The tears of Odysseus -- History : music gives voice to the ineffable -- Tears, chills, and broken bones -- The music itself -- Explaining strong emotional responses to music I -- Explaining strong emotional responses to music II -- The sublime, revisited -- Conclusion : values.

Much work on the sense of agency has focused either on abnormal cases, such as delusions of control, or on simple action tasks in the laboratory. Few studies address the nature of the sense of agency in complex natural settings, or the effect of skill on the sense of agency. Working from 2 case studies of mountain bike riding, we argue that the sense of agency in high-skill individuals incorporates awareness of multiple causal influences on action outcomes. This allows fine-grained (...) differentiation of the contributions of self and external factors to action outcomes. We further argue that the sense of agency incorporates prospective awareness of actions that are possible in a situation and awareness of the limits of control. These forms of sense of agency enable highly flexible, context-sensitive strategic control, and are likely to contribute to high interindividual variability in responses to complex tasks. (shrink)

We investigate flexibility and problem solving in skilled action. We conducted a field study of mountain bike riding that required a learner rider to cope with major changes in technique and equipment. Our results indicate that relatively inexperienced individuals can be capable of fairly complex 'on-the-fly' problem solving which allows them to cope with new conditions. This problem solving is hard to explain for classical theories of skill because the adjustments are too large to be achieved by automatic mechanisms and (...) too complex and rapid to be achieved by cognitive processes as they are usually understood. A recent theory, Mesh, can explain these results because it posits that skill-specific cognitive abilities develop during skill learning and that control typically involves an interplay between cognitive and automatic mechanisms. Here we develop Mesh further, providing a detailed explanation for these problem solving abilities. We argue that causal representation, metacognitive awareness and other forms of performance awareness combine in the formulation and control of action strategies. We also argue that the structure of control present in this case is inconsistent with Bratman's model of intentions, and that, in the face of high uncertainty and risk, intentions can be much more labile than Bratman recognises. In addition, we found limitations and flaws in problem solving which illuminate the representations involved. Finally, we highlight the crucial role of social and cultural learning in the development of complex skills. (shrink)

This is a transcript of a conversation between P F Strawson and Gareth Evans in 1973, filmed for The Open University. Under the title 'Truth', Strawson and Evans discuss the question as to whether the distinction between genuinely fact-stating uses of language and other uses can be grounded on a theory of truth, especially a 'thin' notion of truth in the tradition of F P Ramsey.

The notion of a simulating termination analyzer is examined at the concrete level of pairs of C functions. This is similar to AProVE: Non-Termination Witnesses for C Programs. The termination status decision is made on the basis of the dynamic behavior of the input. This paper explores what happens when a simulating termination analyzer is applied to an input that calls itself.

In this paper, I reply to 18 of the essays on panpsychism in this issue. Along the way, I sketch out what a post-Galilean science of consciousness, one in which consciousness is taken to be a fundamental feature of reality, might look like.

Some scientific categories seem to correspond to genuine features of the world and are indispensable for successful science in some domain; in short, they are natural kinds. This book gives a general account of what it is to be a natural kind and puts the account to work illuminating numerous specific examples.

Tradução para o português do ensaio "Freedom and Resentment”, de P. F. Strawson. Publicado originalmente em Proceedings of the British Academy, v. 48, 1960. Republicado em Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 2-28]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da UFSC, 2015. ISBN: 9788532807250.

Tradução para o português do ensaio "Social Morality and Individual Ideal”. Publicado originalmente em Philosophy: The Journal of the Royal Institute of Philosophy, vol. XXXVI, n. 136, p. 1-17, Jan. 1961. Republicado em: STRAWSON, P. F. Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 26-44]. ]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da (...) UFSC, 2015. ISBN: 9788532807250. (shrink)

Tradução para o português do livro "Ceticismo e naturalismo: algumas variedades", Strawson, P. F. . São Leopoldo, RS: Editora da Unisinos, 2008, 114 p. Coleção: Ideias. ISBN: 9788574313214. Capítulo 1 - Ceticismo, naturalismo e argumentos transcendentais 1. Notas introdutórias; 2. Ceticismo tradicional; 3. Hume: Razão e Natureza; 4. Hume e Wittgenstein; 5. “Apenas relacionar”: O papel dos argumentos transcendentais; 6. Três citações; 7. Historicismo: e o passado.

If two theory formulations are merely different expressions of the same theory, then any problem of choosing between them cannot be due to the underdetermination of theories by data. So one might suspect that we need to be able to tell distinct theories from mere alternate formulations before we can say anything substantive about underdetermination, that we need to solve the problem of identical rivals before addressing the problem of underdetermination. Here I consider two possible solutions: Quine proposes that we (...) call two theories identical if they are equivalent under a reconstrual of predicates, but this would mishandle important cases. Another proposal is to defer to the particular judgements of actual scientists. Consideration of an historical episodethe alleged equivalence of wave and matrix mechanicsshows that this second proposal also fails. Nevertheless, I suggest, the original suspicion is wrong; there are ways to enquire into underdetermination without having solved the problem of identical rivals. (shrink)

Some philosophers understand natural kinds to be the categories which are constraints on enquiry. In order to elaborate the metaphysics appropriate to such an account, I consider the complicated history of scurvy, citrus, and vitamin C. It may be tempting to understand these categories in a shallow way (as mere property clusters) or in a deep way (as fundamental properties). Neither approach is adequate, and the case instead calls for middle-range ontology: starting from categories which we identify in the world (...) and elaborating their structure, but not pretending to jump ahead to a complete story about fundamental being. (shrink)

P. F. Strawson; II*—Scruton and Wright on Anti-Realism Etc., Proceedings of the Aristotelian Society, Volume 77, Issue 1, 1 June 1977, Pages 15–22, https://doi.

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is yes (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork's overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden, aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., "the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically prurient perspective on its female lead.'' Such a "non-summative" judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like "it's a 6/10" or "it's a pretty good movie!" I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people's character. (shrink)

Philosophy in Africa has for more than a decade now been dominated by the discussion of one compound question, namely, is there an African philosophy, and if there is, what is it? The first part of the question has generally been unhesitatingly answered in the affirmative. Dispute has been primarily over the second part of the question as various specimens of African philosophy presented do not seem to pass muster. Those of us who refuse to accept certain specimens as philosophy (...) have generally been rather illogically said also to deny an affirmative answer to the first part of the question. In a paper presented at the International Symposium in Memory of Dr William Amo, the Ghanaian philosopher who taught in German universities in the early part of the eighteenth century, Professor Odera Oruka identified four trends, perhaps more appropriately approaches, in current African philosophy. (shrink)

The Argument from Inductive Risk (AIR) is taken to show that values are inevitably involved in making judgements or forming beliefs. After reviewing this conclusion, I pose cases which are prima facie counterexamples: the unreflective application of conventions, use of black-boxed instruments, reliance on opaque algorithms, and unskilled observation reports. These cases are counterexamples to the AIR posed in ethical terms as a matter of personal values. Nevertheless, it need not be understood in those terms. The values which load a (...) theory choice may be those of institutions or past actors. This means that the challenge of responsibly handling inductive risk is not merely an ethical issue, but is also social, political, and historical. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

The no-miracles argument and the pessimistic induction are arguably the main considerations for and against scientific realism. Recently these arguments have been accused of embodying a familiar, seductive fallacy. In each case, we are tricked by a base rate fallacy, one much-discussed in the psychological literature. In this paper we consider this accusation and use it as an explanation for why the two most prominent `wholesale' arguments in the literature seem irresolvable. Framed probabilistically, we can see very clearly why realists (...) and anti-realists have been talking past one another. We then formulate a dilemma for advocates of either argument, answer potential objections to our criticism, discuss what remains (if anything) of these two major arguments, and then speculate about a future philosophy of science freed from these two arguments. In so doing, we connect the point about base rates to the wholesale/retail distinction; we believe it hints at an answer of how to distinguish profitable from unprofitable realism debates. In short, we offer a probabilistic analysis of the feeling of ennui afflicting contemporary philosophy of science. (shrink)

I've previously suggested that the historical evidence used to challenge scientific realism should lead us to embrace what I call Uniformitarianism, but many recently influential forms of scientific realism seem happy to share this commitment. I trace a number of further points of common ground that collectively constitute an appealing Middle Path between classical forms of realism and instrumentalism, and I suggest that many contemporary realists and instrumentalists have already become fellow travelers on this Middle Path without recognizing how far (...) they have thereby diverged from those who share their labels and slogans. I conclude by describing their central remaining disagreement and the sorts of evidence needed to resolve it. (shrink)

In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.

There is a history of thinking that photographs provide a special kind of access to the objects depicted in them, beyond the access that would be provided by a painting or drawing. What is included in the photograph does not depend on the photographer’s beliefs about what is in front of the camera. This feature leads Kendall Walton to argue that photographs literally allow us to see the objects which appear in them. Current generative algorithms produce images in response to (...) users’ text prompts. Depending on the parameters, the output can resemble specific people or things which are named in the prompt. This resemblance does not depend on the user’s beliefs, so generated images are in this sense like photographs. Given this parallel, how should we think about AI-generated images? (shrink)

A critical note on Christopher Bartel and Jack M. C. Kwong, ‘Pluralism, Eliminativism, and the Definition of Art’, Estetika 58 (2021): 100–113. Art pluralism is the view that there is no single, correct account of what art is. Instead, art is understood through a plurality of art concepts and with considerations that are different for particular arts. Although avowed pluralists have retained the word ‘art’ in their discussions, it is natural to ask whether the considerations that motivate pluralism should lead (...) us to abandon art talk altogether; that is, should pluralism lead to eliminativism? This paper addresses arguments both for and against this move. We ultimately argue that pluralism allows one to retain the word ‘art’, if one wants it, but only in a loose, conversational sense. The upshot of pluralism is that talk of art in general cannot be asked to do theoretical and philosophical work. (shrink)

Some philosophers think that there is a gap between is and ought which necessarily makes normative enquiry a different kind of thing than empirical science. This position gains support from our ability to explicate our inferential practices in a way that makes it impermissible to move from descriptive premises to a normative conclusion. But we can also explicate them in a way that allows such moves. So there is no categorical answer as to whether there is or is not a (...) gap. The question of an is-ought gap is a practical and strategic matter rather than a logical one, and it may properly be answered in different ways for different questions or at different times. (shrink)

Kyle Stanford has recently claimed to offer a new challenge to scientific realism. Taking his inspiration from the familiar Pessimistic Induction (PI), Stanford proposes a New Induction (NI). Contra Anjan Chakravartty’s suggestion that the NI is a ‘red herring’, I argue that it reveals something deep and important about science. The Problem of Unconceived Alternatives, which lies at the heart of the NI, yields a richer anti-realism than the PI. It explains why science falls short when it falls short, and (...) so it might figure in the most coherent account of scientific practice. However, this best account will be antirealist in some respects and about some theories. It will not be a sweeping antirealism about all or most of science. (shrink)

It is now commonly held that values play a role in scientific judgment, but many arguments for that conclusion are limited. First, many arguments do not show that values are, strictly speaking, indispensable. The role of values could in principle be filled by a random or arbitrary decision. Second, many arguments concern scientific theories and concepts which have obvious practical consequences, thus suggesting or at least leaving open the possibility that abstruse sciences without such a connection could be value-free. Third, (...) many arguments concern the role values play in inferring from evidence, thus taking evidence as given. This paper argues that these limitations do not hold in general. There are values involved in every scientific judgment. They cannot even conceivably be replaced by a coin toss, they arise as much for exotic as for practical sciences, and they are at issue as much for observation as for explicit inference. (shrink)

When we ask what natural kinds are, there are two different things we might have in mind. The first, which I’ll call the taxonomy question, is what distinguishes a category which is a natural kind from an arbitrary class. The second, which I’ll call the ontology question, is what manner of stuff there is that realizes the category. Many philosophers have systematically conflated the two questions. The confusion is exhibited both by essentialists and by philosophers who pose their accounts in (...) terms of similarity. It also leads to misreading philosophers who do make the distinction. Distinguishing the questions allows for a more subtle understanding of both natural kinds and their underlying metaphysics. (shrink)

Imperatives cannot be true, but they can be obeyed or binding: `Surrender!' is obeyed if you surrender and is binding if you have a reason to surrender. A pure declarative argument — whose premisses and conclusion are declaratives — is valid exactly if, necessarily, its conclusion is true if the conjunction of its premisses is true; similarly, I suggest, a pure imperative argument — whose premisses and conclusion are imperatives — is obedience-valid (alternatively: bindingness-valid) exactly if, necessarily, its conclusion is (...) obeyed (alternatively: binding) if the conjunction of its premisses is. I argue that there are two kinds of bindingness, and that a vacillation between two corresponding variants of bindingness-validity largely explains conflicting intuitions concerning the validity of some pure imperative arguments. I prove that for each of those two variants of bindingness-validity there is an equivalent variant of obedience-validity. Finally, I address alternative accounts of pure imperative inference. (shrink)

The accepted narrative treats John Stuart Mill’s Kinds as the historical prototype for our natural kinds, but Mill actually employs two separate notions: Kinds and natural groups. Considering these, along with the accounts of Mill’s nineteenth-century interlocutors, forces us to recognize two distinct questions. First, what marks a natural kind as worthy of inclusion in taxonomy? Second, what exists in the world that makes a category meet that criterion? Mill’s two notions offer separate answers to the two questions: natural groups (...) for taxonomy and Kinds for ontology. This distinction is ignored in many contemporary debates about natural kinds and is obscured by the standard narrative that treats our natural kinds just as a development of Mill’s Kinds. (shrink)

Homeostatic property clusters (HPCs) are offered as a way of understanding natural kinds, especially biological species. I review the HPC approach and then discuss an objection by Ereshefsky and Matthen, to the effect that an HPC qua cluster seems ill-fitted as a description of a polymorphic species. The standard response by champions of the HPC approach is to say that all members of a polymorphic species have things in common, namely dispositions or conditional properties. I argue that this response fails. (...) Instances of an HPC kind need not all be similar in their exhibited properties. Instead, HPCs should instead be understood as unified by the underlying causal mechanism that maintains them. The causal mechanism can both produce and explain some systematic differences between a kind’s members. An HPC kind is best understood not as a single cluster of properties maintained in stasis by causal forces, but as a complex of related property clusters kept in relation by an underlying causal process. This approach requires recognizing that taxonomic systems serve both explanatory and inductive purposes. (shrink)

This note outlines a Theory of Everything consistent with the PF interpretation of quantum mechanics.

William James’ argument against William Clifford in The Will to Believe is often understood in terms of doxastic efficacy, the power of belief to influence an outcome. Although that is one strand of James’ argument, there is another which is driven by ampliative risk. The second strand of James’ argument, when applied to scientific cases, is tantamount to what is now called the Argument from Inductive Risk. Either strand of James’ argument is sufficient to rebut Clifford's strong evidentialism and show (...) that it is sometimes permissible to believe in the absence of compelling evidence. However, the two considerations have different scope and force. Doxastic efficacy applies in only some cases but allows any values to play a role in determining belief; risk applies in all cases but only allows particular conditional values to play a role. (shrink)

The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of “the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories” (Stanford 2001, (...) p. S12). This paper examines Stanford’s New Induction and argues that it – like the other forms of underdetermination that he criticizes – merely recapitulates familiar philosophical conundra. (shrink)

Part of a book symposium on Anjan Chakravartty's Scientific ontology: integrating naturalized metaphysics and voluntarist epistemology (Oxford University Press, 2017).

This discussion note addresses Caleb Hazelwood’s ‘Practice-Centered Pluralism and a Disjunctive Theory of Art’. Hazelwood advances a disjunctive definition of art on the basis of an analogy with species concept pluralism in the philosophy of biology. We recognize the analogy between species and art, we applaud attention to practice, and we are bullish on pluralism—but it is a mistake to take these as the basis for a disjunctive definition.

There are two senses of ‘what scientists know’: An individual sense (the separate opinions of individual scientists) and a collective sense (the state of the discipline). The latter is what matters for policy and planning, but it is not something that can be directly observed or reported. A function can be defined to map individual judgments onto an aggregate judgment. I argue that such a function cannot effectively capture community opinion, especially in cases that matter to us.

Although some authors hold that natural kinds are necessarily relative to disciplinary domains, many authors presume that natural kinds must be absolute, categorical features of the reality —often assuming that without even mentioning the alternative. Recognizing both possibilities, one may ask whether the difference especially matters. I argue that it does. Looking at recent arguments about natural kind realism, I argue that we can best make sense of the realism question by thinking of natural kindness as a relation that holds (...) between a category and a domain. (shrink)

Cover songs are a familiar feature of contemporary popular music. Musicians describe their own performances as covers, and audiences use the category to organize their listening and appreciation. However, until now philosophers have not had much to say about them. This book explores how to think about covers, appreciating covers, and the metaphysics of covers and songs. Along the way, it explores a range of issues raised by covers, from the question of what precisely constitutes a cover, to the history (...) and taxonomy of the category, the various relationships that hold between songs, performances, and tracks, and the appreciation and evaluation of covers. (shrink)

To stimulate research and innovation (R&I), to contribute to the solution of societal challenges and to align R&I with societal values, the European Commission has launched the governance framework of Responsible Research and Innovation (RRI). RRI figures in many high-level EU policies as a means to promote smart growth, and a growing community of R&I practitioners from both the public and private sectors appears committed to it. Although debates on what RRI precisely entails have not reached closure yet, RRI provides (...) an interesting avenue to explore ways of making R&I more societally germane. While recognizing the usefulness of keeping critical reflection on RRI’s meaning alive, we suggest that to make the step from theorizing to implementation, RRI could benefit from a clearer conceptualization. This chapter presents the iterative trajectory in conceptualizing RRI followed as part of RRI Tools, one of a number of EC-funded research projects and support acts aimed at fleshing out what RRI can and should be, and the conceptualization of RRI that this led to. It suggests that RRI is best captured if in R&I governance attention is paid to the five p’s of Purpose, Products, Processes, Preconditions and People, and that further elaborations on the meaning of RRI should happen in dialogue with attempts at practicing RRI. (shrink)

Christy Mag Uidhir has recently argued (a) that there is no in principle aesthetic difference between a live performance and a recording of that performance, and (b) that the proper aesthetic object is a type which is instantiated by the performance and potentially repeatable when recordings are played back. This paper considers several objections to (a) and finds them lacking. I then consider improvised music, a subject that Mag Uidhir explicitly brackets in his discussion. Improvisation reveals problems with (b), because (...) the performance-event and the performance-type are distinct but equally proper aesthetic objects. (shrink)

Given the fact that many people use Wikipedia, we should ask: Can we trust it? The empirical evidence suggests that Wikipedia articles are sometimes quite good but that they vary a great deal. As such, it is wrong to ask for a monolithic verdict on Wikipedia. Interacting with Wikipedia involves assessing where it is likely to be reliable and where not. I identify five strategies that we use to assess claims from other sources and argue that, to a greater of (...) lesser degree, Wikipedia frustrates all of them. Interacting responsibly with something like Wikipedia requires new epistemic methods and strategies. (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

The underdetermination of theory by evidence is supposed to be a reason to rethink science. It is not. Many authors claim that underdetermination has momentous consequences for the status of scientific claims, but such claims are hidden in an umbra of obscurity and a penumbra of equivocation. So many various phenomena pass for `underdetermination' that it's tempting to think that it is no unified phenomenon at all, so I begin by providing a framework within which all these worries can be (...) seen as species of one genus: A claim of underdetermination involves (at least implicitly) a set of rival theories, a standard of responsible judgment, and a scope of circumstances in which responsible choice between the rivals is impossible. Within this framework, I show that one variety of underdetermination motivated modern scepticism and thus is a familiar problem at the heart of epistemology. I survey arguments that infer from underdetermination to some reëvaluation of science: top-down arguments infer a priori from the ubiquity of underdetermination to some conclusion about science; bottom-up arguments infer from specific instances of underdetermination, to the claim that underdetermination is widespread, and then to some conclusion about science. The top-down arguments either fail to deliver underdetermination of any great significance or (as with modern scepticism) deliver some well-worn epistemic concern. The bottom-up arguments must rely on cases. I consider several promising cases and find them to either be so specialized that they cannot underwrite conclusions about science in general or not be underdetermined at all. Neither top-down nor bottom-up arguments can motivate any deep reconsideration of science. (shrink)

The problem considered in this chapter emerges from the tension we find when looking at the design and architecture of chatbots on the one hand and their conversational aptitude on the other. In the way that LLM chatbots are designed and built, we have good reason to suppose they don't possess second-order capacities such as intention, belief or knowledge. Yet theories of conversation make great use of second-order capacities of speakers and their audiences to explain how aspects of interaction succeed. (...) As we can all bear witness to now though, at the point of use chatbots appear capable of performing language tasks at a level close to that of humans. This creates a tension when we consider something like, for example, the classic Gricean theory of implicature. On a broad summary of this type of account, to utter p and implicate q requires the reflexive occurrence of an audience supposing a speaker believes that q, and the speaker believing that their audience can determine they believe it when they utter p. So taken at face value, if a chatbot doesn’t have the capacity for belief, then either in their role as speaker or audience, they would not seem capable of either generating or comprehending implicatures. Yet on the surface it does seem that chatbots are capable of dealing with (some) implicatures, and as such it raises questions about how we should then correlate this with what we think occurs in cases of implicature with chatbots. (shrink)

According to the standard narrative, natural kind is a technical notion that was introduced by John Stuart Mill in the 1840s and the recent craze for natural kinds, launched by Putnam and Kripke, is a continuation of that tradition. I argue that the standard narrative is mistaken. The Millian tradition of kinds was not particularly influential in the 20th-century, and the Putnam-Kripke revolution did not clearly engage with even the remnants that were left of it. The presently active tradition of (...) natural kinds is less than half a century old. Recognizing this might help us better appreciate both Mill and natural kinds. (shrink)

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

One approach to science treats science as a cognitive accomplishment of individuals and defines a scientific community as an aggregate of individual inquirers. Another treats science as a fundamentally collective endeavor and defines a scientist as a member of a scientific community. Distributed cognition has been offered as a framework that could be used to reconcile these two approaches. Adam Toon has recently asked if the cognitive and the social can be friends at last. He answers that they probably cannot, (...) posing objections to the would-be rapprochement. We clarify both the animosity and the tonic proposed to resolve it, ultimately arguing that worries raised by Toon and others are uncompelling. (shrink)