Putnam Indispensability thesis. The proofs validate holonomic metamathematics, meta-ontology, new number theory, new proof theory, new philosophy of logic, and unconditional disproof of the P/NP problem. The proofs, metatheory, and definitions are also confirmed and verified with graphic proof of intrinsic enabling and sustaining principles of reality.

Traditionally, consistency is the only criterion for the quality of a theory in logic-based approaches to reasoning about actions. This work goes beyond that and contributes to the metatheory of actions by investigating what other properties a good domain description should have. We state some metatheoretical postulates concerning this sore spot. When all postulates are satisfied we call the action theory modular. Besides being easier to understand and more elaboration tolerant in McCarthy’s sense, modular theories have interesting properties. We (...) point out the problems that arise when the postulates about modularity are violated, and propose algorithmic checks that can help the designer of an action theory to overcome them. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very (...) logic it is designed to study. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper (...) is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

The work provides comprehensively definitive, unconditional proofs of Riemann's hypothesis, Goldbach's conjecture, the 'twin primes' conjecture, the Collatz conjecture, the Newcomb-Benford theorem, and the Quine-Putnam Indispensability thesis. The proofs validate holonomic metamathematics, meta-ontology, new number theory, new proof theory, new philosophy of logic, and unconditional disproof of the P/NP problem. The proofs, metatheory, and definitions are also confirmed and verified with graphic proof of intrinsic enabling and sustaining principles of reality.

Due to the wide scope of (in particular linear) homotopy type theory (using quantum natural language processing), a metatheory can be applied not just to theorizing the metatheory of scientific progress, but ordinary language or any public language defined by sociality/social agents as the precondition for the realizability of (general) intelligence via an inferential network from which judgement can be made. How this metatheory of science generalizes to public language is through the recent advances of quantum natural (...) language processing, but the traditional metalogical encodings (of Tarski) is relatively comparable through universes such as the type of types or type of types of types found in the inherent inferentialism of UF/HoTT via infinity-groupoids. The "computational trinity" of proofs=programs=algebra in HoTT also means reason is defined functionally as "what it does" by what it computes (proofs are programs). Following Reza Negarestani's recent book, through the self's self-realizability, achieving self-consciousness and consciousness beyond selfhood, "geistig manifestation" is achieved in the form of general intelligence, but only through an inferential network of social agents intrinsically encoded through computation. (shrink)

Applied technological developments are represented by (1) genetic engineering as management tools of biological evolution and (2) socio-economic engineering as management tools of civilizational and socio-cultural development. This binary structure logically follows from the postulated three-module organization of the sustainable evolutionary strategy of the sentient human being. Naturphilosophy once again acquires the status of the basis of the theory of evolution in an explicit way. There is a system of metaphysical postulates and ontological categories derived from the anthropic principle of (...) participation. For modern neoliberal political democracy, bio-power and biopolitics look like the most effective technology for stabilizing the scenarios and trends of the global evolutionary process that are optimal within this ideological system. Conclusions.Transbipolitics in our understanding is a political problematic related to the rationalization of the global evolutionary process. In the coming decades transbipolitics will become the carrier element of the global process of evolution of the noosphere with the consequent complication and increase of cohesion between the individual socio-cultural types that are part of the system of modern globalizing civilization. (shrink)

Addiction is one of the most significant problems facing contemporary society. Consequently many scholars, institutions and clinicians have sought to understand this complex phenomenon, as is evident in the abundance of etiological models of addiction in existence today. A literature review pointed that there is little consensus regarding the nature and etiopathogenesis of addiction, and integrative models have not yet been able to provide the sought-after integration. In addressing this problem, this study offers a theoretical analysis of the paradigmatic and (...) meta-paradigmatic suitability of Integral Theory in the design of an integrated metatheory of addiction. The data consisted of the most prominent etiological theories and models of addiction. The study focused on several essential features constituting the architectonic of any metatheory that attempts to provide conceptual scaffolding for the construction of a comprehensive metatheory of addiction. The criteria for the construction of a metatheory were conceptual integration, ontological span, ontological depth, empirical validity and internal consistency. Integral Theory was critically assessed in terms of each of the abovementioned criteria. The study suggests that Integral Theory is eminently suitable as a philosophical foundation for the development of an integrated metatheory of addiction. (shrink)

This thesis-on macro-ontology, physics, logic, and metalogical principles presents the findings, results, theorems, and metatheory that correct long-standing defects and deficiencies of current standard model (SM) physics and cosmology. It eliminates artificial SM anomalies, paradoxes, logical fallacies, absurdities, and conflicts with reality (and the findings of plasma physics, astronomy, ontology, epistemics, etc.). New theorems and metatheorems eliminate the illogic maintaining distortions of post-Einsteinian physics, its wildly speculative conjectures, and shibboleths (its unrealistic assumptions commonly accepted as facts). In critiques of (...) misperceptions, misconceptions and misinterpretations of observations and data, this work exposes the common failure to recognize the severe deficiencies of theory, science, ontology, and metamathematics. New results prove that chronic failure to differentiate realities from theorems, hypotheses, conjectures, opinions, and beliefs prevents progress to better physics and STEM education. Therefore, this work also enables resolution of the long-standing logical incongruency of physics, psychology, cognitive science, and philosophy, especially ontology. So, the facts and proofs presented here can enable a new era of discovery, creativity, and technological progress. (shrink)

This thesis-on macro-ontology, physics, logic, and metalogical principles presents the findings, results, theorems, and metatheory that correct long-standing defects and deficiencies of current standard model (SM) physics and cosmology. It eliminates artificial SM anomalies, paradoxes, logical fallacies, absurdities, and conflicts with reality (and the findings of plasma physics, astronomy, ontology, epistemics, etc.). New theorems and metatheorems eliminate the illogic maintaining distortions of post-Einsteinian physics, its wildly speculative conjectures, and shibboleths (its unrealistic assumptions commonly accepted as facts). In critiques of (...) misperceptions, misconceptions and misinterpretations of observations and data, this work exposes the common failure to recognize the severe deficiencies of theory, science, ontology, and metamathematics. New results prove that chronic failure to differentiate realities from theorems, hypotheses, conjectures, opinions, and beliefs prevents progress to better physics and STEM education. Therefore, this work also enables resolution of the long-standing logical incongruency of physics, psychology, cognitive science, and philosophy, especially ontology. So, the facts and proofs presented here can enable a new era of discovery, creativity, and technological progress. (shrink)

This thesis-on macro-ontology, physics, logic, and metalogical principles presents the findings, results, theorems, and metatheory that correct long-standing defects and deficiencies of current standard model (SM) physics and cosmology. It eliminates artificial SM anomalies, paradoxes, logical fallacies, absurdities, and conflicts with reality (and the findings of plasma physics, astronomy, ontology, epistemics, etc.). New theorems and metatheorems eliminate the illogic maintaining distortions of post-Einsteinian physics, its wildly speculative conjectures, and shibboleths (its unrealistic assumptions commonly accepted as facts). In critiques of (...) misperceptions, misconceptions and misinterpretations of observations and data, this work exposes the common failure to recognize the severe deficiencies of theory, science, ontology, and metamathematics. New results prove that chronic failure to differentiate realities from theorems, hypotheses, conjectures, opinions, and beliefs prevents progress to better physics and STEM education. Therefore, this work also enables resolution of the long-standing logical incongruency of physics, psychology, cognitive science, and philosophy, especially ontology. So, the facts and proofs presented here can enable a new era of discovery, creativity, and technological progress. (shrink)

Lecture Notes On Eric Schmid's "Prospectus to a Homotopic Metatheory of Language" Presented at the Book Release Event at Triest Gallery (NYC) on January 19, 2024 -/- Prospectus to a Homotopic Metatheory of Language by Eric Schmid proposes that mathematics does not involve the discovery of a synthetic a priori. In other words, mathematics is not a stable transcendent object of knowledge. Instead, Schmid defines math as a language that depends on an infinitely large network topology of inferences. (...) Importantly, this metatheory can be applied not just to the disciplinary specific languages of computer & natural science, but also ordinary & public languages. Mathematics is not the discovery of transcendent concepts, but a dynamic evolving language of inquiry. (shrink)

ABSTRACT In my previous work I explored how Integral Theory can be applied as a meta‐theoretical and transdisciplinary framework, in an attempt to arrive at integrally informed metatheory of addiction, yet indispensable aspects were overlooked. Moreover, an overemphasis was placed on Integral Methodological Pluralism, without clarifying the ontological pluralism of addiction as a multiple object enacted by various methodologies. I believe what is needed in an attempt at a comprehensive integral metatheory of addiction is to include Sean Esbjörn‐Hargens (...) and Michael Zimmerman’s Integral Pluralism and Integral Enactment Theory. Integral Enactment Theory highlights the phenomenon of addiction as a multiple and dynamic object arising along a continuum of ontological complexity. Integral Enactment Theory adeptly points out how etiological models “co‐arise”, in relation to methodology (methodological pluralism) and enacts a particular reality of addiction (ontological pluralism), while being mediated by the world view of the subject (epistemological pluralism) applying the method. This paper briefly explores the significance of including Integral Pluralism and Integral Enactment theory in the quest of an integral metatheory of addiction . (shrink)

Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e., a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs.

The author argues that Quine’s criticism of Kantian analytical/synthetic distinction, as well as transcendentalist reductionism, is not entirely adequate. Furthermore, the author states that Kant’s and Quine’s theories of experience and cognition (transcendentalist and holistic) are based on a common dogma, the one of consistency. Taking into account their uncritical ac-ceptance of experience as a system that is able to adjust new and old elements to each other, both philosophers have much more in common than Quine and his followers might (...) have ex- pected. (shrink)

First, we will address the unnecessary link between symbio-studies and Gaia, asking for the historical and epistemological reasons why they become associated. In particular, we contend that the association is mediated by the common interest in large-scale physico-chemical and biochemical patterns, rather than by an emphasis on harmony, equilibrium, and cooperation (Visvader 1992). Second, we will ask what Gaia is in a metatheoretical sense: is it a scientific hypothesis, a theory, a metaphor, an inspired invention, or a resurgence of antiscientific (...) attitude? After examining some alternatives that show the importance of metatheorizing, we will define Gaia a ‘scientific narrative’, this being a technical term in a sketchy metatheory. Let us just say, for now, that by narrative we don’t mean fairytale or artistic fiction, but rather a way of telling the history of our planet. We are not going to answer the question whether or not we should ban Gaia from any scientific discourse, nor the question how symbio-students should deal with the traditional association of their field with Gaia. But we hope to frame the dilemma in which symbio-students and the scientific community at large are held in a better way than simply insisting on classic demarcations between science and non-science. (shrink)

Das grundsätzliche Fragen liegt immer und ständig dem Wissen zugrunde. Ein grundsätzliches Fragen ist notwendig, wenn man die Komplexität unserer Zeit und unserer Welt verstehen will. Was uns aber heutzutage fehlt, ist die Verbindung zwischen der elementaren Situation jedes grundsätzlichen Fragens und der inflationären Vervielfachung von Wissensformen und partiellen Theorien. Damit einhergehend verliert die Philosophie den Sinn der Form eines ersten Wissens (prôtê epistêmê) als vorrangige Form eines Denkens, das den Wissensformen Einheit geben und den Sinn des Wissens für den (...) Menschen erschließen könnte. Das Buch zielt darauf ab, im Dialog mit der phänomenologischen sowie mit der analytischen Tradition eine neue Schau zu entwickeln, welche die elementare Situation der Frage nach dem Sinn und die Komplexität des Realen wieder miteinander in Verbindung bringt. Ausgehend von der Frage nach dem Sinn kommen Grundfragen in den Blick, welche, jede auf ihre Art und Weise, einen Horizont öffnen, in dem das Denken eine Erweiterung seines Verstehens erreicht: der Horizont der Metaegologie, der Metatheorie, der Metaontologie und zuletzt der Metametaphysik. Durch die Entwicklung der Korrespondenz zwischen Grundfragen und Horizonten des Denkens öffnet sich nicht nur die Perspektive einer Archäologie, sondern die Perspektive der Zukunft des Wissens. (shrink)

Formal ontology as a main branch of metaphysics investigates categories of being. In the formal ontological approach to metaphysics, these ontological categories are analysed by ontological forms. This analysis, which we illustrate by some category systems, provides a tool to assess the clarity, exactness and intelligibility of different category systems or formal ontologies. We discuss critically different accounts of ontological form in the literature. Of ontological form, we propose a character- neutral relational account. In this metatheory, ontological forms of (...) entities are their standings in internal relations whose holding is neutral on the character of their relata. These relations are “formal ontological relations”. Entities belong to ontological categories because they stand in the same formal ontological relations. We hold a nominalist relationalism about ontological categories and forms. We conclude by showing that our metatheory is useful for understanding categorial fundamentality/non- fundamentality, different formal ontologies, and for unifying metaphysical questions. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, (...) Löwenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

In this paper, I elaborate on the Strong Nuclear Theory (SNT) of tropes and substances, which I have defended elsewhere, using my metatheory about formal ontology and especially fundamental ontological form. According to my metatheory, for an entity to have an ontological form is for it to be a relatum of a formal ontological relation or relations jointly in an order. The full fundamental ontological form is generically identical to a simple formal ontological relation or relations jointly in (...) an order. Regarding generic identity, I follow Fabrice Correia and Alexander Skiles, who consider it a form of generalized identity as distinguished from numerical identity. The SNT states that for any trope to have the full fundamental ontological form is for it to be a strongly rigidly or generically (existentially) dependent individual simple part. Therefore, the common dichotomous set-up of asking whether tropes are fundamentally properties rather than objects or vice versa is a non-starter to me in formal ontological terms. The elaboration of the SNT also supplies me with the resources to respond to the arguments against tropes by Douglas Ehring, Robert K. Garcia and Herbert Hochberg. Finally, I argue that non-fundamentally but necessarily, every trope is a proper part of a substance and is concrete in the SNT. (You may access the published paper via the external link below.). (shrink)

Although we may find the concept of anomie in Greek thought, it is since Durkheim that the concept begins to be used specifically as a sociological concept. However, a theory of anomie only becomes consolidated since “Social Structure and Anomie” by Robert K. Merton (Merton 1938). The theory becomes important and conquers its space in the rest of the century as one of the most productive theories about deviance. In this study, based on a contemporary conception of scientific theory, that (...) of the structuralist metatheory, a reconstruction of Merton’s approach is proposed, allowing to make explicit the deep structure of the theory. (shrink)

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics (...) match with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

The perhaps most important criticism of the nontransitive approach to semantic paradoxes is that it cannot truthfully express exactly which metarules preserve validity. I argue that this criticism overlooks that the admissibility of metarules cannot be expressed in any logic that allows us to formulate validity-Curry sentences and that is formulated in a classical metalanguage. Hence, the criticism applies to all approaches that do their metatheory in classical logic. If we do the metatheory of nontransitive logics in a (...) nontransitive logic, however, there is no reason to think that the argument behind the criticism goes through. In general, asking a logic to express its own admissible metarules may not be a good idea. (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)

Here's the thing: when you look at it from just the right angle, it's entirely obvious how semantics for second-order relevant logics ought to go. Or at least, if you've understood how semantics for first-order relevant logics ought to go, there are perspectives like this. What's more is that from any such angle, the metatheory that needs doing can be summed up in one line: everything is just as in the first-order case, but with more indices. Of course, it's (...) no small matter finding the magical angle from which everything becomes obvious. And even having found this perspective, one cannot assume one's audience will find things as obvious as oneself. All that to say this: if the results in the paper below strike you as obvious, pay attention to the perspective that makes that possible. And if they don't, feel free to ignore this preamble in its entirety. (shrink)

In the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that the syntax of (...) the object language is specified exactly enough, and that the metatheory has a certain amount of set theoretic power,2 one can explicitly define truth in the object language. And what can be explicitly defined can be eliminated. It follows that the defined concept cannot give rise to any inconsistencies (that is, paradoxes). This gave new respectability to the concept of truth and related notions. Nevertheless, philosophers’ judgements on the nature and philosophical relevance of Tarski’s work have varied. It is my aim here to review and evaluate some threads in this debate. (shrink)

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...) the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

Modern science, based on the laws of physics, claims validity for all events in space and time. However, it also reveals its own limitations, such as the indeterminacy of quantum physics, the limits of decidability, and, presumably, limits of decodability of the mind-brain relationship. At the philosophical level, these intrinsic limitations allow for different interpretations of the relation between human cognition and the natural order. In particular, modern science may be logically consistent with religious as well as agnostic views of (...) humans and the universe. These points are exemplified through the transcript of a discussion between Kurt Gödel and Rudolf Carnap that took place in 1940. Gödel, discoverer of mathematical undecidability, took a proreligious view; Carnap, one of the founders of analytical philosophy, an antireligious view. By the time of the discussion, Carnap had liberalized his ideas on theoretical concepts of science: he believed that observational terms do not suffice for an exhaustive definition of theoretical concepts. Then, responded Gödel, one should formulate a theory or metatheory that is consistent with scientific rationality, yet also encompasses theology. Carnap considered such theories unproductive. The controversy remained unresolved, but its emphasis shifted from rationality to wisdom, not only in the Gödel-Carnap discussion but also in our time. -/- . (shrink)

The investigation into logical form and structure of natural sciences and mathematics covers a significant part of contemporary philosophy. In contrast to this, the metatheory of normative theories is a slowly developing research area in spite of its great predecessors, such as Aristotle, who discovered the sui generis character of practical logic, or Hume, who posed the “is-ought” problem. The intrinsic reason for this situation lies in the complex nature of practical logic. The metatheory of normative educational philosophy (...) and theory inherits all the difficulties inherent in the general metatheory but has also significantly contributed to its advancement. In particular, the discussion on its mixed normative-descriptive character and complex composition has remained an important part of research in educational philosophy and theory. The two points seem to be indisputable. First, the content of educational philosophy and theory is a complex one, connecting different disciplines. Second, these disciplines are integrated within the logical form of practical inference or means-end reasoning. On the other hand, the character of consequence relation in this field, although generally recognized as specific, represents an unresolved prob- lem, a solution of which requires a sophisticated logical theory and promises to influence the self- understanding of educational philosophy and theory. (shrink)

Is there more to the recent surge in political realism than just a debate on how best to continue doing what political theorists are already doing? I use two recent books, by Michael Freeden and Matt Sleat, as a testing ground for realism’s claims about its import on the discipline. I argue that both book take realism beyond the Methodenstreit, though each in a different direction: Freeden’s takes us in the realm of meta-metatheory, Sleat’s is a genuine exercise in (...) grounding liberal normative theory in a non-moralistic way. I conclude with wider methodological observations. I argue that unlike communitarianism (the previous contender for the discipline’s renewal), realism has the potential to open new vistas, though their novelty is to a large extent relative to the last forty years or so: realism is best thought of as a return to a more traditional way of doing political philosophy. (shrink)

I recast the DWE ("Doing Well Enough") deontic framework as an Andersonian-Kangerian modal framework and explore its metatheory systematically.

Since 1976 Hilary Putnam has on many occasions proposed an argument, founded on some model-theoretic results, to the effect that any philosophical programme whose purpose is to naturalize semantics would fail to account for an important feature of every natural language, the determinacy of reference. Here, after having presented the argument, I will suggest that it does not work, because it simply assumes what it should prove, that is that we cannot extend the metatheory: Putnam appears to think that (...) all we may determinately say about the relations between words and entities in the world is what the model theory tells us, but he has never offered justifications for that. At the end of the article, I will discuss the apparently reliable intuition that seems to me to be at the root of the argument, that is that, given a formal theory, there is an infinite number of ways of connecting it to, or of projecting it onto, the world. I will suggest that we should resist this intuition, because it rests on a very doubtful notion of world, which assumes that for any class of objects there is a corresponding property. (shrink)

This synthesis of 5 prominent conflict management paradigms uses power differential as the single most contributing variable to their process and outcome of conflict. Efforts of scholars to integrate or synthesize conflict paradigms have been unsuccessful or clumsy by the scholars’ own assessments. The 5 selected paradigms represent an interdisciplinary set of normative and descriptive paradigms from different social contexts and intellectual frameworks. The 5 share the common traits of rival goals, three levels of socially constructed power differential, and outcomes (...) relative to the total value of the rival goal. An inverse relationship between power differential and the total value of conflict outcomes is supported by all 5 paradigms and empirical data. Explanatory metatheory is the methodology used for synthesis. An increase in power differential results in a decrease in total value of the rival goal. Power differential is constructed using Max Weber’s ideal-type method. The power differentials are abstracted from the paradigms themselves. Empirical work form secondary sources and case studies complete the analysis. (shrink)

The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.

Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e. a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs. (Translation of our German paper "Ein Redehandlungskalkül. Ein (...) pragmatisierter Kalkül des natürlichen Schließens nebst Metatheorie"; online available at http://philpapers.org/rec/CORERE.). (shrink)

What's wrong with modalities in (Wittgenstein 1922)? In (Suszko 1968), the writer argued that "Wittgenstein was somewhat confused and wrong in certain points. For example, he did not see the clear-cut distinction between language (theory) and metalanguage (metatheory): a confusion between use and mention of expressions". Furthermore, a modal logic was proposed in (von Wright 1986) as depicting Wittgenstein's bipolarity thesis in a S5 frame. -/- The aim of the present paper is to deal with the specific case of (...) epistemic modal logic: such a logic of propositional attitudes assumes a philosophy of language that would violate Wittgenstein's two main assumptions. (shrink)

The authors argue that the consciousness debate inhabits the same problem space today as it did in the 17th century. They attribute the lack of progress to a mindset still polarized by Descartes’ real distinction between mind and body, resulting in a standoff between humanistic and scientistic approaches. They suggest that consciousness can be adequately studied only by a multiplicity of disciplines so that the paramount problem is how to integrate diverse disciplinary perspectives into a coherent metatheory. Process philosophy (...) is well qualified to attempt such a synthesis. The rationale for the volume is summed up in the book's unifying thesis: normal, focal-attentive consciousness is not the sui generis phenomenon it is usually taken to be, but part of a wider spectrum of experience (including marginal, deviant, and non-human experience) that can only be studied by approaches as diverse as phenomenology, psycho- and neuropathology, biology, and zoology. (shrink)

Most of us are either philosophically naïve scientists or scientifically naïve philosophers, so we misjudged Schrödinger’s “very burlesque” portrait of Quantum Theory (QT) as a profound conundrum. The clear signs of a strawman argument were ignored. The Ontic Probability Interpretation (TOPI) is a metatheory: a theory about the meaning of QT. Ironically, equating Reality with Actuality cannot explain actual data, justifying the century-long philosophical struggle. The actual is real but not everything real is actual. The ontic character of the (...) Probable has been elusive for so long because it cannot be grasped directly from experiment; it can only be inferred from physical setups that do not morph it into the Actual. In this Part III, Born’s Rule and the quantum formalism for the microworld are intuitively surmised from instances in our macroworld. The posited reality of the quanton’s probable states and properties is probed and proved. After almost a century, TOPI aims at setting the record straight: the so-called ‘Basis’ and ‘Measurement’ problems are ill-advised. About the first, all bases are legitimate regardless of state and milieu. As for the second, its premise is false: there is no need for a physical ‘collapse’ process that would convert many states into a single state. Under TOPI, a more sensible variant of the ‘measurement problem’ can be reformulated in non-anthropic terms as a real problem. Yet, as such, it is not part of QT per se and will be tackled in future papers. As for the mythical cat, the ontic state of a radioactive nucleus is not pure, so its evolution is not governed by Schrödinger’s equation – let alone the rest of his “hellish machine”. Einstein was right: “The Lord is subtle but not malicious”. However, ‘The Lord’ turned out to be much subtler than what Einstein and Schrödinger could have ever accepted. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [1]. (shrink)

The paper identifies defining characteristics of the principal models of problem-solving behavior which are useful in developing a general theory of problem-solving. An attempt is made both to make explicit those disagreements between theorists of different persuasions which have served as obstacles to an integrated approach, and to show that these disagreements have arisen from a number of conceptual confusions: The conflict between information processors and behavioral analysts has resulted from a common failure to understand theoretical sufficiency, and hence these (...) theorists have been at a loss to understand one another. Two directions of research in problem-solving, mechanical algorithmic problem-solving and the psychology of invention, have been thought to be divergent, but in fact complement one another once it is clear that problem-solving involves neither discovery nor invention, but rather is a matter of perceptual encoding and processing. Successful problem-solving behavior can be described as adaptive, learning behavior in which organization skills are effectively associated with situationally determined perceptual encoding processes of the individual mechanical or biological problem-solver. (shrink)

Stephen Hawking claims: Philosophy is dead! Natural scientists use terms like 'natural law', 'matter', 'nature' and 'theories'. Often these terms are taken for granted without reflection. The task of philosophy of science as a metatheory of science is to clarify these terms. In doing so, philosophy of science is confronted with epistemological, ontological and metaphysical questions. But it also deals with questions such as "How do we define the boundaries between different scientific disciplines?" or "How do we distinguish science (...) from pseudoscience?". In addition, philosophy of science deals with ethical problems of modern technology, with methodological issues, with reconstructing the structure and development of scientific theories, and with exposing ideological paternalism of science. The optimistic conclusion is: Philosophy is not dead - but philosophers must discuss with scientists on an equal footing. (shrink)

In “The Routledge Handbook of Philosophy and Science of Addiction” Robert West highlights a pervasive challenge for more conceptual clarity and consensus within the field of addiction studies. In an attempt to address the challenge I provide the conceptual building blocks or architectonic of a metatheory of addiction, referred to as the Integrated Metatheoretical Model of Addiction (IMMA). The IMMA is not a general theory of addiction, but rather an exploratory attempt at providing the architectonic of an metaparadigmatic heuristic, (...) that may potentially provide the conceptual scaffolding needed for developing a general theory of addiction. (shrink)

The article concerns the meta-epistemological problem of the justification of a theory of knowledge and provides a reconstruction of the history of its formulations. In the first section, I analyse the connections between Sextus Empiricus' diallelus, Montaigne's rouet and Chisholm's problem of criterion; in the second section I focus on the link between thediallelus and the Cartesian circle; in the third section I reconstruct the origin of Fries' trilemma; finally, in the last section I draw some general conclusions about the (...) issue qua a general problem for a theory of knowledge. (shrink)

Abstract: This is necessarily an evolutionary work in progress. Its purpose and goal is enabling real progress of science, mathematics, society, and civilization. Thus, to accomplish the mission, upgrading the current sociocultural paradigm is essential. That makes holistic ontology and optimal epistemics essential to ongoing work and to further development of new theory and metatheory. Hence, the current listings of key terms, definitions, and explanations presented here provide some core concepts and supporting theorems, metatheorems, equations, and examples. That enables (...) remedial revision of relevant domains of thought and discourse. The project is also intended to inspire collaborative extension and ongoing refinement of the work. The appendices provide additional perspective. ~ A preprint draft, v.2e, for review and comment only. (shrink)

Gödel's incompleteness theorems establish the stunning result that mathematics cannot be fully formalized and, further, that any formal system containing a modicum of number or set theory cannot establish its own consistency. Wilfried Sieg and Clinton Field, in their paper Automated Search for Gödel's Proofs, presented automated proofs of Gödel's theorems at an abstract axiomatic level; they used an appropriate expansion of the strategic considerations that guide the search of the automated theorem prover AProS. The representability conditions that allow the (...) syntactic notions of the metalanguage to be represented inside the object language were taken as axioms in the automated proofs. The concrete task I am taking on in this project is to extend the search by formally verifying these conditions. Using a formal metatheory defined in the language of binary trees, the syntactic objects of the metatheory lend themselves naturally to a direct encoding in Zermelo's theory of sets. The metatheoretic notions can then be inductively defined and shown to be representable in the object-theory using appropriate inductive arguments. Formal verification of the representability conditions is the first step towards an automated proof thereof which, in turn, brings the automated verification of Gödel's theorems one step closer to completion. (shrink)

The latest draft (posted 05/14/22) of this short, concise work of proof, theory, and metatheory provides summary meta-proofs and verification of the work and results presented in the Theory and Metatheory of Atemporal Primacy and Riemann, Metatheory, and Proof. In this version, several new and revised definitions of terms were added to subsection SS.1; and many corrected equations, theorems, metatheorems, proofs, and explanations are included in the main text. The body of the text is approximately 18 pages, (...) with 3 sections; 1, an Introduction (with a 108 page listing of key terms & definitions), sect. 2, the Results, sect. 3, Discussion (commentary & predictions), and sect. 4, Works Cited. As much as possible, the style is intended for readability and understanding by very bright children (with some interest & knowledge of maths, etc.) and very interested nonprofessionals. The results of this project also enable upgrades of number theory, set theory, proof theory, metamathematics, the foundations of science, and quantum mechanics theory (etc.). (shrink)

ABSTRACT In previous work I explored how Integral Theory can be applied as a metatheoretical and transdisciplinary framework, in an attempt to arrive at an integrally informed metatheory of addiction. There was an overemphasis on Integral Methodological Pluralism in that thread of research, without clarifying the ontological pluralism of addiction as a multiple object enacted by various methodologies. To arrive at a comprehensive integral metatheory and integral ontology of addiction, I believe it is necessary to include the conception (...) of Integral Pluralism and Integral Enactment Theory as posited by Sean Esbjörn-Hargens. Integral Enactment Theory highlights the phenomenon of addiction as a multiple and dynamic object arising along a continuum of ontological complexity; it adeptly points out how etiological models “co-arise” in relation to methodology (methodological pluralism) to enact a particular reality of addiction (ontological pluralism) while being mediated by the worldview of the subject (epistemological pluralism) applying the method. This article briefly explores the significance of including Integral Pluralism and Integral Enactment Theory in the quest of an integral metatheory and integral ontology of addiction. (shrink)

This article outlines an integrally informed model for addictionon treatment and recover that is being pioneered and developed at Tabankulu Secondary Addiction Recovery Center in Cape Town, South Africa. Tabankulu is the world’s first inpatient Addictionon treatment center to implement an integrally informed treatment model. The Integrated Recovery model is a comprehensive, balanced, multi-phased, and multi-disciplinary approach to the treatment of and recovery from addiction. Its philosophy is derived from integrang a 12 Step abstinence-based methodology, mindfulness-based interventions, positive psychology, and (...) Integral Theory. The case is made that addictionon treatment facilities, therapists working with this population, and recovering addicts will become more proficient, effective, and consequently have higher success rates by becoming integrally informed. (shrink)

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.