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 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)

The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind of bilateralist reasoning, since they (...) do not only internalize processes of verifcation or provability but also the dual processes in terms of falsifcation or what is called dual provability. In [Wansing, 2017] a normal form theorem for N2Int is stated, here, I want to prove a cut-elimination theorem for SC2Int, i.e., if successful, this would extend the results existing so far. (shrink)

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a (...) serious problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty. (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)

This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a (...) term forming operator. In the final section rules for I for negative free and classical logic are also mentioned. (shrink)

I argue that Alvin Goldman has failed to save process reliabilism from my critique in earlier work of consequentialist or teleological epistemic theories. First, Goldman misconstrues the nature of my challenge: two of the cases he discusses I never claimed to be counterexamples to process reliabilism. Second, Goldman’s reply to the type of case I actually claimed to be a counterexample to process reliabilism is unsuccessful. He proposes a variety of responses, but all of them either feature an implausible restriction (...) on process types, or fail to rule out cases with the sort of structure that generates the worry, or both. (shrink)

ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can be found (...) in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)

In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of (...) Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities. (shrink)

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which (...) establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

The proposed project is based on a Dietitian app. The proposed app lets us discover what should we eat based on our weight, height, age, sex, and physical activity. It calculates BMI and BMR and tells us how many calories should we ideally need to intake per day. The calories we should intake will be feed in and based on the RETE algorithm the amount of food intake for the day will be decided. The proposed application is for any type (...) of body person, it is also suited for any range of weight people. It will ideally inform how should we cut down the weight using target programs such as 1LB per week gain/loss. The given system will suggest a food list according to the meal that is if it’s breakfast lunch or dinner. It will accordingly organize heavy calorie food & light calorie food. The system will give more accurate results as it accepts the data entered by the user and processes it depending on some metrics already known to the application on the basis of which a diet plan is generated and ask the user if the user accepts the diet plan. If not accepted the system may also give an alternative diet plan. (shrink)

I discuss Greg Restall’s attempt to generate an account of logical consequence from the incoherence of certain packages of assertions and denials. I take up his justification of the cut rule and argue that, in order to avoid counterexamples to cut, he needs, at least, to introduce a notion of logical form. I then suggest a few problems that will arise for his account if a notion of logical form is assumed. I close by sketching what I take to (...) be the most natural minimal way of distinguishing content and form and suggest further problems arising for this route. (shrink)

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

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)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (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)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we (...) show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...) completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to (...) change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

Realists about aesthetic judgment believe something like the following: for an aesthetic judgment of be correct, it must respond to the intrinsic aesthetic properties possessed by the object in question (e.g., Meskin et al., 2013; Kieran 2010). However, Cutting’s (2003) empirical research on aesthetic judgment puts pressure on that position. His work indicates that unconscious considerations extrinsic to an artwork can underpin said judgements. This paper takes Cutting’s conclusion a step further: If philosophers grant that it’s possible to appreciate artwork (...) on the basis of unconscious biases, then we never can be fully confident that our aesthetic judgment is undergirded by the intrinsic aesthetic properties of an artwork. Furthermore, if judgment on the basis of unconscious, external reasons cannot be ruled out, we cannot be confident that our aesthetic judgments are ‘correct’. I argue that Cutting’s research is just the tip of the iceberg regarding the extrinsic, unconscious factors that influence aesthetic judgment. Expectation bias formed via social influence and context greatly influence aesthetic judgments and are unavoidable: we inevitably form expectations based on all kinds of contextual cues independently of any actual exposure to the item in question. Such factors make it terribly difficult to be confident in our aesthetic judgments. Even if there are objective properties that mark out some items as aesthetically superior to others, we cannot be sure that our judgments are responding to those properties. (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)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...) semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

Despite recent breakthroughs in the field of artificial intelligence (AI) – or more specifically machine learning (ML) algorithms for object recognition and natural language processing – it seems to be the majority view that current AI approaches are still no real match for natural intelligence (NI). More importantly, philosophers have collected a long catalogue of features which imply that NI works differently from current AI not only in a gradual sense, but in a more substantial way: NI is closely related (...) to consciousness, intentionality and experiential features like qualia (the subjective contents of mental states)1 and allows for understanding (e.g., taking insight into causal relationships instead of ‘blindly’ relying on correlations), as well as aesthetical and ethical judgement beyond what we can put into (explicit or data-induced implicit) rules to program machines with. Additionally, Psychologists find NI to range from unconscious psychological processes to focused information processing, and from embodied and implicit cognition to ‘true’ agency and creativity. NI thus seems to transcend any neurobiological functionalism by operating on ‘bits of meaning’ instead of information in the sense of data, quite unlike both the ‘good old fashioned’, symbolic AI of the past, as well as the current wave of deep neural network based, ‘sub-symbolic’ AI, which both share the idea of thinking as (only) information processing: In symbolic AI, the name explicitly references to its formal system based, i.e. essentially rule-based, nature, but also sub-symbolic AI is (implicitly) rule-based, only now via globally parametrized, nested functions. In the following I propose an alternative view of NI as information processing plus ‘bundle pushing’, discuss an example which illustrates how bundle pushing can cut information processing short,and suggest first ideas for scientific experiments in neuro-biology and information theory as further investigations. (shrink)

“ A man orders a whole pizza pie for himself and is asked whether he would like it cut into eight or four slices. He responds, ‘Four, I’m on a diet ”’ (Noël Carroll) -/- While not hilarious --so funny that it induces chortling punctuated with outrageous vomiting--this little gem is amusing. We recognize that something has gone wrong. On a first reading it might not compute, something doesn’t quite make sense. Then, aha! , we understand the hapless dieter has (...) misapplied general rules of thumb, mental short-cuts, or heuristics, that we were also initially committed to and that would usually be good enough to rely upon— fewer slices equals fewer calories; diets require fewer calories, etc—but in this particular case they fail, and the feeling of mirth is our reward for making this discovery. We don’t say all of that after a punchline, of course, but that’s what is happening according to the Humor as Error-Detection Theory : our sense of humor can sense our errors. This chapter will focus on the overlap and benefits of a humorous and philosophical attitude toward the world and our place in it. The historian of philosophy Will Durant tells us that genuine philosophy begins when one learns to doubt; we can say something similar with humor--trust me. (shrink)

Within his overarching program aiming to defend an epistemic conception of analyticity, Boghossian (1996 and 1997) has offered a clear-cut explanation of how we can acquire a priori knowledge of logical truths and logical rules through implicit definition. The explanation is based on a special template or general form of argument. Ebert (2005) has argued that an enhanced version of this template is flawed because a segment of it is unable to transmit warrant from its premises to the conclusion. This (...) article aims to defend the template from this objection. We provide an accurate description of the type of non-transmissivity that Ebert attributes to the template and clarify why this is a novel type of non-transmissivity. Then, we argue that Jenkins (2008)’s response to Ebert fails because it focuses on doxastic rather than propositional warrant. Finally, we rebut Ebert’s objection on Boghossian’s behalf by showing that it rests on an unwarranted assumption and is internally incoherent. (shrink)

This article addresses Rancière’s critique of Aristotle’s political theory as parapolitics in order to show that Aristotle is a resource for developing an inclusionary notion of political community. Rancière argues that Aristotle attempts to cut off politics and merely police (maintain) the community by eliminating the political claim of the poor by including it. I respond to three critiques that Rancière makes of Aristotle: that he ends the political dispute by including the demos in the government; that he includes the (...) free masses only incidentally because, by chance, the rule is political, not based on mastery; and that he attempts to close off politics by determining in advance what speech counts as speech. I argue that Aristotle attempts to institute this contest by accepting the incommensurable claims of arithmetic and geometric equality. Aristotle puts this conflict at the root of political life in such a way that serves Rancière’s larger project of perpetuating politics. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

Placebo-trials on HIV-infected pregnant women in developing countries like Thailand and Uganda have provoked recent controversy. Such experiments aim to find a treatment that will cut the rate of vertical transmission more efficiently than existing treatments like zidovudine. This scenario is first stated as generally as possible, before three ethical principles found in the Belmont Report, itself a sharpening of the Helsinki Declaration, are stated. These three principles are the Principle of Utility, the Principle of Autonomy and the Principle of (...) Justice. These are taken as voices of moral imperative. But although each has intuitive appeal, it can be shown that there are possible scenarios in which they give conflicting prescriptions. To achieve consistency, one must be subordinate to the others. The voice of utility is taken as subordinate to those of justice and autonomy and it is shown that given plausible assumptions about the level of poverty and education in the developing country targeted, the experiment is ruled morally wrong in the name of both justice and autonomy. Moreover, it is argued that no justification can be found for the inclusion of a placebo group, when strictly defined. By contrast, a ‘no- treatment’ control arm might be justified, but only when the demands of autonomy are satisfied, demands that are more stringent than they might appear. A utilitarian defence of the experiment is examined, namely that the would-be participants are in a no-loss situation, and it is shown that this defence is seriously flawed. Finally, it is concluded that there is no justification for amending the Declaration of Helsinki. (shrink)

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the (...) class='Hi'>rule is determined by mathematics. (shrink)

The separation of powers principle deeply heritaged in the US constitutionalism affected and continues to influence the law and public policy in the nation. The tripartite scheme of government was quarreled over the history how we have to perceive any best adequate interaction among the Congress, Executive and Judiciary. The Constitution itself merely quibbles on this point, and the Supreme Court justices, in some cases, would not be done as a clear cut for the scope of constitutional power conferred on (...) each branch. As the stare decisis is a rule in the common law countries, it is less prospective to anticipate that a quantum leap can be made for the new paradigm of constitutional government in the US. In this challenge, the paper deals with the sensitive area of three powers involving the issue of presidential privilege and immunity, justiceability and standing, as well as judicial control of public agencies. In the course of discussion, several landmark cases were illustrated to make a point for the angulated controversies, typically involving the pressing pubic issues and officers of absolute or qualified immunity. Given the diverse structure of government, the US model had been followed by many new born republics in 20th centuries. The author would wish that the paper provides a comparative lesson for the circle of those countries. (shrink)

This paper discusses the prospects of a dispositional solution to the Kripke–Wittgenstein rule-following puzzle. Recent attempts to employ dispositional approaches to this puzzle have appealed to the ideas of finks and antidotes—interfering dispositions and conditions—to explain why the rule-following disposition is not always manifested. We argue that this approach fails: agents cannot be supposed to have straightforward dispositions to follow a rule which are in some fashion masked by other, contrary dispositions of the agent, because in all (...) cases, at least some of the interfering dispositions are both relatively permanent and intrinsic to the agent. The presence of these intrinsic and relatively permanent states renders the ascription of a rule-following disposition to the agent false. (shrink)

Cutting God in Half argues that, in order to tackle climate change, world poverty, extinction of species and our other global problems rather better than we are doing at present we need to bring about a revolution in science, and in academia more generally. We need to put our problems of living – personal, social, global – at the heart of the academic enterprise. How our human world, imbued with meaning and value, can exist and best flourish embedded in the (...) physical universe is, the book argues, our basic problem. It is our fundamental philosophical problem, our fundamental problem of knowledge and understanding, and our fundamental practical problem of living. It is this problem that we fail, at present, to recognize as fundamental – to our cost. It can be understood to arise as a result of cutting God in half – severing the God of Cosmic Power from the God of Value. The first is Einstein’s God, the underlying unity in the physical universe that determines how events occur. The second is what is of most value associated with human life – and sentient life more generally. Having cut God in half in this way, the problem then becomes to see how the two halves can be put together again. This book tackles outstanding aspects of this problem, and in doing so throws out original ideas about science, education, religion, evolutionary theory, free will, quantum theory, and how we should go about tackling our impending global crises. It transpires that bringing our basic problem into sharp focus has revolutionary implications. It becomes clear how and why many aspects of our social and cultural world urgently need to be transformed. Cutting God in Half is written in a lively, accessible style, and ought to be essential reading for anyone concerned about ultimate questions – the nature of the universe, the meaning of life, the future of humanity. (shrink)

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...) cut-conditions in the absence of finitariness or of monotonicity. (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)

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (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)

The aim of this paper is to give an account of what it is to internalize a rule. I claim that internalization is the process of redistributing the burden of instruction from the teacher to the student. The process is complete when instruction is no longer needed, and the rule has reshaped perceptual classification of the circumstances in which it applies. Teaching a rule is the initiation of this process. We internalize rules by simulating instruction coming from (...) someone else. Running these simulations enables us to toggle between the perspective of the instructor and our own perspective. By doing this we coordinate our perspectives with that of the teacher. The account given here provides a deeper explanation of why internalizing a rule involves the dispositions and reactive attitudes proponents of Rule Consequentialism often say it does, why moral reflection is variably demanding, how intergenerational moral progress is made possible by our cognitive architectures, and why the adoption of a rule should be understood in terms of teaching that rule. (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)

Many philosophers think that games like chess, languages like English, and speech acts like assertion are constituted by rules. Lots of others disagree. To argue over this productively, it would be first useful to know what it would be for these things to be rule-constituted. Searle famously claimed in Speech Acts that rules constitute things in the sense that they make possible the performance of actions related to those things (Searle 1969). On this view, rules constitute games, languages, and (...) speech acts in the sense that they make possible playing them, speaking them and performing them. This raises the question what it is to perform rule-constituted actions (e. g. play, speak, assert) and the question what makes constitutive rules distinctive such that only they make possible the performance of new actions (e. g. playing). In this paper I will criticize Searle’s answers to these questions. However, my main aim is to develop a better view, explain how it works in the case of each of games, language, and assertion and illustrate its appeal by showing how it enables rule-based views of these things to respond to various objections. (shrink)

The going-on problem (GOP) is the central concern of Wittgenstein's later philosophy. It informs not only his epistemology and philosophy of mind, but also his views on mathematics, universals, and religion. In section I, I frame this issue as a matter of accounting for intentionality. Here I follow Saul Kripke's lead. My departure therefrom follows: first, a criticism of Wittgenstein's “straight” conventionalism and, secondly, a defense of a solution Kripke rejects. I proceed under the assumption, borne out in the end, (...) that statements of rule-following have truth-conditions and are not, as Kripke seems willing to concede, merely "assertible" in circumstances of a specified sort. Ultimately, my goal is to demonstrate that intending can be understood in terms of an individual's dispositions rather than those of the community to which she belongs. (shrink)

In this paper, a metal cutting machine position control have been designed and simulated using Matlab/Simulink Toolbox successfully. The open loop response of the system analysis shows that the system needs performance improvement. Static output feedback and full state feedback H 2 controllers have been used to increase the performance of the system. Comparison of the metal cutting machine position using static output feedback and full state feedback H 2 controllers have been done to track a set point position using (...) step and sine wave input signals and a promising results have been analyzed. (shrink)

In the middle of the 20th century, it was a common Wittgenstein-inspired idea in philosophy that for a linguistic expression to have a meaning is for it to be governed by a rule of use. In other words, it was widely believed that meanings are to be identified with use-conditions. However, as things stand, this idea is widely taken to be vague and mysterious, inconsistent with “truth-conditional semantics”, and subject to the Frege-Geach problem. In this paper I reinvigorate the (...) ideas that meaningfulness is a matter of being governed by rules of use and that meanings are best thought of in terms of use-conditions. I will do this by sketching the Rule-Governance view of the nature of linguistic meaningfulness, showing that the view isn’t by itself subject to the two problems, and explain why the idea has had a lasting appeal to philosophers from Strawson to Kaplan and why we should find it continually attractive. (shrink)

I introduce an account of when a rule normatively sustains a practice. My basic proposal is that a rule normatively sustains a practice when the value achieved by following the rule explains why agents continue following that rule, thus establishing and sustaining a pattern of activity. I apply this model to practices of belief management and identifies a substantive normative connection between knowledge and belief. More specifically, I proposes one special way that knowledge might set the (...) normative standard for belief: knowing is essentially the unique way of normatively sustaining cognition and, thereby, inquiry. In this respect, my proposal can be seen as one way of elaborating a “knowledge-first” normative theory. (shrink)

Rule-Consequentialism faces “the problem of partial acceptance”: How should the ideal code be selected given the possibility that its rules may not be universally accepted? A new contender, “Calculated Rates” Rule-Consequentialism claims to solve this problem. However, I argue that Calculated Rates merely relocates the partial acceptance question. Nevertheless, there is a significant lesson from this failure of Calculated Rates. Rule-Consequentialism’s problem of partial acceptance is more helpfully understood as an instance of the broader problem of selecting (...) the ideal code given various assumptions—assumptions about who will accept and comply with the rules, but also about how the rules will be taught and enforced, and how similar the future will be. Previous rich discussions about partial acceptance provide a taxonomy and groundwork for formulating the best version of Rule-Consequentialism. (shrink)

Brad Hooker; II*—Rule-Consequentialism, Incoherence, Fairness1, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 19–36, https://d.

This is a short response to Aaron Cotnoir's 'Composition as General Identity', in which I suggest some further applications of his ideas, and try to press the question of why we should think of his 'general identity relation' as a genuine identity relation.

Mental content normativists hold that the mind’s conceptual contents are essentially normative. Many hold the view because they think that facts of the form “subject S possesses concept c” imply that S is enjoined by rules concerning the application of c in theoretical judgments. Some opponents independently raise an intuitive objection: even if there are such rules, S’s possession of the concept is not the source of the enjoinment. Hence, these rules do not support mental content normativism. Call this the (...) “Source Objection.” This paper refutes the Source Objection, outlining a key strand of the relationship between judgments and their contents in the process. Theoretical judgment and mental conceptual content are equally the source of enjoinment; norms for judging with contents do not derive from one at the expense of the other. (shrink)

Timothy Williamson famously argued that assertion is constituted either by the knowledge rule or some similar epistemic rule. If true, the proposal has important implications for criticism of assertions. If assertions are analogical to other rule-constituted kinds like games, we can criticize assertions either on external or internal grounds, depending on whether the criticism draws from the necessary norms of assertion or some contingent ones. More recently, authors like Goldberg and MacFarlane have argued against other theories of (...) assertion on the grounds that they cannot explain the possibility of internal criticism for assertions. This paper raises methodological problems with these arguments. The main idea is to show that alternative, non-normative accounts of assertion can also explain the apparent differences in grounds of criticism without assuming that assertion is necessarily governed by some epistemic norm. (shrink)