Given an intermediate prepositional logic L, denote by L –d its disjuctionless fragment. We introduce an infinite sequence {J n}n1 of propositional formulas, and prove:(1)For any L: L –d =I –d (I=intuitionistic logic) if and only if J n L for every n 1.

We introduce, in a general setting, an ‘‘analytic’’ version of standard equational calculi of combinatory logic. Analyticity lies on the one side in the fact that these calculi are characterized by the presence of combinatory introduction rules in place of combinatory axioms, and on the other side in that the transitivity rule proves to be eliminable. Apart from consistency, which follows immediately, we discuss other almost direct consequences of analyticity and the main transitivity elimination theorem; in particular the Church−Rosser and (...) the leftmostreduction theorems for the associated notions of reduction. The last two sections deal with analytic combinatory calculi with the extensionality rule added. Here, as far as the elimination of transitivity is concerned, we have only partial results, which unfortunately do not cover, at present, full CL + Ext. Yet, they are sufficient to prove the decidability of weaker combinatory calculi with extensionality, including e.g. BCK + Ext. (shrink)

LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = (( ) ) (Scott), andKP = ()()() (Kreisel-Putnam). Using Kripke's semantics, we prove:1) SKP has the finite model property; 2) SKP has the disjunction property. In the last section of the paper we give some results about Scott's logic S = I+S.

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken. (shrink)

It has often been remarked that the metatheory of strong reduction $\succ$ , the combinatory analogue of βη-reduction ${\twoheadrightarrow_{\beta\eta}}$ in λ-calculus, is rather complicated. In particular, although the confluence of $\succ$ is an easy consequence of ${\twoheadrightarrow_{\beta\eta}}$ being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of $\succ$ , one which makes no detour through λ-calculus. We answer positively to this question, by extending (...) and exploiting the technique of transitivity elimination for ‘analytic’ combinatory proof systems, which has been introduced in previous papers of ours. Indeed, a very short proof of the confluence of $\succ$ immediately follows from the main result of the present paper, namely that a certain analytic proof system G e [ $\mathbb {C}$ ] , which is equivalent to the standard proof system CL ext of Combinatory Logic with extensionality, admits effective transitivity elimination. In turn, the proof of transitivity elimination—which, by the way, we are able to provide not only for G e [ $\mathbb {C}$ ] but also, in full generality, for arbitrary analytic combinatory systems with extensionality—employs purely proof-theoretical techniques, and is entirely contained within the theory of combinators. (shrink)

We give completeness results — with respect to Kripke's semantic — for the negation-free intermediate predicate calculi.

We introduce a certain extension of -calculus, and show that it has the Church-Rosser property. The associated open-term extensional combinatory algebra is used as a basis to construct models for theories of Explict Mathematics (formulated in the language of "types and names") with positive stratified comprehension. In such models, types are interpreted as collections of solutions (of terms) w.r. to a set of numerals. Exploiting extensionality, we prove some consistency results for special ontological axioms which are refutable under elementary comprehension.

The paper settles an open question concerning Negri-style labeled sequent calculi for modal logics and also, indirectly, other proof systems which make (more or less) explicit use of semantic parameters in the syntax and are thus subsumed by labeled calculi, like Brünnler’s deep sequent calculi, Poggiolesi’s tree-hypersequent calculi and Fitting’s prefixed tableau systems. Specifically, the main result we prove (through a semantic argument) is that labeled calculi for the modal logics K and D remain complete w.r.t. valid sequents whose relational (...) part encodes a tree-like structure, when the unique rule which contains an harmful implicit contraction—by which the condition that the premises be less complex than the conclusion is violated—is modified into a contraction-free one respecting the latter condition, thus making the proof-search space finite. (shrink)

As evidenced by high-throughput sequencers, genomic technologies have recently undergone radical advances. These technologies enable comprehensive sequencing of personal genomes considerably more efficiently and less expensively than heretofore. These developments present a challenge to the conventional framework of biomedical ethics; under these changing circumstances, each research project has to develop a pragmatic research policy. Based on the experience with a new large-scale project—the Genome Science Project—this article presents a novel approach to conducting a specific policy for personal genome research in (...) the Japanese context. In creating an original informed-consent form template for the project, we present a two-tiered process: making the draft of the template following an analysis of national and international policies; refining the draft template in conjunction with genome project researchers for practical application. Through practical use of the template, we have gained valuable experience in addressing challenges in the ethical review process, such as the importance of sharing details of the latest developments in genomics with members of research ethics committees. We discuss certain limitations of the conventional concept of informed consent and its governance system and suggest the potential of an alternative process using information technology. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) ; as opposed to what he may have taught secretly to his pupils. Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken.In that part of the dialogue where the question is under examination whether or not knowledge and perception are the same, Socrates uses an idealized concept of knowledge. That is, he restricts the use of the word by setting down what he will consider to be the essential characteristics of knowledge, the sufficient and necessary conditions of its being instantiated. An excellent piece of philosophical procedure. (shrink)

We aim at clarifying to what extent the work of the English mathematician George Boole on the algebra of logic is taken into consideration and discussed in the work of early Husserl, focusing in particular on Husserl’s lecture “Über die neueren Forschungen zur deduktiven Logik” of 1895, in which an entire section is devoted to Boole. We confront Husserl’s representation of the problem-solving processes with the analysis of “symbolic reasoning” proposed by George Boole in the Laws of Thought and try (...) to show how and why Husserl, while praising Boole’s calculus, strongly criticizes his attempt at a philosophical clarification and justification of it. (shrink)

For each ordinal $\alpha > 0, L(\alpha)$ is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable $\eta (> 0)$ , there exists a countable ordinal of the form β + η such that L(α (...) + η) = L(β + η). On the other hand, such a reduction of ordinals to countable ones is impossible for a logic L(α) if α is an uncountable regular ordinal. Moreover, it will be proved that the mapping L is injective if it is restricted to ordinals less than ω ω , i.e. α ≠ β implies L(α) ≠ L(β) for each ordinal $\alpha,\beta. (shrink)

We aim at clarifying to what extent the work of the German mathematician Ernst Schröder on the algebra of logic is taken into consideration and rehashed in the work of the early Husserl, focusing on Husserl’s 1891 Review of the first volume of Schröder’s monumental Vorlesungen über die Algebra der Logik and on Husserl’s text Der Folgerungskalkül und die Inhaltslogik written in the same year. We will try to show how and why Husserl, while praising Schröder’s calculus, strongly criticizes Schröder’s (...) attempt at a philosophical clarification and justification of it. (shrink)

This paper deals with the infinitary modal propositional logic Kω1, featuring countable disjunctions and conjunc- tions. It is known that the natural infinitary extension LK.

Because anticipated and retrospective regret play important roles in practical deliberation and motivation, better understanding them can illuminate the contours of human agency. However, the possibility of self-ignorance and the fact that we change over time can make regret—especially anticipatory regret—not only a poor predictor of where the agent will be in the future but also an unreliable indicator of where the agent stands. Granting these, this paper examines the way in which prospective and, particularly, retrospective regret can nevertheless yield (...) important insight into the sorts of creatures we are, both generally and individually. The experience of retrospective regret can show a person she values something in a way she did not know or that she is (or was) a different person than she had thought, insights which can factor into forward-looking, or prospective, deliberation. Such instances of revelatory regret reveal something to the agent about herself as agent. I examine two cases of agential self-ignorance. In the first, the experience of regret reveals what the agent values, not only to others but even to the agent himself. In the second, the agent anticipates experiencing regret for an action but does not experience the regret, suggesting that the agent did not value the rejected alternative in the way she thought. Anticipatory regret is forward-looking and can play an important role in practical deliberation. But insofar as anticipatory regret flows from one’s imperfect judgment and prospection about oneself, retrospective regret can be an important corrective in helping the agent understand her own standpoint. (shrink)

In his newly updated version of The Anatomy of a Constitutional Law Case, Alan F. Westin provides a documentary portrait of historically important constitutional law case, 'Youngstown Sheet & Tube Co. v. Sawyer, ' from its rise in a bargaining dispute in the steel industry during 1952 to the aftermath of its decision by the United States Supreme Court. Westin has added to his classic book additional materials and personal commentaries collected since the work was first published. The new information (...) covers what went on within the Truman administration, what went on within the Supreme Court when analyzing and resolving issues that come before it. Westin includes selections from transcripts, briefs and other official proceedings, adds notes describing each phase of the constitutional process, and a section of commentary and questions relating this case to others. (shrink)

We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW + . Next, we show that POW + can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.

We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jager's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW$^+$. Next, we show that POW$^+$ can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.

It is not quite as easy to see that there is in fact no formula of this modal language having the same truth conditions (in terms of S5 Kripke semantics) as (1). This was rst conjectured by Allen Hazen2 and later proved by Harold Hodes3. We present a simple direct proof of this result and discuss some consequences for the logical analysis of ordinary modal discourse.

In recent years, there has been a heated debate about how to interpret findings that seem to show that humans rapidly and automatically calculate the visual perspectives of others. In the current study, we investigated the question of whether automatic interference effects found in the dot-perspective task (Samson, Apperly, Braithwaite, Andrews, & Bodley Scott, 2010) are the product of domain-specific perspective-taking processes or of domain-general “submentalizing” processes (Heyes, 2014). Previous attempts to address this question have done so by implementing inanimate (...) controls, such as arrows, as stimuli. The rationale for this is that submentalizing processes that respond to directionality should be engaged by such stimuli, whereas domain-specific perspective-taking mechanisms, if they exist, should not. These previous attempts have been limited, however, by the implied intentionality of the stimuli they have used (e.g. arrows), which may have invited participants to imbue them with perspectival agency. Drawing inspiration from “novel entity” paradigms from infant gaze-following research, we designed a version of the dot-perspective task that allowed us to precisely control whether a central stimulus was viewed as animate or inanimate. Across four experiments, we found no evidence that automatic “perspective-taking” effects in the dot-perspective task are modulated by beliefs about the animacy of the central stimulus. Our results also suggest that these effects may be due to the task-switching elements of the dot-perspective paradigm, rather than automatic directional orienting. Together, these results indicate that neither the perspective-taking nor the standard submentalizing interpretations of the dot-perspective task are fully correct. (shrink)

Are we witnessing progress or regress in the recent increasing popularity and electoral success of populist politicians and parties in consolidated democratic nations? ... Is the innovative use of popular referendum in Great Britain to settle fundamental constitutional questions a progressive or regressive innovation? ... Similarly, is the increasing use of constituent assemblies to change constitutions across the world evidence of progress in democratic constitutionalism, or, a worryingly regressive change back toward unmediated popular majoritarianism? ... This paper reflects on some (...) of the perils and promise of framing such questions with the conceptual couplet of progress and regress. It considers four compelling critiques of the use of ‘progress’ and its cognates in sociopolitical theory, as well as arguing that such concepts are nevertheless ineliminable for our normative theories. The paper concludes by suggesting that we can avoid the most serious problems by employing only conceptions of political progress and regress that are piecemeal, pragmatic, and processual. (shrink)

The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of (...) selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS studies. (shrink)

_BMC Medical Ethics_ is an open access journal publishing original peer-reviewed research articles in relation to the ethical aspects of biomedical research and clinical practice, including professional choices and conduct, medical technologies, healthcare systems and health policies. _BMC __Medical Ethics _is part of the _BMC_ series which publishes subject-specific journals focused on the needs of individual research communities across all areas of biology and medicine. We do not make editorial decisions on the basis of the interest of a study or (...) its likely impact. Studies must be scientifically valid; for research articles this includes a scientifically sound research question, the use of suitable methods and analysis, and following community-agreed standards relevant to the research field. Specific criteria for other article types can be found in the submission guidelines. _BMC series - open, inclusive and trusted_. (shrink)

We introduce new proof systems G[β] and G ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule admits effective elimination. This key feature, besides its intrinsic conceptual significance, turns out to provide a common logical background to new and comparatively simple demonstrations—rooted in nice proof-theoretical properties of transitivity-free derivations—of a number (...) of well-known and central results concerning β- and βη-reduction. The latter include the Church–Rosser theorem for both reductions, the Standardization theorem for β- reduction, as well as the Normalization (Leftmost reduction) theorem and the Postponement of η-reduction theorem for βη-reduction. (shrink)

Theorists of public reason such as John Rawls often idealize constitutional courts as exemplars of public reason. This paper raises questions about the seduction and limits of analogies between theorists’ account of public reason and actual constitutional jurisprudence. Examining the work product of the United States Supreme Court, the paper argues that while it does engage in reason-giving to support its decisions—as the public reason strategy suggests— those reasons are (largely) legalistic and specifically juristic reasons—not the theorists’ idealized moral-political reasons (...) on matters of fundamental principle. But if constitutional courts do not engage on matters of fundamental principle, then a public reason strategy for assuaging democratic worries about judicial review would no longer be open: prominent liberal and deliberative democratic theorists could no longer point to the alleged superiority of constitutional courts to speak in the name of, and for, the people’s shared political principles. The paper extends beyond the U.S. case study by pointing to three institutional factors explaining the disanalogy between what some constitutional courts do and what public reason theories require them to do. It concludes with considerations about whether the public reason strategy might be more successfully applied to international courts. (shrink)

Autobiography and Teacher Development in China investigates the roles of autobiography in teacher education, as several scholars in China recontextualize Western conceptions of teacher development, combining them with uniquely Chinese cultural conceptions to articulate a reconceptualization of teacher development that holds worldwide significance. Framed by the work of Zhang Hua and William F. Pinar, these theoretical and practical essays point to an internationally inflected reconceptualization of teachers' professional development, pre-service and in-service. This volume addresses multiple movements of teacher education reform (...) worldwide, focused on crafting a nationally distinctive course not only internationally, but also culturally, historically, and locally. (shrink)

From climate change to fossil fuel dependency, from the uneven effects of natural disasters to the loss of biodiversity: complex socio-environmental problems indicate the urgency for cross-disciplinary research into the ways in which the social, the natural and the technological are ever more entangled. This ground breaking text moves between environmental sociology and environmental geography, political and social ecology and critical design studies to provide a definitive mapping of the state of environmental social theory in the age of the anthropocene. (...) Environments, Natures and Social Theory provokes dialogue and confrontation between critical political economists, actor network theorists, neo-Malthusians and environmental justice advocates. It maps out the new environmental politics of hybridity moving from hybrid neo-liberals to end times ecologists, from post environmentalists to cyborg eco-socialists. White, Rudy and Gareau insist on the necessity of a critical but optimistic hybrid politics, arguing that a more just, egalitarian, democratic and sustainable anthropocene is within our grasp. This will only be brought into being, however, by reclaiming, celebrating and channeling the reconstructive potential of entangled hybrid humans as inventive hominids, creative gardeners, critical publics and political agents. Written in an accessible style, Environments, Natures and Social Theory is an essential resource for undergraduate and postgraduate students across the social sciences. (shrink)

Since Mueller’s 1958 article calling Hegelian dialectics a “legend,” it has been fashionable to deny that Hegel used thesis-antithesis-synthesis dialectics. But in truth, Hegel’s Phenomenology of Spirit has 28 dialectics hidden on four outline levels, and The Philosophy of History has 10 more on three outline levels. In Phenomenology’s macrodialectic, Hegel’s nonsupernatural Spirit–all reality, everything in the universe, including man and artificial objects–advances from unconscious + union (thesis) to conscious + separation (antithesis) to a synthesis of conscious (from the antithesis) (...) + union (from the thesis). Previous interpretations of Phenomenology have missed this dialectic: they have assumed that Spirit’s journey begins with consciousness, whereas the journey actually begins in the primordial state of nature, before man arrives and provides Spirit with its Mind (the collective mind of man). Mind then misperceives itself as a multitude of separate alien “objects”–things other than itself. The macrodialectic and all other dialectics are based on Christianity’s Johannine separation-and-return mythology; all Hegelian dialectics separate from a concept in the thesis, going to that something’s opposite (antithesis), and then return to the thesis concept. Thus, in Hegel’s master-and-slave dialectic (God = master, man = slave), man advances from potential + freedom to actual + bondage (religiosity) to actual + freedom (atheism). Only Marx and Tillich understood Hegelian dialectics. Marx’s basic dialectic (one of four) saw history separating from and returning to Communism, going from communal ownership + poverty (primitive communism, or gens) to private ownership + wealth (slavery, feudalism, capitalism) to communal ownership + wealth (final communism). Tillich’s basic dialectic (one of many) separates from and returns to God, advancing from Yes to God + Yes to supernaturalism (theism) to No to God + No to supernaturalism (atheism) to Yes to God + No to supernaturalism (humanism: humanity is the nonsupernatural “God above the God of theism”). (shrink)

To find more information about Rowman and Littlefield titles, please visit www.rowmanlittlefield.com.