Conciliatory views of peer disagreement hold that when an agent encounters peer disagreement she should conciliate by adjusting her doxastic attitude towards that of her peer. In this paper I distinguish different ways conciliation can be understood and argue that the way conciliationism is typically understood violates the principle of commutativity of evidence. Commutativity of evidence holds that the order in which evidence is acquired should not influence what it is reasonable to believe based on that evidence. I argue that (...) when an agent encounters more than one peer, and applies the process of conciliation serially, the order she encounters the peers influences the resulting credence. I argue this is a problem for conciliatory views of disagreement, and suggest some responses available to advocates of conciliation. (shrink)

The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest in substitutional quantification, namely, theories (...) of truth and ontological commitment. (shrink)

The moral significance of blockchain technologies is a highly debated and polarised topic, ranging from accusations that cryptocurrencies are tools serving only nefarious purposes such as cybercrime and money laundering, to the assessment of blockchain technology as an enabler for revolutionary positive social transformations of all kinds. Such technological determinism, however, hardly provides insights of sufficient depth on the moral significance of blockchain technology. This thesis argues rather, that very much like the cryptographic tools before them, blockchains develop in a (...) constant feedback loop. Blockchain applications are driven by values, normative assumptions, and personal commitments of researchers, which shape moral effects of technology. At the same time these very assumption are often embedded in preexisting moral conception and ethical theories, implicitly or explicitly accepted by blockchain developers. And just as the introduction of one flawed element in the cryptographic application can have mass scale effects, the introduction of flawed normative assumptions can have far reaching consequences in blockchain applications. This thesis argues that we should not take normative assumptions present in blockchain applications as given. Just like the open-source code is developed through the public revision and scrutiny, we should aim to make normative assumptions transparent and be ready to revise them in case we find some bugs. How can we qualify claims that blockchain technologies enable new types of institutions? Can blockchain technologies eliminate trust in complex socio-technical systems? What does individual sovereignty mean in the context of private data control and privacy? Whether property in private data enabled by blockchain applications can solve moral issues of privacy and commercial surveillance? Answers to these and other questions map some of the key normative assumptions present in the current blockchain applications and serve as a contribution to the open-source project of the future society built on the fundamental human values. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

Understanding enjoys a special kind of value, one not held by lesser epistemic states such as knowledge and true belief. I explain the value of understanding via a seemingly unrelated topic, the implausibility of veritism. Veritism holds that true belief is the sole ultimate epistemic good and all other epistemic goods derive their value from the epistemic value of true belief. Veritism entails that if you have a true belief that p, you have all the epistemic good qua p. Veritism (...) is a plausible and widely held view; I argue that it is untenable. I argue that integration among beliefs possesses epistemic value independent from the good of true belief, and so has value veritism cannot account for. I argue further that this integration among beliefs comprises the distinctive epistemic value of understanding. (shrink)

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...) relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

In this study, I reconstruct and compare Alain Badiou’s Being and Event (2005) and Graham Priest’s One (2014), arguing that the ontologies pursued within the two texts are intriguingly analogous in a number of ways. Both Badiou and Priest are committed to thinking through classically ontological problems without denying the validity of the paradoxes they raise; both regard Plato’s Parmenides as an early and formative account of these paradoxes; both establish conclusions to the effect that unity – or “oneness” – (...) is indeed a contradictory phenomenon; and both, as a corollary of this conclusion, develop frameworks which confer ontological prominence upon "the void" and "emptiness" respectively, thereby arriving at what appears to be a shared ontological nihilism. In this comparative study, I not only enquire whether the frameworks adopted by Badiou and Priest really do lead to nihilist conclusions, but also attempt to clearly outline their trajectories of thought for the benefit of those who might be tempted to dismiss their seemingly outlandish theses out of hand. (shrink)

Moral encroachment holds that the epistemic justification of a belief can be affected by moral factors. If the belief might wrong a person or group more evidence is required to justify the belief. Moral encroachment thereby opposes evidentialism, and kindred views, which holds that epistemic justification is determined solely by factors pertaining to evidence and truth. In this essay I explain how beliefs such as ‘that woman is probably an administrative assistant’—based on the evidence that most women employees at the (...) firm are administrative assistants—motivate moral encroachment. I then describe weaknesses of moral encroachment. Finally I explain how we can countenance the moral properties of such beliefs without endorsing moral encroachment, and I argue that the moral status of such beliefs cannot be evaluated independently from the understanding in which they are embedded. (shrink)

This essay presents a unified account of safety, sensitivity, and severe testing. S’s belief is safe iff, roughly, S could not easily have falsely believed p, and S’s belief is sensitive iff were p false S would not believe p. These two conditions are typically viewed as rivals but, we argue, they instead play symbiotic roles. Safety and sensitivity are both valuable epistemic conditions, and the relevant alternatives framework provides the scaffolding for their mutually supportive roles. The relevant alternatives condition (...) holds that a belief is warranted only if the evidence rules out relevant error possibilities. The safety condition helps categorise relevant from irrelevant possibilities. The sensitivity condition captures ‘ruling out’. Safety, sensitivity, and the relevant alternatives condition are typically presented as conditions on warranted belief or knowledge. But these properties, once generalised, help characterise other epistemic phenomena, including warranted inference, legal verdicts, scientific claims, reaching conclusions, addressing questions, warranted assertion, and the epistemic force of corroborating evidence. We introduce and explain Mayo’s severe testing account of statistical inference. A hypothesis is severely tested to the extent it passes tests that probably would have found errors, were they present. We argue Mayo’s account is fruitfully understood using the resulting relevant alternatives framework. Recasting Mayo’s condition using the conceptual framework of contemporary epistemology helps forge fruitful connections between two research areas—philosophy of statistics and the analysis of knowledge—not currently in sufficient dialogue. The resulting union benefits both research areas. (shrink)

The epistemology of risk examines how risks bear on epistemic properties. A common framework for examining the epistemology of risk holds that strength of evidential support is best modelled as numerical probability given the available evidence. In this essay I develop and motivate a rival ‘relevant alternatives’ framework for theorising about the epistemology of risk. I describe three loci for thinking about the epistemology of risk. The first locus concerns consequences of relying on a belief for action, where those consequences (...) are significant if the belief is false. The second locus concerns whether beliefs themselves—regardless of action—can be risky, costly, or harmful. The third locus concerns epistemic risks we confront as social epistemic agents. I aim to motivate the relevant alternatives framework as a fruitful approach to the epistemology of risk. I first articulate a ‘relevant alternatives’ model of the relationship between stakes, evidence, and action. I then employ the relevant alternatives framework to undermine the motivation for moral encroachment. Finally, I argue the relevant alternatives framework illuminates epistemic phenomena such as gaslighting, conspiracy theories, and crying wolf, and I draw on the framework to diagnose the undue skepticism endemic to rape accusations. (shrink)

The paper questions the scientific rather than ideological problem of an eventual biological successor of the mankind. The concept of superhumans is usually linked to Nietzsche or to Heidegger’s criticism or even to the ideology of Nazism. However, the superhuman can be also viewed as that biological species who will originate from humans eventually in the course of evolution.While the society is reached a natural limitation of globalism, technics depends on the amount of utilized energy, and the mind is restricted (...) by its carrier, i.e. by the brain, it is language which seems to be the frontier of any future development of humans or superhumans. Language is a symbolization of the world and thus doubling in an ideal or virtual world fruitful for creativity and the modeling of the former. Consequently, the gap between the material and the ideal world is both produced by and productive for language. (shrink)

The text discusses Linnaeus’ binominal classification and the idea of mathesis unversalis of Leibniz in the ground of Michel Foucault’s conception of ‘epistema’ as well the connexion of XVIII century’s representation of universal order with viewpoints of Descartes (Rules for the Direction of the Mind) and Kant (The Critique of Pure Reason, The Critique of (the Power of) Judgment).

Alternatives to dairy products are becoming part of mainstream food culture in Western societies amidst growing concerns for more sustainable and healthy diets, and improved animal welfare. As more citizens opt for plant-based milks, markets have responded with an abundance of alternatives to facilitate the transition. Previous systematic reviews have examined the environmental and health impacts of plant-based products compared with dairy, yet a synthesis of empirical research on the social and environmental justice impacts of dairy alternatives is lacking. This (...) systematic scoping review aims to explore the extent, range, and nature of peer-reviewed studies on dairy alternatives that address their outcomes for justice. Publications were sought through systematic search of two comprehensive electronic databases (Scopus and Web of Science) and screened by two independent reviewers following eligibility criteria. Included studies predominantly focused on consumer identities and values, and the market-led nature of dairy alternatives consumption. Gaps in the literature included impacts on nutritional equity and the innovation and adaptive capabilities of food producers and workers across geographies. We conclude that the heavy-handed regulation of dairy alternative terminology and the market-driven nature of this transition raise questions about injustices in governance and innovation in this sector. (shrink)

The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...) measurement. The quantity of quantum information is the transfinite ordinal number corresponding to the infinity series in question. The transfinite ordinal numbers can be defined as ambiguously corresponding “transfinite natural numbers” generalizing the natural numbers of Peano arithmetic to “Hilbert arithmetic” allowing for the unification of the foundations of mathematics and quantum mechanics. (shrink)

According to a common conception of legal proof, satisfying a legal burden requires establishing a claim to a numerical threshold. Beyond reasonable doubt, for example, is often glossed as 90% or 95% likelihood given the evidence. Preponderance of evidence is interpreted as meaning at least 50% likelihood given the evidence. In light of problems with the common conception, I propose a new ‘relevant alternatives’ framework for legal standards of proof. Relevant alternative accounts of knowledge state that a person knows a (...) proposition when their evidence rules out all relevant error possibilities. I adapt this framework to model three legal standards of proof—the preponderance of evidence, clear and convincing evidence, and beyond reasonable doubt standards. I describe virtues of this framework. I argue that, by eschewing numerical thresholds, the relevant alternatives framework avoids problems inherent to rival models. I conclude by articulating aspects of legal normativity and practice illuminated by the relevant alternatives framework. (shrink)

Many theorists hold that outright verdicts based on bare statistical evidence are unwarranted. Bare statistical evidence may support high credence, on these views, but does not support outright belief or legal verdicts of culpability. The vignettes that constitute the lottery paradox and the proof paradox are marshalled to support this claim. Some theorists argue, furthermore, that examples of profiling also indicate that bare statistical evidence is insufficient for warranting outright verdicts.I examine Pritchard's and Buchak's treatments of these three kinds of (...) case. Pritchard argues that his safety condition explains the insufficiency of bare statistical evidence for outright verdicts in each of the three cases, while Buchak argues that her treatment of the distinction between credence and belief explains this. In these discussions the three kinds of cases – lottery, proof paradox, and profiling – are treated alike. The cases are taken to exhibit the same epistemic features. I identity significant overlooked epistemic differences amongst these three cases; these differences cast doubt on Pritchard's explanation of the insufficiency of bare statistical evidence for outright verdicts. Finally, I raise the question of whether we should aim for a unified explanation of the three paradoxes. (shrink)

This paper examines the plays of African-American playwright Adrienne Kennedy, Funnyhouse of a Negro (1962) and The Owl Answers (1963), which remain important for their engagement with notions of African-American identity, resistance and agency through their attention to mixed race female characters or mulattos who experience bodily and psychological traumas that demonstrate the abuse of the colonized on a deeply visceral level. Kennedy's plays have remained controversial because of their failure to comply with the nationalistic orientation of the Black Arts (...) Movement (BAM) of 1960s America. I aim to examine these plays through a framework of postcolonial-feminist performance analysis that finds its way back to histories of colonization and slavery, enabling through such returns, a compelling critique of the manoeuvrings of racial hierarchies and power imbalances. As well, I argue that Kennedy's protagonists are de-essentialized fractured beings who fail to embody either White superiority or Black nationalist pride, as they oscillate between two polarities. Such failure (on the part of Kennedy's mulattos) allows for a strategic de-essentialization of identity that interrogates fixed categorization. As well, through a form that is fluid, fragmented and blurs the distinctions among history, memory, space and time, her works impart political agency to the characters and enable an empowered sense of the ‘self-in-process.’. (shrink)

In der vorliegenden Arbeit soll ein in der analytischen Philosophie aufgestelltes Programm zur Explikation der kausalen Begrifflichkeit kritisch untersucht werden. Seine kritische Analyse mag im Hinblick auf die Rolle von Interesse sein, welche die kausalen Begriffe in einer allgemeinen Theorie der wissenschaftlichen Erklärung zu spielen haben. Diese Analyse könnte außerdem m.E. zur Bestimmung des Ausgangspunktes einer positiven Behandlung der mit den kausalen Begriffen zusammenhängenden Sinnfragen beitragen.

The article analyzes some key motives of both classical German phenomenology and contemporary French phenomenology. The theme of sense-formation, a recurring thread throughout Husserl's entire body of work, serves as a discussion starting point.A special emphasis is put on one of Husserl's posthumously published texts from 1933, in which he distinguishes between the open process of sense-formation [Sinnbildung] and the closed sense-structures [Sinngebilde]. The “phenomenon” to which phenomenological philosophy refers here is not a “pre-given thing” yet, but rather the horizon (...) in which its sense is shaped. This fundamental intuition is crucially important for the project of “nonstandard” phenomenology, which Richir is developing in the context of Francophone philosophy. Drawing equally from Maurice Merleau-Ponty’ phenomenology of language, Richir refers to “the sense that creates itself.” In this way, he is continuing to develop one of the key intuitio... (shrink)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases suggests (...) standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

This essay is not about what love is. It is about what self-ascriptions of love do. People typically self-ascribe romantic love when a nexus of feelings, beliefs, attitudes, values, commitments, experiences, and personal histories matches their conception of romantic love. But what shapes this conception? And (how) can we adjudicate amongst conflicting conceptions? -/- Self-ascriptions of love do not merely describe the underlying nexus of attitudes and beliefs. They also change it. This essay describes how conceptions of love affect romantic (...) experience. I limn distinctions between love and obsessive infatuation and explore ways language can cultivate queer romantic preferences. Since conceptions of love are shaped, often implicitly, by terms available in one’s linguistic community, the resulting nexus of concepts and conceptions manifests linguistic luck. I suggest ways we might sculpt the language of love to better understand—and change—ourselves. Love can help us flourish and so can our “love” language. (shrink)

The teleological approach to an epistemic concept investigates it by asking questions such as ‘what is the purpose of the concept?’, ‘What role has it played in the past?’, or ‘If we imagine a society without the concept, why would they feel the need to invent it?’ The idea behind the teleological approach is that examining the function of the concept illuminates the contours of the concept itself. This approach is a relatively new development in epistemology, and as yet there (...) are few works examining it. This paper aims to fill this gap and engender further understanding of the teleological method. I first contrast the teleological method with more orthodox approaches in epistemology. I then draw a three-way taxonomy of different kinds of teleological approach and provide an example of each kind. The teleological approach is often presented as antithetical to the more orthodox approaches in epistemology, and so in competition with them. I demur. I argue that the methods can be fruitfully combined in epistemological theorising; in the final section I suggest specific ways the teleological approach can be incorporated alongside more orthodox methods in a general methodological reflective equilibrium. (shrink)

Abstract.The German zoologist and geneticist Ludwig Plate was a pupil and successor of the “German Darwin” Ernst Haeckel as the director of the Institute of Zoology at Jena University. Plate campaigned for a revival of the original Darwinism. His research program, which he labelled “old-Darwinism”, proclaimed the synthesis of selectionism with “moderate Lamarckism” and orthogenesis.This article reconstructs and analyses Plate’s “old-Darwinian” synthesis and sheds light on Plate’s controversial biography, especially his conflict with Haeckel.

In criminal trials the state must establish, to a particular standard of proof, the defendant's guilt. The most widely used and important standard of proof for criminal conviction is the ‘beyond a reasonable doubt' standard. But what legitimates this standard, rather than an alternative? One view holds the standard of proof should be determined or justified – at least in large part – by its consequences. In this spirit, Laudan uses crime statistics to estimate risks the average citizen runs of (...) being violently victimised and falsely convicted. He argues that since the former risk is higher, and the aggregate harms are worse, the standard of proof should be substantially lowered. He presents a formula for calculating the preferred standard. In this article I outline various ways Laudan's uses of crime statistics are flawed, and explain how he substantially overestimates risks of victimhood and underestimates costs of false convictions. I also explain why his formula is mistaken, and illuminate consequences Laudan neglects. I conclude that, even if consequences determine the appropriate standard of proof, Laudan's arguments fail to show the standard is too high. I conclude by suggesting that the inadequacies of Laudan's reasoning might be good news for consequence-based justifications of the standard of proof. (shrink)

In the early 1960s, American philosopher of science Thomas Kuhn contributed to a “crisis of rationality” with his hypothesis that science develops by means of paradigm shifts. He challenged the positivist concept of cumulative and continuous scientific progress. According to Kuhn, the relation between two succeeding scientific traditions ‘separated by a scientific revolution’ is characterized by conceptual incommensurability that constrains the interpretation of science as a cumulative, steadily progressing enterprise. Thomas Kuhn’s philosophy was heavily criticized by German-American biologist Ernst Mayr (...) as unapplicable to the history of biology. Mayr, one of the most outstanding evolutionary biologists of the 20th century and a “co-architect” of the so-called Modern Synthesis (contemporary Darwinism), published extensively on the history and philosophy of biology as he thought that theoretical biology cannot progress without proper philosophy of science. Being convinced of the progressive development of Darwinism, Mayr pointed out that Kuhn’s concept of scientific revolutions does not reflect conceptual changes in evolutionary biology. Here we summarize Mayr’s critiques of Kuhn and, based on our own research, take Mayr’s side in the controversy between two great thinkers. (shrink)

Theoria, Volume 87, Issue 1, Page 136-151, February 2021.

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...) of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links (...) it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)

Some expressions of English, like the demonstratives ‘this’ and ‘that’, are referentially promiscuous: distinct free occurrences of them in the same sentence can differ in content relative to the same context. One lesson of referentially promiscuous expressions is that basic logical properties like validity and logical truth obtain or fail to obtain only relative to a context. This approach to logic can be developed in just as rigorous a manner as David Kaplan’s classic logic of demonstratives. The result is a (...) logic that applies to arguments in English containing multiple occurrences of referentially promiscuous expressions. (shrink)

Along with “epoché” or his “reductions”, Husserl’s “noema” and “noesis”, being neologisms invented by him, are main concepts in phenomenology able to represent its originality. Following the trace of a recent paper (Penchev 2021 July 23), its formal and philosophical approach is extended to both correlative notions, in the present article. They are able to reveal the genesis of the world from consciousness in a transcendental method relevant to Husserl, but furthermore described formally as a process of how subjective (...) temporality appears being isomorphic to objective temporality of the “world by itself” (an abstraction meaning it out of consciousness or transcendental consciousness): thus, it shares the same mathematical structure, which is embodied in the physical process of decoherence by the physical quantity of quantum information. The temporal world is able to appear naturally (rather as a ridiculous effect of the mythical “Big Bang”). The same process translated by formal and mathematical tools as interpreted in terms of “noema”, “noesis”, or transcendental consciousness is isomorphic to how “Self” (including in an individual and psychological sense) appears in virtue of transcendental consciousness. (shrink)

The GOOGLE and XPRIZE $5,000,000 for the practical and socially useful utilization of the quantum computer is the starting point for ontomathematical reflections for what it can really serve. Its “output by measurement” is opposed to the conjecture for a coherent ray able alternatively to deliver the ultimate result of any quantum calculation immediately as a Dirac -function therefore accomplishing the transition of the sequence of increasingly narrow probability density distributions to their limit. The GOOGLE and XPRIZE problem’s solution needs (...) the initial understanding that the result of any quantum calculation is a wave function, or respectively, a probability (density or not) distribution unlike the Turing machine one, and only a “calculating ray” is able to transform the former into the later without any “curving” disturbances. Thus, the unique capability of the quantum computer due to its inherent quantum parallelism can be conserved for all Gödel unresolvable problems, only on the fast “NP” track of which the quantum computer “Achilles” is able practically to overrun the Turing machine “Tortoise” since the latter can “sprint” only by any “P” calculating speed even on it and unlike “Achilles” himself able for “NP” velocities as well. The way for any material body to “calculate” the certain trajectory of least action also resolves the “traveling salesman problem” in fact, therefore illustrating furthermore what the “NP” output of a quantum computer by a “calculating ray” should mean. Another example is the problem of the number of all prime numbers less than “N”, which is suggested to visualize once again the quantum computer capability to resolve problems by a “NP” speed and thus qualitatively to overrun any competing Turing machine. The technically implemented idea of laser is now reinterpreted to “radiate a wave function” in order to explain the “calculating ray” option for a quantum computer “NP” output. The generalization of an entanglement “trigger ray” described by any non-Hermitian operator (unlike a laser) is suggested as well as those “sci-fi” horizons which it reveals. One of them is meant for elucidating the practical meaning of the “Yang-Mills existence and mass gap problem”, one more of the CMI “Millennium Problems” after that of “P vs NP”. -/- . (shrink)

Building on recent work by Delia Graff Fara and Ora Matushansky on appellative constructions like ‘Mirka called Roger handsome’, I argue that if Millianism about proper names is true, then the quantifier ‘something’ in ‘Mirka called Roger something’ is best understood as a kind of substitutional quantifier. Any adequate semantics for such quantifiers must explain both the logical behavior of ‘Mirka called Roger something’ and the acceptability of ‘so’-anaphora in ‘Mirka called Roger something, and everyone so called is handsome’. Millianism (...) about proper names is inconsistent with such quantifiers being standard non-substitutional second-order quantifiers. But this is not the only option for Millianism: I provide two different propositional semantics for substitutional quantification, each of which is adequate in the sense above, given Millianism. One of these is based on Tobias Rosefeldt’s work on non-nominal quantification, and I identify in what way Rosefeldt’s semantics is substitutional. (shrink)

My essay ‘Attunement: On the Cognitive Virtues of Attention’ is the lead essay in a symposium. Adam Carter and Sandy Goldberg each respond to the ‘Attunement’ essay. This is my rejoinder. -/- (i.) Carter argues that resources from virtue reliabilism can explain the source of attention normativity. He modifies this virtue reliabilist AAA-framework to apply to attentional normativity. I raise concerns about Carter’s project. I suggest that true belief and proper attentional habits are not relevantly similar. -/- (ii.) Goldberg claims (...) that social roles underwrite kinds of attentional normativity that are not well-captured by virtue theory. I critically assess this claim. (shrink)

I motivate three claims: Firstly, attentional traits can be cognitive virtues and vices. Secondly, groups and collectives can possess attentional virtues and vices. Thirdly, attention has epistemic, moral, social, and political importance. An epistemology of attention is needed to better understand our social-epistemic landscape, including media, social media, search engines, political polarisation, and the aims of protest. I apply attentional normativity to undermine recent arguments for moral encroachment and to illuminate a distinctive epistemic value of occupying particular social positions. A (...) recurring theme is that disproportionate attention can distort, mislead, and misrepresent even when all the relevant claims are true and well supported by evidence. In the informational cacophony of the internet age, epistemology must foreground the cognitive virtues of attunement. (shrink)

Thought experiments as counterexamples are a familiar tool in philosophy. Frequently understanding a vignette seems to generate a challenge to a target theory. In this paper I explore the content of the judgement that we have in response to these vignettes. I first introduce several competing proposals for the content of our judgement, and explain why they are inadequate. I then advance an alternative view. I argue that when we hear vignettes we consider the normal instances of the vignette. If (...) the normal instance of the vignette exhibits a counter-instance, the vignette constitutes a challenge to the target theory. I argue that this proposal shows how responses to vignettes are an ordinary, everyday judgement, and I explain how the proposal avoids the problems generated by competing theories. Finally, I argue this ‘normalcy proposal’ most naturally accords with our understanding of the method. (shrink)

Radio Free Europe used balloons to drop leaflets in an attempt to supplement radio with printed words in the 1950s—a historical moment when closing borders, censoring the press, jamming foreign radios, tapping telephone lines, and tracking letters from abroad created an almost hermetically sealed space without many means for exchanging information across the Iron Curtain. This article traces how distorted and limited information shaped Cold War propaganda and practices of information-gathering. The article further examines unpredictable environmental factors that were transformed (...) into persuasive political rhetoric. A comparative analysis of communist media shows similarities of imagination in a visual propaganda campaign across five communist countries. Fantasies evolved into an object of public interest when propaganda strategies embraced a language of facts. (shrink)

An annotated bibliography of legal epistemology.

In an earlier defense of the view that the fundamental logical properties of logical truth and logical consequence obtain or fail to obtain only relative to contexts, I focused on a variation of Kaplan’s own modal logic of indexicals. In this paper, I state a semantics and sketch a system of proof for a first-order logic of demonstratives, and sketch proofs of soundness and completeness. (I omit details for readability.) That these results obtain for the first-order logic of demonstratives shows (...) that the significance of demonstratives for logic exceeds their behavior as rigid designators in counterfactual reasoning, or reasoning about alternative possibilities. Furthermore, the results in this paper help address one common objection to the view that logical truth and consequence obtain only relative to contexts. According to this objection, the view entails that logical consequence is not formal. (shrink)