In this paper, a modified form of Collatz conjecture for neutrosophic numbers n ∈ (Z U I) is defined. We see for any n ∈ (Z U I) the related sequence using the formula (3a + 1) + (3b + 1)I converges to any one of the 55 elements mentioned in this paper. Using the akin formula of Collatz conjecture viz. (3a- 1) + (3b -1)I the neutrosophic numbers converges to any one of the 55 (...) elements mentioned with appropriate modifications. Thus, it is conjectured that every n ∈ (Z U I) has a finite sequence which converges to any one of the 55 elements. (shrink)

In previous papers (see Van Bendegem [1993], [1996], [1998], [2000], [2004], [2005], and jointly with Van Kerkhove [2005]) we have proposed the idea that, if we look at what mathematicians do in their daily work, one will find that conceiving and writing down proofs does not fully capture their activity. In other words, it is of course true that mathematicians spend lots of time proving theorems, but at the same time they also spend lots of time preparing the ground, if (...) you like, to construct a proof. (shrink)

Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions . Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered . Two derivations of the same sequent are equivalent if and only if (...) all their interpretations in K are equal. In fact, the assignment of values to atoms is defined constructively for each pair of derivations. Taking into account a mistake in R. Voreadou's proof of the “abstract coherence theorem” found by the author, it was necessary to modify her description of the class of non-commutative diagrams in SMC categories; our proof of S. Mac Lane conjecture also proves the correctness of the modified description. (shrink)

1. On at least one usage of ‘mean’, performing an action that leads someone else to think that P, is not, on its own, sufficient for meaning that P. Nor is performing an action that is intended to get someone to think this. Instead one must make one’s intention overt. Grice’s way of developing this overtness requirement requires audience-directed intentions: for an agent, on this approach, to mean that P, she must perform a publicly accessible action with the intention of (...) producing in an addressee the belief that P, while further intending that her addressee enter that state at least in part by recognition of her intention. 11 Different types of intended cognitive state and content correspond to different illocutionary forces. Thus an imperatival utterance might be made with the aim of producing an intention to do something; and one might mean P as a conjecture rather than as an assertion by intending to produce in an addressee not a belief but some less committal cognitive state such as tentative acceptance. (shrink)

BackgroundDecision-making in out-of-hospital cardiac arrest should ideally include clinical and ethical factors. Little is known about the extent of ethical considerations and their influence on prehospital resuscitation. We aimed to determine the transparency in medical records regarding decision-making in prehospital resuscitation with a specific focus on ethically relevant information and consideration in resuscitation providers’ documentation.MethodsThis was a Danish nationwide retrospective observational study of out-of-hospital cardiac arrests from 2016 through 2018. After an initial screening using broadly defined inclusion criteria, two experienced (...) philosophers performed a qualitative content analysis of the included medical records according to a preliminary codebook. We identified ethically relevant content in free-text fields and categorised the information according to Beauchamp and Childress’ four basic bioethical principles: autonomy, non-maleficence, beneficence, and justice. ResultsOf 16,495 medical records, we identified 759 (4.6%) with potentially relevant information; 710 records (4.3%) contained ethically relevant information, whereas 49 did not. In general, the documentation was vague and unclear. We identified four kinds of ethically relevant information: patients’ wishes and perspectives on life; relatives’ wishes and perspectives on patients’ life; healthcare professionals’ opinions and perspectives on resuscitation; and do-not-resuscitate orders. We identified some “best practice” examples that included all perspectives of decision-making. ConclusionsThere is sparse and unclear evidence on ethically relevant information in the medical records documenting resuscitation after out-of-hospital cardiac arrests. However, the “best practice” examples show that providing sufficient documentation of decision-making is, in fact, feasible. To ensure transparency surrounding prehospital decisions in cardiac arrests, we believe that it is necessary to ensure more systematic documentation of decision-making in prehospital resuscitation. (shrink)

Modifying the conjecture of Wolfgang Helbig by means of the distinction between Xenophon and his various narrators introduced by Benjamin McCloskey, this paper uses the insights of Hartvig Frisch to show how drawing a distinction between the first-person speaker in pseudo-Xenophon’s Constitution of the Athenians and its author indicates that the former is Alcibiades and the latter is Xenophon himself.

It is conjectured that a suitably modified Bondi-type expansion of the gravitational field in the radiation zone is a rapidly convergent series. It is also conjectured that the source behavior in the inner zone is insensitive to the initial conditions imposed on the gravitational field in solving the initial-value problem in this zone. Consequences of these conjectures for the problem of relating source motion to the Bondi news function are discussed.

How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects of the theory. Because the philosophical side has radical elements, so does the physical-theory side. The philosophical side is radical, first, in proposing that the productivity or dynamism in the universe that many believe to be responsible for (...) its systematic regularities is actually itself a physical constituent of the universe, along with more familiar entities. Indeed, it proposes that instances of dynamism can themselves take part in physical interactions with other entities, this interaction then being “meta-dynamism” (a type of meta-causation). Secondly, the theory is radical, and unique, in arguing that consciousness is necessarily partly constituted of meta-dynamic auto-sensitivity, in other words it must react via meta-dynamism to its own dynamism, and also in conjecturing that some specific form of this sensitivity is sufficient for and indeed constitutive of consciousness. The article proposes a way for physical laws to be modified to accommodate meta-dynamism, via the radical step of including elements that explicitly refer to dynamism itself. Additionally, laws become, explicitly, temporally non-local in referring directly to quantity values holding at times prior to a given instant of application of the law. The approach therefore implicitly brings in considerations about what information determines states. Because of the temporal non-locality, and also because of the deep connections between dynamism and time-flow, the approach also implicitly connects to the topic of entropy insofar as this is related to time. (shrink)

We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

A notion of feasible function of finite type based on the typed lambda calculus is introduced which generalizes the familiar type 1 polynomial-time functions. An intuitionistic theory IPVω is presented for reasoning about these functions. Interpretations for IPVω are developed both in the style of Kreisel's modified realizability and Gödel's Dialectica interpretation. Applications include alternative proofs for Buss's results concerning the classical first-order system S12 and its intuitionistic counterpart IS12 as well as proofs of some of Buss's conjectures concerning (...) IS12, and a proof that IS12 cannot prove that extended Frege systems are not polynomially bounded. (shrink)

A naturalistic theory of intentionality is proposed that differs from previous evolutionary and tracking theories. Full-blown intentionality is constructed through a series of evolvable refinements. A first, minimal version of intentionality originates from a conjectured internal process that estimates an organism’s own fitness and that continually modifies the organism. This process produces the directedness of intentionality. The internal estimator can be parsed into intentional components that point to components of the process that produces fitness. It is argued that such intentional (...) components can point to mistaken or non-existing entities. Different Fregian senses of the same reference correspond to different components that have different roles in the estimator. Intentional components that point to intentional components in other organisms produce directedness towards semi-abstract entities. Finally, adding a general, population-wide means of communication enables intentional components that point to fully abstract entities. Intentionality thus naturalized has all of its expected properties: being directed; potentially making errors; possibly pointing to non-existent, abstract, or rigid entities; capable of pointing many-to-one and one-to-many; distinguishing sense and reference; having perspective and grain; and having determinate content. Several examples, such as ‘swampman’ and ‘brain-in-a-vat’, illustrate how the theory can be applied. (shrink)

We may think of principles which purport to fairly and reasonably adjudicate conflicting claims among human beings as principles of justice. To identify such principles John Rawls investigates what principles would be chosen by rational, self-interested persons who are ignorant of certain features of themselves which might be taken into account to promote their own advantage. The impartial viewpoint obtained by participants in a modified “original position” might be used, to identify principles which would reasonably and fairly adjudicate conflicting (...) claims among sentient creatures, i.e., human beings and animals. In what follows I attempt to sketch the beginnings of such a strategy, some reasons for exploring it, and conjecture as to a few of its implications for current disputes about the treatment of animals. (shrink)

In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary gradient, spoiling Gauss's law. The secondary first-class constraint p^i,_i=0 still holds, but being a function of derivatives of momenta, it is not directly about E. Only a special combination of the two first-class constraints, the Anderson-Bergmann -Castellani gauge generator G, leaves E (...) unchanged. This problem is avoided if one uses a first-class constraint as the generator of a _canonical transformation_; but that partly strips the canonical coordinates of physical meaning as electromagnetic potentials and makes the electric field depend on the smearing function, bad behavior illustrating the wisdom of the Anderson-Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation dot{q}- dH/dp= -E_i -p^i=0 supports using the primary Hamiltonian rather than the extended Hamiltonian. The results extend the Lagrangian-oriented reforms of Castellani, Sugano, Pons, Salisbury, Shepley, _etc._ by showing the inequivalence of the extended Hamiltonian to the primary Hamiltonian even for _observables_, properly construed in the sense implying empirical equivalence. Dirac and others have noticed the arbitrary velocities multiplying the primary constraints outside the canonical Hamiltonian while apparently overlooking the corresponding arbitrary coordinates multiplying the secondary constraints _inside_ the canonical Hamiltonian, and so wrongly ascribed the gauge quality to the primaries alone, not the primary-secondary team G. Hence the Dirac conjecture about secondary first-class constraints rests upon a false presupposition. The usual concept of Dirac observables should also be modified to employ the gauge generator G, not the first-class constraints separately, so that the Hamiltonian observables become equivalent to the Lagrangian ones such as the electromagnetic field F. (shrink)

Dirac's approach to gauge symmetries is discussed. We follow closely the steps that led him from his conjecture concerning the generators of gauge transformations {\it at a given time} ---to be contrasted with the common view of gauge transformations as maps from solutions of the equations of motion into other solutions--- to his decision to artificially modify the dynamics, substituting the extended Hamiltonian for the total Hamiltonian. We show in detail that Dirac's analysis was incomplete and, in completing it, (...) we prove that the fulfilment of Dirac's conjecture ---in the ``non-pathological" cases--- does not imply any need to modify the dynamics. We give a couple of simple but significant examples. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Evolution of Pragmatism in India: Ambedkar, Dewey, and the Rhetoric of Reconstruction by Scott R. StroudAlbert R. SpencerBy Scott R. StroudThe Evolution of Pragmatism in India: Ambedkar, Dewey, and the Rhetoric of Reconstruction Chicago and London: The University of Chicago Press, 2023. 302 pp., incl. indexMore scholarly attention needs to be paid to the mutual influences between Asian and American thought, especially with regards to the development, (...) legacy, and future of pragmatism. Fortunately, there have been several notable attempts. Throughout his works, Richard Shusterman frequently incorporates the perspectives of various East Asian philosophies into his articulation of somaesthetics. Multiple scholars have explored John Dewey’s lectures in China and their political and educational impact, such as Jessica Ching-Sze Wang’s John Dewey in China or The Democracy of the Dead by Roger T. Ames and David L. Hall. Still others have highlighted the influence of Indian thought on pragmatism’s forerunners, such as American Philosophy Before Pragmatism (Goodman 2015), American Pragmatism: An Introduction (Spencer 2020), and The Ethics of Oneness (Engles 2021). Perhaps the most interesting inquiries into this influence can be found in a special volume of The Journal of Aesthetic Education (Vol. 43, No. 1) where multiple scholars discuss pragmatism’s connections and comparisons to The Bhagavad Gita, Confucianism, and Taoism. Among these scholars is Scott Stroud whose most recent publication The Evolution of Pragmatism in India (2023) represents the culmination of nearly two decades of research on the subject with special attention to the continuities between pragmatism and Indian thought. In it, he meticulously explores the influence of John Dewey on one of his students, Bhimrao Ambedkar (1891–1956), who was a transformative figure in the founding of the nascent Republic of India. The result is a work of scholarship that shows the global relevance of pragmatism in the 20th Century, [End Page 456] introduces the fascinating philosophy of Ambedkar to a non-Indian audience, and provides an entry for further scholarship on this profound thinker and activist.Bhimrao Ambedkar was a critical figure in the birth of modern India. Born an “untouchable” due to the rigid caste system, he tirelessly advocated for the right of Dalits (“crushed” or “untouchables”). By the mid-20th century, he had greatly influenced Indian politics, safeguarded the interests of the oppressed, and played a key role in drafting the Indian Constitution. Separate to his role as a statesman, Ambedkar promoted Buddhism in the 1950s as an escape from caste oppression, culminating in his publication, The Buddha and His Dhamma (1957). While his name is less familiar outside of India, he was voted the “Greatest Indian” in a 2012 poll due to his profound impact on the nation’s post-independence development. These accomplishments were supported by an extensive education, but unlike most subjects of the British Empire, Ambedkar also studied in the United States. Stroud initiates his study by focusing on this formative period, specifically his time at Columbia University and the influence of the philosopher and psychologist John Dewey. While their relationship has been acknowledged, Stroud is the first to explore this relationship in depth and he not only reconstructs the influence of Dewey on Ambedkar’s Navayana Pragmatism but illuminates the ways that Ambedkar integrated, modified, and even resisted Dewey’s pragmatism.Stroud masterfully builds his reconstruction of this synergy between Dewey’s pragmatism and Ambedkar’s philosophy not out of ephemeral conjecture or pithy textual evidence, but through painstaking, detailed, and exhaustive scholarship. He draws on comparative evidence in their major and minor works, their private correspondence, interviews of Ambedekar’s cohort at Columbia, Dewey’s voluminous lecture notes, and even the marginalia and notecards found between the pages of Ambedkar’s pragmatism bookshelf. Indeed, I often found myself pleasantly distracted as I imagined Stroud’s academic pilgrimage throughout India, Columbia University, and the Center for Dewey Studies to find every scrap of relevant information. In our age of instant information and digital archives, it is refreshing and inspiring to encounter a scholar still willing to trek across the globe for answers to his inquiries. Despite his passion to uncover the influence of Dewey on Ambedekar, Stroud never reduces the... (shrink)

A Polish group G is tame if for any continuous action of G, the corresponding orbit equivalence relation is Borel. When [Formula: see text] for countable abelian [Formula: see text], Solecki [Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995) 4765–4777] gave a characterization for when G is tame. In [L. Ding and S. Gao, Non-archimedean abelian Polish groups and their actions, Adv. Math. 307 (2017) 312–343], Ding and Gao showed that for such G, the (...) orbit equivalence relation must in fact be potentially [Formula: see text], while conjecturing that the optimal bound could be [Formula: see text]. We show that the optimal bound is [Formula: see text] by constructing an action of such a group G which is not potentially [Formula: see text], and show how to modify the analysis of [L. Ding and S. Gao, Non-archimedean abelian Polish groups and their actions, Adv. Math. 307 (2017) 312–343] to get this slightly better upper bound. It follows, using the results of Hjorth et al. [Borel equivalence relations induced by actions of the symmetric group, Ann. Pure Appl. Logic 92 (1998) 63–112], that this is the optimal bound for the potential complexity of actions of tame abelian product groups. Our lower-bound analysis involves forcing over models of set theory where choice fails for sequences of finite sets. (shrink)

Classical proof forests are a proof formalism for first-order classical logic based on Herbrand’s Theorem and backtracking games in the style of Coquand. First described by Miller in a cut-free setting as an economical representation of first-order and higher-order classical proof, defining features of the forests are a strict focus on witnessing terms for quantifiers and the absence of inessential structure, or ‘bureaucracy’.This paper presents classical proof forests as a graphical proof formalism and investigates the possibility of composing forests by (...) cut-elimination. Cut-reduction steps take the form of a local rewrite relation that arises from the structure of the forests in a natural way. Yet reductions, which are significantly different from those of the sequent calculus, are combinatorially intricate and do not exclude the possibility of infinite reduction traces, of which an example is given.Cut-elimination, in the form of a weak normalisation theorem, is obtained using a modified version of the rewrite relation inspired by the game-theoretic interpretation of the forests. It is conjectured that the modified reduction relation is, in fact, strongly normalising. (shrink)

Science is increasingly becoming automated. Tasks yet to be fully automated include the conjecturing, modifying, extending and testing of hypotheses. At present scientists have an array of methods to help them carry out those tasks. These range from the well-articulated, formal and unexceptional rules to the semi-articulated and variously understood rules-of-thumb and intuitive hunches. If we are to hand over at least some of the aforementioned tasks to machines, we need to clarify, refine and make formal, not to mention computable, (...) even the more obscure of the methods scientists successfully employ in their inquiries. The focus of this essay is one such less-than-transparent methodological rule. I am here referring to the rule that ad hoc hypotheses ought to be spurned. This essay begins with a brief examination of some notable conceptions of ad hoc-ness in the philosophical literature. It is pointed out that there is a general problem afflicting most such conceptions, namely the intuitive judgments that are supposed to motivate them are not universally shared. Instead of getting bogged down in what ad hoc-ness exactly means, I shift the focus of the analysis to one undesirable feature often present in alleged cases of ad hoc-ness. I call this feature the ‘monstrousness’ of a hypothesis. A fully articulated formal account of this feature is presented by specifying what it is about the internal constitution of a hypothesis that makes it monstrous. Using this account, a monstrousness measure is then proposed and somewhat sketchily compared with the minimum description length approach. (shrink)

There have been many interpretations of Catullus’ poem 2 and especially of verses 5-8. The first part of this study presents the status quaestionis, listing the main interpretations and conjectures. In the second part two new interpretations of vv. 5-8 are advanced, without modifying the text of manuscripts OGR. According to the first, the words cum desiderio meo … lubet iocari are understood as a substantive clause dependent on the verb credo, which also governs et solaciolum as a predicative. Alternatively, (...) solaciolum may be taken as predicative of an understood object te referring to passer in the first verse. In either case, ut cum with the transmitted future acquiescet can have temporal force, as recently argued by Paul Claes 56. (shrink)

Over 25 years ago, the first author conjectured in [15] that the existence of arbitrarily large primes is provable from the axioms I Δ₀(π) + def(π), where π(x) is the number of primes not exceeding x, IΔ₀(π) denotes the theory of Δ₀ induction for the language of arithmetic including the new function symbol π, and de f(π) is an axiom expressing the usual recursive definition of π. We prove a modified version in which π is replaced by a more (...) general function ξ that counts some of the primes below x (which primes depends on the values of parameters in ξ), and has the property that π is provably Δ₀(ξ) definable. (shrink)

ABSTRACT Jason Brennan’s recent epistemic argument for epistocracy relies on the assumption that voter competence requires knowledge of economics and political science. He conjectures that people who would qualify as competent are mostly white, upper-middle- to upper-class, educated, employed men, who know better how to promote the interests of the disadvantaged than the disadvantaged themselves. My paper, first, shows that this account of voter competence is too narrow and, second, proposes a modified account of this concept. Brennan mistakenly reasons (...) as though it is obvious that socially disadvantaged and oppressed people, by virtue of lacking sufficient knowledge of political science and economics, do not belong on an epistocratic council. This is because there is another way of being competent: possessing first-personal experience and knowledge unique to disadvantaged or oppressed situatedness. Once voter competence is characterized accurately and more holistically, epistocracy’s problematic implications of privileging already dominant genders, races, and classes, which characterize Brennan’s account, no longer arise. (shrink)

This paper is motivated by the idea of interaction between two directions of research in knowledge representation: the design of action description languages and the development of libraries of reusable, general-purpose knowledge components. Writing an action description that characterizes actions in terms of their effects, as common today, can be compared to writing a program that does not use standard subroutines. We conjecture that a library of standard descriptions for a number of “basic” actions can facilitate writing, understanding and (...) modifying action descriptions. In this paper, we take some steps towards determining how such a library, written in the action language C+, can be used. When using an instance of a library action description, we relate the library constants to the domain-specific constants by providing definitions. Therefore, a theory of explicit definitions in C+ is developed. To illustrate the use of the library, we show how the action PushBox in the Monkey and Bananas domain can be described as a special case of the “library action” Move. (shrink)

This is James Diggle's OCT , with a modified apparatus. The lacuna at 186 prompted two conjectures by Willink: υτθυ and the ingenious αλθυ . I wonder, however, whether an adverb is what we want: the anadiplosis of λακυ would not have come amiss to lend a touch of hysterical urgency to the cry of the rapist's victim; but that would not give us the rhythm we need . Something approaching the effect of the suggested anadiplosis might be obtained (...) by the supplement πoλλοσιυ. Although it lacks the palaeographical plausibility of αλθυ, it gives us an expression that is characteristically Euripidean in contexts pertaining to souls in torment: Ale. 185 πoλλυ δακρωυ, 938 πολλυ δ μχθωυ Su. 1119 ἂλγσι πoλλος, Tr. 28 πολλος δ κωκυτοσιυ, 38 δκρυα χουσα πολλ, etc. The adjective applied to sound is not unknown:Rh. 290–1 πολλι γᾰρ χι Θρικιοςωυ στρατς1στιχ. It can also be used to describe the frequency of sung laments accompanied by hysterical self-mutilation: S. El. 88–90 πολλς μυ θρυωυ ιδς, 1 πολλᾰς δ’ υτρις ισθxυ 1 στρυωυ πλαγᾰς αμασσομυωυ. (shrink)

There is now a huge amount of interest in consciousness among scientists as well as philosophers, yet there is so much confusion and ambiguity in the claims and counter-claims that it is hard to tell whether any progress is being made. This ``position paper'' suggests that we can make progress by temporarily putting to one side questions about what consciousness is or which animals or machines have it or how it evolved. Instead we should focus on questions about the sorts (...) of architectures that are possible for behaving systems and ask what sorts of capabilities, states and processes, might be supported by different sorts of architectures. We can then ask which organisms and machines have which sorts of architectures. This combines the standpoint of philosopher, biologist and engineer. If we can find a general theory of the variety of possible architectures (a characterisation of ``design space'') and the variety of environments, tasks and roles to which such architectures are well suited (a characterisation of ``niche space'') we may be able to use such a theory as a basis for formulating new more precisely defined concepts with which to articulate less ambiguous questions about the space of possible minds. For instance our initially ill-defined concept (``consciousness'') might split into a collection of more precisely defined concepts which can be used to ask unambiguous questions with definite answers. As a first step this paper explores a collection of conjectures regarding architectures and their evolution. In particular we explore architectures involving a combination of coexisting architectural levels including: (a) reactive mechanisms which evolved very early, (b) deliberative mechanisms which evolved later in response to pressures on information processing resources and (c) meta-management mechanisms that can explicitly inspect evaluate and modify some of the contents of various internal information structures. It is conjectured that in response to the needs of these layers, perceptual and action subsystems also developed layers, and also that an ``alarm'' system which initially existed only within the reactive layer may have become increasingly sophisticated and extensive as its inputs and outputs were linked to the newer layers. Processes involving the meta-management layer in the architecture could explain the origin of the notion of ``qualia''. Processes involving the ``alarm'' mechanism and mechanisms concerned with resource limits in the second and third layers gives us an explanation of three main forms of emotion, helping to account for some of the ambiguities which have bedevilled the study of emotion. Further theoretical and practical benefits may come from further work based on this design-based approach to consciousness. A deeper longer term implication is the possibility of a new science investigating laws governing possible trajectories in design space and niche space, as these form parts of high order feedback loops in the biosphere. (shrink)

This classic remains one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history.

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

_Conjectures and Refutations_ is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

_Conjectures and Refutations_ is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

Clayton and Stevens argue that political liberals should engage with the religiously unreasonable by offering religious responses and showing that their religious views are mistaken, instead of refusing to engage with them. Yet they recognize that political liberals will face a dilemma due to such religious responses: either their responses will alienate certain reasonable citizens, or their engagements will appear disingenuous. Thus, there should be a division of justificatory labour. The duty of engagement should be delegated to religious citizens. In (...) this comment, I will argue that the division of justificatory labour is indefensible. This dilemma can be avoided if politicians and political philosophers correctly use conjecture, a form of discourse that involves non-public reason. As a conditional response, conjecture avoids alienating any reasonable citizens. Also, if conjecture is given in a sincere and open-minded manner, then the problem of disingenuousness can be overcome. My comment concludes that while the engagement of politicians and political philosophers does not necessarily jeopardize overlapping consensus, they should be permitted, or perhaps even required, to engage with the religiously unreasonable due to the natural duty of justice. (shrink)

The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism: that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable'. Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us (...) understand the difficulties of the problems which we try to solve. This is how we become better acquainted with our problem, and able to propose more mature solutions: the very refutation of a theory - that is, of a tentative solution to our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows, even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason here for despair of reason. And since we can never know for certain, the can be no authority here for any claim to authority, for conceit over our knowledge, or for smugness. The essays and lectures of which this book is composed apply this thesis to many topics, ranging from problems of the philosophy and history of the physical and social sciences to historical and political problems. (shrink)

As space travel and intentions to colonise other planets are becoming the norm in public debate and scholarship, we must also confront the technical and survival challenges that emerge from these hostile environments. This paper aims to evaluate the various arguments proposed to meet the challenges of human space travel and extraterrestrial planetary colonisation. In particular, two primary solutions have been present in the literature as the most straightforward solutions to the rigours of extraterrestrial survival and flourishing: (1) geoengineering, where (...) the environment is modified to become hospitable to its inhabitants, and (2) human (bio)enhancement where the genetic heritage of humans is modified to make them more resilient to the difficulties they may encounter as well as to permit them to thrive in non-terrestrial environments. Both positions have strong arguments supporting them but also severe philosophical and practical drawbacks when exposed to different circumstances. This paper aims to show that a principled stance where one position is accepted wholesale necessarily comes at the opportunity cost of the other where the other might be better suited, practically and morally. This paper concludes that case-by-case evaluations of the solutions to space travel and extraterrestrial colonisation are necessary to ensure moral congruency and the survival and flourishing of astronauts now and into the future. (shrink)

The Busy Beaver Competition is held by Turing machines. The better ones halt taking much time or leaving many marks, when starting from a blank tape. In order to understand the behavior of some Turing machines that were once record holders in the five-state Busy Beaver Competition, we analyze their halting problem on all inputs. We prove that the halting problem for these machines amounts to a well-known problem of number theory, that of the behavior of the repeated iteration of (...) Collatz-like functions, that is functions defined by cases according to congruence classes. (shrink)

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

In this paper I argue that, in at least two cases - his discussions of the temporal precedence o f polytheism over monotheism and of the origins of civil society - we see Hume consigning to historical development certain aspects of reason which, as a comparison with Locke will show, have sometimes been held to be uniform. In the first of these cases Hume has recourse to claims about the general historical development of human thought. In the second case, the (...) origin of the civil institution of justice and government is not linked directly to external circumstances and the principles of human nature, as it is in contractarian theories, but makes a detour through the historical acquisition of certain concepts. Because Hume's position does not conform in any simple sense to Dugald Stewart's 'incontrovertible logical maxim' that the capacities of the human mind have been the same in all ages, Stewart's account of the method of conjectural history is, in any simple sense, inadequate as a description of Hume's practice. (shrink)

This is a conjecture about the conditions and operating structures that are required for the phenomenality of certain mental states. Specifically, full-blown phenomenality is assumed, as contrasted with constrained examples of phenomenal experience such as sensations of color and pain. Propositional attitudes and content, while not phenomenal per se, are standardly concurrent and may condition phenomenal states (e.g., when tied to false beliefs). It is conjectured that full phenomenality natively arises in coherent processes of situated sensory synthesis and representation (...) (with conceptual content) that are looped, mereologically whole and multi-dimensional. And that phenomenal states are typically phase-states within a parameterized conjoint structure of world and experiencer processes that are causally modulated across Markov blankets (which are conditionally independent and may be nested: cf. M. Kirchoff, et. al., 2017, 2018; and T. Burge, 2010, re: anti-individualism). Though they may, it is not accepted that phenomenally conscious states must be targets of higher-order representations (cf. A. Byrne, 2004). (shrink)

We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.

We give a plausible-sounding conjecture involving the number of n-equivalence classes of structures of size m which would imply that the complement of a spectrum is also a spectrum.

The modifier effect is the reduction in perceived likelihood of a generic property sentence, when the head noun is modified. We investigated the prediction that the modifier effect would be stronger for mutable than for central properties, without finding evidence for this predicted interaction over the course of five experiments. However Experiment 6, which provided a brief context for the modified concepts to lend them greater credibility, did reveal the predicted interaction. It is argued that the modifier effect (...) arises primarily from a general lack of confidence in generic statements about the typical properties of unfamiliar concepts. Neither prototype nor classical models of concept combination receive support from the phenomenon. 2010 Elsevier Inc. All rights reserved. (shrink)

The Conjectural Body combines continental philosophy with musicology, popular music studies, and feminist, critical race, and postcolonial theories to offer a unique perspective on issues of gender, race, and the philosophy of music. It is one of the few books in philosophy to take popular music seriously, and is one of the few books in continental feminism to privilege music over the visual.

Dylan Thomas made his name with one particular poem, ‘The Force that Through the Green Fuse Drives the Flower’, which he wrote and published in his teens. Not only the theme but also the imagery in detail is too close to certain passages in Schopenhauer for a coincidence to be likely. It is more probable that there was some influence. This is made more likely by the fact that there are good reasons to believe that the young Thomas had read (...) a book called Thomas Hardy's Universe, by Ernest Brennecke, which contains many quotations from Schopenhauer, including, in its first chapter, the one closest to Thomas's poem. (shrink)