Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, independence (...) conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (shrink)

Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders’s proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind’s Habilitationsrede, to which Manders’s account is compared. I (...) conclude with an examination of three possible stances towards extensions via ideal elements. (shrink)

Radical enactive and embodied approaches to cognitive science oppose the received view in the sciences of the mind in denying that cognition fundamentally involves contentful mental representation. This paper argues that the fate of representationalism in cognitive science matters significantly to how best to understand the extent of cognition. It seeks to establish that any move away from representationalism toward pure, empirical functionalism fails to provide a substantive “mark of the cognitive” and is bereft of other adequate means for individuating (...) cognitive activity. It also argues that giving proper attention to the way the folk use their psychological concepts requires questioning the legitimacy of commonsense functionalism. In place of extended functionalism—empirical or commonsensical—we promote the fortunes of extensive enactivism, clarifying in which ways it is distinct from notions of extended mind and distributed cognition. (shrink)

This paper brings together several strands of thought from both the analytic and phenomenological traditions in order to critically examine accounts of cognitive enhancement that rely on the idea of cognitive extension. First, I explain the idea of cognitive extension, the metaphysics of mind on which it depends, and how it has figured in recent discussions of cognitive enhancement. Then, I develop ideas from Husserl that emphasize the agential character of thought and the distinctive way that conscious thoughts are related (...) to one another. I argue that these considerations are necessary for understanding why forms of cognitive extension may diminish our cognitive lives in different ways. This does not lead to a categorical rejection of cognitive enhancement as unethical or bad for human flourishing, but does warrant a conservative approach to the design and implementation of cognitive artifacts. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , (...) K4, and S4, with □ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between □ and a natural presentation of ♢. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

According to an influential idea in the philosophy of set theory, certain mathematical concepts, such as the notion of a well-order and set, are indefinitely extensible. Following Parsons (1983), this has often been cashed out in modal terms. This paper explores instead an extensional articulation of the idea, formulated in higher-order logic, that flat-footedly formalizes some remarks of Zermelo. The resulting picture is incompatible with the idea that the entire universe can be well-ordered, but entirely consistent with the idea that (...) the sets of any set-theoretic universe can be. (shrink)

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint (...) the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined. (shrink)

The principle of sufficient reason threatens modal collapse. Some have suggested that by appealing to the indefinite extensibility of contingent truth, the threat is neutralized. This paper argues that this is not so. If the indefinite extensibility of contingent truth is developed in an analogous fashion to the most promising models of the indefinite extensibility of the concept set, plausible principles permit the derivation of modal collapse.

In a recent publication in this journal, Asle Kiran and Peter-Paul Verbeek (hereafter K&V) argue that extension theory and the notion of trust it implies are flawed. In this commentary, I defend extension theory against their critique. I first briefly introduce extension theory, then reconstruct K&V’s five arguments against extension theory and demonstrate that four of their five arguments are misplaced.

The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)

Recent progress in geroscience holds the promise of significantly slowing down or even reversing ageing and age-related diseases, and thus increasing our healthspans. In this paper, I offer a novel argument in favour of developing such technology and making it unconditionally available to everyone. In particular, I argue that justice requires that each person be provided with sufficient opportunities to have a ‘complete life’, that many people currently lack such opportunities, and that we would substantially improve the status quo by (...) giving them access to anti-ageing technology. (shrink)

Extension project implementers ensure that activities and community linkages are not hampered by the challenges posed by the Coronavirus Disease 2019 (COVID-19) pandemic. This study presents the lived experiences of extension project implementers in providing community services in the midst of pandemic. Specifically, their experiences, reflections, and insights in the implementation of extension projects were enumerated. Eleven extensionists who were directly involved in and capable of conducting University extension projects were purposefully chosen as participants. Descriptive phenomenology research design was employed. (...) Data were analyzed through Colaizzi’s (1978) method. The experiences of the extension project implementers were themed as follows: difficulties in planning and implementation; support system; reflections and insights; and outstanding characteristics of the implementers. These experiences, as well as the extent to which extension projects have been implemented, will be taken into account in future planning, implementation, and impact assessments. (shrink)

In Kant’s logical texts the reference of the form S is P to an “unknown = x” is well known, but its understanding still remains controversial. Due to the universality of all concepts, the subject as much as the predicate is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, this Kantian interpretation of the S-P relationship leads to the question about the relations between intuition and concept in judgment. (...) In contrast to intuition, if no concept, due to its universality, refers immediately to an object, how should one understand the relations of S and P to one another, as well as their relations to intuition, which corresponds to the possible individuality of the object in general = x? To answer this question, it is necessary to understand Kant’s notion of extension, and to prove its irreducibility to the Port-Royal notion of extension as well as to the Fregean one. (shrink)

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the ℏ→0 limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for such extensions. Moreover, (...) we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the ℏ→0 case) on the fiber C*-algebras. (shrink)

This article argues, first, that there is plenty of agreement among philosophers on philosophically substantive claims, which fall into three categories: reasons for or against certain views, elementary truths regarding fundamental notions, and highly conditionalized claims. This agreement suggests that there is important philosophical progress. It then argues that although it's easy to list several potential kinds of philosophical progress, it is much harder to determine whether the potential is actual. Then the article attempts to articulate the truth that the (...) deniers of philosophical progress are latching on to. Finally, it comments on the significance of the agreement and progress. (shrink)

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

We might worry that our seamless reliance on AI systems makes us prone to adopting the strange errors that these systems commit. One proposed solution is to design AI systems so that they are not phenomenally transparent to their users. This stops cognitive extension and the automatic uptake of errors. Although we acknowledge that some aspects of AI extension are concerning, we can address these concerns without discouraging transparent employment altogether. First, we believe that the potential danger should be put (...) into perspective – many unreliable technologies are unlikely to be used transparently precisely because they are unreliable. Second, an agent who transparently employs a resource may also reflect (opaquely) on its reliability. Finally, agents can rely on a process transparently and be yanked out of their transparent use when it turns unreliable. When an agent is responsive to the reliability of their process in this way, they have epistemically integrated it, and the beliefs they form with it are formed responsibly. This prevents the agent from automatically incorporating problematic beliefs. Responsible (and transparent) use of AI resources – and consequently responsible AI extension – is hence possible. We end the paper with several design and policy recommendations that encourage epistemic integration of AI-involving belief-forming processes. (shrink)

The quantified argument calculus (Quarc) is a novel logic that departs in several ways from mainstream first-order logic. In particular, its quantifiers are not sentential operators attached to variables, but attach to unary predicates to form arguments – quantified arguments – of other predicates. Furthermore, Quarc includes devices to account for anaphora, active-passive-voice distinctions, and sentence- versus predicate-negation. While this base system has already been shown to be sound and complete, modal extensions still lack such results. The present paper fills (...) this lacuna by developing a modal extension of Quarc, including identity. The semantics will invalidate the Quarc-analogues of the Barcan-formula and its converse, as well as treat identity as contingent by default. Furthermore, an unlabelled Gentzen-style natural deduction system will be presented, which includes the full expressive power of Quarc. It will be shown to be strongly sound and complete with respect to relational frames. The paper closes off with considerations on how to extend the system to cover other normal modal logics as well as extensions to suitable three-valued semantics that capture relevant types of presupposition-failure. (shrink)

The Mindoro State University Bongabong Campus extension unit is still opera- tional amid the COVID-19 pandemic. This paper evaluates the implementation of the "eSupport: Continuation of Extension Services Amid Covid-19 Pandemic," an extension program by the College of Computer Studies faculty and students. This ex- tension program included six topics delivered via a free webinar series and online training programs through Google Meet, Zoom, MS Teams, and Facebook Live and some conducted face-to-face. Participants or beneficiaries in the webinars, online and (...) face-to-face training, and extensionists served as respondents of the study. The narrative research design was used, and the data were treated using the weighted mean. The instrument used in the study was a university evaluation questionnaire on extension services. The evaluation sheet was divided into strategy, speaker, and services. The study revealed that community beneficiaries gave positive assessments and feedback on the College of Computer Studies' extension project. Participants' and extensionists' or implementers' experiences and recommendations will be considered in future planning, implementation, and impact assessments. (shrink)

ABSTRACT Joseph Halpern and Judea Pearl draw upon structural equation models to develop an attractive analysis of ‘actual cause’. Their analysis is designed for the case of deterministic causation. I show that their account can be naturally extended to provide an elegant treatment of probabilistic causation. 1Introduction 2Preemption 3Structural Equation Models 4The Halpern and Pearl Definition of ‘Actual Cause’ 5Preemption Again 6The Probabilistic Case 7Probabilistic Causal Models 8A Proposed Probabilistic Extension of Halpern and Pearl’s Definition 9Twardy and Korb’s Account 10Probabilistic (...) Fizzling 11Conclusion. (shrink)

I discuss Clark’s predictive processing/extended mind hybrid, diagnosing a problem: Clark’s hybrid suggests that, when we use them, we pay attention to mind-extending external resources. This clashes with a commonly accepted necessary condition of cognitive extension; namely, that mind-extending resources must be phenomenally transparent when used. I then propose a solution to this problem claiming that the phenomenal transparency condition should be rejected. To do so, I put forth a parity argument to the effect that phenomenal transparency cannot be a (...) necessary condition on cognitive extension: roughly, since internal cognitive resources can fail to be transparent when used, by parity, external resources can fail to be phenomenally transparent too. Further, I argue that phenomenal transparency is not even a reliable indicator of cognitive extension; hence its absence should not be considered a problem for Clark’s extended mind-predictive processing hybrid. Lastly, I consider and allay a number of worries my proposal might raise, and conclude the paper. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

Would be fairer to call Peirce’s philosophy of language “extensionalist” or “intensionalist”? The extensionalisms of Carnap and Quine are examined, and Peirce’s view is found to be prima facie similar, except for his commitment to the importance of “hypostatic abstraction”. Rather than dismissing this form of abstraction (famously derided by Molière) as useless scholasticism, Peirce argues that it represents a crucial (though largely unnoticed) step in much working inference. This, it is argued, allows Peirce to transcend the extensionalist-intensionalist dichotomy itself, (...) through his unique triadic analysis of reference and meaning, by transcending the distinction between (as Quine put it) “things” and “attributes”. (shrink)

Este breve ensayo se inscribe en la tradición de buscar similitudes entre los epítetos y otros fenómenos lingüísticos, tanto inofensivos como discriminatorios. En particular, trataré de motivar la introducción de una distinción entre el blanco de un epíteto y su extensión y mostraré cómo esta distinción nos sirve para ver similitudes entre el comportamiento de este tipo de expresiones y el del complemento “de verdad” en expresiones como “tacos de verdad”. De paso, trataré también de explorar si estas teorías, (...) desarrolladas en su mayor parte en los Estados Unidos de América, sirven de herramienta teórica para dar cuenta de como ciertas expresiones contribuyen a la exclusión y discriminación de grupos minoritarios en nuestro contexto, es decir, en el castellano de México. (shrink)

The purpose of this essay is exegesis. I explicate Nicolas Malebranche's (1674, 1678, 1688, 1714) concept of intelligible extension. I begin by detailing how the concept matured throughout Malebranche's work, and the new functions it took on within his metaphysical system. I then examine Gustav Bergmann's “axiomatic” interpretation, as well as the criticism of it offered by Daise Radner. I argue that Radner's criticism of the interpretation is only partly successful; some of her objections can be met; others cannot. I (...) then develop a novel interpretation of the concept, given insights from this dispute. I call it the “programmatic interpretation.” I argue that this interpretation coheres well with Malebranche's famous Vision in God thesis, as well as many of his other commitments. I conclude by considering a certain pertinent objection to my proposal, summarizing the dialectic, and forcefully restating my case. (shrink)

A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which (...) the tetrahedron's in-sphere touches those faces. Part I presents an overview of these results and some necessary but little-known background in areal geometry. Part II derives the promised extension, and ends with a conjecture as to how the formula extends to n-dimensional simplices for all n>3. Part III explains how, for n=3, the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios; it further proves that these unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ42, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subvariety. Part IV consists of five appendices which show, among other things, that the algebraic structure of the zeros in the affine plane naturally defines the associated four-element, rank 3 chirotope, aka affine oriented matroid. (shrink)

This paper attempts to resolve the puzzle associated with the non-spatiality of monads by investigating the possibility that Leibniz employed a version of the extension of power doctrine, a Scholastic concept that explains the relationship between immaterial and material beings. As will be demonstrated, not only does the extension of power doctrine lead to a better understanding of Leibniz’ reasons for claiming that monads are non-spatial, but it also supports those interpretations of Leibniz’ metaphysics that accepts the real extension of (...) bodies. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware (...) of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

In this chapter I give an account of the epistemology underlying the concept of “extension” in the Mengzi, an early Confucian text written in the fourth century BCE. Mengzi suggests in a conversation with King Xuan of Qi that a solution to the King’s problem of how one comes to act in a kingly manner is that one engages in “extension”. I argue that a long-standing scholarly debate on the exact nature of Mengzian “extension” can be resolved by closely investigating (...) the epistemological assumptions that must be in place for “extension” to be a viable solution to King Xuan’s problem. More specifically, my argument is that knowledge of a certain kind, namely knowing-to, is both necessary and sufficient for extension to take place. In other words, for a person S to extend X, where X is a capacity for action, S at least needs to have knowing-to. (shrink)

In this paper, we focus on the most efficacious AI applications for life extension and anti-aging at three expected stages of AI development: narrow AI, AGI and superintelligence. First, we overview the existing research and commercial work performed by a select number of startups and academic projects. We find that at the current stage of “narrow” AI, the most promising areas for life extension are geroprotector-combination discovery, detection of aging biomarkers, and personalized anti-aging therapy. These advances could help currently living (...) people reach longevity escape velocity and survive until more advanced AI appears. When AI comes close to human level, the main contribution to life extension will come from AI integration with humans through brain-computer interfaces, integrated AI assistants capable of autonomously diagnosing and treating health issues, and cyber systems embedded into human bodies. Lastly, we speculate about the more remote future, when AI reaches the level of superintelligence and such life-extension methods as uploading human minds and creating nanotechnological bodies may become possible, thus lowering the probability of human death close to zero. We suggest that medical AI based superintelligence could be safer than, say, military AI, as it may help humans to evolve into part of the future superintelligence via brain augmentation, uploading, and a network of self-improving humans. Medical AI’s value system is focused on human benefit. (shrink)

I argue that the Conceptual Ethics and Conceptual Engineering framework, in its pragmatist version as recently defended by Thomasson (2017, 2020), provides a means of articulating and defending the conventionalist interpretation of projects of conceptual extension (e.g. the extended mind, the extended phenotype) in biology and psychology. This promises to be illuminating in both directions: it helps to make sense of, and provides an explicit methodology for, pragmatic conceptual extension in science, while offering further evidence for the value and fruitfulness (...) of the conceptual ethics/engineering framework itself, in particular with respect to conceptual change within science, which has thus-far received little attention in the literature on conceptual ethics/engineering. (shrink)

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued (...) fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to some implicit counter-property corresponding to the bipolar-valued fuzzy set. By using single-valued bipolar fuzzy numbers, the MULTIMOORA method can be more efficient for solving some specific problems whose solving requires assessment and prediction. The suitability of the proposed approach is presented through an example. (shrink)

In this chapter I give an account of the epistemology underlying the concept of “extension” in the Mengzi, an early Confucian text written in the fourth century BCE. Mengzi suggests in a conversation with King Xuan of Qi that a solution to the King’s problem of how one comes to act in a kingly manner is that one engages in “extension”. I argue that a long-standing scholarly debate on the exact nature of Mengzian “extension” can be resolved by closely investigating (...) the epistemological assumptions that must be in place for “extension” to be a viable solution to King Xuan’s problem. More specifically, my argument is that knowledge of a certain kind, namely knowing-to, is both necessary and sufficient for extension to take place. In other words, for a person S to extend X, where X is a capacity for action, S at least needs to have knowing-to. (shrink)

Plants from a handful of species provide the primary source of food for all people, yet this source is vulnerable to multiple stressors, such as disease, drought, and nutrient deficiency. With rapid population growth and climate uncertainty, the need to produce crops that can tolerate or resist plant stressors is more crucial than ever. Traditional plant breeding methods may not be sufficient to overcome this challenge, and methods such as highOthroughput sequencing and automated scoring of phenotypes can provide significant new (...) insights. Ontologies are essential tools for accessing and analysing the large quantities of data that come with these newer methods. As part of a larger project to develop ontologies that describe plant phenotypes and stresses, we are developing a plant disease extension of the Infectious Disease Ontology (IDOPlant). The IDOPlant is envisioned as a reference ontology designed to cover any plant infectious disease. In addition to novel terms for infectious diseases, IDOPlant includes terms imported from other ontologies that describe plants, pathogens, and vectors, the geographic location and ecology of diseases and hosts, and molecular functions and interactions of hosts and pathogens. To encompass this range of data, we are suggesting inOhouse ontology development complemented with reuse of terms from orthogonal ontologies developed as part of the Open Biomedical Ontologies (OBO) Foundry. The study of plant diseases provides an example of how an ontological framework can be used to model complex biological phenomena such as plant disease, and how plant infectious diseases differ from, and are similar to, infectious diseases in other organism. (shrink)

Is the Smartphone (SP) an extension of consciousness or just an (other) externalization of the mind and an extension of the social? The concept of externalizing the mind more appropriately describes a series of processes that tend to be considered extensions of the mind. The human mind has evolved concurrently with various externalizations, such as utensils and language, as contributions to the development of the common environment of humanity: culture and civilization. Externalizations indicate the appearance of the human mind while (...) the extensions take into account the possibility of passing to another level (the singularity of consciousness). SP is a handy tool that mediates the personal relationship with the world, benefiting from a level of integration into the global workspace of the mind. Externalization called the SP could be a bridge from the externalization of the mind to its extensions, making the ontological leap from the utensil status to that of "part of the mind". SP is a mediator of an environment: it mediates between the mind and a special social environment called the Internet (mediates access to cognitive support provided by society through the virtual world), which is gradually becoming another reality. SP is part of the extension of human society by introducing tools into the network of personal relationships. Not the mind is expanded, but the social network, increasing the number of entities with which the human can create and maintain relationships. SP may be an extension of the social rather than an extension of the mind because it mediates an increase in the complexity of social relations that can lead to the emergence of "collective minds" (causing a change in the ontological status of society). Changing cognitive demands is a feature of the world's progress. Progress brings along with it cognitive costs of integration, technical solutions like SP, aimed at reducing these costs, generating an evolutionary advantage in the new social context. From an evolutionist perspective, the world means precisely this kind of modification of cognitive demands necessary for survival, SP joining the set of tools that mediate the cognitive progress of the world in which the human is inserted. We propose the use of an evolutionary cognitive economy principle, based on avoiding unnecessary costs, reducing losses and optimizing cognitive gains. (shrink)

This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and R T of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and R T, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way.

The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties.

If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would still (...) expect it to follow that a sum of connected self-connected individuals is self-connected too. In this paper, we present some surprising countermodels which show that this conjecture is incorrect. (shrink)

Extended cognition holds that cognitive processes sometimes leak into the world (Dawson, 2013). A recent trend among proponents of extended cognition has been to put pressure on phenomena thought to be safe havens for internalists (Sneddon, 2011; Wilson, 2010; Wilson & Lenart, 2014). This paper attempts to continue this trend by arguing that music perception is an extended phenomenon. It is claimed that because music perception involves the detection of musical invariants within an “acoustic array”, the interaction between the auditory (...) system and the musical invariants can be characterized as an extended computational cognitive system. In articulating this view, the work of J. J. Gibson (1966, 1986) and Robert Wilson (1994, 1995, 2004) is drawn on. The view is defended from several objections and its implications outlined. The paper concludes with a comparison to Krueger’s (2014) view of the “musically extended emotional mind”. (shrink)

In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and Anti-Commutative CI-algebras are not BE-algebras.

The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional expressions. (...) The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

Drawing on 49 oral-history interviews with Scottish family business owner-managers, six key-informant interviews, and secondary sources, this interdisciplinary study analyses the decline of kinship-based connections and the emergence of new kinds of elite networks around the 1980s. As the socioeconomic context changed rapidly during this time, cooperation built primarily around literal family ties could not survive unaltered. Instead of finding unity through bio-legal family connections, elite networks now came to redefine their ‘family businesses’ in terms of affectively loaded ‘family values’ (...) such as loyalty, care, commitment, and even ‘love’. Consciously nurturing ‘as-if-family’ emotional and ethical connections arose as a psychologically effective way to bring together network members who did not necessarily share pre-existing connections of bio-legal kinship. The social-psychological processes involved in this extension of the ‘family’ can be understood using theories of the moral sentiments first developed in the Scottish Enlightenment. These theories suggest that, when the context is amenable, family-like emotional bonds can be extended via sympathy to those to whom one is not literally related. As a result of this ‘progress of sentiments’, one now earns his/her place in a Scottish family business, not by inheriting or marrying into it, but by performing family-like behaviours motivated by shared ethics and affects. (shrink)

This paper is my very first publication, please feel free to give me feedback and constructive criticism. I hope to be able to pitch into the discussion around the extension of mind and the philosophy of mind in general. It is my Bachelor's thesis, supervised and graded by a lecturer and assistant professor at the Munich Center for Mathematical Philosophy. Simply for their own privacy, I have censored their name from the publication. -/- Thank you for reading.

Reichenbach’s early solution to the scientific problem of how abstract mathematical representations can successfully express real phenomena is rooted in his view of coordination. In this paper, I claim that a Reichenbach-inspired, ‘layered’ view of coordination provides us with an effective tool to systematically analyse some epistemic and conceptual intricacies resulting from a widespread theorising strategy in evolutionary biology, recently discussed by Okasha (2018) as ‘endogenization’. First, I argue that endogenization is a form of extension of natural selection theory that (...) comprises three stages: quasi-axiomatisation, functional extension, and semantic extension. Then, I argue that the functional extension of one core principle of natural selection theory, namely, the principle of heritability, requires the semantic extension of the concept of inheritance. This is because the semantic extension of ‘inheritance’ is necessary to establish a novel form of coordination between the principle of heritability and the extended domain of phenomena that it is supposed to represent. Finally, I suggest that – despite the current lack of consensus on the right semantic extension of ‘inheritance’ – we can fruitfully understand the reconceptualization of ‘inheritance’ provided by niche construction theorists as the result of a novel form of coordination. (shrink)

This paper aims to reassess a notion in the works of the later Husserl that is both historically important and philosophically insightful, but remains understudied, namely, that of type. In opposition to a standard reading which treats Husserl’s type presentations as pre-conceptual habits, this paper argues that these representations are a specific kind of concept. More precisely, it shows that Husserl’s account of type presentations is akin to the contemporary prototype theory of concepts. This is historically important, since the predecessor (...) of the prototype theory is usually said to be Wittgenstein. From a philosophical standpoint, the paper shows that Husserl has an innovative account of the connection between type concepts and their extension. Contrary to the standard view of extensions as sets and thus sharp entities, Husserl develops a correlationalist theory of concepts, according to which, for the specific characteristics in the structure of a concept, there are corresponding characteristics in the arrangement of its members, and vice versa. According to this theory, while sharp concepts lead to sharp extensions, vague concepts such as (proto)type concepts lead to vague extensions. The paper presents this understanding of Husserl in detail and explains its philosophical significance. (shrink)