We discuss the effectivity of Arslanov’s completeness criterion. In particular, we show that a parameterized version, similar to the recursion theorem with parameters, fails. We also discuss the effectivity of another extension of the recursion theorem, namely Visser’s ADN theorem, as well as that of a joint generalization of the ADN theorem and Arslanov’s completeness criterion.

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a (...) purely combinatorial characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

We prove a completeness criterion for quasi-reducibility and generalize it to higher levels of the arithmetical hierarchy. As an application of the criterion we obtain Q-completeness of the set of all pairs such that the prefix-free Kolmogorov complexity of x is less than n.

Previous research has found that funding disparities are driven by applications’ final impact scores and that only a portion of the black/white funding gap can be explained by bibliometrics and topic choice. Using National Institutes of Health R01 applications for council years 2014–2016, we examine assigned reviewers’ preliminary overall impact and criterion scores to evaluate whether racial disparities in impact scores can be explained by application and applicant characteristics. We hypothesize that differences in commensuration—the process of combining criterion (...) scores into overall impact scores—disadvantage black applicants. Using multilevel models and matching on key variables including career stage, gender, and area of science, we find little evidence for racial disparities emerging in the process of combining preliminary criterion scores into preliminary overall impact scores. Instead, preliminary criterion scores fully account for racial disparities—yet do not explain all of the variability—in preliminary overall impact scores. (shrink)

Summary Giancarlo Trombini presents the continuation of his research on the question of which criteria can be used to assess the progress of therapy in an objectively verifiable way and to make the decision on the completion of therapy. In the first phase of his research, the phenomenological criterion of a qualitative change in the patient’s relations toward the positive and higher complexity was proposed for this purpose. In terms of the working method in analytic therapy, this meant concretely: (...) attention should be paid to what development is shown in the comparison of the relationships that occur in the dream narrative and in the subsequent associations. This criterion was therefore given the name manifest dream/association comparison (MDAC)—comparison between the manifest dream and the subsequent associations. The idea can easily be transferred to those therapy methods, which do not primarily work with reports of dream memories and subsequent associations—also, in other ways of working, it is possible to pay attention, in the way suggested by Trombini, to the qualitative development of the relationships which are thematized by the clients in the course of an hour. To this first criterion, another phenomenological criterion is now added in the present article: that of the “concluding therapeutic turn” (CTT). If the patient’s development reaches this turn in the course of the therapy in one session, this indicates, according to Trombini, that the therapy can soon be concluded. The fulfillment of this criterion can be recognized by the fact that in the sequence of dream narration and subsequent associations in a session, a relational dynamic toward the positive and higher complexity becomes recognizable and that is, at the same time, connected with a reconciliation of the three temporal reference systems (past, present, and future). The achievement of this CTT indicates that the patient is aware of the changes made in therapy and makes it evident to the therapist that the therapy is nearing completion. (shrink)

In this paper, I offer an examination of the two existing criteria of change, one indicated, implicitly, by Aristotle and the other proposed, quite formally, by Russell. Both criteria engender problems. While the Aristotelian criterion is both too narrow and too broad, as it includes bogus changes and excludes subjectless changes, the Russellian criterion avoids the distinction between genuine changes and bogus changes completely. The aim of the paper is to address these problems and to show how these (...) two existing criteria of change can be made to deal with the problems through revision and integration. (shrink)

Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional (...) identity than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation. (shrink)

Abstract:Disturbing cases continue to be published of patients declared brain dead who later were found to have a few intact brain functions. We address the reasons for the mismatch between the whole-brain criterion and brain death tests, and suggest solutions. Many of the cases result from diagnostic errors in brain death determination. Others probably result from a tiny amount of residual blood flow to the brain despite intracranial circulatory arrest. Strategies to lessen the mismatch include improving brain death determination (...) training for physicians, mandating a test showing complete intracranial circulatory arrest, or revising the whole-brain criterion. (shrink)

We propose a criterion to regard a property of a theory (in first or second order logic) as virtuous: the property must have significant mathematical consequences for the theory (or its models). We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying it. The stability hierarchy (...) extends this virtue to other complete theories. The interaction of model theory and traditional mathematics is examined by considering the views of such as Bourbaki, Hrushovski, Kazhdan, and Shelah to flesh out the argument that the main impact of formal methods on mathematics is using formal definability to obtain results in ‘mainstream’ mathematics. Moreover, these methods (e.g., the stability hierarchy) provide an organization for much mathematics which gives specific content to dreams of Bourbaki about the architecture of mathematics. (shrink)

The debate about Habermas' use of the system and lifeworld distinction has not focused on the explanation of social pathologies that he offers, but rather only on conceptual problems with the theories that he uses. Twill argue that the explanation offered by his thesis that "systems colonize the lifeworld" fits the main criterion for adequacy for macro-micro explanation: because it establishes macro-micro linkage, it is at least potentially complete. Such an analysis fits the empirical approach to traditional debates between (...) collectivists and individualists among macrosociologists. I shall apply this approach here in three steps. First, I shall use the controversy about functionalist explanation in the social sciences to develop the criterion of completeness for macrosociological explanations (1). Second, I shall generalize the conditions of adequacy for functionalist explanations to macrosociology as a whole and show that Habermas'explanation of the colonization of the lifeworld is at least potentially complete, as an explanation sketch that lacks empirical detail (2). Third, I shall show that this approach also requires that Habermas modify his overly Weberian claims about the effects of bureaucracy, since his stronger notion of reification is based on the incompletness in his explanation of this aspect of the micromacrolinkage (3). Moreover; a more complete account has clearer practical consequences for agency in the form of collective action. (shrink)

For any unit vector in an inner product space S, we define a mapping on the system of all ⊥-closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems (...) of subspaces. Finally, the result will be generalized to general inner product spaces. (shrink)

The debate about the criterion of truth has always been closely linked with the battle lines of philosophy. Philosophers of different philosophical lines use different criteria of truth, each of which is consistent with the criterion of truth common to its philosophical line. Idealist philosophies advocate the primacy of thinking [, implying more the structure or process of thought, as compared to "thought" , implying a more or less coherent idea, viewpoint, or system, the result of thinking - (...) Tr.] and regard the material world as secondary, believing that human thought and truth are dropped from heaven, or are generated by the subjective consciousness itself. The idealist criterion of truth is sought in thought itself. Idealist philosophers cannot use the criterion of practice because the entire theory of idealism, including its view of truth, is made up wholly of subjective and empty constructs which would not pass the test of practice. If idealist philosophy used the criterion of practice it would undoubtedly refute itself. Only the materialist philosophical line is linked by its very nature with the criterion of practice. Materialism affirms the primacy of the material world, and the secondary nature of thinking as a reflection of the material world, regarding truth as a correct or accurate reflection of objective things. To test whether or not such a reflection is correct, it is not permissible to appeal to thought itself; we must rely on social practice. To discuss the truth of thinking, separate from social practice, would be to abandon materialism and fall into idealism. Therefore we say that the materialist philosophical line, as part of its basic fundamental nature, embraces the acceptance of the criterion of practice, or we say that it is fundamentally linked to the criterion of practice. Of course, to say that the materialist philosophical line is fundamentally linked to the criterion of practice is not to say that every materialist is able to consciously adopt the criterion of practice, rather that materialism ought to use social practice as the criterion of truth. Only in this way can one maintain a thoroughgoing materialism. However, ought to is one thing, while reality is quite another. In reality, the materialists coming before Marx did not self-consciously adopt the criterion of practice, but for the most part used subjective criteria. For example, the well-known materialist [Ludwig] Feuerbach [1804-18721 thought that "agreement of the majority" or "common opinion" was a criterion of truth. "Agreement" and "opinion" are subjective, and such a theory of the criterion of truth stands in contradiction to the materialist line that Feuerbach advocated. With a criterion of that sort, not only would it be impossible to validate the objective truth that Feuerbach sought; on the contrary, one could refute objective truth totally, refute the materialist line. Since subjective criteria of truth solve the problem of truth within the subjective realm and must refute the objective nature of truth, subjective criteria of truth are therefore fundamentally incompatible with the materialist line of thought. Only the criterion of practice accepts objective truth, and is compatible with the materialist line of thought. That materialists before Marx were unable to self-consciously employ the criterion of practice and used subjective criteria of truth reveals the limited and partial nature of materialism. By introducing social practice into the theory of knowledge and by determining that practice is the criterion of truth, thereby overcoming the limitations and incompleteness of the old materialism, Marxism developed the materialist theory of knowledge into a completely scientific theory. This was an enormous contribution to the history of philosophy. However, the acceptance or rejection of the criterion of practice is not a minor problem, but rather a major problem that affects all philosophical lines of thought. To uphold the criterion of practice is to stand on the side of materialism. On the other hand, to use the criterion of thought to refute the criterion of practice is to fall into idealism. (shrink)

One criterion of constructive logics is the disjunction, property (DP). The Halldén-completeness is a weak DP, and is related to the relevance principle and variable separation. This concept is well-understood in the case of propositional logics. We extend this notion to predicate logics. Then three counterparts naturally arise. We discuss relationships between these properties and meet-irreducibility in the lattice of logics.

Economists evaluate their models in terms of credibility. For example, Rothschild and Stiglitz argued from a model of a completive insurance market that under the “plausible” (632) assumption of information asymmetry, one can “credibly” infer the non-existence of equilibria in specific situations – despite the fact that, as they admit, the real ‘market … for insurance is probably not competitive’ (648).1 Another example is Richard Thaler’s column on anomalies of (micro-) economic theory. From 1987 to 2001, he headed every article (...) with the following sentence: ‘An empirical result is anomalous if it is difficult to rationalize, or if implausible assumptions are necessary to explain it within the paradigm’.2 Or, yet another example, Hans Lind concludes in a survey of mathematical models of rent control that ‘what is shown in the model[s]…is just one type of argument…for why a certain story is more credible than a competing story. (shrink)

By using algebraic-categorical tools, we establish four criteria in order to disprove canonicity, strong completeness, w-canonicity and strong w-completeness, respectively, of an intermediate propositional logic. We then apply the second criterion in order to get the following result: all the logics defined by extra-intuitionistic one-variable schemata, except four of them, are not strongly complete. We also apply the fourth criterion in order to prove that the Gabbay-de Jongh logic D1 is not strongly w-complete.

Although William of Occam’s early epistemological quote “Entities must not be multiplied beyond necessity” attempted to put an end to the uncontrollable ontological confusion of his time, Occam’s Razor as its modern epistemological version considers as unscientific any non- measurable entity. However, words such as “immaterial”, “spirit” and “free will” have never ceased to exist in everyday human communication. According to Linguistics every word that has not historically ceased to be used by the total of people (or most of their (...) societies) corresponds to a commonly accepted entity for which its users generally recognize the same distinguishable characteristics. A new, revised and complete–in the standards of the universal human communication–epistemological criterion is required fully now adapted in the linguistic criterion–the language people commonly communicate and use. (shrink)

This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ, where x occurs only positively in γ, we obtain the flat modal fixpoint language by adding to the language of polymodal logic a connective γ for each γΓ. The term γ is meant to be interpreted as the least fixed point of the functional interpretation of the term γ. We consider the (...) following problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen–Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite. (shrink)

We suggest some new ways to effectivize the definitions of several classes of simple sets. On this basis, new completeness criterions for simple sets are obtained. In particular, we give descriptions of the class of complete maximal sets.

Although it has been largely neglected in contemporary philosophy , the problem of the criterion raises questions which must be addressed by any complete account of knowledge . But the problem of the criterion suffers not onl.

One central objection to the maximin payoff criterion is that it focuses on the state that yields the lowest payoffs regardless of how low these are. We allow different states to have different sets of possible outcomes and show that the original axioms of Milnor (1954) continue to characterize the maximin payoff criterion, provided that the sets of payoffs achievable across states overlap. If instead payoffs in some states are always lower than in all others then ignoring the (...) “bad” states is no longer inconsistent with these axioms. Similar dependence on overlap of outcome spaces across states holds for the minimax regret and maximin joy criteria. (shrink)

Peirce’s anti-psychologism hinges on two main assumptions. First, logic and psychology belong to two separate disciplines – respectively, the normative sciences and the experimental sciences. Second, externalism must be understood as a crucial and inescapable epistemological criterion. The introspectionist illusion, according to which individuals have direct and epistemologically flawless access to their own internal states, should be dismissed. As Colapietro (2003) and Calcaterra (2006) observe, Peirce’s standpoint is far different from the Kantian classical account of anti-psychologism. This original take (...) on anti-psychologism leaves room for a functional distinction between logic and psychology, emerging from a semiotic and communicative continuity. This means that psychology, unlike logic as a formal doctrine of signs, will be epistemologically appropriate for dealing with internal psychological states, on the condition that this inquiry be focused on the communicative processes through which these internal states are expressed and conveyed. Such a Peircean account of anti-psychologism forms the epistemological background of this paper. My goal is to show how Peirce’s approach to communication and semiosis can be applied in order to discuss a specific psychological theory, in this case, attachment theory. Specifically, I propose employing Giovanni Maddalena’s Peircean distinction between complete and incomplete gestures (Maddalena 2015) to account for the distinction between secure, dismissing and preoccupied attachment patterns. To this end, I will be discussing three different measurements of attachment: the Adult Attachment Interview (AAI, George, Kaplan & Main 1985), the Adult Attachment Projection (AAP, George & West 2006), and the Patient Attachment Coding System (PACS, Talia, Miller-Bottome & Daniel 2015). Throughout this discussion, I will examine the connection between the semiotic and phenomenological category of completeness, and the psychological category of security. This connection involves an interesting normative import, which I briefly discuss in the conclusions. (shrink)

Providing a principled characterization of the distinction between logical and non-logical expressions is a longstanding issue in the philosophy of logic. In the Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by "syntactic" means which sentences are valid and which are (...) not. Despite a renewed interest in the philosophical benefits of analyticity, both inside and outside of Carnap scholarship, Carnap's definition of logical expressions seems to have drawn too little attention. I shall argue that it is worth a second look. More precisely, my aim will be to defend this idea against some technical problems faced by Carnap's way of implementing it and against Quinean attacks on syntax-based conventionalism. Section 1 presents Carnap's definition in the context of Logical Syntax of Language, that is, how exactly the definition works, and why Carnap needs it. In section 2, I review three challenges that have been raised in the literature, and I propose to revise the definition accordingly. I argue that its modified version is immune to the previous challenges, and, to some extent, immune to new challenges as well. In the last section, I suggest that the definition has a philosophical interest of its own, because standard Quinean objections are not as conclusive as one might think when attention is paid to the fact that Carnap requires complete syntactic specification of validities. (shrink)

Describing resources and their relationships with organisms seems to be a useful approach to a ‘unified ecology’, contributing to fill the gap between natural and human oriented processes, and opening new perspectives in dealing with biological complexity. This Resource Criterion defines the main properties of resources, describes the mechanisms that link them to individual species, and gives a particular emphasis to the biosemiotic approach that allows resources to be identified inside a heterogeneous ecological medium adopting the eco-field model. In (...) particular, this Criterion allows to couple matter, structured energy and information composing the ecological systems to the biosemiotic and cognitive mechanisms adopted by individual species to track resources, transforming neutral surroundings into meaningful species-specific Umwelten. The expansion of the human semiotic niche that is a relevant evolutionary process of the present time, assigns the role of powerful and efficient agency to the Resources Criterion to evaluate the effect of human intrusion into the natural systems with habits of key stone species, under the challenge of a growing use of alloctonous, immaterial and symbolic resources of the actual globalized societal models. The Resource Criterion interprets the ecological dynamics contributing to complete the epistemology of the ecology, to open a bridge toward economy and other societal sciences, and to contribute to formulate a General Theory of Resources. (shrink)

The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many different consistent sets, and it has been argued that a complete interpretation should be accompanied with a natural mechanism leading to a (possibly) unique preferred consistent set. The existence of multiple consistent sets becomes more problematic because it allows the existence of contrary inferences [1]. We analyse (...) the conceptual difficulties that arise from the existence of multiple consistent sets and provide a suggestion for a natural set selection criterion. This criterion does not lead to a unique physical consistent set, however it evades the existence of consistent sets with contrary inferences. The criterion is based on the concept of preclusion and the requirement that probability one propositions and their inferences should be non-contextual. The allowed consistent sets turn-out to be compatible with coevents which are the ontology of an alternative, histories based, formulation [2–4]. (shrink)

Consider a general class of structural inference rules such as exchange, weakening, contraction and their generalizations. Among them, some are harmless but others do harm to cut elimination. Hence it is natural to ask under which condition cut elimination is preserved when a set of structural rules is added to a structure-free logic. The aim of this work is to give such a condition by using algebraic semantics. We consider full Lambek calculus (FL), i.e., intuitionistic logic without any structural rules, (...) as our basic framework. Residuated lattices are the algebraic structures corresponding to FL. In this setting, we introduce a criterion, called the propagation property, that can be stated both in syntactic and algebraic terminologies. We then show that, for any set R of structural rules, the cut elimination theorem holds for FL enriched with R if and only if R satisfies the propagation property. As an application, we show that any set R of structural rules can be "completed" into another set R*, so that the cut elimination theorem holds for FL enriched with R*, while the provability remains the same. (shrink)

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity, where novel empirical data are lacking. One principle widely adopted in the search for QG is ultraviolet completion: the idea that a theory should hold up to all possible high energies. We argue— contra standard scientific practice—that UV-completion is poorly motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we (...) explore the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV-completion is used, and how it should be used, in various specific approaches to QG. 1Introduction 1.1Principles in theory development and evaluation 2Primer on UV-Completion, Renormalizability, and All That 2.1Renormalizability and UV-completion 2.2Other forms of UV-completion 3Why Should QG Be UV-Complete? 3.1UV-completion and fundamentality 3.2UV-completion and minimal length 4UV-Completion in Different Approaches to QG 4.1String theory 4.2Asymptotic safety 4.3Causal dynamical triangulation 4.4Higher derivative approaches 4.5Supergravity 4.6Causal set theory 4.7Canonical QG 4.8Loop quantum gravity 4.9Approaches based on alternative gravitational theories 4.10Emergent gravity approaches 5UV-Completion as a Guiding Principle in QG 6Conclusion. (shrink)

In this journal (Studia Logica), D. Rizza [2010: 176] expounded a solution of what he called “the indiscernibility problem for ante rem structuralism”, which is the problem to make sense of the presence, in structures, of objects that are indiscernible yet distinct, by only appealing to what that structure provides. We argue that Rizza’s solution is circular and expound a different solution that not only solves the problem for completely extensive structures, treated by Rizza, but for nearly (but not) all (...) mathematical structures. (shrink)

A semantics for logical necessity, based on Carnap's criterion of adequacy, is given with respect to the ontology of logical atomism. A calculus for sentential (propositional) modal logic is described and shown to be complete with respect to this semantics. The semantics is then modified in terms of a restricted notion of 'all possible worlds' in the interpretation of necessity and shown to yield a completeness theorem for the modal logic S5. Such a restricted notion introduces material content (...) into the meaning of necessity so that, in addition to atomic facts, there are "modal facts" that distinguish one world from another. (shrink)

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs (...) in CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

In the United States, the dominant model of decision‐making capacity (DMC) is the “four abilities model,” which judges DMC according to four criteria: understanding, appreciation, reasoning, and communicating a choice. Some critics argue that this model is “too cognitive” because it ignores the role of emotions and values in decision‐making. But so far there is no consensus about how to incorporate such factors into a model of DMC while still ensuring that patients with unusual or socially disapproved values still have (...) their autonomous decisions respected. In this paper, we aim to give an account of the role of values in decision‐making which can answer some of the lingering questions about capacity. In the current literature, defenders of the inclusion of values in DMC tend to propose solutions which focus on the distorted or incoherent attributes of the values themselves. We argue that shifting the focus onto valuing as an ability is a better solution and that a complete picture of capacity includes understanding, appreciation, reasoning, communicating a choice, and the ability to value. On the basis of a conceptual analysis of the necessary conditions for autonomous decision‐making, we derive a conception of the ability to value. On our account, the ability to value has four components: the possession of values, the ability to access those values, the ability to engage in practical reasoning with one's values, and the ability to act on the result of that reasoning. We describe the positive components of the ability to value, some indicators of impairment, and some implications of our account. (shrink)

We can think of functional completeness in systems of propositional logic as a form of expressive completeness: while every logical constant in such system expresses a truth-function of finitely many arguments, functional completeness garantees that every truth-function of finitely many arguments can be expressed with the constants in the system. From this point of view, a functionnaly complete system of propositionnal logic can thus be seen as one where no logical constant is missing. Can a similar question (...) be formulated for quantified first-order logics ? How to make sense of the question whether, e.g., ordinary first-order logic is "functionaly" complete or have no logical constant missing ? In this note, we build on a suggestive proposal made by Bonnay(2006) and shows that it is equivalent to the criterion that a first-order logic L be functionaly complete if and only if every class of structures closed under L-elementary equivalence is L-elementary. Ordinary first-order logic is not complete in this sense. We raise the question whether any logic can be. -/- . (shrink)

The problem of logical constants consists in finding a principled way to draw the line between those expressions of a language that are logical and those that are not. The criterion of invariance under permutation, attributed to Tarski, is probably the most common answer to this problem, at least within the semantic tradition. However, as the received view on the matter, it has recently come under heavy attack. Does this mean that the criterion should be amended, or maybe (...) even that it should be abandoned? I shall review the different types of objections that have been made against invariance as a logicality criterion and distinguish between three kinds of objections, skeptical worries against the very relevance of such a demarcation, intensional warnings against the level at which the criterion operates, and extensional quarrels against the results that are obtained. I shall argue that the first two kinds of objections are at least partly misguided and that the third kind of objection calls for amendment rather than abandonment. (shrink)

In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in (...) this context. (shrink)

The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible torsion within all norm-composing parallelizable manifolds. A profound interplay is thus uncovered between the existence and strength of quantum correlations and the parallelizability of the spheres S^0, S^1, S^3, and S^7 necessitated by the four real division algebras. In particular, parallelization within a unit (...) 3-sphere is shown to be responsible for the existence of EPR and Hardy type correlations, whereas that within a unit 7-sphere is shown to be responsible for the existence of all GHZ type correlations. Moreover, parallelizability in general is shown to be equivalent to the completeness criterion of EPR, in addition to necessitating the locality condition of Bell. It is therefore shown to predetermine both the local outcomes as well as the quantum correlations among the remote outcomes, dictated by the infinite factorizability of points within the spheres S^3 and S^7. The twin illusions of quantum entanglement and non-locality are thus shown to stem from the topologically incomplete accountings of the measurement results. (shrink)

The average, general readings in philosophy anthology have five to seven readings on necessary truth. This volume has fourteen. The old workhorses are here: Kant on synthetic and analytic propositions, Mill on necessary truths, Ayer on the a priori, Quine, Grice, and Strawson on dogmas of empiricism. In addition, Pap has two items, one in the middle of an exchange with Putnam over reds, greens, and the synthetic a priori. There is a tough logical analysis by Hintikka, contributions by Jonathan (...) Bennett and Hanson, and a final exchange between Katz and Quine. The selections are by no means comprehensive, but, as the editors note, this would have been impossible. A seventeen-page bibliography comes closer to fulfilling the completeness criterion. The editors include a short introduction, which really should have been expanded, since it raises some of the ontological issues that implicitly guide the debate that takes place among the selections.--E. A. R. (shrink)

Harmony and conservative extension are two criteria proposed to discern between acceptable and unacceptable rules. Despite some interesting works in this field, the exact relation between them is still not clear. In this article, some standard counterexamples to the equivalence between them are summarized, and a recent formulation of the notion of stability is used to express a more refined conjecture about their relation. Then Prawitz's proposal of a counterexample based on the truth predicate to this refined conjecture is shown (...) to rest on dubious assumptions. As a consequence, two new counterexamples are proposed: one uses the extension of logic with a small amount of arithmetic, while the other uses the extension of a small fragment of arithmetic with a problematic operator defined by Peano. It is argued that both these new counterexamples work fine to reject the conjecture and that the last one works also as a rejection of harmony as a complete criterion of acceptability of rules. (shrink)

This paper details efforts by the Purdue School of Engineering and Technology at Indiana University Purdue University Indianapolis to create a single instrument for honors science, technology, engineering and mathematics students wishing to demonstrate competence in the IUPUI Principles of Undergraduate Learning and Accreditation Board for Engineering and Technology Engineering Accreditation Criterion and Technology Accreditation Criterion 2, a through k. Honors courses in Human Behavior, Ethical Decision-Making, Applied Leadership, International Issues and Leadership Theories and Processes were created along (...) with a specific menu of activities and an assessment rubric based on PUL’s and ABET criteria to evaluate student performance in the aforementioned courses. Students who complete the series of 18 Honors Credit hours are eligible for an Honors Certificate in Leadership Studies from the Department of Organizational Leadership and Supervision. Finally, an accounting of how various university assessment criteria, in this case the IUPUI Principles of Undergraduate Learning, can be linked to ABET outcomes and prove student competence in both, using the aforementioned courses, menu of items, and assessment rubrics; these will be analyzed and discussed. (shrink)

What is the criterion for distinguishing between the excellence of the excellent constitution κατ’ εὐχήν in Politics VII and the excellence of the other excellent constitutions? Every constitution includes in its composition necessity and good. Yet, unlike what happens in the other excellent constitutions, in the best constitution of Politics VII there is a convergence, not an opposition, between necessity and goodness. This point is confirmed by a change in the meaning of the word ἀναγκαῖον. In the constitution delineated (...) in Book VII, ultimately matter and form are identical. Both the convergence between necessity and good and the fact that every citizen should be a good man or a ‘maker of virtue’ lead to equate the excellent constitution with the completed form of political capacity. Hence, the relationship between πολιτεία and ἀρίστη πολιτεία is similar to the relationship between ἔργον κιθαριστοῦ and ἔργον σπουδαίου κιθαριστοῦ. (shrink)

In this paper, I argue that the ‘modified youngest first’ principle provides a morally appropriate criterion for making decisions regarding the distribution of scarce medical resources, and that it is morally preferable to the simple ‘youngest first’ principle. Based on the complete lives system's goal of maximizing complete lives rather than individual life episodes, I argue that essential to the value we see in complete lives is the first person value attributed by the experiencer of that life. For a (...) life to be ‘complete’ or ‘incomplete,’ the subject of that life must be able to understand the concept of a complete life, to have started goals and projects, and to know what it would be for that life to be complete. As the very young are not able to do this, it can reasonably be said that their characteristically human lives have not yet begun, giving those accepting a complete lives approach good reason to accept the modified youngest first principle over a simple ‘youngest first’ approach. (shrink)

Alongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum’s Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko’s Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style (...) entailment relation over a single-conclusion one. (shrink)

On the definition of genre of Dostoevsky's works. The article mostly addresses Dostoevsk's own definitions of genres of his works, either explicated in the texts (subtitles, prefaces) or contained in the writer's letters; or rather the relationship between the scholarly strategies of defining genres and the writer's own view, as evidenced. by subtitles which, in some sense, are part of the text (in nearly, but not precisely, the same way as the titles themselves are). The writer's own definitions, then, can (...) be regarded as possible objects of the scholarly interpretation. Agreement, or lack thereof, between the author's and the scholars' definitions may be due both to similarity vs dissimilarity between the definition standards inherent in the respective epochs and to specific interpretation aspects. In the latter case, agreement is more cornman in studies focusing on vastly different problems unrelated to genre, whereas disagreement is more frequent in studies concerned with the genres of Dostoevsky's works. One of the reasons why his own definitions must be critically revisited is that certain titles of his workscan be basically viewed as subtitles or genre definitions insofar as they in some way define the variety of the text regardless of the underlying criterion: narrative, "discourse", type of source, genre, or genre variety. Indeed, both these subtitles and, sometimes, the writer's own genre definitions tum out to be pretense, an imitation of "standard" subtitles or genre definitions, respectively. Titles themselves sometimes look like subtitles, thus "exposing the device" and demonstrating this mimicry not merely by violating semantic and syntactic relations in the case of subtitles (sign/name/title/ subtitle and virtual reference/"reality" of text - and relationships such as those between title and subtitle; title and the principal text; and subtitle and principal text), but also by the fact that their position is "marked". Dostoevsky not just failed to follow his own "final genre definitions" within the text, as reflected in the subtitles, and not just changed them repeatedly in his letters, but in the official documents, too, he sometimes defined genres in a way which did not agree with either the subtitles or his own definitions given in his letters.Dostoevsky frequently changed the genre definitions not merely during his work on a text, which would be only natural, and not merely many years after it had been completed, published, revised, and republished (which might be ascribed to memory errors), but also shortly after the completed manuscript had been shipped to the publishers or after the text had been published or republished. While the logic underlying these changes must be studied and interpreted, it is evident that the scholars are often unable to accept the author's own "final genre definitions" both because these are often unavailable in subtitles, and because of the "Proteic" nature of their use by the writer in various contexts. (shrink)

In spite of the fact that there is a common reality, people know very little about death. However, the person who sees the limited life as an obstacle in the way of encountering in life has always been in search of immortality. As a result of this quest, death has occupied different positions in human life. These positions can be grouped under three headings as tamed death, foreign death, and unspoken death. In this context, according to the last approach which (...) is effective in the modern world, the death which is completely removed from the life of the individual has been turned into a phenomenon which should be avoided/ postponed, not something to be dealt with. Thus, death, becoming a lonely phenomenon rather than a social phenomenon, has become a business problem rather than an occupation that people are interested in. Death, on the other hand, must be a criterion that determines life rather than being an object determined by life. The purpose of studying in this context is to question the position occupied in the life of the modern individual by moving from the understanding of deaths developed in the historical process. (shrink)

In this paper I propose a new argument for moderate autonomism. I call this the ‘critical argument’ to distinguish it from the empirical argument of James C. Anderson and Jeffrey T. Dean, and the no-error argument of James Harold. My strategy is to first employ the criticism of Matthew Arnold and F.R. Leavis to demonstrate the moralist failure to account for the complexity of the relationship between literature and morality, and then offer a more promising alternative. I set out the (...) autonomist, moralist, and immoralist positions in the value interaction debate in §1, and identify problems with classifying the two critics in contemporary terms. In §2 I discuss Arnold’s cultural criticism as both a part of – and a reaction to – the public moralist tradition that dominated Britain in the nineteenth century, drawing attention to his criterion of ‘seriousness’. §3 examines Leavis’ literary criticism, focusing on his conception of the relationship between composition and life, and his criterion of ‘maturity’. Drawing on the similarities between Arnold and Leavis, I demonstrate that their concern with morality differs from that of the contemporary moralists in §4. In §5 I employ John Gibson’s distinction between normative and informative values to complete the argument for moderate autonomism. I test my argument against an extreme case, a hypothetical literary equivalent to The Birth of a Nation, in §6, and conclude that moderate autonomism provides the most compelling solution to the value interaction debate. (shrink)