This article aims at a constructive and argumentative engagement between the cognitive science of religion (CSR) and philosophical and theological reflection on the imago Dei. The Swiss theologian Emil Brunner argued that the theological notion that humans were created in the image of God entails that there is a “point of contact” for revelation to occur. This article argues that Brunner's notion resonates quite strongly with the findings of the CSR. The first part will give a short overview of (...) the CSR. The second part deals with Brunner's idea of the imago Dei and the “point of contact.” The third and final part of the article outlines a model of revelation that is in line with Brunner's thought and the CSR. The aim of this article is to show how the naturalistic methodology of the CSR provides a fertile new perspective on several theological issues and thereby enriches theological reflection. (shrink)
This biography of Emil du Bois-Reymond, the most important forgotten intellectual of the nineteenth century, received an Honorable Mention for History of Science, Medicine, and Technology at the 2013 PROSE Awards, was shortlisted for the 2014 John Pickstone Prize (Britain's most prestigious award for the best scholarly book in the history of science), and was named by the American Association for the Advancement of Science as one of the Best Books of 2014. -/- In his own time (1818–1896) du (...) Bois-Reymond grew famous for his groundbreaking research in neuroscience and his provocative addresses on politics and culture. His discovery of the electrical transmission of nerve signals, his innovations in laboratory instrumentation, and his reductionist methodology all helped lay the foundations of modern neuroscience. -/- In addition to describing the pioneering experiments that earned du Bois-Reymond a seat in the Prussian Academy of Sciences and a professorship at the University of Berlin, this book also recounts du Bois-Reymond’s family origins, private life, public service, and lasting influence. In talks that touched on science, philosophy, history, and literature, du Bois-Reymond introduced Darwin to German students (triggering two days of debate in the Prussian parliament), asked on the eve of the Franco-Prussian War whether France had forfeited its right to exist, and proclaimed the mystery of consciousness, heralding the age of doubt. The first modern biography in any language, "Emil du Bois-Reymond" recovers an important chapter in the history of science, the history of ideas, and the history of Germany. (shrink)
We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.
We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev . We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia (...) theorem and the theory of modal companions to systems of multiple-conclusion rules or (finitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property. (shrink)
We study the extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove that (...) dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (shrink)
We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from . We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV₁ + dWPHP(PV).
We develop an arithmetical theory and its variant , corresponding to “slightly nonuniform” . Our theories sit between and , and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propositional translations of -formulas provable in admit L-uniform polynomial-size Frege proofs.
This paper explores in detail an argument for epistemic expressivism, what we call the Argument from Motivation. While the Argument from Motivation has sometimes been anticipated, it has never been set out in detail. The argument has three premises, roughly, that certain judgments expressed in attributions of knowledge are intrinsically motivating in a distinct way (P1); that motivation for action requires desire-like states or conative attitudes (HTM); and that the semantic content of knowledge attributions cannot be specified without reference to (...) the intrinsically motivating judgments that such attributions express (P2). We argue that these premises entail a version of ecumenical expressivism. Since the argument from motivation has not been explicitly stated before, there is no current discussion of the argument. In this paper we therefore consider and reject various objections that one might propose to the argument, including some that stem from the idea that knowledge is factive, or that knowledge involves evidence that rules out relevant alternatives. Other objections to (P1) specifically might be derived from cases of apparent lack of epistemic motivation considered in in Kvanvig (The value of knowledge and the pursuit of understanding, 2003) and Brown (Nous 42(2):167–189, 2008), as well as from general forms of externalism about epistemic motivation. We consider these and find them wanting. Finally, the paper offers some critical remarks about the prospect of denying (P2). (shrink)
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...) existential theories in the process. (shrink)
We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...) of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)
Timothy Michael Fowler has argued that, as a consequence of their commitment to neutrality in regard to comprehensive doctrines, political liberals face a dilemma. In essence, the dilemma for political liberals is that either they have to give up their commitment to neutrality (which is an indispensible part of their view), or they have to allow harm to children. Fowler’s case for this dilemma depends on ascribing to political liberals a view which grants parents a great degree of freedom in (...) deciding on the education of their children. I show that ascribing this view to political liberals rests upon a misinterpretation of political liberalism. Since political liberals have access to reasons based upon the interests of children, they need not yield to parent’s wishes about the education of their children. A correct understanding of political liberalism thus shows that political liberals do not face the dilemma envisaged by Fowler. (shrink)
It has been argued that Hume’s denial of infinite divisibility entails the falsity of most of the familiar theorems of Euclidean geometry, including the Pythagorean theorem and the bisection theorem. I argue that Hume’s thesis that there are indivisibles is not incompatible with the Pythagorean theorem and other central theorems of Euclidean geometry, but only with those theorems that deal with matters of minuteness. The key to understanding Hume’s view of geometry is the distinction he draws between a precise and (...) an imprecise standard of equality in extension. Hume’s project is different from the attempt made by Berkeley in some of his later writings to save Euclidean geometry. Unlike Berkeley, who interprets the theorems of Euclidean geometry as false albeit useful approximations of geometrical facts, Hume is able to save most of the central theorems as true. (shrink)
Mixed strategies have been used to show that Pascal’s Wager fails to offer sufficient pragmatic reasons for believing in God. Their proponents have argued that, in addition to outright belief in God, rational agents can follow alternatives strategies whose expected utility is infinite as well. One objection that has been raised against this way of blocking Pascal’s Wager is that applying a mixed strategy in Pascal’s case is tantamount to applying an iterated mixed strategy which, properly understood, collapses into the (...) pure strategy of becoming a theist. I argue that since the assumptions used to develop the iterated mixed strategies response are even more questionable than those the initial objection relies on, this type of response to the mixed strategy objection fails. (shrink)
We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.
This article provides a summary overview of the ideas on medical anthropology and anthropological medicine of the German philosopher-psychiatrist Viktor Emil von Gebsattel (1883–1974), and discusses in more detail his views on the doctor-patient relationship. It is argued that Von Gebsattel''s warning against a dehumanization of medicine when the person of both patient and physician are not explicitly present in their relationship remains valid notwithstanding the modern emphasis on respect for patient (and provider) autonomy.
We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most (...) nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal. (shrink)
In Beyond the Limits of Thought , Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink (...) virtually all orthodox solutions', and that the Inclosure Schema cannot be the structure that underlies the Liar paradox. Moreover, Ramsey was right in thinking that logical and semantic paradoxes are paradoxes of different kinds. (shrink)
We formalize the construction of Paterson’s variant of the Ajtai–Komlós–Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory , under the assumption of the existence of suitable expander graphs. We derive a conditional p-simulation of the propositional sequent calculus in the monotone sequent calculus.
By a well-known result of Cook and Reckhow [S.A. Cook, R.A. Reckhow, The relative efficiency of propositional proof systems, Journal of Symbolic Logic 44 36–50; R.A. Reckhow, On the lengths of proofs in the propositional calculus, Ph.D. Thesis, Department of Computer Science, University of Toronto, 1976], all Frege systems for the classical propositional calculus are polynomially equivalent. Mints and Kojevnikov [G. Mints, A. Kojevnikov, Intuitionistic Frege systems are polynomially equivalent, Zapiski Nauchnyh Seminarov POMI 316 129–146] have recently shown p-equivalence of (...) Frege systems for the intuitionistic propositional calculus in the standard language, building on a description of admissible rules of IPC by Iemhoff [R. Iemhoff, On the admissible rules of intuitionistic propositional logic, Journal of Symbolic Logic 66 281–294]. We prove a similar result for an infinite family of normal modal logics, including K4, GL, S4, and. (shrink)
Williamson and others have argued that contextualist theories of the semantics of ‘know’ have a special problem of accounting for our practices of ‘consuming’ knowledge attributions and denials made in other contexts. In what follows, I shall understand the objection as the idea that contextualism has a special problem of accounting for how we are able to acquire epistemically useful information from knowledge claims made in other contexts. I respond to the objection by arguing that the defeasibility of knowledge makes (...) it difficult for everyone to acquire epistemically useful information from knowledge claims made in other contexts, and that there is no special problem for contextualism when it comes to acquiring epistemically useful information from knowledge claims made in other contexts. (shrink)
Page generated Sun Jul 25 11:16:56 2021 on philpapers-web-786f65f869-jmfbq
cache stats: hit=16926, miss=15607, save= autohandler : 1504 ms called component : 1487 ms search.pl : 1217 ms render loop : 1146 ms next : 555 ms addfields : 538 ms publicCats : 452 ms autosense : 179 ms match_other : 159 ms save cache object : 99 ms menu : 82 ms retrieve cache object : 72 ms quotes : 71 ms initIterator : 68 ms search_quotes : 40 ms prepCit : 20 ms match_cats : 18 ms applytpl : 6 ms intermediate : 1 ms match_authors : 1 ms init renderer : 0 ms setup : 0 ms auth : 0 ms writelog : 0 ms