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 and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...) the model-theoretic concepts, based on those in [7], that guide the rest of this paper. Section 3 presents Natural Deduction systems IK and CK, formalizations of intuitionistic and classical one-step versions of K. In these systems, occurrences of step-markers allow deductions to display deductive structure that is covered over in familiar “no step” proof-theoretic systems for such logics. Box and Diamond are governed by Introduction and Elimination rules; the familiar K rule and Necessitation are derived (i.e. admissible) rules. CK will be the result of adding the 0-version of the Rule of Excluded Middle to the rules which generate IK. Note: IK is the result of merely dropping that rule from those generating CK, without addition of further rules or axioms (as was needed in [7]). These proof-theoretic systems yield intuitionistic and classical consequence relations by the obvious definition. Section 4 provides some examples of what can be deduced in IK. Section 5 defines some proof-theoretic concepts that are used in Section 6 to prove the soundness of the consequence relation for IK (relative to the class of models defined in Section 2.) Section 7 proves its completeness (relative to that class). Section 8 extends these results to the consequence relation for CK. (Looking ahead: Part 2 will investigate one-step proof-theoretic systems formalizing intuitionistic and classical one-step versions of some familiar logics stronger than K.). (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)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is (...) a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

I argue for the thesis (UL) that there are certain logical abilities that any rational creature must have. Opposition to UL comes from naturalized epistemologists who hold that it is a purely empirical question which logical abilities a rational creature has. I provide arguments that any creatures meeting certain conditions—plausible necessary conditions on rationality—must have certain specific logical concepts and be able to use them in certain specific ways. For example, I argue that any creature able to grasp theories must (...) have a concept of conjunction subject to the usual introduction and elimination rules. I also deal with disjunction, conditionality and negation. Finally, I put UL to work in showing how it could be used to define a notion of logical obviousness that would be well suited to certain contexts—e.g. radical translation and epistemic logic—in which a concept of obviousness is often invoked. (shrink)

In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, (...) known as reduction and expansion . We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules. (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)

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the (...) existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition. (shrink)

This short paper has two loosely connected parts. In the first part, I discuss the difference between classical and intuitionist logic in relation to different the role of hypotheses play in each logic. Harmony is normally understood as a relation between two ways of manipulating formulas in systems of natural deduction: their introduction and elimination. I argue, however, that there is at least a third way of manipulating formulas, namely the discharge of assumption, and that the difference between (...) classical and intuitionist logic can be characterised as a difference of the conditions under which discharge is allowed. Harmony, as ordinarily understood, has nothing to say about discharge. This raises the question whether the notion of harmony can be suitably extended. This requires there to be a suitable fourth way of manipulating formulas that discharge can stand in harmony to. The question is whether there is such a notion: what might it be that stands to discharge of formulas as introduction stands to elimination? One that immediately comes to mind is the making of assumptions. I leave it as an open question for further research whether the notion of harmony can be fruitfully extended in the way suggested here. In the second part, I discuss bilateralism, which proposes a wholesale revision of what it is that is assumed and manipulated by rules of inference in deductions: rules apply to speech acts – assertions and denials – rather than propositions. I point out two problems for bilateralism. First, bilaterlists cannot, contrary to what they claim to be able to do, draw a distinction between the truth and assertibility of a proposition. Secondly, it is not clear what it means to assume an expression such as '+ A' that is supposed to stand for an assertion. Worse than that, it is plausible that making an assumption is a particular speech act, as argued by Dummett (Frege: Philosophy of Language, p.309ff). Bilaterlists accept that speech acts cannot be embedded in other speech acts. But then it is meaningless to assume + A or − A. (shrink)

The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: (...) non- factive grounding claims, if true, are zero-grounded in the sense of Fine. (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)

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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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)

In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made to (...) axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system. (shrink)

This is a short introduction to a book symposium on Paul Gowder's recent book, _The Rule of Law in thee Real World_ (Cambridge University Press, 2016). The book symposium will appear in the St. Luis University Law Journal, 62 St. Louis U. L.J., -- (2018), with commentaries on Gowder's book by colleen Murphy, Robin West, Chad Flanders, and Matthew Lister, along with replies by Paul Gowder.

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (...) (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that (...) are parameterized with formal grammars, and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.

This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, (...) and rejective elimination rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguish it from Francez's. (shrink)

Lewis Carroll’s 1895 paper “Achilles and the Tortoise” showed that we need a distinction between rules of inference and premises. We cannot, on pain of regress, treat all rules simply as further premises in an argument. But Carroll’s paper doesn’t say very much about what rules there must be. Indeed, it is consistent with what Carroll says there to think that the only rule is -elimination. You might think that modern Bayesians, who seem to think that (...) the only rule of inference they need is conditionalisation, have taken just this lesson from Carroll. But obviously nothing in Carroll’s argument rules out there being other rules as well. (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, 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.

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism (...) links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)

In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction rules \, what are the strongest elimination (...) rules that are validated by an assertability conditional meaning-theory based on \? I prove that the intuitionistic introduction rules are the strongest rules that are validated by the intuitionistic elimination rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discussion revolves around the problem of iterated grounding-claims. Suppose that \ grounds \; what grounds that \ grounds that \? I argue that unless we can get a satisfactory answer to this question the notion of grounding will be useless. I discuss and reject some proposed accounts of iterated grounding claims. I then develop a new way of expressing grounding, propose an account of iterated grounding-claims and show how we can develop logics for grounding. In “Is the Vagueness Argument Valid?” I argue that the Vagueness Argument in favor of unrestricted composition isn’t valid. However, if the premisses of the argument are true and the conclusion false, mereological facts fail to supervene on non-mereological facts. I argue that this failure of supervenience is an artifact of the interplay between the necessity and determinacy operators and that it does not mean that mereological facts fail to depend on non-mereological facts. I sketch a deflationary view of ontology to establish this. (shrink)

“Critical thinking is one of the biggest hiatuses in our education system. Learning to distinguish sense from nonsense is of great importance in the information age that we live in. In a systematic way, this book helps you to gain insight into, and subsequently eliminate, the most important reasoning errors that we all tend to make. It also helps you to debunk weak and fallacious arguments and unreliable information. -/- In addition to understanding what critical and scientific thinking entails, you (...) will learn more about what makes science reliable. In times of skepticism regarding science, where (sometimes dangerous) pseudoscientific and conspiracy theories run rampant, this is particularly important. -/- Critical thinking is not a matter of intellectual preference or even self-interest (although one certainly benefits from thinking critically). It is first and foremost a matter of moral and social responsibility. Better thinking leads to a better world. With this book I hope to contribute to that important goal and you, dear student or reader, can do the same!” - Michael Vlerick -/- . (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)

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)

Article Authors Metrics Comments Media Coverage Abstract Author Summary Introduction Results Discussion Supporting information Acknowledgments Author Contributions References Reader Comments (0) Media Coverage (0) Figures Abstract During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked (...) to predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them. (shrink)

This is an introduction to an edited volume of critical reactions to Derek Parfit's book On What Matters. It outlines Parfit's key ideas on reasons and rationality, his revisionary interpretations of Kantian ethics, his versions of Kantian Contractualism and Rule Consequentialism, and his master argument that attempts to show how the best versions of these ethical theories converge. The introduction also intoruces the essays of the volume.

In their Introduction to Logic, Copi and Cohen suggest that students construct a formal proof by "working backwards from the conclusion by looking for some statement or statements from which it can be deduced and then trying to deduce those intermediate statements from the premises. What follows is an elaboration of this suggestion. I describe an almost mechanical procedure for determining from which statement(s) the conclusion can be deduced and the rules by which the required inferences can be (...) made. This method is designed to forestall the quandary in which many beginners find themselves: not knowing how to get started. (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)

The first thing we must keep in mind is that when saying that China says this or China does that, we are not speaking of the Chinese people, but of the Sociopaths who control the CCP -- Chinese Communist Party, i.e., the Seven Senile Sociopathic Serial Killers (SSSSK) of the Standing Committee of the CCP or the 25 members of the Politburo etc.. -/- The CCP’s plans for WW3 and total domination are laid out quite clearly in Chinese govt publications (...) and speeches and this is Xi Jinping’s “China Dream”. It is a dream only for the tiny minority (perhaps a few dozen to a few hundred) who rule China and a nightmare for everyone else (including 1.4 billion Chinese). The 10 billion dollars yearly enables them or their puppets to own or control newspapers, magazines, TV and radio channels and place fake news in most major media everywhere every day. In addition, they have an army (maybe millions of people) who troll all the media placing more propaganda and drowning out legitimate commentary (the 50 cent army). -/- In addition to stripping the 3rd world of resources, a major thrust of the multi-trillion dollar Belt and Road Initiative is building military bases worldwide. They are forcing the free world into a massive high-tech arms race that makes the cold war with the Soviet Union look like a picnic. -/- Though the SSSSK, and the rest of the world’s military, are spending huge sums on advanced hardware, it is highly likely that WW3 (or the smaller engagements leading up to it) will be software dominated. It is not out of the question that the SSSSK, with probably more hackers (coders) working for them then all the rest of the world combined, will win future wars with minimal physical conflict, just by paralyzing their enemies via the net. No satellites, no phones, no communications, no financial transactions, no power grid, no internet, no advanced weapons, no vehicles, trains, ships or planes. -/- There are only two main paths to removing the CCP, freeing 1.4 billion Chinese prisoners, and ending the lunatic march to WW3. The peaceful one is to launch an all-out trade war to devastate the Chinese economy until the military gets fed up and boots out the CCP. -/- An alternative to shutting down China’s economy is a limited war, such as a targeted strike by say 50 thermobaric drones on the 20th Congress of the CCP, when all the top members are in one place, but that won’t take place until 2022 so one could hit the annual plenary meeting. The Chinese would be informed, as the attack happened, that they must lay down their arms and prepare to hold a democratic election or be nuked into the stone age. The other alternative is an all-out nuclear attack. Military confrontation is unavoidable given the CCP’s present course. It will likely happen over the islands in the South China Sea or Taiwan within a few decades, but as they establish military bases worldwide it could happen anywhere (see Crouching Tiger etc.). Future conflicts will have hardkill and softkill aspects with the stated objectives of the CCP to emphasize cyberwar by hacking and paralyzing control systems of all military and industrial communications, equipment, power plants, satellites, internet, banks, and any device or vehicle connected to the net. The SS are slowly fielding a worldwide array of manned and autonomous surface and underwater subs or drones capable of launching conventional or nuclear weapons that may lie dormant awaiting a signal from China or even looking for the signature of US ships or planes. While destroying our satellites, thus eliminating communication between the USA and our forces worldwide, they will use theirs, in conjunction with drones to target and destroy our currently superior naval forces. Of course, all of this is increasingly done automatically by AI. -/- By far the biggest ally of the CCP is the Democratic party of the USA. -/- The choice is to stop the CCP now or watch as they extend the Chinese prison over the whole world. -/- Of course, universal surveillance and digitizing of our lives is inevitable everywhere. Anyone who does not think so is profoundly out of touch. -/- Of course, it is the optimists who expect the Chinese sociopaths to rule the world while the pessimists (who view themselves as realists) expect AI sociopathy (or AS as I call it – i.e., Artificial Stupidity or Artificial Sociopathy) to take over, perhaps by 2030. -/- Those interested in further details on the lunatic path of modern society may consult my other works such as Suicide by Democracy-an Obituary for America and the World 4th Edition 2019 and Suicidal Utopian Delusions in the 21st Century: Philosophy, Human Nature and the Collapse of Civilization 5th ed (2019) . (shrink)

The legal progression in China is portrayed negatively by western scholars who often argue that the state institutions in China are subordinate to the control of Chinese Communist Party’s leadership which makes these institutions politically insignificant. We consider that the legal progression in China has an instrumental role in achieving “Harmonious Socialist Society.” The purpose of this thesis is to provide an analytical literature review of scholastic work to explain the legality of rule of law in China and to elaborate (...) the outcomes of China’s recent legal developments. This paper has two main subjects. First, it examines the nature of law and rule of law in China through the prism of different legal theories. Secondly, by arguing from different political theories, it explains the necessity of customized legal system in China for establishing a Harmonious Socialist Society. By giving different examples from contemporary China, this thesis argues that the legality of the rule of law in China ought to be understood in the context of China’s economic and social progression rather than the western legal scholarship. China’s economic progress demands a customized legal system. In our thesis, we claim that the regular upgradation of laws and introduction of constitutional amendments in China, should be recognized as important achievement which is required for the institutional innovation. Legal progression in China during last decade perfectly fit into the framework of “Socialism with Chinese Characteristics” and is very crucial for building a harmonious socialist society. It is vivid from China’s economic growth and developed international relations. Finally, this paper suggests that the Chinese legal progression can be taken as successful example of legal experimentalism. (shrink)

If a theory addressing problems that are global in scope aims to be convincing outside its own tradition, it should be robust-enough to deal with the simple observation that, around the world, there are multiple systems of norms, rules and institutionalized normative orders.

Conceptual therapy seeks to eliminate from our vocabulary of concepts those that are conceptually pathological. The very use of such concepts—which is much of the time—brings about dysfunctional thinking: thought, that is to say, that leads us astray, paving the way for beliefs and claims to knowledge that are fundamentally nonsensical. A therapy for such concepts may be likened to holding a selective sieve and pouring the ideas with which we attempt to make sense of the world through it, allowing (...) the sieve to filter out those that would otherwise infect our thinking with meaninglessness. -/- Conceptual Therapy: An Introduction to Framework-relative Epistemology was written by the author as an introductory text for university classes in applied skills in epistemological analysis. (shrink)

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and (...) allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

ABSTRACT The individual-community relationship has always been one of the most fundamental topics of social sciences. In sociology, this is known as the micro-macro relationship while in economics it refers to the processes, through which, individual actions lead to macroeconomic phenomena. Based on philosophical discourse and systems theory, many sociologists even use the term "emergence" in their understanding of micro-macro relationship, which refers to collective phenomena that are created by the cooperation of individuals, but cannot be reduced to individual actions. (...) "Emergence" theories attempt to explain the nature of society as a complex system by examining how individuals and their relationships lead to the creation of integrated and macro-social phenomena such as markets, educational systems, cultural beliefs, and shared social practices. As a prelude to activity, every researcher has to answer the question from the methodological point of view, how is it possible to study the behavior of social groups and how can we gain knowledge about the laws related to social groups? Anyone who deals with humanities and social sciences or any reality and phenomenon that affects human beings, inevitably deals with the reality that is emerging. In fact, emergence occurs when one level of reality emerges radically from another level. Examples of emergent levels of reality include how the mind emerges from the body; or the way society emerges from human beings. Therefore, when there is an emerging factor, different scientific disciplines should be used, because it is inevitable to talk about social affairs, psychology and neurobiology, as well as physical and even chemical. -/- INTRODUCTION Since its beginning in the 19th century, sociology has faced the fundamental question of what a social phenomena stands for? At a glance, sociologists deal with the study of social groups, collective behavior, institutions, social structures, social networks, and social dynamics, and ultimately all such phenomena are composed of individuals. Therefore, social phenomena seem to have no independent ontological status, and in this case, sociology is ultimately about reducible individuals. Different approaches about the micro-macro relationship, using the concept of "emergence", argue that although collective phenomena are created by individuals, they cannot be reduced to individual action. The term "emergence" is used to distinguish "emergent results" from " Procedural results". Results are called Procedural that can only be calculated by adding or subtracting the causes that act together. On the contrary, they are emergent outcomes that are qualitatively novel compared to the causes from which they originate. An example of such emergent results is mental characteristics that emerge from neural processes, but are not considered among the characteristics of neural processes of components - which are their origin. Philosophical debates about emergentism and reductionism focus on the mind-brain relationship, but as many philosophers have noted, they can be generalized to apply to any hierarchical set of features. The cognitive revolution reactivated a 19th century controversy between theorists of Identity and dualism. The theorists of Identity believe in reductionist materialism and elimination of metaphysics, according to which the mind is nothing more than the biological, while the dualists believe that the mind and the brain are distinct from each other. Emergence has been considered as a third way between the theories of Identity and dualism. -/- METHODOLOGY Interdisciplinarity Is fundamentally indicated by the dominance of open systems as well as social and emerging systems at different levels. Therefore, as long as we are facing a new emergentism, there will necessarily be different fields and an interdisciplinary method. The commonality of social sciences and cognitive sciences on the issue of emergence provides the possibility of interaction and exchange of concepts between these two for deeper research. Therefore, in this research, apart from the concepts of Subvenience and downward causation, we have used multiple realization and wildly disjunctive, which are used to explain the emerging concept in cognitive sciences, including neurobiology, psychology, and philosophy. For analytical and interdisciplinary approaches, after examining the concepts of subvenience, and wildly disjunctive, Individualistic and collectivist emergentism have been reviewed. And then their adequacy is criticized and evaluated in meeting strong emergence conditions. -/- FINDINGS Philosophers of the mind have been able to define the conditions of irreducibility and downward causation, which are essential for strong emergence, by using the principle of subvenience with the help of multiple realization and wildly disjunctive principles. Therefore, by definition, emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and emergentist collectivism faces the challenge of reification. The analysis of the challenges facing the two methodological approaches of individualism and collectivism leads us to three unresolved issues about the emerging phenomenon, which are realism, downward causality, and mechanism. Despite the differences in the stances of these two approaches regarding the aforementioned triple problems, individualists and collectivists both agree that some social characteristics are reducible; and some others are irreducible due to their complexity, the determination of which, depends on the case study of the mechanism of emergence of each social characteristic. -/- CONCLUSION An emergence that is consistent with reductionism is called a weak emergence. And strong emergence includes the principle of irreducibility and downward causality. According to strong emergence, the characteristics of social phenomena have downward causal power, which cannot be reduced to the causal forces. The principle of subvenience, together with multiple realization and wildly disjunctive, can provide the conditions of irreducibility and downward causality, which are essential conditions of strong emergence. Based on the philosophical analysis of two methodological approaches, individualist and collectivist, it can be concluded that emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and reification collectivism faces the challenge of reification. The analysis of the problems faced by these two approaches leads us to three unresolved issues, which are realism, downward causality, and mechanism. individualist emergentists acknowledge the existence of emergent social characteristics, but despite this, they believe that these characteristics are not real but merely analytical constructs that require explanation based on individuals and their mutual actions. But collectivists argue that emergentism yields a categorical ontology and supports social realism. They accept the dependence of social characteristics on individuals, but claim that social entities and structures are ontologically independent. Individualists and collectivists both agree that some social characteristics are reducible; and others are irreducible due to their complexity; and the only way to recognize this is to engage in empirical studies of the mechanisms and temporal processes of "emergence" that create social characteristics. -/- NOVELTY The newness of this compact article is as follows: a) Presenting an interdisciplinary approach using the analysis of philosophy of cognitive sciences, including the philosophy of mind, neurobiology and psychology to formulate the issue of social emergence; b) Criticizing individualist and collectivist methodological approaches to the issue of social emergence and explaining the sufficiency and shortcomings of both in providing weak and strong emerging conditions; c) Explaining and categorizing the challenges facing methodological approaches in explaining the phenomenon of social emergence, in three categories: realism, downward causality, and mechanism. BIBLIOGRAPHY Beckermann, A., Flohr, H., & Kim, J. (eds.) (1992). Emergence or reduction? Essays on the prospects of nonreductive physicalism. Berlin: Walter de Gruyter. Bhaskar, R. (1979). The possibility of Naturalism. New York: Routledge. Bhaskar, R., Danermark, B. & Price, L. (2018). Interdisciplinarity and wellbeing: A critical realist general theory of interdisciplinarity. London and New York: Routledge. Blau, P.M. (1981). Introduction: diverse views of social structure and their common denominator. In Blau, P.M. & Merton, R.K. (eds.), Continuity in Structural Inquiry (pp. 1–23). Beverly Hills: Sage. Blau, P.M. (1987). Microprocess and macrostructure. In K.S. Cook (ed.), Social Exchange Theory (pp. 83–100). Newbury Park, CA: Sage. Brooks, R.A., & Maes, P. (eds). (1994). Artificial life IV; proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems. Cambridge, Mass: MIT Press. Clark, A. (1997). Being there: Putting brain, body, and world together again. Cambridge, Mass.: MIT Press. Coleman, J. S. (1987). Microfoundations and macrosocial behavior. In: J. C. Alexander, B. Giesen, R. Munch, & Neil J. Smelser (Eds.). The Micro-Macro Link (pp. 153–73). Berkeley: University of California. Coleman, J. S. (1990). Foundations of social theory. Cambridge, MA: Harvard University Press. Elster, J. (1985). Making sense of Marx. New York: Cambridge University Press. Fodor, J.A. (1974). Special sciences (Or: The disunity of science as a working hypothesis). Synthese, 28(2), 97–115. Fodor, J.A. (1989). Making mind matter more. Philosophical Topics, 17, 59-79. Giddens, A. (1984). The constitution of society: Outline of the theory of structuration. Berkeley: University of California Press. Hempel, C.G. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press. Horgan, T. (1993). From supervenience to superdupervenience: meeting the demands of a material world. Mind, 102, 555-586. Humphreys, P. (1997). How properties emerge”. Philosophy of Science, 64, 1-17. Kim, J. (1999). Making sense of emergence. Philosophical Studies, 95, 3–36. Kincaid, H. (1997). Individualism and the unity of science. New York: Rowman & Littlefield. Lewis, D.K. (1986). The plurality of worlds. Oxford: Oxford University Press. Nigel, G., & Conte, R. (eds.) (1995). Artificial societies; The computer simulation of social life. London: UCL Press. O’Connor, T. (1994). Emergent properties. American Philosophical Quarterly, 31, 91-104. Popper, K.R. (1968). Conjectures and refutations: The Growth of Scientific Knowledge. New York: Harper & Row. Sawyer, R. K. (2001). Emergence in sociology: contemporary philosophy of mind and some implications for sociological theory. American Journal of Sociology, 107, 551-585. Sawyer, R. K. (2004). The mechanisms of emergence. Philosophy of the Social Sciences, 34, 260–282. Sawyer, R. K. (2005). Social emergence: societies as complex systems. Cambridge: Cambridge University Press. Sawyer, R.K. (2003). Nonreductive individualism: Part 2, Social causation. Philosophy of the Social Sciences, 33, 203–224. Winch, P. (1993). The idea of a social science and its relation to philosophy‭ (SAMT, Trans.). Tehran, Iran: SAMT. (shrink)

My goal is to illuminate truth-making by way of illuminating the relation of making. My strategy is not to ask what making is, in the hope of a metaphysical theory about is nature. It's rather to look first to the language of making. The metaphor behind making refers to agency. It would be absurd to suggest that claims about making are claims about agency. It is not absurd, however, to propose that the concept of making somehow emerges from some feature (...) to do with agency. That's the contention to be explore in this paper. The way to do this is through expressivism,. Truth-making claims, and making-claims generfally, are claims in which we express mental states linked to our maipulation of concepts, like truth. In particular, they express disposition to undertake derivations using inference rules, in which introduction rules have a specific role. I then show how this theory explains our intuitions about truth's asymmetric dependence on being. (shrink)

Kant's notion of ‘discipline’ has received considerable attention from scholars of his philosophy of education, but its role in his theoretical philosophy has been largely ignored. This omission is surprising since his discussion of discipline in the first Critique is not only more extensive and expansive in scope than his other discussions but also predates them. The goal of this essay is to provide a comprehensive reading of the Discipline that emphasizes its systematic importance in the first Critique. I argue (...) that its goal is to establish a set of rules for the use of pure reason that, if followed, will mitigate and perhaps even eliminate our tendency to make judgments about supersensible objects. Since Kant's justification for these rules relies crucially on claims he has defended in the Doctrine of Elements, I argue further that, far from being a dispensable part of the Critique as commentators have tended to claim, the Discipline is, in fact, the culmination of Kant's critique of metaphysics. (shrink)

Learning from Arguments advances accessible versions of key philosophical arguments, in a form that students can emulate in their own writing, and with the primary aim of cultivating an understanding of the dynamics of philosophical argumentation. -/- The book contains ten core chapters, covering the problem of evil, Pascal’s wager, personal identity, the irrationality of fearing death, free will and determinism, Cartesian skepticism, the problem of induction, the problem of political authority, the violinist argument, the future-like-ours argument, the ethics of (...) eating meat, utilitarianism (both act and rule), and the trolley problem. Additionally, there is an introductory chapter explaining what arguments are and surveying some common argumentative strategies, an appendix on logic explaining the mechanics and varieties of valid arguments, and an appendix providing detailed advice for writing philosophy papers. -/- Each of the ten core chapters offers a sustained argument for some controversial thesis, specifically written for an audience of beginners. The aim is to introduce newcomers to the dynamics of philosophical argumentation, using some of the arguments standardly covered in an introductory philosophy course, but without the additional hurdles one encounters when reading the primary sources of the arguments: challenging writing, specialized jargon, and references to unfamiliar books, philosophers, or schools of thought. (shrink)

In the introduction I argue that the basic element (or primitive) for constructing the physical universe is "displacement from a prior level", and the basic structure is "a sequence of such displacements" (summarized as postulates 1 and 2). The displacements are then defined as one-dimensional objects with a direction (postulate 3). The relations between these displacements are stated in postulate 4. In section 2 we discuss basic consequences of the postulates, and in section 3 we use the postulates to (...) derive a (3+1)-dimensional structure, interpreted as ordinary space and time. We then derive further properties of space --- isotropy, homogeneity, and a rapid early expansion (i.e. inflation). Time, comporting with experience, is shown to be a one-dimensional stream --- with a direction. In section 4 we associate energy with the displacements, and find that the same factors that construct ordinary space (and make it isotropic and homogeneous) also smear the locations of entities/particles across that space --- thereby providing a mechanism/explanation for that iconic and enigmatic aspect of quantum mechanics. We also determine that there must be a continual, uniformly-distributed stream of (non-zero-point) energy coming into the system that constructs new space (i.e. dark energy). The streaming natures of both time and dark energy are shown to have the same basic cause: the processes that input dark energy into the system, and that construct time, are themselves independent of time --- and so they are continual processes. Further consequences follow from the model, including an explanation for why the presence of energy affects space and time, and why quantum vacuum energy is an exception to this rule (i.e. does not gravitate) --- thereby eliminating the cosmological constant problem. A key benefit of the model is that it liberates us from always having to think about the construction of the universe in terms of spatio-temporal relations and evolution (e.g. the big bang model), which is problematic because presumably (and as we will indeed see) space and time are products of the fundamental construction process, not things that govern it. (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 COVID-19 pandemic demonstrated the benefits of international data sharing. Data sharing enabled the health care policy makers to make decisions based on real-time data, it enabled the tracking of the virus, and importantly it enabled the development of vaccines that were crucial to mitigating the impact of the virus. This data sharing is not the norm as data sharing needs to navigate complex ethical and legal rules, and in particular, the fragmented application of the General Data Protection Regulation (...) (GDPR). The introduction of the draft regulation for a European Health Data Space (EHDS) in May 2022 seeks to address some of these legal issues. If passed, it will create an obligation to share electronic health data for certain secondary purposes. While there is a clear need to address the legal complexities involved with data sharing, it is critical that any proposed reforms are in line with ethical principles and the expectations of the data subjects. In this paper we offer a critique of the EHDS and offer some recommendations for this evolving regulatory space. (shrink)

This article proposes a new interpretation of mutual information. We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the problem of (...) measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. _1_ Introduction _2_ Formal Analyses of the Three Interpretations _2.1_ Reduction in doubt _2.2_ Reduction in uncertainty _2.3_ Divergence _3_ Inconsistency with Epistemic Value of Information _4_ Problem of Measure Sensitivity _5_ Reduction in Expected Inaccuracy _6_ Resolution of the Problem of Measure Sensitivity _6.1_ Alternative measures of inaccuracy _6.2_ Resolution by strict propriety _6.3_ Range of applications _7_ Global Scoring Rules _8_ Conclusion. (shrink)

Matthew Adler's Measuring Social Welfare is an introduction to the social welfare function (SWF) methodology. This essay questions some ideas at the core of the SWF methodology having to do with the relation between the SWF and the measure of well-being. The facts about individual well-being do not single out a particular scale on which well-being must be measured. As with physical quantities, there are multiple scales that can be used to represent the same information about well-being; no one (...) scale is special. Like physical laws, the SWF and its ranking of distributions cannot depend on exactly which of these scales we use. Adler and other theorists in the SWF tradition have used this idea to derive highly restrictive constraints on the shape of the SWF. These constraints rule out seemingly plausible views about distributive justice and population ethics. I argue, however, that these constraints stem from a simple but instructive mistake. The SWF should not be applied to vectors of numbers such as 1 and 2, but rather to vectors of dimensioned quantities such as 1 util and 2 utils. This seemingly pedantic suggestion turns out to have far-reaching consequences. Unlike the orthodox SWF approach, treating welfare levels as dimensioned quantities lets us distinguish between real changes in well-being and mere changes in the unit of measurement. It does this without making the SWF depend on the scale on which welfare is measured, and in a way that avoids the restrictive constraints on the shape of the SWF. (shrink)

The tenth proposition of Spinoza’s Ethics reads: ‘Each attribute of substance must be conceived through itself.’ Developing and defending the argument for this single proposition, it turns out, is vital to Spinoza’s philosophical project. Indeed, it’s virtually impossible to overstate its importance. Spinoza and his interpreters have used EIp10 to prove central claims in his metaphysics and philosophy of mind (i.e., substance monism, mind-body parallelism, mind-body identity, and finite subject individuation). It’s crucial for making sense of his epistemology (i.e., Spinoza’s (...) account of knowledge and response to skepticism) and in resolving puzzles within the Ethics (i.e., explaining human ignorance of all but two attributes). Even those who do not attribute some of the above claims to Spinoza need EIp10 to defend much of what they believe about Spinoza’s system. This paper locates a previously unnoticed argument for this proposition in Spinoza’s Short Treatise on God, Man, and His Well Being. There, Spinoza shows himself concerned with a powerful and underappreciated form of philosophical skepticism, one with surprising echoes in the work of his contemporary Leibniz as well as in the later Wittgenstein. Spinoza’s introduction of E1p10 in the Ethics circumvents this form of skepticism, solving the problem the Short Treatise envisions while also explaining that text’s argument’s absence from the explicit justificatory structure of the Ethics. (shrink)

Can new technology enhance purpose-driven, democratic dialogue in groups, governments, and societies? Online Deliberation: Design, Research, and Practice is the first book that attempts to sample the full range of work on online deliberation, forging new connections between academic research, technology designers, and practitioners. Since some of the most exciting innovations have occurred outside of traditional institutions, and those involved have often worked in relative isolation from each other, work in this growing field has often failed to reflect the full (...) set of perspectives on online deliberation. This volume is aimed at those working at the crossroads of information/communication technology and social science, and documents early findings in, and perspectives on, this new field by many of its pioneers. -/- CONTENTS: -/- Introduction: The Blossoming Field of Online Deliberation (Todd Davies, pp. 1-19) -/- Part I - Prospects for Online Civic Engagement -/- Chapter 1: Virtual Public Consultation: Prospects for Internet Deliberative Democracy (James S. Fishkin, pp. 23-35) -/- Chapter 2: Citizens Deliberating Online: Theory and Some Evidence (Vincent Price, pp. 37-58) -/- Chapter 3: Can Online Deliberation Improve Politics? Scientific Foundations for Success (Arthur Lupia, pp. 59-69) -/- Chapter 4: Deliberative Democracy, Online Discussion, and Project PICOLA (Public Informed Citizen Online Assembly) (Robert Cavalier with Miso Kim and Zachary Sam Zaiss, pp. 71-79) -/- Part II - Online Dialogue in the Wild -/- Chapter 5: Friends, Foes, and Fringe: Norms and Structure in Political Discussion Networks (John Kelly, Danyel Fisher, and Marc Smith, pp. 83-93) -/- Chapter 6: Searching the Net for Differences of Opinion (Warren Sack, John Kelly, and Michael Dale, pp. 95-104) -/- Chapter 7: Happy Accidents: Deliberation and Online Exposure to Opposing Views (Azi Lev-On and Bernard Manin, pp. 105-122) -/- Chapter 8: Rethinking Local Conversations on the Web (Sameer Ahuja, Manuel Pérez-Quiñones, and Andrea Kavanaugh, pp. 123-129) -/- Part III - Online Public Consultation -/- Chapter 9: Deliberation in E-Rulemaking? The Problem of Mass Participation (David Schlosberg, Steve Zavestoski, and Stuart Shulman, pp. 133-148) -/- Chapter 10: Turning GOLD into EPG: Lessons from Low-Tech Democratic Experimentalism for Electronic Rulemaking and Other Ventures in Cyberdemocracy (Peter M. Shane, pp. 149-162) -/- Chapter 11: Baudrillard and the Virtual Cow: Simulation Games and Citizen Participation (Hélène Michel and Dominique Kreziak, pp. 163-166) -/- Chapter 12: Using Web-Based Group Support Systems to Enhance Procedural Fairness in Administrative Decision Making in South Africa (Hossana Twinomurinzi and Jackie Phahlamohlaka, pp. 167-169) -/- Chapter 13: Citizen Participation Is Critical: An Example from Sweden (Tomas Ohlin, pp. 171-173) -/- Part IV - Online Deliberation in Organizations -/- Chapter 14: Online Deliberation in the Government of Canada: Organizing the Back Office (Elisabeth Richard, pp. 177-191) -/- Chapter 15: Political Action and Organization Building: An Internet-Based Engagement Model (Mark Cooper, pp. 193-202) -/- Chapter 16: Wiki Collaboration Within Political Parties: Benefits and Challenges (Kate Raynes-Goldie and David Fono, pp. 203-205) -/- Chapter 17: Debian’s Democracy (Gunnar Ristroph, pp. 207-211) -/- Chapter 18: Software Support for Face-to-Face Parliamentary Procedure (Dana Dahlstrom and Bayle Shanks, pp. 213-220) -/- Part V - Online Facilitation -/- Chapter 19: Deliberation on the Net: Lessons from a Field Experiment (June Woong Rhee and Eun-mee Kim, pp. 223-232) -/- Chapter 20: The Role of the Moderator: Problems and Possibilities for Government-Run Online Discussion Forums (Scott Wright, pp. 233-242) -/- Chapter 21: Silencing the Clatter: Removing Anonymity from a Corporate Online Community (Gilly Leshed, pp. 243-251) -/- Chapter 22: Facilitation and Inclusive Deliberation (Matthias Trénel, pp. 253-257) -/- Chapter 23: Rethinking the ‘Informed’ Participant: Precautions and Recommendations for the Design of Online Deliberation (Kevin S. Ramsey and Matthew W. Wilson, pp. 259-267) -/- Chapter 24: PerlNomic: Rule Making and Enforcement in Digital Shared Spaces (Mark E. Phair and Adam Bliss, pp. 269-271) -/- Part VI - Design of Deliberation Tools -/- Chapter 25: An Online Environment for Democratic Deliberation: Motivations, Principles, and Design (Todd Davies, Brendan O’Connor, Alex Cochran, Jonathan J. Effrat, Andrew Parker, Benjamin Newman, and Aaron Tam, pp. 275-292) -/- Chapter 26: Online Civic Deliberation with E-Liberate (Douglas Schuler, pp. 293-302) -/- Chapter 27: Parliament: A Module for Parliamentary Procedure Software (Bayle Shanks and Dana Dahlstrom, pp. 303-307) -/- Chapter 28: Decision Structure: A New Approach to Three Problems in Deliberation (Raymond J. Pingree, pp. 309-316) -/- Chapter 29: Design Requirements of Argument Mapping Software for Teaching Deliberation (Matthew W. Easterday, Jordan S. Kanarek, and Maralee Harrell, pp. 317-323) -/- Chapter 30: Email-Embedded Voting with eVote/Clerk (Marilyn Davis, pp. 325-327) -/- Epilogue: Understanding Diversity in the Field of Online Deliberation (Seeta Peña Gangadharan, pp. 329-358). -/- For individual chapter downloads, go to odbook.stanford.edu. (shrink)

The article considers the features of ensuring the economic security of enterprises in the conditions of intensive introduction of information technologies in their activities in the process of forming the digital economy. It is determined that digitalization creates important advantages for enterprises in terms of implementing a long-term strategy for their development, strengthening economic security, and achieving significant competitive advantages in doing business. It is studied that the system of economic security of the enterprise is an organized set of (...) elements of the management infrastructure of the enterprise, which are focused on ensuring stable and effective development of the business entity, neutralization, and elimination of internal and external threats. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)