We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Gödel’s functional “Dialectica” interpretation, the new interpretation does not care for precise witnesses of existential statements, but only for bounds for them. New principles are supported by our interpretation, including the FAN theorem, weak König’s lemma and the lesser limited principle of omniscience. Conspicuous among these principles are also refutations of some laws of classical logic. Notwithstanding, we end up discussing some applications of the (...) new interpretation to theories of classical arithmetic and analysis. (shrink)

Generative artificial intelligence systems based on transformers, including both text-generators like GPT-4 and image generators like DALL-E 3, have recently entered the popular consciousness. These tools, while impressive, are liable to reproduce, exacerbate, and reinforce extant human social biases, such as gender and racial biases. In this paper, we systematically review the extent to which DALL-E Mini suffers from this problem. In line with the Model Card published alongside DALL-E Mini by its creators, we find that the images it produces (...) tend to represent dozens of different occupations as populated either solely by men (e.g., pilot, builder, plumber) or solely by women (e.g., hairdresser, receptionist, dietitian). In addition, the images DALL-E Mini produces tend to represent most occupations as populated primarily or solely by White people (e.g., farmer, painter, prison officer, software engineer) and very few by non-White people (e.g., pastor, rapper). These findings suggest that exciting new AI technologies should be critically scrutinized and perhaps regulated before they are unleashed on society. (shrink)

This paper builds on existing research investigating CSR and ethical consumption within luxury contexts, and makes several contributions to the literature. First, it addresses existing knowledge gaps by exploring the ways in which consumers perform ethical luxury purchases of fine jewellery through interpretive research. Second, the paper is the first to examine such issues of consumer ethics by extending the application of theories of practice to a luxury product context, and by building on Magaudda’s :15–36, 2011) circuit of practice framework. (...) This is significant in that, to date, consumer research using practice theories has focused mainly on routine and habitual practices. Our findings and discussion provide an analysis of intentional and less intentional ethical consumer performances within the interconnected nexus of activities of consumers’ fine jewellery consumption practice, where meanings, understandings and intelligibility of social phenomena are worked through the various activities that shape such a practice. Finally, the paper concludes with significant managerial and policy-related implications, as our extended circuit of practice analysis conveys that if ethics and sustainability dimensions are to be embedded in fine jewellery consumption practice, they must first be made an intrinsic part of the nexus of the social and material environment of trading and consumption places. (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 Δ₁¹-comprehension (...) schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)

Machery argues that concepts do not constitute a natural kind. We argue that this is a mistake. When appropriately construed, his discussion in fact bolsters the claim that concepts are a natural kind.

One of the most basic functions of human language is to convey who did what to whom. In the world's languages, the order of these three constituents (subject [S], verb [V], and object [O]) is uneven, with SOV and SVO being most common. Recent experiments using experimentally elicited pantomime provide a possible explanation of the prevalence of SOV, but extant explanations for the prevalence of SVO could benefit from further empirical support. Here, we test whether SVO might emerge because (a) (...) SOV is not well suited for describing reversible events (a woman pushing a boy) and (b) pressures to be efficient and mention subjects before objects conspire to rule out many other alternatives. We tested this by asking participants to describe reversible and non‐reversible events in pantomime, and we instructed some participants to be consistent in the form of their gestures and to teach them to the experimenter. These manipulations led to the emergence of SVO in speakers of both English (SVO) and Turkish (SOV). (shrink)

As the use of algorithmic decision‐making becomes more commonplace, so too does the worry that these algorithms are often inscrutable and our use of them is a threat to our agency. Since we do not understand why an inscrutable process recommends one option over another, we lose our ability to judge whether the guidance is appropriate and are vulnerable to being led astray. In response, I claim that a process being inscrutable does not automatically make its guidance inappropriate. This phenomenon (...) is not restricted to algorithms, and there are many social processes which we should conform to but are similarly unable to judge for ourselves. I provide a framework for how we can depend on inscrutable processes by introducing a distinction between knowing conformity (where I understand what justifies the guidance) from mere conformity (where I merely do what I am told) and showing how mere conformity is often positively valuable because it allows for extended processes that in turn allow us to accomplish more than we could on our own. This is in effect a division of deliberative labour, which I argue is something commonplace but not often recognised, of which algorithmic guidance can be an example. (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.

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 Δ11-comprehension (...) schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)

Este artigo busca encontrar na teoria crítica da racionalidade moderna de Jürgen Habermas (1929-) elementos de uma paideia. O primeiro tópico lança o substrato epistemológico sobre a existência das racionalidades estratégica e comunicativa. O segundo, afirma que o desengate entre o sistema e o mundo da vida, e a colonização deste por aquele, causam as patologias modernas e colaboram para a formulação de pedagogias coordenadas pela ação estratégica. O terceiro, propõe que o reacoplamento do sistema ao mundo vivido proporciona que (...) todas as dimensões da existência humana sejam orientadas pela ação comunicativa, na qual se encontram os traços de uma paideia emancipadora e revolucionária. (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.

This research investigated the metacognitive underpinnings of moral judgment. Participants in two studies were asked to provide quick intuitive responses to moral dilemmas and to indicate their fee...

In “Judy Benjamin is a Sleeping Beauty” (2010) Bovens recognises a certain similarity between the Sleeping Beauty (SB) and the Judy Benjamin (JB). But he does not recognise the dissimilarity between underlying protocols (as spelled out in Shafer (1985). Protocols are expressed in conditional probability tables that spell out the probability of coming to learn various propositions conditional on the actual state of the world. The principle of total evidence requires that we not update on the content of the proposition (...) learned but rather on the fact that we learn the proposition in question. Now attention to protocols drives a wedge between the SB and the JB. We have shown that the solution to a close variant of the SB which involves a clear protocol is P*(Heads) = 1/3 and since Beauty’s has precisely the same information at her disposal in the original SB at the time that she is asked to state her credence for Heads, the same solution should hold. The solution to the JB, on the other hand, is dependent on Judy’s probability distribution over protocols. One reasonable protocol yields P(Red) = 1/2, but Judy could also defend alternative values or a range of values in the interval [1/3, 1/2] depending on her probability distribution over protocols. (shrink)

What are the effects of word-by-word predictability on sentence processing times during the natural reading of a text? Although information complexity metrics such as surprisal and entropy reduction have been useful in addressing this question, these metrics tend to be estimated using computational language models, which require some degree of commitment to a particular theory of language processing. Taking a different approach, this study implemented a large-scale cumulative cloze task to collect word-by-word predictability data for 40 passages and compute surprisal (...) and entropy reduction values in a theory-neutral manner. A separate group of participants read the same texts while their eye movements were recorded. Results showed that increases in surprisal and entropy reduction were both associated with increases in reading times. Furthermore, these effects did not depend on the global difficulty of the text. The findings suggest that surprisal and entropy reduction independently contribute to variation in reading times, as these metrics seem to capture different aspects of lexical predictability. (shrink)

Recently several authors have proposed proxies of welfare that equate some (as opposed to all) choices with welfare. In this paper, I first distinguish between two prominent proxies: one based oncontext-independent choicesand the other based onreason-based choices. I then propose an original proxy based on choices that individuals state they would want themselves to repeat at the time of the welfare/policy evaluation (confirmed choices). I articulate three complementary arguments that, I claim, support confirmed choices as a more reliable proxy of (...) welfare than context-independent and reason-based choices. Finally, I discuss the implications of these arguments fornudgesandboosts. (shrink)

We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically true. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we obtain (...) a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

We introduce a new typed combinatory calculus with a type constructor that, to each type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, associates the star type σ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^*$$\end{document} of the nonempty finite subsets of elements of type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory (...) calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. (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)

In Frege’s logicism, numbers are logical objects in the sense that they are extensions of certain concepts. Frege’s logical system is inconsistent, but Richard Heck showed that its restriction to predicative quantification is consistent. This predicative fragment is, nevertheless, too weak to develop arithmetic. In this paper, I will consider an extension of Heck’s system with impredicative quantifiers. In this extended system, both predicative and impredicative quantifiers co-exist but it is only permissible to take extensions of concepts formulated in the (...) predicative fragment of the language. This system is consistent. Moreover, it proves the principle of reducibility applied to concepts true of only finitely many objects. With the aid of this form of reducibility, it is possible to develop arithmetic in a thoroughly Fregean way. (shrink)

We present a functional interpretation of Peano arithmetic that uses Gödel’s computable functionals and which systematically injects uniformities into the statements of finite-type arithmetic. As a consequence, some uniform boundedness principles are interpreted while maintaining unmoved the -sentences of arithmetic. We explain why this interpretation is tailored to yield conservation results.

The epistemic position of an agent often depends on their position in a larger network of other agents who provide them with information. In general, agents are better off if they have diverse and independent sources. Sullivan et al. [19] developed a method for quantitatively characterizing the epistemic position of individuals in a network that takes into account both diversity and independence; and presented a proof-of-concept, closed-source implementation on a small graph derived from Twitter data [19]. This paper reports on (...) an open-source reimplementation of their algorithm in Python, optimized to be usable on much larger networks. In addition to the algorithm and package, we also show the ability to scale up our package to large synthetic social network graph profiling, and finally demonstrate its utility in analyzing real-world empirical evidence of ‘echo chambers’ on online social media, as well as evidence of interdisciplinary diversity in an academic communications network. (shrink)

According to attention-based theories, to explain organizational attention is to explain organizational behavior. In our study, we test the model of situated attention and firm behavior by examining the effects of attention structures and allocation of attention on organizational outcomes. We hypothesize a positive relationship between attention structures and the allocation of organizational attention that, in turn, has an effect on financial performance. Using a unique data set composed of indicators of social responsibility published by 338 Brazilian organizations between 2001 (...) and 2007, we find support for our hypotheses. Our findings suggest that organizational attention to social issues fully mediates the relationship between attention structures and financial performance. (shrink)

The increasing use of digital technologies in judicial and arbitration proceedings increases the usage of digital evidence by the parties, which brings the necessity of creating patterns for adjudicators to admit and assess this new type of evidence. This paper generally addresses digital evidence focusing on the second moment in international arbitration proceedings. It also narrows the topic to hacked and leaked evidence and its admissibility in international arbitration. The literature review showed a significant amount of research devoted to the (...) evidence in arbitration. Some considered electronic evidence within one jurisdiction; others focused on certain forms of digital evidence such as electronic signatures. Papers on digital evidence in international arbitration approach arbitration rules for digital evidence but skip admissibility issues. No systemic and complex works research digital evidence in arbitration, explicitly focusing on the admissibility of hacked and leaked digital evidence from a comparative perspective. Also, no research deals with enforcing international arbitration awards relying on illegally obtained digital evidence. In these cases, there could be a possible violation of domestic public policy under the New York Convention terms (art. V, 2, b). That is why the paper aims to offer the concept of digital evidence in international arbitration, including hacked and leaked evidence, criteria of its admissibility and relevance, and design the arbitration guidelines for assessing hacked and leaked evidence. Comparative legal analysis of the international arbitration rules and national procedure law allowed us to compare the regulatory approaches to the definition of digital evidence and its admissibility worldwide. The method of legal modeling allowed designing model guidelines for arbitral tribunals to evaluate the admissibility and relevance of digital evidence, including hacked and leaked evidence. Moreover, the case study method allowed us to analyze jurisprudence and define criteria for admission of hacked and leaked evidence. We conclude that the admissibility of hacked and leaked evidence depends solely on the arbitrator’s broad discretion to assess the evidence. Nevertheless, thorough evidence analysis and a well-reasoned award are always mandatory. (shrink)

This article is the first attempt to justify the "next" milestone in the development of legal realism: hyperrealism. The implications of digitalization have become the new fuel for the legal realist's jurisprudence prediction theory, that is, empirical research to predict the judge's or the court's decision. Indeed, that was impossible for American realists in the early twentieth century, and all the attempts failed. Therefore, tools such as Judicial Analytics allow us to prove that personal motives and prejudices affect a dispute's (...) resolution. Based on a systemic, comparative, and interdisciplinary analysis that intermingles legal theory, data analytics and digital technologies, the article substantiates the concept of hyperrealism itself. It evaluates the advantages and disadvantages of its primary tool—judicial analytics. The authors state the necessity of creating regulatory mechanisms of "curbing" to use them to improve justice and minimize the risk of rights violations. They propose using tools of expert evaluation, standardization, and ethical regulation of forensic analysis. (shrink)

It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system F at, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the (...) intuitionistic propositional logic in which commuting conversions are not needed. (shrink)

The purpose of this article is to reflect on the changes that the implementation of artificial wombs would bring to society, the family, and the concept of motherhood and fatherhood through the lens of two recent books: Helen Sedgwick’s The Growing Season and Rebecca Ann Smith’s Baby X. Each of the two novels, set in a near future, follows the work of a scientist who develops artificial womb technology. Significantly, both women experience concerns about the technology and its long-term effects (...) that make both of them leave their laboratories and rethink the technology they invented, while considering its many ethical implications. Both novels can be seen as feminist revisionary rewritings of Aldous Huxley’s Brave New World, rejecting the vision of rows of mass-produced, anonymous babies in artificial wombs, stressing instead the closeness of the parents to their offspring. They nevertheless critically evaluate not only the many potential benefits for women of ectogenetic technology but also the possible disadvantages and pitfalls. (shrink)

We study an alternative embedding of IPC into atomic system F whose translation of proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination rules for disjunction and absurdity. As compared to the embedding based on instantiation overflow, the alternative embedding works equally well at the levels of provability and preservation of proof identity, but it produces shorter derivations and shorter simulations of reduction sequences. Lambda-terms are employed in the technical development so that the algorithmic (...) content is made explicit, both for the alternative and the original embeddings. The investigation of preservation of proof-reduction steps by the alternative embedding enables the analysis of generation of “administrative” redexes. These are the key, on the one hand, to understand the difference between the two embeddings; on the other hand, to understand whether the final word on the embedding of IPC into atomic system F has been said. (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.

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)

Artificial intelligence (AI) systems are increasingly being used not only to classify and analyze but also to generate images and text. As recent work on the content produced by text and image Generative AIs has shown (e.g., Cheong et al., 2024, Acerbi & Stubbersfield, 2023), there is a risk that harms of representation and bias, already documented in prior AI and natural language processing (NLP) algorithms may also be present in generative models. These harms relate to protected categories such as (...) gender, race, age, and religion. There are several kinds of harms of representation to consider in this context, including stereotyping, lack of recognition, denigration, under-representation, and many others (Crawford in Soundings 41:45–55, 2009; in: Barocas et al., SIGCIS Conference, 2017). Whereas the bulk of researchers’ attention thus far has been given to stereotyping and denigration, in this study we examine ‘exnomination’, as conceived by Roland Barthes (1972), of religious groups. Our case study is DALL-E, a tool that generates images from natural language prompts. Using DALL-E mini, we generate images from generic prompts such as “religious person.” We then examine whether the generated images are recognizably members of a nominated group. Thus, we assess whether the generated images normalize some religions while neglecting others. We hypothesize that Christianity will be recognizably represented more frequently than other religious groups. Our results partially support this hypothesis but introduce further complexities, which we then explore. (shrink)

The present paper stems from the biosemiotic modelling of individual artificial cognition proposed by Ferreira and Caldas (2012) but goes further by introducing the concept of Umwelt Overlap. The introduction of this concept is of fundamental importance making the present model closer to natural cognition. In fact cognition can only be viewed as a purely individual phenomenon for analytical purposes. In nature it always involves the crisscrossing of the spheres of action of those sharing the same environmental bubble. Plus, the (...) incorporation of that concept is vital to understand the complex semiosis that sustains collective tissues, societies, regulating collective cognition and consequently cooperative action. The concept of Umwelt Overlap broadens the range of applicability of the previous model to several distinct domains allowing for example for its application to multi-agent cooperative autonomous systems. In this paper a Middle Size League RoboCup soccer team is used as an example of a possible application. (shrink)

We show that there is a purely proof-theoretic proof of the Rasiowa–Harrop disjunction property for the full intuitionistic propositional calculus ), via natural deduction, in which commuting conversions are not needed. Such proof is based on a sound and faithful embedding of \ into an atomic polymorphic system. This result strengthens a homologous result for the disjunction property of \ and answers a question then posed by Pierluigi Minari.

Most studies investigating the relationship between cultural constructs and ethical perception have focused on individual- and societal-level values without much attention to other type of cultural constructs such as social beliefs. In addition, we need to better understand how social beliefs are linked to ethical perception and the level of analysis at which social beliefs may best predict ethical perceptions. This research contributes to the cross-cultural ethical perception literature by examining the relationship of individual-level social cynicism belief, one of five (...) universally endorsed social beliefs, together with individual social dominance orientation and the perception of unethical behavior. By means of two studies, we examine these relationships across societies that significantly differ on societal-level social cynicism belief. Using 371 business students from Russia and the U.S. in Study 1 and 268 professionals from Portugal and the U.S. in Study 2, we found that individual-level social cynicism belief was positively associated with social dominance orientation. Social dominance orientation, in turn, mediated the relationship between individual social cynicism belief and the perception of unethical behavior. Although we found significant societal-level differences in social cynicism belief in both studies, the relationships between individual-level social cynicism belief, social dominance orientation, and the perception of unethical behavior were structurally equivalent across societies in both studies, suggesting that societal-level differences did not significantly affect these relationships. Implications for cross-cultural business ethics research and practice are discussed. (shrink)