This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form (...) and that deductions in normal form have the subformula property. (shrink)

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a (...) general introduction rule for implication. The general introduction rule for negation has a similar form. Maximal formulas with implication or negation as main operator require reduction procedures of a more intricate kind not present in normalisation for intuitionist logic. (shrink)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for (...) bilateral proof rules has a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.

Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The (...) Thesis has also had an influence on the philosophy of language: some prominent writers in that area, notably Dummett and Robert Brandom, have taken it to be a special case of a more general requirement that the grounds for asserting a statement must cohere with its consequences. This essay considers various ways of making the Harmony Thesis precise and scrutinizes the most influential arguments for it. The verdict is negative: all the extant arguments for the Thesis are weak, and no version of it is remotely plausible. (shrink)

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be (...) used with any Copi-style set of inference rules, so it is quite adaptable to many mainstream symbolic logic textbooks. Consequently, PARC may be especially attractive to logic teachers who find Jaskowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules. The PARC system is also keyboard-friendly in comparison to the widely adopted Jaskowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams. (shrink)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help (...) make explicit the restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist (also called 'syntactic') one based on introduction and elimination rules, and the representationalist (also called 'semantic') one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my (...) argument is that there are different notions of conjunction at play in standard first order logic, and that the technical and philosophical connections between them are far from well established. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties (...) from its associated labelled calculus. (shrink)

Quine has been charged with eliminating the normative dimension from his naturalized epistemology. The aim of the paper is to look at the role of empathy in Quine's language learning situation, which in its simplest form is constituted by the parent-child relation. We will explore the normativity of the role of empathy thereof by exploiting the sociality of the language learning situation. Since the sociality of Quine's notion of empathy is implicit, to explore the normativity expression thereof, we will examine (...) the explicit sociality of Wittgenstein's language learning situation-also constituted in its simplest form by the master-novice relation-and the normative character of it. By explicating the normativity of the calibrating role of the master and of rule following generally, we will parse the social dimensions of the empathizing role of the linguist in Quine's language learning situation. Finally, by examining the nature of normativity in empathizing, we will establish that the normativity of empathizing involved in Quine's language learning situation is socially grounded without denying its individual dimension. We will conclude that the normativity objection against Quine's naturalism thus stands refuted. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

The conceptual model of United Nations reform - "UN 3.0" includes the General Program of Action on UN Reform, consisting of two stages. The first stage for 2020-2025 envisages the transformation of the main organs of the UN - the General Assembly and the Security Council with measures to improve the effectiveness of the management system, address the "veto problem", problem of financing, improve staff work and administrative and financial control, strengthen UN media, improvement of work with the (...) global civil society. The General Assembly is converted into the General All-Parliamentary Assembly of the UN. In the structure of the Assembly, the Council for Law is being established, which coordinates the activities of UN structures in the field of law. To coordinate the activities of the UN in the field of human rights and civil society, ethical issues, the General all-parliamentary Assembly creates the Council on ethics, human rights and civil society and transforms the Committee on information into the Council on public information and communication with civil society. The structure of the Council includes all UN media. The reform of the UN Security Council is carried out in three sub-stages. At the 1st sub-stage (2020-2021) the Security Council is transformed into the Council of Existential Security (CES). The membership of the CES is increased to 25 member countries, of which five countries have the right of the unconditional (absolute, eternal) veto: Great Britain, France, China, Russian Federation, USA. The General All-Parliamentary Assembly elects 15 new permanent members of the Council of Existential Security with the right of the conditional (limited) veto: Argentina, Australia, Brazil, Canada, Egypt, Germany, India, Indonesia, Italy, Mexico, South Africa, Nigeria, Pakistan , Turkey, Japan (if they fulfill the mandatory restrictive conditions). At this sub-stage, the CES elects also five non-permanent members with the right of a conditional (limited) veto when they meet the mandatory restrictive conditions, with a rotation period of 2 years from geographical regions (or regional unions): Africa, Latin America and the Caribbean, Asia and the Pacific Ocean (2 places), Eastern Europe. On the second sub-stage (2022-2023), subject to the effective activity of the CES of the enlarged composition and compliance with mandatory restrictive conditions, new permanent members of the "Existential Security Council" are elected with the right of a conditional (limited) veto: Iran, Spain, Poland, Saudi Arabia. Members of the CES may be regional unions, whose member countries are not represented in the CES, but still have one vote with the right of a conditional (limited) veto. -/- Two essential levels of the veto: 1. Unconditional (absolute, eternal) veto is the historical right of veto of the five permanent members of the Council of Existential Security - Great Britain, China, Russia, USA, France; 2. Сonditional (limited) veto is the veto of other permanent and non-permanent members of the Council of Existential Security. The right of veto is a unique international school for the achievement of consensus, a school of high democracy for Humanity, a reliable guarantee of the viability of the UN structure. The Council for Existential Security centralises the management of the UN subsidiary bodies with the expansion of their security functions: the Military Staff Committee, the Counter-Terrorism Committee, the Committee for the Prevention of the Spread of Nuclear, Chemical and Biological Weapons, the Sanctions Committees and other committees. On the basis of the decision of the Council of Existential Security, the General All-Parliamentary Assembly creates permanent contingents of UN peacekeeping and counter-terrorism forces. In addition, two Centers are being created in the structure of the Council for Existential Security: the World Center for the Elimination of the Effects of Technogenic and Natural Disasters with branches on all continents and the World Center for the Analysis of Existential Risks and the Overall Security Strategy. The Center is developing the Programs of research and monitoring of global existential threats and risks. In order to increase the level of legitimacy and authority of the Secretary General of the United Nations, the Rules of procedure for elections to this post are changing. Each member country of the Council for Existential Security represents one of the most authoritative candidates for election to the post of Secretary General at the session of the General All-Parliamentary Assembly, with the possibility of nominating candidates from other countries, including those not members of the Council for Existential Security. Elections are held in two rounds during one day of the session of the Assembly. The Legal Committee of the UN General Assembly is developing a Program for the Reform of the Judicial System of the United Nations, which takes into account the proposals of the previous international discussion and determines the scope and terms of the reform of the courts. In accordance with the Program of Action on UN Reform for 2020-2025, reforms are under way in the structure of the Economic and Social Council. The central task of the reform is to strengthen the coordinating role of ECOSOC in the entire system of UN-related specialized agencies, funds and programs related to the Council. The key task of the UN reform is the solution of the financing problem. A unified "UN Open Budget "Solidarity XXI" is being created, including the financing of peacekeeping operations and other expenses. Each country, a member of the United Nations, lists in an established period, once a year, an Existential contribution - the Earth Tax. The Earth Tax for each UN member state is established on the basis of four scales of calculation: Scale I - for 5 permanent members of the Council of Existential Security, who have the right of absolute (absolute) veto; Scale II - for the permanent members of the SEB, who have the right to a conditional (limited) veto; Scale III - for non-permanent members of the SEB, who have the right to a conditional (limited) veto; Scale IV - for all other UN member countries. The program of action on UN reform includes a set of measures to ensure transparent work of the International Civil Service Commission with the involvement of the UN media. To strengthen control functions in the sphere of personnel policy, administrative and financial management, the General All-Parliamentary Assembly of the United Nations establishes the Permanent Commission on Ethics and Administrative and Financial Control. All members of the Commission, members of the Committees and auditors are independent in their activities from the leadership of the United Nations, its funds and programs. The General All-Parliamentary Assembly completes the first stage of the Program of Action on UN Reform in 2025 and, following an open discussion, introduces a single language of international communication - Esperanto and approves it as the official language of the United Nations. With a view to more effective work of the central UN governing bodies in the face of increasing existential threats and risks, reducing the current expenses for the maintenance of the central bodies of the UN, the Council for Existential Security and the General All-Parliamentary Assembly decide on the relocation of the UN headquarters to Iceland. The UN building complex in New York is transferred to preferential use of non-governmental organizations, which contribute to the implementation of the goals of the United Nations. At the second stage of the UN reform in the period 2026-2028, additional necessary transformations are being made in the UN system. At the end of the first stage of the reform, taking into account the reforms carried out by the main organs of the United Nations and the internal improvement of the work of all its structures, the United Nations Program of Action for the years 2026-2028 is being developed. (shrink)

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop (...) several extensions of \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...) all booksellers, including Barnes & Noble, Amazon, and brick-and-mortar bookstores under ISBN 978-0-578-88646-6. ●●●●● In light of the length of this book, readers who would like to have a more detailed description of the book's objectives and method may find it helpful to read the detailed and clearly written Wikipedia entry about this work: From the Wikipedia search page, use the search phrase "Critique of Impure Reason". At least at the time of this writing (11/29/2021), the Wikipedia entry is well-researched and accurate. ●●●●● In addition, a "Primer on Bartlett's CRITIQUE OF IMPURE REASON" has been made available by the author. It is available under its title through PhilPapers and other philosophy online archives. ●●●●● COMMENDATIONS OF THIS WORK, from the back cover of the published edition: ●●●●● “I admire its range of philosophical vision.” – Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh, author of more than 100 books. ●●●●● “Bartlett’s _Critique of Impure Reason_ is an impressive, bold, and ambitious work. Careful scholarship is balanced by original analyses that lead the reader to recognize the limits of meaning, knowledge, and conceptual possibility. The work addresses a host of traditional philosophical problems, among them the nature of space, time, causality, consciousness, the self, other minds, ontology, free will and determinism, and others. The book culminates in a fascinating and profound new understanding of relativity physics and quantum theory.” – Gerhard Preyer, Professor of Philosophy, Goethe-University, Frankfurt am Main, Germany, author of many books including _Concepts of Meaning_, _Beyond Semantics and Pragmatics_, _Intention and Practical Thought_, and _Contextualism in Philosophy_. ●●●●● “[This work’s] goal is of a unique and difficult species: Dr. Bartlett seeks to develop a formal logical calculus on the basis of transcendental philosophical arguments; in fact, he hopes that this calculus will be the formal expression of the transcendental foundation of knowledge.... I consider Dr. Bartlett’s work soundly conceived and executed with great skill.” – C. F. von Weizsäcker, philosopher and physicist, former Director, Max-Planck-Institute, Starnberg, Germany. ●●●●● “Bartlett has written an American “Prolegomena to All Future Metaphysics.” He aims rigorously to eliminate meaningless assertions, reach bedrock, and place philosophy on a firm foundation that will enable it, like science and mathematics, to produce lasting results that generations to come can build on. This is a great book, the fruit of a lifetime of research and reflection, and it deserves serious attention.” — Martin X. Moleski, former Professor, Canisius College, Buffalo, NY, studies of scientific method, the presuppositions of thought, and the self-referential nature of epistemology. ●●●●● “Bartlett has written a book on what might be called the underpinnings of philosophy. It has fascinating depth and breadth, and is all the more striking due to its unifying perspective based on the concepts of reference and self-reference.” – Don Perlis, Professor of Computer Science, University of Maryland, author of numerous publications on self-adjusting autonomous systems and philosophical issues concerning self-reference, mind, and consciousness. ●●●●● ●●●●● The _Critique of Impure Reason: Horizons of Possibility and Meaning_ comprises a major and important contribution to philosophy. Thanks to the generosity of its publisher, this massive 885-page volume has been published as a free open access eBook (3.75MB) as well as an open access printed edition. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. ●●●●● In Kant’s _Critique of Pure Reason_ we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new _Critique_ focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ _conflict_ with the very preconditions of meaning and of knowledge. ●●●●● This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. ●●●●● The _Critique of Impure Reason_ proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. ●●●●● The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of _possible meaning_ are determined. ●●●●● Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, _metalogical projection_. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. ●●●●● Based on original research and rigorous analysis combined with extensive scholarship, the _Critique of Impure Reason_ develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. ●●●●● CONTENTS AT A GLANCE ▪▪▪▪▪ Preface ▪▪▪▪▪ Foreword by Carl Friedrich von Weizsäcker ▪▪▪▪▪ Acknowledgments ▪▪▪▪▪ Avant-propos: A philosopher’s rallying call ▪▪▪▪▪ Introduction ▪▪▪▪▪ A note to the reader ▪▪▪▪▪ A note on conventions ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART I ▪▪▪▪▪ ▪▪▪▪▪ WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN ▪▪▪▪▪ 1 Philosophical-psychological prelude ▪▪▪▪▪ 2 Putting belief in its place: Its psychology and a needed polemic ▪▪▪▪▪ 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference ▪▪▪▪▪ 4 The stepladder to maximum theoretical generality ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART II ▪▪▪▪▪ THE METALOGIC OF REFERENCE ▪▪▪▪▪ A New Approach to Deductive, Transcendental Philosophy ▪▪▪▪▪ 5 Reference, identity, and identification ▪▪▪▪▪ 6 Self-referential argument and the metalogic of reference ▪▪▪▪▪ 7 Possibility theory ▪▪▪▪▪ 8 Presupposition logic, reference, and identification ▪▪▪▪▪ 9 Transcendental argumentation and the metalogic of reference ▪▪▪▪▪ 10 Framework relativity ▪▪▪▪▪ 11 The metalogic of meaning ▪▪▪▪▪ 12 The problem of putative meaning and the logic of meaninglessness ▪▪▪▪▪ 13 Projection ▪▪▪▪▪ 14 Horizons ▪▪▪▪▪ 15 De-projection ▪▪▪▪▪ 16 Self-validation ▪▪▪▪▪ 17 Rationality: Rules of admissibility ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART III ▪▪▪▪▪ PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE ▪▪▪▪▪ Major Problems and Questions of Philosophy and the Philosophy of Science ▪▪▪▪▪ 18 Ontology and the metalogic of reference ▪▪▪▪▪ 19 Discovery or invention in general problem-solving, mathematics, and physics ▪▪▪▪▪ 20 The conceptually unreachable: “The far side” ▪▪▪▪▪ 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism ▪▪▪▪▪ 22 The projections of time, space, and space-time ▪▪▪▪▪ 23 The projections of causality, determinism, and free will ▪▪▪▪▪ 24 Projections of the self and of solipsism ▪▪▪▪▪ 25 Non-relational, agentless reference and referential fields ▪▪▪▪▪ 26 Relativity physics as seen through the lens of the metalogic of reference ▪▪▪▪▪ 27 Quantum theory as seen through the lens of the metalogic of reference ▪▪▪▪▪ 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory ▪▪▪▪▪ ▪▪▪▪▪ PART IV ▪▪▪▪▪ HORIZONS ▪▪▪▪▪ 29 Beyond belief ▪▪▪▪▪ 30 _Critique of Impure Reason_: Its results in retrospect ▪▪▪▪▪ ▪▪▪▪▪ SUPPLEMENT ▪▪▪▪▪ The Formal Structure of the Metalogic of Reference ▪▪▪▪▪ APPENDIX I ▪▪▪▪▪ The Concept of Horizon in the Work of Other Philosophers ▪▪▪▪▪ APPENDIX II ▪▪▪▪▪ Epistemological Intelligence ▪▪▪▪▪ References ▪▪▪▪▪ Index ▪▪▪▪▪ About the author. 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In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If a proposition is true at (...) all epistemically possible worlds for an agent, the proposition is epistemically necessary for the agent, and as such, the agent knows the proposition. -/- This framework presupposes an underlying space of worlds that we can call epistemic space. Traditionally, worlds in epistemic space are identified with possible worlds, where possible worlds are the kinds of entities that at least verify all logical truths. If so, given that epistemic space consists solely of possible worlds, it follows that any world that may remain epistemically possible for an agent verifies all logical truths. As a result, all logical truths are epistemically necessary for any agent, and the corresponding framework only allows us to model logically omniscient agents. This is a well-known consequence of the standard possible world framework, and it is generally taken to imply that the framework cannot be used to model non-ideal agents that fall short of logical omniscience. -/- A familiar attempt to model non-ideal agents within a broadly world involving framework centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in epistemic space, it is easy to avoid logical omniscience. If any logical falsehood is true at some impossible world, then any logical falsehood may remain epistemically possible for some agent. As a result, we can use an impossible world involving framework to model extremely non-ideal agents that do not know any logical truths. -/- A much harder, and considerably less investigated challenge is to ensure that the resulting epistemic space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out impossible worlds that verify obvious logical falsehoods. To model such agents, we need a construction of a non-trivial epistemic space that partly consists of impossible worlds where not "anything goes". This involves imposing substantive constraints on impossible worlds to eliminate from epistemic space, say, trivially impossible worlds that verify obvious logical falsehoods. -/- The central aim of this dissertation is to investigate the nature of such non-trivially impossible worlds and the corresponding epistemic spaces. To flag my conclusions, I argue that successful constructions of epistemic spaces that can safely navigate between the Charybdis of logical omniscience and the Scylla of of “anything goes” are hard, if not impossible to find. (shrink)

The underdetermination of theory by data obtains when, inescapably, evidence is insufficient to allow scientists to decide responsibly between rival theories. One response to would-be underdetermination is to deny that the rival theories are distinct theories at all, insisting instead that they are just different formulations of the same underlying theory; we call this the identical rivals response. An argument adapted from John Norton suggests that the response is presumptively always appropriate, while another from Larry Laudan and Jarrett Leplin suggests (...) that the response is never appropriate. Arguments from Einstein for the special and general theories of relativity may fruitfully be seen as instances of the identical rivals response; since Einstein’s arguments are generally accepted, the response is at least sometimes appropriate. But when is it appropriate? We attempt to steer a middle course between Norton’s view and that of Laudan and Leplin: the identical rivals response is appropriate when there is good reason for adopting a parsimonious ontology. Although in simple cases the identical rivals response need not involve any ontological difference between the theories, in actual scientific cases it typically requires treating apparent posits of the various theories as mere verbal ornaments or computational conveniences. Since these would-be posits are not now detectable, there is no perfectly reliable way to decide whether we should eliminate them or not. As such, there is no rule for deciding whether the identical rivals response is appropriate or not. Nevertheless, there are considerations that suggest for and against the response; we conclude by suggesting two of them. (shrink)

A methodological model of origin and settlement of theory-choice situations (previously tried on the theories of Einstein and Lorentz in electrodynamics) is applied to modern Theory of Gravity. The process of origin and growth of empirically-equivalent relativistic theories of gravitation is theoretically reproduced. It is argued that all of them are proposed within the two rival research programmes – (1) metric (A. Einstein et al.) and (2) nonmetric (H. Poincare et al.). Each programme aims at elimination of the cross-contradiction (...) between the special theory of relativity and Newton’s theory of gravitation. New arguments in favor of Einstein’s programme are given. Nevertheless, this does not imply the necessity to rule out all the nonmetric theories, since Einstein’s and Poincare’s programmes are alternative only as different tools of the cross-contradiction elimination. In the other respects these programmes are complementary: description, explanation and prediction of gravitational experimental data entails the usage of the languages of nonmetric theories as well as of metric ones. The part of the present investigation elucidating the necessity of nonmetric theories is an implementation of the ideas of A.Z. Petrov, the founder of Kazan University Relativity Department. Late Alexei Zinovievich had frequently punctuated that the notion of Riemann space-time continuum common for all metric theories obfuscates all the gravitational notions considerably and hampers the analogies with other physical theories at hand. Since the ambiguity is a hallmark of all the general relativism notions, approach to their definitions “should be determined not by analogies and contingent facts, but by general considerations linked the physical measurements theory… No matter how far the events lie out of the frames of classical physical explanations, all the experimental data should be described by classical notions” (Petrov, 1965,pp. 59,66). Key words: Kip S. Thorne, A.P. Lightman, Stepin, theory of gravity . (shrink)

From my ongoing "Metalogical Plato" project. The aim of the diagram is to make reasonably intuitive how the Socratic elenchos (the logic of refutation applied to candidate formulations of virtues or ruling knowledges) looks and works as a whole structure. This is my starting point in the project, in part because of its great familiarity and arguable claim to being the inauguration of western philosophy; getting this point less wrong would have broad and deep consequences, including for philosophy’s self-understanding. -/- (...) (i.) is the first pass at elenchos in which the Socratic interlocutor does not reflect on knowledge being the crux of the problem. (ii.) is the second, rarer, reflective pass in which they are, making the investigation explicitly about knowledge. Its centrality in the Charmides makes that neglected dialogue of superlative importance. This structure is also the gateway through which the discussion/dialectic crosses into the Agathology (discussion of the form of the good) at Republic 505. -/- The problem of elenchos, then, grasped as a whole structure, is that it seems that knowledge can neither satisfactorily be included in nor excluded from its own scope. The development of the ti esti (“what is ---?”) question leads to the introduction of knowledge into its own scope (i. implicitly, as goodness contrasted with blind rule-following ii. explicitly qua knowledge) while the development of the dual peri tinos (“----about what?) question leads to K’s elimination from its own scope. The introductions are motivated to avoid contradiction, but produce regress; the eliminations are motivated to avoid regress, but produce contradiction. In scholarship, and in the history of philosophy, the ti esti question is universally recognized, to the point of being identified with philosophy’s origin and essence; the peri tinos question is neglected textually and never recognized as the equal dual to the ti esti. This, I claim, has blocked the development of a nontrivial logical appreciation of what Plato's Socrates is up to. (One rather disastrous effect of this neglect is taking Aristotle as the beginning of the development of logic, rather than, correctly, for the beginning of logic’s fatal separation from mathematics and dialectic.) -/- Further, because of this monopticism of the ti esti, the function of consistency in the elenchos has not been understood, even with respect to the ti esti. The ti esti is actually in search of completeness, given a norm of consistency; the peri tinos is in search of consistency, given a norm of completeness. Only appreciating the two questions as dual allows space in the structure to clarify these different orientations relative to consistency. (And, dually, to completeness, whose function in the elenchos is generally entirely missed by scholars and relegated to discussions of eros; it's not out of place there, of course, but its significance is secured here.) Recognizing the duality of the ti esti and peri tinos questions is thus the royal road, in the Socratic-Platonic context, to catching sight of what we post-Cantorians can recognize as the metalogical duality of consistency and completeness. (The salutary disruptive effects of this Plato-Cantor proximity have, of course, been traced in complementary ways by Badiou.) -/- Note that the diagram is supposed to provide a relatively accessible orientation, not to stand on its own, and certainly not to be the last word on any subject. An important qualification (telegraphed in the previous paragraph) is that what elenchos shows is not finally circular or paradoxical, though the problem first presents as such (stubbornly, obdurately, as "difficult" Plato's Socrates always says with characteristic understatement). What is depicted here is meant, at a first pass, to be the shape of that first presentation, the form of the problem of elenchos, rather than of its solution. It's not an accident that this problem strongly resembles "Russell's paradox" (not Russell's not a paradox.) Problem is to solution as RP is to the diagonal theorems. (shrink)

: The Hamblin-Karttunen approach has led to many insights about questions in English. In this article the results of this rule-by-rule tradition are reconsidered from a crosslinguistic perspective. Starting from the type-driven XLS theory developed in Bittner (1994a, b), it is argued that evidence from simple questions (in English, Polish, Lakhota and Warlpiri) leads to certain revisions. The revised XLS theory then immediately generalizes to complex questions — including scope marking (Hindi), questions with quantifiers (English) and multiple wh-questions (English, Hindi, (...) Japanese). Eliminating language- and construction-specific information from the compositional rules, in favor of universal semantic filters, leads to analyses that not only generalize across unrelated languages but are also empirically more accurate, not less. (shrink)

In “Two Dogmas”, Quine indicates that Carnap’s Aufbau fails “in principle” to reduce our knowledge of the external world to sense data. This is because in projecting the sensory material to reconstruct the physical world, Carnap gives up the use of operating rules and switches to a procedure informed by general principles. This procedure falls short of providing an eliminative translation for the connective “is at”, which is necessary for the reduction. In dissecting Quine’s objection, I argue that (...) Quine has at best proven the claim that the use of general principles essentially fails the task of radical reductionism. However, in order to establish the conclusion that the Aufbau fails in principle, Quine needs to further vindicate two other claims. They are: first, a switch from operating rules to general principles is necessary; second, the set of general principles Carnap adopts is the best alternative. By disambiguating the notion of “explicit definition” and examining the concept of definability in the Aufbau, I explore the possibility of justifying these two claims that Quine overlooks in his objection. The result suggests that Quine’s objection stands in tension with his radical reductionist reading of the Aufbau. (shrink)

Mental explanations of behaviour are physical explanations of a special kind. Mental events are physical events. Mental explanations of physical behaviour are not mysterious, they designate events with physical causal powers. Mentalistic terms differ from physicalistic ones in the way they specify events: the former cite extrinsic properties, the latter intrinsic properties. The nature of explanation in general is discussed, and a naturalistic view of intentionality is proposed. The author shows why epistemological considerations rule out the elimination of (...) "mentalistic talk" from explanations of behaviour. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

An examination of the role played by general rules in Hume's positive (nonskeptical) epistemology. General rules for Hume are roughly just general beliefs. The difference between justified and unjustified belief is a matter of the influence of good versus bad general rules, the good general rules being the "extensive" and "constant" ones.

This letter was rejected by International Knowledge Press because "we are unable to conclude that these findings would warrant publication in this journal." The letter is suggesting that dark energy, dark matter and universal expansion are intimately related. However, they aren't viewed as revolutions in cosmology which are essential to a complete understanding of the modern universe. They are instead viewed as properties which need to be added to the cosmos when Einstein's theory of gravity (General Relativity) is apparently (...) still not thoroughly comprehended a little over a century since it was published. (shrink)

Divus Augustus Pater. The cult of divine Augustus under the rule of the Julio-Claudian dynasty -/- Summary The cult of divine Augustus was one of the most important phenomena of ideological nature under the rule of the Julio-Claudian dynasty. The crucial point of its development was the apotheosis conducted on 17 September 14 AD. The new cult was derived greatly from numerous borrowings from the rites of various gods of the Roman Pantheon. As divus, Augustus received a separate priest, a (...) private priestess, and a college of priests. The first flamen Augustalis became Germanicus. The holder of this title enjoyed many privileges. It seems unlikely, however, that flamen Augustalis controlled the entire cult of divine Augustus. This was the role of the emperor as both the supreme priest and the inheritor of political power. Sodales Augustales also had special cult functions. This religious fraternity had a mixed private-state character just like many of the institutions of the early principate. It was a cult college of gens Iulia and, most of all, of Augustus. From its beginning it enjoyed high prestige. The members of this religious fraternity were recruited among the Senate elite and the family of the emperor. Sacerdos divi Augusti occupies a different place in the priesthood established to worship Augustus. This female priesthood, despite its humble cult and political role, is of great interest to scholars. In spite of discerning investigations by researchers, there seem to have been only two priestesses in the Julio-Claudian dynasty – Julia Augusta, the widow of the creator of the principate, and Antonia Augusta. There is even no certainty that the latter had preformed the function at all. Augustus, as a god, was given a separate temple under a Senate decree. However, the construction work went slowly ahead. Therefore, divus Augustus was initially worshipped in other places of worship. At first, it was the temple of Mars Ultor. He was also worshipped in the sacrarium on the Palatine. One encounters certain difficulties when trying to identify the places of Augustus’ worship in Rome. Ultimately, there seem to have been two sacraria in the capital of the Empire. There is no certainty, however, whether yet another temple was located next to the templum novum divi Augusti on the Palatine. In trying to analyse the phenomenon of the divinity of the Roman emperors, and Augustus in particular, it is necessary to refer to the genesis of Emperor worship. Within the framework of official religion it is important to distinguish such elements as genius and numen. Although the consecratio act conducted by the Senate meant the crossing of the boundary between the human Augustus and the divine Augustus, it is important to remember that Augustus had prepared his apotheosis for a long time and already enjoyed divine honours during his lifetime. Certain elements of Augustus worship developed under his rule continued to exist for some time after the death of the creator of the principate. Augustus divinity was guarded by the law of maiestas. At the beginning of the rule of Tiberius it mostly protected divus Augustus himself. Gradually, despite some opposition, the law began to serve the ruling emperor. There is little certainty of how many cases were brought under the crimen laesae maiestatis against those who insulted the divine Augustus. The issue of trials for offending the law of maiestas is accounted for one-sidedly by ancient historians, which complicates the work of contemporary researchers. There is, however, no denying that for Tiberius (Augustus’ successor) the trials on the charge of maiestas turned out to be a trap. The cult of divus Augustus was approved throughout the Empire. Nevertheless, some weaker voices of opposition could be heard. These were present in the Senate circles cherishing the memory of the last defenders of the Republic, as well as among some ethnic and religious communities. The latter included Judaism and emerging Christianity. The political consequences of Augustus’ deification were very serious. He significantly contributed to the ruling of the Julio-Claudian dynasty for over 50 years. The main reason for that was the fact that in the Rome of that time the tradition of power succession was not yet well-grounded. Directly after the principate creator’s death, his consecratio took place – he was assigned priests and many godly honours and a temple was erected in his honour. These actions obviously took place under Augustus’ successor Tiberius who, during his rule, constantly tried to emulate the divine predecessor and referred to his decrees on numerous occasions. Tiberius was the emperor who contributed to the cult of his adoptive father to the greatest extent. However, one cannot fail to notice that his actions were somehow ambiguous. It has to be remembered that, in addition to his sincere respect for the divine Augustus, Tiberius also tried to use the authority of the creator of the principate to strengthen his power. This is exemplified by the motto imprinted on coins: DIVVS AVGVSTVS PATER. Caligula took a different approach to the Augustan cult. When assuming power after Tiberius, he was in a different position. The 20-year rule by Augustus’ successor greatly contributed to the strengthening of the idea of the principate ’s stability in the minds of the Romans. This allowed Caligula to pay less heed to the Senate aristocracy, as well as other institutional elements of the Republic. Under these circumstances, the cult of Augustus underwent modifications. Divus Augustus still remained at the heart of the religious propaganda of the Roman state and gens Iulia, but also other members of the family of the young Emperor received a number of honours drawing them closer to the world of gods. Drusilla, for that matter, was made a diva. By this, the idea of domus Augusta received a new confirmation. Caligula himself did not cease to participate in, and support, the rites performed to worship his divine grandfather. The available sources lead us to believe that Augustus constituted for the young princeps a role model and a character to which he often compared himself with. For Claudius, the use of the cult of divine Augustus was important as a tool to strengthen political power. But due to the fact that his personal links with divus Augustus were rather weak, Claudius focused on the cult of his grandmother Livia, Augustus’ wife. He also emphasised the function of sacerdos divi Augusti which his mother Antonia Augusta was to fulfil. Claudius faced the task of the ‘reconstruction’ of the cult of Augustus which had deteriorated, especially during the second part of Caligula’s rule. Claudius took a different direction in imitating Augustus than his two predecessors. Augustus’ model was very capacious, allowing him to find examples which could be adjusted to fit his own political goals and personality. Claudius avoided the stiffness characteristic of Tiberius and, at the same time, respected Augustus’ traditions which he Caligula inadvertently abused. Claudius’ attitude to Augustus is not quite clear. Undoubtedly he kept alive the memory of the first princeps, however, there is a lack of testimony about the new honours conferred on divine Augustus during the rule of this Emperor. Almost all of them concentrate around the person of Claudius or his family. There are, however, no honours conferred on the creator of the principate. This type of attitude caused the cult of divine Augustus to be eclipsed by the cult of the ruling Emperor. Nero, the last representative of the Julio-Claudian dynasty descended, unlike Claudius, directly from the line of Augustus. The new emperor deified his predecessor by using the model of Augustus’ apotheosis. In the first part of his rule he drew greatly from the Augustus model of exercising power. Nero ’s ideological platform seems to be the richest in comparison with other emperors of the Julio-Claudian dynasty. The tradition of links with divus Augustus was, however, only one of many different elements. With time, the tradition appeared to play a still smaller role. The departure from the Augustus model took place on many levels. Some of the steps were very radical, whereas others were less significant. The most serious was the elimination of the members of gens Iulia and gens Claudia, and those who could prove their kinship with both the houses. The devastation in Nero ’s closest family put an end to the concept of domus Augusta. Formally, the Emperor did not renounce the divine creator of the principate but, in practice, the idea of the new domus Augusta no longer aimed at presenting Augustus’ descendants united in a single family. Nero was now alone and any creation of ideological concepts of power under those circumstances had to be based around him. These actions ended in disaster. By giving up the Augustan model, Nero lost the support of the army and, as a result, lost power. Apart from the worship of the state religion in the capital, divus Augustus was the subject of a provincial and municipal cult. Here, the worship of divine Augustus was often a continuation, sometimes in an extended form, of the honours Augustus had been granted during his lifetime. In the cult of divus Augustus, in the provinces one can observe a mutual interweaving of elements copied from the capital model and local traditions. The beginning of the provincial cult of Augustus dates back to the rule of Tiberius. The crucial point for the establishment of the provincial cult in the West was the request of the citizens of Hispania Tarraconensis to build a temple for divine Augustus. It is important to emphasise here that he was appointed on a local initiative. In the East, the genesis of the provincial cult is related to the functioning of koinon. In comparison with the western regions, the cult here was characterised not only by longer history but also an extensive system of priesthood and rich ritual. The intensity of development of municipal and private cult in the West depended on the level of social and economic development of the regions. It assumed the most complex forms in the provinces with well-developed city life – generally in the eastern provinces. Whereas the cult of divine Augustus in the western municipal provinces was similar in character to the cult of the principate’s creator in Italy. The greatest testimony to the cult’s development comes from relatively strongly romanised and, at the same time, the wealthiest regions which had been part of the Empire for a long time. These included the mainly proconsular Africa, Spain and Narbonese Gaul. The sources coming from these regions constitute not only an illustration of the development of the cult of divine Augustus and members of domus Augusta, but are also a sign of the processes of romanisation of great numbers of city populations. It is necessary to note that outside Rome we do not encounter an isolated cult of divine Augustus. Whenever we deal with information concerning temples or rituals dedicated to the deified creator of the principate, other members of the family are also worshipped. In fact, during the whole rule of the Julio-Claudian dynasty we actually deal with the cult of divine Augustus in close association with the worship of domus Augusta – domus divina. (shrink)

In this paper, I examine Hume’s account of an important class of causal belief which he calls “general rules”. I argue that he understands general rules, like all causal beliefs, as lively ideas which are habitually associated with our impressions or memories. However, I argue, he believes that they are unlike any reflectively produced causal beliefs in that they are produced quickly and automatically, such that they occur independently of any other processes of reasoning. Given this, (...) I argue, Hume appears to understand general rules as relatively simple beliefs, expressible only via generic sentences, like “birds lay eggs”. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires (...) that revised beliefs incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also (...) consider sequential quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

Jobst Langrebe’s and Barry Smith’s book Why Machines Will Never Rule the World argues that artificial general intelligence (AGI) will never be realized. Drawing on theories of complexity they argue that it is not only technically, but mathematically impossible to realize AGI. The book is the result of cooperation between a philosopher and a mathematician. In addition to a thorough treatment of mathematical modelling of complex systems the book addresses many fundamental philosophical questions. The authors show that philosophy is (...) still relevant for questions of information technology in general and artificial intelligence in particular. This paper endorses Landgrebe’s and Smith’s arguments that artificial general intelligence cannot be realized, but not their conclusion that machines will never rule the world. It is not only a question of what technology can do. An equally important question is what technology does to us. Machines may not take over the world in a literal sense, but they may have many negative effects. Some of the most serious can be placed under the category of the “degeneration effect”. (shrink)

Eliminative reasoning is a method that has been employed in many significant episodes in the history of science. It has also been advocated by some philosophers as an important means for justifying well-established scientific theories. Arguments for how eliminative reasoning is able to do so, however, have generally relied on a too narrow conception of evidence, and have therefore tended to lapse into merely heuristic or pragmatic justifications for their conclusions. This paper shows how a broader conception of evidence not (...) only can supply the needed justification but also illuminates the methodological significance of eliminative reasoning in a variety of contexts. (shrink)

In this paper, I argue that the disjunction elimination rule presupposes the principle that a true disjunction contains at least one true disjunct. However, in some contexts such as supervaluationism or quantum logic, we have good reasons to reject this principle. Hence, disjunction elimination is restricted in at least one respect: it is not applicable to disjunctions for which this principle does not hold. The insight that disjunction elimination presupposes the principle that a true disjunction contains at (...) least one true disjunct is applied to two arguments which argue for this very principle. I show that these arguments are rule-circular since they rest on disjunction elimination. I claim that rule-circularity better explains why the arguments fail than the explanations provided by Rumfitt (2015), which, for instance, rely on controversial principles about truth. (shrink)

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution is devoted to the basic issues from Wittgenstein to Kripke. Part II will (...) be about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

Bioethics seems preoccupied with establishing, debating, promoting and sometimes debunking principles. While these tasks trade on the status of the word ‘principle’ in our ordinary language, scant attention is paid to the way principles operate in language. In this paper, we explore how principles relate to rules and practices so as to better understand their logic. We argue that principles gain their sense and power from the practices which give them sense. While general principles can be, and are, (...) establishable in abstraction from specific practices, as they are in principlist bioethics, such principles are impotent as moral guides to action. We show that the purchase any principle has as a moral guide to action emerges from its indexical properties as a principle which has sense in a specific practice. The meaning of any principle is internal to the practice and context in which it is invoked and, therefore, principles are not kinds of master rule which dictate moral judgement in new contexts but rather chameleon-like rules which change with the contexture in which they are invoked. (shrink)

What are rules? In this paper I develop a view of regulative rules which takes them to be a distinctive normative kind occupying a middle ground between orders and normative truths. The paradigmatic cases of regulative rules that I’m interested in are social rules like rules of etiquette and legal rules like traffic rules. On the view I’ll propose, a rule is a general normative content that is in force due to human (...) activity: enactment by an authority or acceptance by a community. Rules are unlike orders in being not necessarily communicative, not an expression’s of the giver’s will, not evaluable for sincerity, and in that they have propositional content. And they’re unlike normative truths in that they’re themselves not even truth-evaluable (though their contents are). This is because rules qua things that are in force are not like constatives which have a mind to world direction of fit, but more like performatives. Furthermore, they differ from normative truths in that their normativity is isolated from their background justification and is therefore not dependent on contributory notions like reasons coming together in a weighing explanation. As such, they occupy a middle ground between orders and normative truths, much like in H. L. A. Hart’s opinion law occupies a middle ground between “coercion” and “morality” (Hart 1961/1994). I also illustrate the virtues of this understanding of rules by showing how proper appreciation of how they differ from normative truths helps us defuse a common objection to Hart’s practice theory of rules. (shrink)

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution was devoted to the basic issues from Wittgenstein to Kripke. Part II is (...) about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

Laws can be evaluated as better or worse relative to different normative standards. But the standard set by the Rule of Law defines a kind-relative standard of evaluation: features like generality, publicity, and non-retroactivity make the law better as law. This fact about legal evaluation invites a comparison between law and other “goodness-fixing kinds,” where a kind is goodness-fixing if what it is to be a member of the kind fixes a standard for evaluating instances as better or worse. Indeed, (...) for any goodness-fixing kind, K, that sets a standard, S, for evaluating Ks as Ks, we can ask: (1) How does the nature of Ks explain S? (2) Does being a K depend on meeting a minimum threshold of S-relative goodness? In the case of law and its kind-relative standard defined by the Rule-of-Law virtues, these questions lack settled answers. Although Raz (1979, 2019) offers some discussion, I argue that his answers have the surprising upshot of rendering law sui generis relative to other goodness-fixing kinds, and that preserving continuity with other such kinds involves revising the general picture. On the revised picture, law construed as a system of rules is subject to kind-relative evaluation because it is (a) a functional artifact, (b) with an essential function of realizing a limited normative ideal, and (c) its being minimally good at that function—that is, its realization of the relevant normative ideal to some degree—is a condition and ground of law’s existence, since all functional artifacts appear to be subject to such threshold conditions. (shrink)

Foundational theories of mental content seek to identify the conditions under which a mental representation expresses, in the mind of a particular thinker, a particular content. Normativists endorse the following general sort of foundational theory of mental content: A mental representation r expresses concept C for agent S just in case S ought to use r in conformity with some particular pattern of use associated with C. In response to Normativist theories of content, Kathrin Glüer-Pagin and Åsa Wikforss propose (...) a dilemma, alleging that Normativism either entails a vicious regress or falls prey to a charge of idleness. In this paper, I respond to this argument. I argue that Normativism can avoid the commitments that generate the regress and does not propose the sort of explanation required to charge that its explanation has been shown to be problematically idle. The regress-generating commitment to be avoided is, roughly, that tokened, contentful mental states are the product of rule-following. The explanatory task Normativists should disavow is that of explaining how it is that beliefs and other contentful mental states are produced. I argue that Normativism, properly understood as a theory of content, does not provide this kind of psychological explanation, and therefore does not entail that such explanations are to be given in terms of rule-following. If this is correct, Normativism is not the proper target of the dilemma offered by Glüer-Pagin and Wikforss. Understanding why one might construe Normativism in the way Glüer-Pagin and Wikforss must, and how, properly understood, it avoids their dilemma, can help us to appreciate the attractiveness of a genuinely normative theory of content and the importance of paying careful attention to the sort of normativity involved in norm-based theories of content. (shrink)

In Tulving’s initial characterization, episodic memory was one of multiple memory systems. It was postulated, in pursuit of explanatory depth, as displaying proprietary operations, representations, and substrates such as to explain a range of cognitive, behavioural, and experiential phenomena. Yet the subsequent development of this research program has, paradoxically, introduced surprising doubts about the nature, and indeed existence, of episodic memory. On dominant versions of the ‘common system’ view, on which a single simulation system underlies both remembering and imagining, there (...) are no processes unique to memory to support robust generalizations with inductive potential. Eliminativism about episodic memory seems to follow from the claim that it has no dedicated neurocognitive system of its own. After identifying this under-noticed threat, we push back against modern eliminativists by surveying recent evidence that still indicates specialized mechanisms, computations, and representations that are distinctly mnemic in character. We argue that contemporary realists about episodic memory can retain lessons of the common system approach while resisting the further move to eliminativism. (shrink)

In her seminal article ‘Modern Moral Philosophy’ (1958) Elizabeth Anscombe argued that we need a new ethics, one that uses virtue terms to generate absolute prohibitions against certain act-types. Leading contemporary virtue ethicists have not taken up Anscombe's challenge in justifying absolute prohibitions and have generally downplayed the role of rule-following in their normative theories. That they have not done so is primarily because contemporary virtue ethicists have focused on what is sufficient for characterizing the deliberation and action of the (...) fully virtuous person, and rule-following is inadequate for this task. In this article, I take up Anscombe's challenge by showing that rule-following is necessary for virtuous agency, and that virtue ethics can justify absolute prohibitions. First, I offer a possibility proof by showing how virtue ethics can generate absolute prohibitions in three ways: by considering actions that directly manifest vice or that cannot be performed virtuously; actions that are prohibited by one's institutional roles and practical identities; and actions that are prohibited by the prescriptions of the wise. I then seek to show why virtue ethicists should incorporate rule-following and absolute prohibitions into their theories. I emphasize the central role that rules have in the development of virtue, then motivate the stronger view that fully virtuous agents follow moral rules by considering the importance of hope, uncertainty about consequences, and taking responsibility for what eventuates. Finally, I provide an account of what Anscombe called a ‘corrupt mind’, explaining how our understanding of virtue is corrupted if we think that virtue may require us to do vicious actions. (shrink)

Proponents of the rule of law argue about whether that ideal should be conceived formalistically or in terms of substantive values. Formalistically, the rule of law is associated with principles like generality, clarity, prospectivity, consistency, etc. Substantively, it is associated with market values, with constitutional rights, and with freedom and human dignity. In this paper, I argue for a third layer of complexity: the procedural aspect of the rule of law; the aspects of rule-of-law requirements that have to do with (...) "natural Justice" or "procedural due process." These I believe have been neglected in the jurisprudential literature devoted specifically to the idea of the rule of law and they deserve much greater emphasis. Moreover procedural values go beyond elementary principles like the guarantee of an unbiased tribunal or the opportunity to present and confront evidence. They include the right to argue in a court about what the law is and what its bearing should be on one's situation. The provision that law makes for argument is necessarily unsettling, and so this emphasis on the procedural aspect highlights the point predictability should not be regarded as the be-all and end-all of the rule of law. (shrink)

The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable proof-theoretic properties. We start by showing that, due to a strong form of invertibility of the truth rules, cut is eliminable in the systems via a standard strategy supplemented by a suitable measure of the number of applications of truth rules to formulas in derivations. (...) Next, we notice that cut remains eliminable when suitable arithmetical axioms are added to the system. Finally, we establish a direct link between cut-free derivability in infinitary formulations of the systems considered and fixed-point semantics. Noticeably, unlike what happens with other background logics, such links are established without imposing any restriction to the premisses of the truth rules. (shrink)

There is a fundamental disagreement about which norm regulates assertion. Proponents of factive accounts argue that only true propositions are assertable, whereas proponents of non-factive accounts insist that at least some false propositions are. Puzzlingly, both views are supported by equally plausible (but apparently incompatible) linguistic data. This paper delineates an alternative solution: to understand truth as the aim of assertion, and pair this view with a non-factive rule. The resulting account is able to explain all the relevant linguistic data, (...) and finds independent support from general considerations about the differences between rules and aims. (shrink)

Traditional rule consequentialism faces a problem sometimes called the ideal world objection—the worry that by looking only at the consequences in worlds where rules are universally adhered to, the theory fails to account for problems that arise because adherence to rules in the real world is inevitably imperfect. In response, recent theorists have defended sophisticated versions of rule consequentialism which are sensitive to the consequences in worlds with less utopian levels of adherence. In this paper, I argue that (...) these attempts underestimate the problem they are designed to avoid—the worry about ideal worlds is only one manifestation of a deeper and more general problem, the distant world objection, which threatens not only the sophisticated revisions of rule consequentialism, but any view which determines what we ought to do by evaluating worlds that differ from ours in more than what is up to us. (shrink)

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...) we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction Cn+1 of n + 1 conditional events to the family {Cn,En+1|Hn+1}. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid. (shrink)

In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system (...) treating apparent terms for numbers using these definitions. (shrink)

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (to (...) replace the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of (...) Dummett and his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

Islamic legal maxims (qawāʿʿid fiqhiyyah) provide necessary basis for extracting legal injunctions on the unprecedented cases (fiqh al-nawāzil) and make it possible for the jurists to forego the need of memorizing copious fiqh treatises. In light of this fact, this article attempts to design a framework for harm elimination, utilizing the related legal maxims, which will be arguably of great use in developing an outlook that enables a person to tackle the many challenges he or she finds in the (...) course of removal of harm. After explaining the concept and definition of Islamic legal maxims in general, this research surveys in detail the universal legal maxim “harm must be eliminated”, covering its role and significance in the theories of fiqh and its scope and application in contemporary issues. Employing descriptive, analytical and critical methods, this study categorizes the legal maxims related to the harm elimination into three: (1) maxims related to prevention of harm before its occurrence, (2) maxims related to elimination of harm after it has taken place and (3) maxims related to minimization of harm if complete removal is impractical. Likewise, this research analyses the sub-maxims of harm elimination, discussing their legal bases, various purposes for which they operate, related uṣūlī principles and legal examples, providing at the end a flowchart that represents a sequence of five steps useful in the course of removal of harm. (shrink)

This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section presents the traditional discussion of metaphysical underdetermination regarding the individuality and non-individuality of quantum particles. Section discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism about objects. Section wraps it all up with metametaphysical considerations regarding the epistemology of metaphysics of science.