We link two concepts from the literature, namely hard sequences for the satisfiability problem sat and so‐called pseudo proof systems proposed for study by Krajíček. Pseudo proof systems are elements of a particular nonstandard model constructed by forcing with random variables. We show that the existence of mad pseudo proof systems is equivalent to the existence of a randomized polynomial time procedure with a highly restrictive use of randomness which produces satisfiable formulas whose satisfying assignments are probably hard (...) to find. (shrink)

In the following we show that general property S considered by Cowen [1], Cowen and Kolany in [3] and earlier by Cowen in [2] and Kolany in [4] as hypergraph satisfiability, can be constructively reduced to (3, 2) · SAT , that is to satisfiability of (at most) triples with two-element forbidden sets. This is an analogue of the“classical” result on the reduction of SAT to 3 · SAT.

I argue that George Schlesinger's proposed solution to the problem of evil fails because: (1) the degree of desirability of state of a being is not properly regarded as a trade‐off between happiness on the one hand and potential on the other; (2) degree of desirability of state is not capable of infinite increase; (3) there is no hierarchy of possible beings, but at most an ordering of such beings in terms of preferences; (4) the idea of such a (...) hierarchy is anyway morally repulsive. Schlesinger is right that the problem of evil disappears, but what makes it vanish is a recognition of the limits of our concepts of satisfaction and happiness, not the incoherent claim that satisfaction or happiness is capable of unlimited increase. (shrink)

In this article, I argue that desire-satisfaction theories of well-being face the problem of trivially satisfied desires. First, I motivate the claim that desire-satisfaction theories need an aggregation principle and reconstruct four possible principles desire-satisfactionists can adopt. Second, I contend that one of these principles seems implausible on numerous counts. Third, I argue that the other three principles, which hold that the creation and satisfaction of new desires is good for individuals and can be called proliferationist, are vulnerable to (...) an objection from trivially satisfied desires. They implausibly imply that forming desires that are trivially satisfied is good for individuals. Finally, I argue that trivially satisfied desires may also worsen desire-satisfactionism's classical problem of pointless desires. Together, these claims constitute a challenge to desire-satisfactionism. (shrink)

In first order logic without equality, but with arbitrary relations and functions the ∃*∀∃* class is the unique maximal solvable prefix class. We show that the satisfiability problem for this class is decidable in deterministic exponential time The result is established by a structural analysis of a particular infinite subset of the Herbrand universe and by a polynomial space bounded alternating procedure.

The still unsettled decision problem for the restricted purely universal formulae 0-formulae) of the first order set-theoretic language based over =, ∈ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related finite set-satisfiability problem for the very significant subclass of the 0-formulae consisting of the formulae involving only nested variables of level 1 is proved to be semidecidable on the ground of a reflection property over (...) the hereditarily finite sets, and various extensions of this result are obtained. When variables are restricted to range only over sets, in universes with infinitely many urelements the set-satisfiability problem is shown to be solvable provided the axiom of foundation is assumed; if it is not, then the decidability of a related derivability problem still holds. That, in turn, suggests the alternative adoption of an antifoundation axiom under which the set-satisfiability problem is also solvable . Turning to set theory without urelements, assuming a form of Boffa's antifoundation axiom, the complement of the set-satisfiability problem for the full class of Δ0-formulae is shown to be semidecidable; a result that is known not to hold, for the set-satisfiability problem itself, even for a very restricted subclass of the Δ0-formulae. (shrink)

We consider two‐variable, first‐order logic in which a single distinguished predicate is required to be interpreted as a transitive relation. We show that the finite satisfiability problem for this logic is decidable in triply exponential non‐deterministic time. Complexity falls to doubly exponential non‐deterministic time if the transitive relation is constrained to be a partial order.

According to Zagzebski, understanding something is justified by the exercise of cognitive skills and intellectual virtues the knower possesses. Zagzebski develops her view by suggesting that “understanding has internalist conditions for success”. Against this view, Grimm raises an objection: what justifies understanding is the reliability of the processes by which we come to understand, and we need not be aware of the outcome of all reliable processes. Understanding is no exception, so, given that understanding something results from reliable processes, we (...) need not always be aware of what we understand. I reply to Grimm’s objection; I argue that Zagzebski’s internalist requirement is best conceived as accessibility to conscious reflection. The accessibility condition is satisfied because understanding solves problems on the knower’s research agenda. And whenever problem-solving is non-trivial, the knower needs to reflect on what the best solving strategy is. (shrink)

We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and (...) ATL$^{+}$ are $\Sigma^P_3$-complete. We note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities. (shrink)

The tree-based data structure of -tree for propositional formulas is introduced in an improved and optimised form. The -trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal (...) form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem. (shrink)

We introduce the notion of “δ-complete decision procedures” for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitz-continuous ODEs. Given an SMT problemϕ and a positive rational number δ, a δ-complete decision procedure determines either that ϕ is unsatisfiable, or that the “δ-weakening” of ϕ is satisfiable. Here, the δ-weakening of ϕ is a variant of ϕ that allows δ-bounded numerical perturbations on ϕ. We (...) establish the existence and complexity of δ-complete decision procedures for bounded SMT over reals with functions mentioned above. We propose to use δ-completeness as an ideal requirement for numerically-driven decision procedures. As a concrete example, we formally analyze the DPLL〈ICP〉 framework, which integrates Interval Constraint Propagation in DPLL, and establish necessary and sufficient conditions for its δ-completeness. We discuss practical applications of δ-complete decision procedures for correctness-critical applications including formal verification and theorem proving. (shrink)

The Gettier problem concerns the definition of knowledge as justified true belief. In the paper I argue that Gettier's cases are not cases of justified true belief because Gettier's examples rely on some problematic assumptions. The first is rather elementary definition of justification and the other is that justification is preserved by entailment, that is, (A) for all agents X, if X is justified in believing that p , and X realizes that the truth of p entails the truth (...) of q , then X would also be justified in believing that q . For the simplistic conception of justification has some alarming consequences we pursue more adequate definition of justification which would satisfy the idea that a necessary condition of justification is to entail or to be entailed by a true proposition. We also show that the (A) is not necessary to provide an elegant counter-example to the definition of knowledge if the elementary definition of justification is adopted. (shrink)

The -logic of Terwijn is a variant of first-order logic with the same syntax in which the models are equipped with probability measures and the quantifier is interpreted as ‘there exists a set A of a measure such that for each,...’. Previously, Kuyper and Terwijn proved that the general satisfiability and validity problems for this logic are, i) for rational, respectively -complete and -hard, and ii) for, respectively decidable and -complete. The adjective ‘general’ here means ‘uniformly over all languages’. (...) We extend these results in the scenario of finite models. In particular, we show that the problems of satisfiability and validity with respect to finite models in E-logic are, i) for rational, respectively -complete and -complete, and ii) for, respectively decidable and -complete. Although partial results toward the countable case are also achieved, the computability of E-logic over countable models still remains largely unsolved. In addition, most o... (shrink)

This article is about the problem of the justification of basic logical laws. Starting from an exposition of Lewis Carroll’s regress, I show the inadequacy of dominant current approaches in the epistemology of logic: they are incapable of responding satisfyingly to the central problem raised by the regress. The realisation of this failure motivates the need to adopt a different perspective on our conception of logical laws. I suggest, in the last portion of the article, that we should (...) follow a suggestion made by Paul Boghossian and look carefully at the primitivist conception of the foundations of logic, such as it is put forward by Aristotle. (shrink)

In this paper, we provide non-clausal tableau calculi for the maximum satisfiability problem and its variants. We discuss both basic calculi to characterize the problem and their modifications to reduce the proof size.

Lawyers and philosophers have found it challenging to construct an account of when an act causes harm that is broad enough to address multiple agent problems but not so broad that it fails to distinguish between genuinely harming a person and imposing a condition on a person that we deem undesirable. Thus, we may think an act causes harm only if it makes a difference to a person and, more specifically, makes things worse for that person. If the effect is (...) the same whatever the one agent does in virtue of what a second agent does or is prepared to do, it may seem that what the one agent does makes no difference. Multiple agent problems are endemic. Legal hypotheticals include the example of two fires, each ‘tortiously’ set, converging on a single barn. The physician faces a multiple agent problem when he or she understands that refusing to provide the fertility treatment a patient demands will just lead to another physician providing the treatment instead. And corporations face the problem when they project that conscientiously refraining from drilling for oil at a particular site will not safeguard that site but rather open the door to equally deleterious activities of still other corporations. This paper argues that a useful first step in developing an account of harm in the multiple agent context is to recognize that often, even if the individual agent cannot make things better for a person, the group can. It seems, however, that a fully adequate account will also show how and when the harm that the group imposes on a person devolves to the agent. This paper proposes such an account. Requirements include: that the agent is a member of a group implicated in the harm; that the agent participate in the bringing about of that harm; and that the agent’s non-participation would not have made things worse for the person. To avoid the charge of harm, then, and still participate in the harm that is done by the group, the agent’s participation must make things better for the person; simply not making things worse, once the other conditions are satisfied, is not enough to avoid the charge of harm. Advantages of the proposed account include its ability to discern as an exception cases in which the agent’s non-participation would have made things worse for the person and to distinguish cases involving a mix of natural and man-made causes. (shrink)

Contact Logics provide a natural framework for representing and reasoning about regions in several areas of computer science. In this paper, we focus our attention on reasoning methods for Contact Logics and address the satisfiability problem and the unifiability problem. Firstly, we give sound and complete tableaux-based decision procedures in Contact Logics and we obtain new results about the decidability/complexity of the satisfiability problem in these logics. Secondly, we address the computability of the unifiability (...) class='Hi'>problem in Contact Logics and we obtain new results about the unification type of the unifiability problem in these logics. (shrink)

In the propositional modal treatment of two-variable first-order logic equality is modelled by a ‘diagonal’ constant, interpreted in square products of universal frames as the identity relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is (...) similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first-order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them. (shrink)

There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas (...) and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory. (shrink)

A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A, B, C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C; this result was the precursor of the Banach–Tarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences. The pieces involved were nonmeasurable. (...) In the present paper, we consider the problem of which systems of congruences can be satisfied using open subsets of the sphere ; of course, these open sets cannot form a partition of the sphere, but they can be required to cover "most of" the sphere in the sense that their union is dense. Various versions of the problem arise, depending on whether one uses all isometries of the sphere or restricts oneself to a free group of rotations, or whether one omits the requirement that the open sets have dense union, and so on. While some cases of these problems are solved by simple geometrical dissections, others involve complicated iterative constructions and/or results from the theory of free groups. Many interesting questions remain open. (shrink)

There is evidence that problem-based learning (PBL) is an effective approach to teach team and problem-solving skills, but also to acquire content knowledge. However, there is hardly any literature about using PBL in philosophy classes. One problem is that PBL is resource intensive because a facilitator is needed for each group of students to support learning efforts and monitor group dynamics. In order to establish more PBL classes, the question is whether PBL can be provided without the (...) need for facilitators. We present a combination of five strategies—among them the collaborative argument visualization software AGORA-net—to replace facilitators. Additionally, we present evidence that these strategies are sufficient to provide a PBL experience that achieves intended learning goals in an ethics class and is satisfying for students without facilitators. (shrink)

I explain the shutdown problem: the problem of designing artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I prove three theorems that make the difficulty precise. These theorems show that agents satisfying some innocuous-seeming conditions will often try to prevent or cause the pressing of the shutdown button, even in cases where it’s costly to do (...) so. And patience trades off against shutdownability: the more patient an agent, the greater the costs that agent is willing to incur to manipulate the shutdown button. I end by noting that these theorems can guide our search for solutions. (shrink)

This paper offers a critique of regulation based upon the belief that commissions often try to satisfy conflicting goals.

After reviewing recent literature from physics and philosophy, it is concluded that we are still far from having a satisfying explanation of the nature and origins of irreversibility. It is proposed that the most fruitful approach to this problem is to concentrate on conditions needed for a rigorous derivation of the Boltzmann equation.

For Descartes, the passions are the key to the good life. But he is also wary of the extent to which they may lead us astray. As I argue, there is reason to be skeptical that Descartes himself provides a satisfying resolution of this tension in the Passions of the Soul. The problem concerns our ability to interpret and work through intra-subjective passional conflicts. Descartes seems almost obsessed with the problem of such conflicts in this text. What he (...) needs to provide, however, is a kind of moral therapy by which we can adjudicatethem. This is tantamount to providing a theory of representation for the passions, and it would be similar to the belief therapy that he provides for determining the representational content of other perception types, notably sensations and appetites. But I argue that he does not discharge this philosophical obligation, and indeed he cannot do so given his own understanding of the uniquely ambiguous representational character of the passions. (shrink)

A satisfying theory of knowledge has to explain why knowledge seems to be better than mere true belief. In this paper, I try to show that the best reliabilist explanation (ERA+) is still not able to solve this problem. According to an already elaborated answer (ERA), it is better to possess knowledge that p because this makes likely that one’s future belief of a similar kind will also be true. I begin with a metaphysical comment which gives birth to (...) ERA +, a better formulation of ERA. Then, I raise two objections against ERA+. The first objection shows that the truth of the reliabilist answer requires the conception of a specific theory of instrumental value. In the second objection, I present an example in order to show that ERA+ actually fails to explain why it is better to possess knowledge than a mere true belief. (shrink)

How can we find any satisfying assignment for a Boolean formula that has many satisfying assignments? There exists an obvious randomized algorithm for solving this problem: one can just pick an assignment at random and check the truth value of the formula for this assignment, this is iterated until a satisfying assignment occurs. Does there exist a polynomial-time deterministic algorithm that solves the same problem? This paper presents such an algorithm and shows that its worst-case running time is (...) linear when input formulas are in k-CNF and a fraction of satisfying assignments is greater than a constant. This algorithm is almost the same as the algorithm proposed by Monien and Speckenmeyer in the early 1980s for less than 2n steps 3-SAT decision.Another result of this paper is that if a formula in k-CNF has many satisfying assignments, then there exists a short satisfying assignment, i.e. an assignment of truth values to a small number of variables. The proposed algorithm yields just such a short satisfying assignment. We also show that there exist formulas in general CNF having many satisfying assignments, that have no short satisfying assignments. (shrink)

We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it (...) has a finite model. Moreover, Mortimer showed that every satisfiable FO 2 -sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO 2 -sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO 2 is NEXPTIME-complete. (shrink)

The seminal Satisfiability Coding Lemma of Paturi, Pudlák, and Zane is a coding scheme for satisfying assignments of k-CNF formulas. We generalize it to give a coding scheme for implicants and use this generalized scheme to establish new structural and algorithmic properties of prime implicants of k-CNF formulas. Our first application is a near-optimal bound of n⋅ 3^{n(1-Ω(1/k))} on the number of prime implicants of any n-variable k-CNF formula. This resolves an open problem from the Ph.D. thesis of (...) Talebanfard, who proved such a bound for the special case of constant-read k-CNF formulas. Our proof is algorithmic in nature, yielding an algorithm for computing the set of all prime implicants - the Blake Canonical Form - of a given k-CNF formula. The problem of computing the Blake Canonical Form of a given function is a classic one, dating back to Quine, and our work gives the first non-trivial algorithm for k-CNF formulas. (shrink)

Purpose. The purpose of the article is the analysis of the reasons and grounds of the crisis in the sphere of meaning-making, as well as searching answers to the questions about the meaning of human life in the contemporary world, which are maximally relevant in connection with the escalation of global problems, revealing the points of convergence between various theoretical positions, evaluation of their heuristic potential. Theoretical basis of the research is the historical-philosophical, comparative and system approaches, as well as (...) the analysis of philosophical insights in the field of global studies. Originality. Originality lies in the fact that this article is the first attempt to conduct comprehensive analysis in the problem of the sense of the Existence as it is presented in the first quarter of the 21st century and to relate it with the modern social situation that is characterized by a complex range of interconnected and interdependent anthropological problems of our time. Authors emphasize that the main reason in the crisis of meaning is that a man has lost touch with his roots, which is wildlife. He has created an artificial structure, civilization to satisfy his needs and finds no way to the transcendental, which is the true House of his being. Conclusions. A human must refuse from false self-conceit concerning his potential omniscience and omnipotence, cease dictating his own rules to the Existence, determine the boundaries of his freedom and try to clearly realize his place in the objective structure of being. The global situation can change for the better only if a dramatic change in the area of meaning-making happens. The decisive force, which may encourage nudging to the positive changes, can be either the free will of people who have realized the criticality of the situation or external natural and social circumstances that will make people reorganize radically. The proper prioritizing, a deep awareness of universal goals and solidarity between people could be the value basis that will become the foundation to find the meaning and create a more favorable future. (shrink)

Ethical beliefs may vary across cultures but there are things that must be valued as preconditions to any cultural practice. Physical and mental abilities vital to believing, valuing and practising a culture are such preconditions and it is always important to protect them. If one is to practise a distinct culture, she must at least have these basic abilities. Access to basic healthcare is one way to ensure that vital abilities are protected. John Rawls argued that access to all-purpose primary (...) goods must be ensured. Amartya Sen and Martha Nussbaum claim that universal capabilities are what resources are meant to enable. Len Doyal and Ian Gough identify physical health and autonomy as basic needs of every person in every culture. When we disagree on what to prioritize, when resources to satisfy competing demands are scarce, our common needs can provide a point of normative convergence. Need-based rationing, however, has been criticized for being too indeterminate to give guidance for deciding which healthcare services to prioritize and for tending to create a bottomless-pit problem. But there is a difference between needing something (first-order need) and needing to have the ability to need (second-order need). Even if we disagree about which first-order need to prioritize, we must accept the importance of satisfying our second-order need to have the ability to value things. We all have a second-order need for basic healthcare as a means to protect our vital abilities even if we differ in what our cultures consider to be particular first-order needs. (shrink)

In 1973, Rittel and Webber coined the term ‘wicked problems’, which they viewed as pervasive in the context of social and policy planning.1 Wicked problems have 10 defining characteristics: they are not amenable to definitive formulation; it is not obvious when they have been solved; solutions are not true or false, but good or bad; there is no immediate, or ultimate, test of a solution; every implemented solution is consequential, it leaves traces that cannot be undone; there are no criteria (...) to prove that all potential solutions have been identified and considered; every wicked problem is essentially unique; every wicked problem can be considered to be a symptom of another problem; a wicked problem can be explained in numerous ways and the choice of explanation determines what will count as a solution and the actors are liable for the consequences of the actions they generate.1 One needs only a passing familiarity with the history of HIV prevention research, and with the intellectual traditions of research ethics, to appreciate that the perils and opportunities arising from proposals to conduct research with people who inject drugs in some of the most precarious social and political circumstances around the world and the challenges associated with implementing the findings satisfy Rittel's and Webber's criteria for ‘wicked problems’. HIV prevention research has contributed important new knowledge about the feasibility, efficacy or relative efficacy of various prevention strategies in a variety of contexts around the world. But the pathways and timelines for how this knowledge has contributed to improvements in public health practice and/or the establishment of policies that ensure unfettered access to appropriate healthcare services for PWID are less clear and decidedly non-linear. One account of the transition from trial to policy …. (shrink)

On Choice of Time Metric. What criteria ought to be satisfied by those observable processes which, accompanied by a function assigning values to intervals of that processes, serve as the standard for measurement of time? In how far do the criteria which can reasonably be established admit of an unambigous definition of time metric? That are the questions to which I have addressed myself in the paper. Peter Janich has aimed at solving the problem with careful avoidance of any (...) reference to physical theory. Although this paper owes a great deal to his ‘Protophysik der Zeit’, reasons will be ad-vanced that it is in principle impossible to give a foundation of time metric without any reference to physical theory. It follows that taking results of physical theory into account is unavoidable as far as a definite decision concerning the choice of time metric is aspired. At first sight reference to law-like assertions on the duration of temporal intervals appears to be paradoxical for it means to take something which originally ought to be submitted to experimental test as the standard for measurement. Poincaré is fairly conscious of this problem, yet explicitly acknowledges that there is a mutual relationship between definition of time metric and physical theory. It will be shown that this kind of mutual relationship which even might be termed as circular does not void physical theory of empirical content. Thus in the final part I am concerned to free the position which recommends reference to physical theory from its paradoxical image in order to advance a conventionalist account as a sceptical, but nevertheless fully satisfying solution. (shrink)

In previous work I have argued that classical electrodynamics is beset by deep conceptual problems, which result from the problem of self-interactions. Symptomatic of these problems, I argued, is that the main approach to modeling the interactions between charges and fields is inconsistent with the principle of energy–momentum conservation. Zuchowski reports a formal result that shows that the so-called ‘Abraham model' of a charged particle satisfies energy–momentum conservation and argues that this result amounts to a refutation of my inconsistency (...) claim. In this paper I defend my claims against her criticism and argue that she has succeeded neither in refuting my inconsistency argument nor in showing that the conceptual problems of classical electrodynamics have been solved. (shrink)

A few years ago, believing that human thinking is nonmonotonic, I tried to reconstruct a nonmonotonic reasoning by application of two monotonic procedures. I called them “step forward” and “step backward” (see [4]). The first procedure is just a consequence operation responsible for an extension of the set of beliefs. The second one, defined on the base of the logic of falsehood reconstructed for the given logic of truthfulness, is responsible for a reduction of the set of beliefs. Both procedures (...) taken together were successfully verified by using so-called AGM (see [5]), postulates for expansion, contraction and revision formulated by Alchourrón, Gärdenfors and Makinson (e.g. [1]). Reasoning composed of the mutual application of both procedures seemed to be quite natural for modeling our thinking. At that time, I supposed that it should be nonmonotonic but I was wrong. It turned out impossible to satisfy a definition of the nonmonotonic inference by reasoning composed both steps. To understand why this is impossible, I began to analyze how nonmonotonicity is obtainable in some well-known cases in the literature. I analyzed the problem from two points of view: (1) non-formal examples for nonmonotonicity and (2) formal constructions of nonmonotonic operations/relations. The result of those investigations was astonishing: none of the considered by me cases of nonmonotonicity belonging to point (1) and almost none belonging to (2) satisfies the definition of nonmonotonic inference. Arguments against the nonmonotonic character of well-known examples for nonmonotonicity of human thinking are more precisely presented in [6]. I present them below an abbreviated version of them. (shrink)

Collective impact cases are situations where people collectively bring about a morally significant outcome by each acting in a certain way, and yet each individual action seems to make no, or almost no difference to the outcome. Intuitively, the beneficial or harmful outcomes give individuals moral reason to act (or refrain from acting) in collective impact situations. However, if the individual action does not make a difference to the outcome, it is not clear what those moral reasons are. The (...) class='Hi'>problem of collective impact is the challenge of identifying such moral reasons. Julia Nefsky has presented an account of how an individual action can help without making a difference – call it the Helping Account – that claims to provide a general solution to the problem of collective impact while avoiding problems faced by previously suggested solutions. I present an internal critique of Nefsky’s work. First, I argue that, based on the problems that Nefsky has raised against previously suggested solutions, three success conditions for a general solution to the problem of collective impact can be formulated: The Weightiness condition, the Generalizability condition, and the Connectedness condition. Second, I argue that the Helping Account fails to satisfy the three success conditions, thereby failing, by Nefsky’s own standards, to provide a general solution to the problem. (shrink)

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

Summary Discussions on soul origins are perceived as antiquated at best. However, there is a recent resurgence of interest in the nature and origins of the mind. This is due in part to the recent developments on the nature of “emergent” properties and/or substances in the contemporary literature on the philosophy of mind. As a contribution to this discussion, I examine the two most prominent theories of mental origins and find that each encounter some noteworthy problems. With these in mind, (...) I recommend that some form of Creationism deserves our attention. It provides a solution to the various philosophical and theological concerns associated with the previously mentioned emergence theories of the mind. Finally, I lay out a more satisfying theory of the soul’s creation in a way that accounts for the benefits of emergentism. (shrink)

In its original form, Nozick’s experience machine serves as a potent counterexample to a simplistic form of hedonism. The pleasurable life offered by the experience machine, its seems safe to say, lacks the requisite depth that many of us find necessary to lead a genuinely worthwhile life. Among other things, the experience machine offers no opportunities to establish meaningful relationships, or to engage in long-term artistic, intellectual, or political projects that survive one’s death. This intuitive objection finds some support in (...) recent research regarding the psychological effects of phenomena such as video games or social media use. After a brief discussion of these problems, I will consider a variation of the experience machine in which many of these deficits are remedied. In particular, I’ll explore the consequences of a creating a virtual world populated with strongly intelligent AIs with whom users could interact, and that could be engineered to survive the user’s death. The presence of these agents would allow for the cultivation of morally significant relationships, and the world’s long-term persistence would help ground possibilities for a meaningful, purposeful life in a way that Nozick’s original experience machine could not. While the creation of such a world is obviously beyond the scope of current technology, it represents a natural extension of the existing virtual worlds provided by current video games, and it provides a plausible “ideal case” toward which future virtual worlds will move. While this improved experience machine would seem to represent progress over Nozick’s original, I will argue that it raises a number of new problems stemming from the fact that that the world was created to provide a maximally satisfying and meaningful life for the intended user. This, in turn, raises problems analogous in some ways to the problem(s) of evil faced by theists. In particular, I will suggest that it is precisely those features that would make a world most attractive to potential users—the fact that the AIs are genuinely moral agents whose well-being the user can significantly impact—that render its creation morally problematic, since they require that the AIs inhabiting the world be subject to unnecessary suffering. I will survey the main lines of response to the traditional problem of evil, and will argue that they are irrelevant to this modified case. I will close by considering by consider what constraints on the future creation of virtual worlds, if any, might serve to allay the concerns identified in the previous discussion. I will argue that, insofar as the creation of such worlds would allow us to meet morally valuable purposes that could not be easily met otherwise, we would be unwise to prohibit it altogether. However, if our processes of creation are to be justified, they must take account of the interests of the moral agents that would come to exist as the result of our world creation. (shrink)

Perfectionism, the view that well-being is a matter of developing characteristically human capacities, has relatively few defenders in the literature, but plenty of critics. This paper defends perfectionism against some recent formulations of classic objections, namely, the objection that perfectionism ignores the relevance of pleasure or preference for well-being, and a sophisticated version of the ‘wrong properties’ objection, according to which the intuitive plausibility of the perfectionist ideal is threatened by an absence of theoretical pressure to accept putative wrong properties (...) cases. The paper argues these objections are unsuccessful, but introduce a new worry, the Deep Problem: Perfectionism fails to offer a satisfying foundational justification for why developing the human essence is valuable. The paper responds to the deep problem, ultimately arguing that it is a puzzle put to all theories of well-being to provide a justification for their normative significance. (shrink)

There is a certain view abroad in the land concerning the philosophical problems raised by Tarskian semantics. This view has it that a Tarskian theory of truth in a language accomplishes nothing of interest beyond the definition of truth in terms of satisfaction, and, further, that what is missing — the only thing that would yield a solution to the philosophical problem of truth when added to Tarskian semantics — is a reduction of satisfaction to a non-semantic relation. It (...) seems to me that this view either misidentifies the philosophical problem altogether, or encourages a seriously misleading picture of the nature of the problem.The view I have in mind is nowhere more persuasively at work than in a recent paper by Hartry Field.1 In this paper Field argues that a Tarskian theory of truth for a natural language is impossible if we insist on Tarski's case-by-case elimination of ‘satisfies'. More fundamentally, however, he argues that a Tarskian theory could provide nothing of philosophical interest beyond the admittedly interesting reduction of truth to satisfaction, and his ground for this claim is, roughly, that a Tarskian theory does not reduce its primitive semantic relation — satisfaction — to a non-semantic relation. (shrink)

Biological agents can act in ways that express a sensitivity to context-dependent relevance. So far it has proven difficult to engineer this capacity for context-dependent sensitivity to relevance in artificial agents. We give this problem the label the “problem of meaning”. The problem of meaning could be circumvented if artificial intelligence researchers were to design agents based on the assumption of the continuity of life and mind. In this paper, we focus on the proposal made by enactive (...) cognitive scientists to design artificial agents that possess sensorimotor autonomy—stable, self-sustaining patterns of sensorimotor interaction that can ground values, norms and goals necessary for encountering a meaningful environment. More specifically, we consider whether the Free Energy Principle (FEP) can provide formal tools for modeling sensorimotor autonomy. There is currently no consensus on how to understand the relationship between enactive cognitive science and the FEP. However, a number of recent papers have argued that the two frameworks are fundamentally incompatible. Some argue that biological systems exhibit historical path-dependent learning that is absent from systems that minimize free energy. Others have argued that a free energy minimizing system would fail to satisfy a key condition for sensorimotor agency referred to as “interactional asymmetry”. These critics question the claim we defend in this paper that the FEP can be used to formally model autonomy and adaptivity. We will argue it is too soon to conclude that the two frameworks are incompatible. There are undeniable conceptual differences between the two frameworks but in our view each has something important and necessary to offer. The FEP needs enactive cognitive science for the solution it provides to the problem of meaning. Enactive cognitive science needs the FEP to formally model the properties it argues to be constitutive of agency. Our conclusion will be that active inference models based on the FEP provides a way by which scientists can think about how to address the problems of engineering autonomy and adaptivity in artificial agents in formal terms. In the end engaging more closely with this formalism and its further developments will benefit those working within the enactive framework. -/- . (shrink)

It has been argued that all compatibilist accounts of free action and moral responsibility succumb to the manipulation problem: evil neurologists or their like may manipulate an agent, in the absence of the agent's awareness of being so manipulated, so that when the agent performs an action, requirements of the compatibilist contender at issue are satisfied. But intuitively, the agent is not responsible for the action. We propose that the manipulation problem be construed as a problem of (...) deviance. In troubling cases of manipulation, psychological elements such as desires and beliefs, among other things, are acquired via causal routes that are deviant relative to causal routes deemed normal or baseline. We develop and defend rudiments of a baseline that is acceptable independently of whether one has compatibilist or incompatibilist leanings. (shrink)

The desire-satisfaction theory of welfare says, roughly, that one's life goes well to the extent that one's desires are satisfied. On standard 'actualist' versions of the theory, it doesn't matter what you desire. So long as you are getting what you actually want – whatever it is – things are going well for you. There is widespread agreement that these standard versions are incorrect, because we can desire things that are bad for us -– in other words, because there are (...) 'defective desires'. The aim of this paper is to defend the actualist desire-satisfaction theory against the problem of defective desires. I aim to show how the theory can accommodate the obvious fact that we can desire things that are bad for us. Admittedly, there are kinds of allegedly defective desire the theory cannot accommodate, but these desires, I argue, turn out not to be defective in the relevant way. (shrink)

In days past, epistemologists expended a good deal of effort trying to analyze the basing relation—the relation between a belief and its basis. No satisfying account was offered, and the project was largely abandoned. Younger epistemologists, however, have begun to yearn for an adequate theory of basing. I aim to deliver one. After establishing some data and arguing that traditional accounts of basing are unsatisfying, I introduce a novel theory of the basing relation: the dispositional theory. It begins with the (...) pedestrian observation that beliefs stand or fall with their bases. The theory I offer is an elucidation and refinement of this thought. (shrink)