Charting the development of the British tradition of naturalism from the 17th to the 19th century, this book provides fascinating insight into a wide range of thinkers, both Catholic and Protestant, who explored the themes of proof, practice, and the role of common sense. Reappraising what these thinkers can teach us about the relations between belief, action, and skepticism, Ferreira contributes to the philosophical study of naturalist replies to skepticism, as well as to a deeper appreciation of this particular (...) segment of British intellectual history. (shrink)
Bovens (2010) points out that there is a structural analogy between the Judy Benjamin problem (JB) and the Sleeping Beauty problem (SB). On grounds of this structural analogy, he argues that both should receive the same solution, viz. the posterior probability of the eastern region of the matrix in Table 1 should equal 1/3. Hence, P*(Red) = 1/3 in the JB and P*(Heads) = 1/3 in the SB. Bovens’s argument rests on a standard error in implementing Bayesian updating, which is (...) spelled out in Shafer 1985. When we are informed of some proposition, we do not only learn the proposition in question, but also that we have learned the proposition as one of the many propositions that we might have learned. The information is generated by a protocol, which determines the various propositions that we might learn. We should then update not on the proposition in question, but rather on the fact that we learned this proposition as one of the many propositions that we might have learned. A well-known application of this insight is the Monty Hall problem (MH) as Speed (1985: 276) points out in a discussion of Shafer 1985. As an illustration, let us apply Shafer’s insight to the MH. In the MH, the contestant in a game show learns that there is a goat behind two of three doors X, Y and Z and a car behind one door. She is asked to pick one of the three doors. The contestant picks door X. Monty will then open one of the remaining doors, which he knows to have a goat behind it. Suppose Monty opens door Y. The contestant is then asked whether she wants to …. (shrink)
Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...) extended system. (shrink)
Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predicate calculus into a second-order predicative system for which there is no need for commuting conversions. Furthermore, we show that the redex (...) and the conversum of a commuting conversion of the original calculus translate into equivalent derivations by means of a series of bidirectional applications of standard conversions. (shrink)
It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing 1 (...) 1-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)
Introduction: Reading Kierkegaard -- Either or and the first upbuilding discourses -- Repetition, fear, and trembling, and more discourses -- Philosophical fragments, the concept of anxiety, and discourses -- Concluding unscientific postscript and two ages -- Works of love, discourses, and other writings -- The sickness unto death and discourses -- Practice in Christianity, discourses, and the attack -- Looking back and looking ahead.
Recently, Feferman and Hellman (and Aczel) showed how to establish the existence and categoricity of a natural number system by predicative means given the primitive notion of a finite set of individuals and given also a suitable pairing function operating on individuals. This short paper shows that this existence and categoricity result does not rely (even indirectly) on finite-set induction, thereby sustaining Feferman and Hellman''s point in favor of the view that natural number induction can be derived from a very (...) weak fragment of finite-set theory, so weak that finite-set induction is not assumed. Many basic features of finiteness fail to hold in these weak fragments, conspicuously the principle that finite sets are in one-one correspondence with a proper initial segments of a (any) natural number structure. In the last part of the paper, we propose two prima facie evident principles for finite sets that, when added to these fragments, entail this principle. (shrink)
Kierkegaard's "Works of Love" provocatively presses for a reconsideration of impartiality, partiality, and equality. Past readings of this text have typically (1) criticized its focus on the abstract category of "human being," ignoring its attention to distinctiveness and difference; (2) defended it from the charge of abstraction by accenting its treatment of distinctiveness and difference, playing down its assumptions about the "essentially" human; (3) acknowledged its emphases on both essence and difference, arguing that they are incompatible and irreconcilable; or (4) (...) acknowledged both emphases, assuming they are compatible without exploring or accounting for the apparent incompatibility. As a means of resolving this seeming inconsistency, I will focus on Kierkegaard's recommendation of moral blindness and its implications for moral vision, and I will argue that "Works of Love" contains resources for an understanding of impartiality that allows moral attention to concrete difference. (shrink)
We construct a weak second-order theory of arithmetic which includes Weak König's Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with Σ b 1 -graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.
In the course of ten short sections, we comment on Gödel's seminal dialectica paper of fifty years ago and its aftermath. We start by suggesting that Gödel's use of functionals of finite type is yet another instance of the realistic attitude of Gödel towards mathematics, in tune with his defense of the postulation of ever increasing higher types in foundational studies. We also make some observations concerning Gödel's recasting of intuitionistic arithmetic via the dialectica interpretation, discuss the extra principles that (...) the interpretation validates and comment on extensionality and higher order equality. The latter sections focus on the role of majorizability considerations within the dialectica and related interpretations for extracting computational information from ordinary proofs in mathematics. (shrink)
Levinas's ethics of other-centered service has been criticized at the theoretical level for failing to offer a conception of moral agency adequate to ground its imperative and at the practical level for encouraging self-hatred. Levinas's explicit resistance to the incorporation of the phrase "as yourself" in the Judaeo-Christian love command might seem to validate the critics' complaints. The author argues, on the contrary, that Levinas does offer a strong and compelling conception of moral agency and that his ethics, properly understood, (...) does not entail self-abnegation. Levinas's attempt to counter excessive and manipulative self-concern and self-inflation by insisting on the dependent and situational position of the self has been wrongly overinterpreted as an abandonment of the self and its just claims. The author seeks to establish a more balanced understanding by focusing attention on the "ethics of welcome," on Levinas's distinctive conception of passivity, and on the role of "the third" in all human relations. (shrink)
Empirical reports on scientific competition show that scientists can be depicted as self-interested, strategically behaving agents. Nevertheless, we argue that recognition-seeking scientists will have an interest in establishing methodological norms which tend to select theories of a high epistemic value, and that these norms will be still more stringent if the epistemic value of theories appears in the utility function of scientists, either directly or instrumentally. (Published Online July 11 2006) Footnotes1 The author gratefully acknowledges financial support from DGI grant (...) BEC2002-03715 (Ministerio de Educación y Cultura). 2 The author gratefully acknowledges financial support from grants PB98-0495-C08-01 and BFF2002-03656 (Ministerio de Educación y Cultura). (shrink)
We show how to interpret intuitionistic propositional logic into a predicative second-order intuitionistic propositional system having only the conditional and the universal second-order quantifier. We comment on this fact. We argue that it supports the legitimacy of using classical logic in a predicative setting, even though the philosophical cast of predicativism is nonrealistic. We also note that the absence of disjunction and existential quantifications allows one to have a process of normalization of proofs that avoids the use of "commuting conversions.".
In "'Yes" and "No'" (2000), Ian Rumfitt proposed bilateralism--a use-based account of the logical words, according to which the sense of a sentence is determined by the conditions under which it is asserted and denied. One of Rumfitt's key claims is that bilateralism can provide a justification of classical logic. This paper raises a techical problem for Rumfitt's proposal, one that seems to undermine the bilateralist programme.
A separation between interpretive and post-interpretive processes is central to Caplan & Waters's theory of language comprehension. This commentary raises some issues that are intended to help sharpen the distinction.
As regular readers of The Pluralist are aware, there appeared in 2008 an issue devoted to Jan Olof Bengtsson's The Worldview of Personalism.1 The issue included five articles, each concerned with a different aspect of the book; and after each article, there was a "Reply" by Bengtsson. In what follows, I shall say something about Bengtsson's reply to my own contribution, "Absolute and Personal Idealism." However, first let me briefly describe that article's argument.In "Absolute and Personal Idealism," I examined the (...) personalist attack on absolutism as formulated by Andrew Seth Pringle-Pattison in two works: Hegelianism and Personality and The Idea of God in the Light of Recent Philosophy. In the first section of .. (shrink)
Pickering & Garrod's (P&G's) mechanistic theory of dialogue is a major advance for psycholinguistics. But the commitment to representational parity in production and comprehension is problematic. Recent research suggests that speakers frequently produce a structure that listeners find ungrammatical and have trouble understanding. If the grammars of the two systems are different, then the assumption of representational parity must be relaxed.
An ordering ( $\leq_K$ ) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size c and decreasing chains of length $\mathfrak{c}^+$ bellow every element. Assuming $\mathfrak{t} = \mathfrak{c}$ a MAD family equivalent to all of its restrictions is constructed. It is also shown here that the Continuum Hypothesis implies that for every $\omega^\omega-bounding$ forcing P of size c there is a (...) Cohen-destructible, $\mathbb{P}-indestructible$ MAD family. Finally, two other orderings on MAD families are suggested and an old construction of $Mr\acute{o}wka$ is revisited. (shrink)
Externality games are studied in Grafe et al. (1998, Math. Methods Op. Res. 48, 71). We define a generalization of this class of games and show, using the methodology in Izquierdo and Rafels (1996, 2001, Working paper, Univ Barcelona; Games Econ. Behav. 36, 174), some properties of the new class of generalized externality games. They include, among others, the algebraic structure of the game, convexity, and their implications for the study of cooperative solutions. Also the proportional rule is characterized for (...) this class of games. (shrink)
Levelt, Roelofs & Meyer present a comprehensive and sophisticated theory of lexical access in production, but we question its reliance on binding-by-checking as opposed to binding-by-timing and we discuss how the timing of retrieval events is a major factor in both correct and errorful production.
Frege's "Grundgesetze der Arithmetik" is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege's Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the "Grundgesetze" is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...) extended system. (shrink)
This paper develops the very basic notions of analysis in a weak second-order theory of arithmetic BTFA whose provably total functions are the polynomial time computable functions. We formalize within BTFA the real number system and the notion of a continuous real function of a real variable. The theory BTFA is able to prove the intermediate value theorem, wherefore it follows that the system of real numbers is a real closed ordered field. In the last section of the paper, we (...) show how to interpret the theory BTFA in Robinson's theory of arithmetic Q. This fact entails that the elementary theory of the real closed ordered fields is interpretable in Q. (shrink)
Søren Kierkegaard (in the Climacus writings) and John Henry Newman have starkly opposed formulations of the relation between faith and reason. In this essay I focus on a possible convergence in their respective understandings of the transition to religious belief or faith, as embodied in metaphors they use for a qualitative transition. I explore the ways in which attention to the legitimate dimension of discontinuity highlighted by the Climacan metaphor of the 'leap' can illuminate Newman's use of the (...) metaphor of a 'polygon inscribed in a circle', as well as the ways in which Newman's metaphor can illuminate the dimension of continuity operative in the Climacan appreciation of qualitative transition. (shrink)
Any complete theory of lexical access in production must address how words are produced in prosodic contexts. Levelt, Roelofs & Meyer make some progress on this point: for example, they discuss resyllabification in multiword utterances. I present work demonstrating that word articulation takes into account overall prosodic context. This research supports Levelt et al.'s hypothesized separation between metrical and segmental information.
The LNCS series reports state-of-the-art results in computer science research, development, and education, at a high level and in both printed and electronic form.
The surprise exam paradox has attracted the attention of prominent logicians, mathematicians and philosophers for decades. Although the paradox itself has been resolved at least since Quine (1953), some aspects of it are still being discussed. In this paper we propose, following Sober (1998), to translate the paradox into the language of game theory to clarify these aspects. Our main conclusions are that a much simpler game?theoretic analysis of the paradox is possible, which solves most of the puzzles related (...) to it, and that this way of analysing the paradox can also throw light on our comprehension of the pragmatics of linguistic communication. (shrink)
The research team measured the enterprise web accessibility levels of the Forbes 250 largest enterprises using the fully automatic accessibility evaluation tool Sortsite, and presented the compliance of the evaluated websites to WCAG 1.0, WCAG 2.0 and Section 508 accessibility levels. Given the recent attention to organizational leaders having ethical duties towards their dedicated employees, we propose that ‘societal citizenship behaviour’ concerns ethical duties of organizational leaders towards society in general and in particular to those who have less means to (...) assert their needs. In effect, we found enterprise website accessibility levels to be in need of significant improvement. An interpretation of a positive path forward to better enterprise website accessibility levels is put forth based on a focus-group interaction and using BNML—a novel Business Narrative Modelling Language. (shrink)
We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov's principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak König's lemma. We discuss some applications, as well as some previous results in the literature.
