The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. This paper lays the ground for (...) an investigation of intuitionistic analogues of systems stronger thanK. A brief survey is given of the existing literature on intuitionistic modal logic. (shrink)

Chciałem Go pożegnać. Kilkakrotnie próbowałem napisać choć parę słów. O Nim samym. Okazało się, że nie potrafię. Udało mi się tylko przedstawić Jego poglądy na reizm Tadeusza Kotarbińskiego, ale uczyniłem to gdzie indziej. Muszę tu poprzestać na ofiarowaniu Mu tego, co napisałem na Jego dziewięćdziesiąte urodziny, w osiemdziesięciolecie naszej przyjaźni.

:There are manifold intriguing issues located within largely unexplored borderlands of bioethics, future studies, and astrobiology. Human enhancement has for quite some time been among the foci of bioethical debates, but the same cannot be said about its global, transgenerational, and even cosmological consequences. In recent years, discussions of posthuman and, in general terms, postbiological civilization have slowly gained a measure of academic respect, in parallel with the renewed interest in the entire field of future studies and the great strides (...) made in understanding of the origin and evolution of life and intelligence in their widest, cosmic context. These developments promise much deeper synergic answers to questions regarding the long-term future of enhancement: how far can it go? Is human enhancement a further step toward building a true postbiological civilization? Should we actively participate and help shape this process? Is the future of humanity “typical” in the same Copernican sense as our location in space and time is typical in the galaxy, and if so, can we derive important insights about the evolutionary pathways of postbiological evolution from astrobiological and Search for ExtraTerrestrial Intelligence studies? These and similar questions could be understood as parts of a possible unifying research program attempting to connect cultural and moral evolution with what we know and understand about their cosmological and biological counterparts. (shrink)

Recent discussion of the alleged adverse consequences of space colonization by Phil Torres in this journal is critically assessed. While the concern for suffering risks should be part of any strategic discussion of the cosmic future of humanity, the Hobbesian picture painted by Torres is largely flawed and unpersuasive. Instead, there is a very real risk that the skeptical arguments will be taken too seriously and future human flourishing in space delayed or prevented.

This article approaches the paradigm shift of datafication from the perspective of civil society. Looking at how individuals and groups engage with datafication, it complements the notion of “data politics” by exploring what we call the “contentious politics of data”. By contentious politics of data we indicate the bottom-up, transformative initiatives interfering with and/or hijacking dominant processes of datafication, contesting existing power relations or re-appropriating data practices and infrastructure for purposes distinct from the intended. Said contentious politics of data is (...) articulated in an array of practices of data activism taking a critical stance towards datafication. In data activism, data as mediators take a central role, both as part of an action repertoire or as objects of struggle in their own right. Leveraging social movement studies and science and technology studies, this theoretical essay argues that data activism can be mapped along two analytical dimensions: “data as stakes” vs. “data as repertoires”, and “individual practice vs. collective action”. Mapping action repertoires and tactics along these axes allows us to chart the potential emergence of a political data subject at the intersection of these two dimensions. This furthers our understanding of people’s engagement with data in relation to other forms of activism and existing work in social movement studies. It also helps us interpreting potential trajectories of contemporary social movements, as they increasingly interface with data, devices and platforms. (shrink)

We historically trace various non-conventional explanations for the origin of the cosmic microwave background and discuss their merit, while analyzing the dynamics of their rejection, as well as the relevant physical and methodological reasons for it. It turns out that there have been many such unorthodox interpretations; not only those developed in the context of theories rejecting the relativistic paradigm entirely but also those coming from the camp of original thinkers firmly entrenched in the relativistic milieu. In fact, the orthodox (...) interpretation has only incrementally won out against the alternatives over the course of the three decades of its multi-stage development. While on the whole, none of the alternatives to the hot Big Bang scenario is persuasive today, we discuss the epistemic ramifications of establishing orthodoxy and eliminating alternatives in science, an issue recently discussed by philosophers and historians of science for other areas of physics. Finally, we single out some plausible and possibly fruitful ideas offered by the alternatives. (shrink)

Cosmology seems extremely remote from everyday human practice and experience. It is usually taken for granted that cosmological data cannot rationally influence our beliefs about the fate of humanity—and possible other intelligent species—except perhaps in the extremely distant future, when the issue of “heat death” (in an ever-expanding universe) becomes actual. Here, an attempt is made to show that it may become a practical question much sooner, if an intelligent community wishes to maximize its creative potential. We estimate, on the (...) basis of a greatly simplified model, the rate of loss of potentially useful information due to the delay in undertaking the colonization of the largest gravitationally bound structures in an accelerating universe. In addition, we argue for a natural cosmological extension of the classical taxonomy of advanced technological communities given by Kardashev. New developments in the fields of anthropic self-selection and physical eschatology give, for the first time, solid foundations to such results. This may open some new (and possibly urgent) issues in the areas of future policy making and transhumanist studies generally. It may also give us a slightly better perspective on the SETI endeavor. (shrink)

The paper addresses the ‘rational choice only’ reconstruction, characterization, and interpretation of classical and neoclassical economics. It argues that such a reconstruction is inaccurate failing to do justice to the dual theoretical character of classical/neoclassical economics. The paper instead proposes and shows that the latter involves not only elements of ‘rational choice theory’ but also those of an alternative conception. It identifies various and important ideas, observations, and implications of irrational choice and action within classical/neoclassical economics. One class of such (...) ingredients involves forms, expressions, and cases—i.e. specification and classification—of irrational choices in the economy. Another class comprises the social and other factors—i.e. economic sociology or social economics—of irrational choices in the economy. The paper’s intended contribution is to help identify and clarify the extant sources and alternatives of rational choice theory in conventional economics.... (shrink)

The article reconsiders the generalization of neoclassical economics by modern rational choice theory. Hence, it reexamines the possible theoretical grounds or lack thereof within neoclassical economics for economic imperialism implied in much of rational choice theory. Some indicative instances of rational choice theory's generalization of neoclassical economics are reviewed. The main portion of the article addresses the question as to whether neoclassical economics allows its generalization in rational choice theory and thus legitimizes economic imperialism. Presented are a number of pertinent (...) theoretical reasons why neoclassical economics does not fully justify its generalization into rational choice as a general social theory, particularly into an overarching economic approach to social action and society. Also discussed are some theoretical implications of the rational choice generalization of neoclassical economics. The main contribution of the article is to detect lack of a strong theoretical rationale in much of neoclassical economics for rational choice theory's manifest or latent economic imperialism. (shrink)

We describe a significant practical consequence of taking anthropic biases into account in deriving predictions for rare stochastic catastrophic events. The risks associated with catastrophes such as asteroidal/cometary impacts, supervolcanic episodes, and explosions of supernovae/gamma-ray bursts are based on their observed frequencies. As a result, the frequencies of catastrophes that destroy or are otherwise incompatible with the existence of observers are systematically underestimated. We describe the consequences of the anthropic bias for estimation of catastrophic risks, and suggest some directions for (...) future work. (shrink)

The recent surge of interest in the origin of the temporal asymmetry of thermodynamical systems (including the accessible part of the universe itself) has put forward two possible explanatory approaches to this age-old problem. Hereby we show that there is a third possible alternative, based on the generalization of the classical (“Boltzmann–Schuetz”) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann's statistical measure at its face (...) value, and accomodating it within the quantum cosmological concept of the multiverse. We argue that conventional objections raised against the Boltzmann–Schuetz view are less forceful and serious than it is usually assumed. A fortiori, they are incapable of rendering the generalized theory untenable. On the contrary, this analysis highlights some of the other advantages of the multiverse approach to the thermodynamical arrow of time. (shrink)

This text is the first part of a larger study about Alexander Radishchev, one of the leading representatives of Enlightenment in Russia's XVIII Century. Analyzing Voltaire's and Diderot's relationship with Catherine II, the Empress of Russia, in the Introduction of this article, the author formulates the reasons for thematization of Russian reception of Enlightenment. Since Radishchev is considered as 'the father of Russian intelligentsia', different approaches to the meaning of the concept of 'Russian intelligentsia' are considered in the first chapter. (...) Radishchev's biography is interpreted in the second chapter in order to facilitate the understanding of his ideas. Interpretation of his ideas, as well as of Catherina's 'enlightened absolutism', will be subject to further consideration in the second part of the study. Tekst je prvi deo obimnije studije u kojoj je analizirano delo Aleksandra Radisceva, vodeceg predstavnika Prosvetiteljstva u Rusiji XVIII veka. Polazeci od odnosa Voltera i Didroa prema ruskoj imperatorki Katarini Velikoj, autor u uvodnom delu rada formulise razloge za bavljenje ruskom recepcijom Prosvetiteljstva. U prvom poglavlju interpretirane su razlicita tumacenja fenomena 'ruske inteligencije' jer se Radiscev smatra njenim rodonacelnikom. U drugom delu izlozena je biografija Radisceva koja olaksava razmatranje njegovih ideja. Analiza tih ideja, kao i 'prosvecenog apsolutizma' Katarine II, bice predmet razmatranja u nastavku ovog rada. (shrink)

This paper interprets and analyzes the debate having taken place in 1995 between E. Gellner and A. Smith concerning the problem of the emergence of nations. This discussion is used as an example to show the basic general features of two approaches in theories of nationalism - the modernist and the ethno symbolic ones. Pointing to the common assumptions shared by Gellner's and Smith's theories of nations, the author interprets ethno-symbolism as a sort of internal self-criticism of the modernist standpoint. (...) This polemic is therefore interpreted not as a debate between "creationist" and "evolutionist" solutions to the problem of the emergence of nations, but rather as a debate between two theoretical paradigms defining different research priorities in studying nations and nationalisms. From this perspective, the author concludes that the ethno symbolic approach to the genealogy of nations has broader heuristic capacities than the modernist paradigm, at least when the emergence of "peripheral nations" and the understanding of the dynamic of their nationalisms are concerned. U radu je interpretiran i analiziran spor koji su vodili E. Gelner i A. Smit 1995. godine o problemu nastanka nacija. Na primenu ove diskusije prikazane su osnovne opste karakteristike dva pristupa u teorijama nacionalizma modernistickog i etnosimbolickog. Ukazujuci na zajednicke pretpostavke Gelnerove i Smitove teorije nacija, autor je etnosimbolizam tumacio kao jednu vrstu unutrasnje samokritike modernistickog stanovista. Na taj nacin, ova polemika nije interpretirana kao spor izmedju "kreacionistickog" i "evolucionistickog" resenja problema nastanka nacija, vec prevashodno kao spor dve teorijske paradigme koje razlicito odredjuju istrazivacke prioritete u tematizaciji nacija i nacionalizama. Sa tog stanovista, autor je zakljucio da etnosimbolicki pristup genealogiji nacija ima vece heuristicke kapacitete od modernisticke paradigme, bar kada je u pitanju problem nastanka "perifernih nacija " i razumevanja dinamike njihovih nacionalizama. (shrink)

A modern assessment of the classical Boltzmann-Schuetz argument for large-scale entropy fluctuations as the origin of our observable cosmological domain is given.The emphasis is put on the central implication of this picture which flatly contradicts the weak anthropic principle as an epistemological statement about the universe. Therefore, to associate this picture with the anthropic principle as it is usually done is unwarranted. In particular, Feynman's criticism of theanthropic principle based on the entropy-fluctuation picture is a product of this semantic confusion.

This article explores the historical and sociological relations between contemporary conservatism and medievalism. It first registers the reemergence and increasing prominence of conservatism in contemporary society, most notably in America during the late 20th and the early 21st centuries. It then places conservatism and medievalism and their relationship within a historical-comparative framework. The article concludes that modern conservatism originates in and continues, with some adaptations or innovations, medievalism seen as the ‘golden past’, becoming the original and persisting conservative ideal and (...) model of society and history. (shrink)

In bioethical discussions of human cloning there are sometimes employed definitions broadening the denotation of the term human being to include also, on an equal footing, human embryos. Also, the fact of being human is being equated with being a person. Consequently, embryos are treated as having dignity and calls are heard in the name of justice to protect the rights and interests of embryos whenever these clash with the interests of mature human beings. The author, being a layman in (...) the area of human cloning, limits himself to indicating views he agrees with and those he finds doubtful. He expects human cloning will be taking place, albeit on a small scale, regardless of any bans which would only force the practice to become clandestine. Arguments in favor of controlled human cloning include not only the need to preserve freedom in scientific research, but also hopes for minimizing the adverse effects of cloning. The author indicates factors of an emotional nature which hamper discussions of cloning. He also argues that objections to experiments with humans and demands to make them conditional on prior consent of the people being experimented on are ineffective and often impossible to satisfy. The author also believes that it is impossible to unconditionally obey the commandment "You shall not kill". He does not see any threats posed by the fact that the clone and the cloned person will be identical. While not overlooking the potential dangers to clones (such as genetic defects), the author also sees potential advantages of cloning and transplantology (therapeutic, psychic, social). (shrink)

An ideal I defined on a group G is called idempotent if for every $A \in I, \{g \in G: Ag^{-1} \not\in I\} \in I$ . We show that a countably complete idempotent ideal on an abelian group cannot be prime but may have strong saturation properties.

Gdy człowiek, który – jak ja obecnie – ma dziewięćdziesiąt jeden lat, rezygnuje z jakiejś działalności, nie musi specjalnie się wysilać, aby usprawiedliwić swą decyzję. Lepiej, by sam wybrał ten moment i uprzedził o tym otoczenie, niżby miała zań zdecydować natura i zaskoczyć zarówno jego, jak innych...