We show that critically accumulating "difficult" problems, contradictions and stagnation in modern science have the unified and well-specified mathematical origin in the explicit, artificial reduction of any interaction problem solution to an "exact", dynamically single-valued (or unitary) function, while in reality any unreduced interaction development leads to a dynamically multivalued solution describing many incompatible system configurations, or "realisations", that permanently replace one another in causally random order. We obtain thus the universal concept of dynamic complexity and chaos impossible in (...) unitary mathematics. This huge difference between the unreduced mathematics of real-world dynamics and strongly limited unitary “models” of traditional mathematics inevitably induces a growing series of “unsolvable” problems and other “mysteries” that culminate now in the crisis of the “end of science”, where the stagnating unitary “science” in question includes only the described limitation of the traditional mathematical framework (unfortunately accepted as the unique possible basis for any scientific knowledge). In this brief review, we show that science extension to the unreduced, dynamically multivalued mathematics of the intrinsically complex real-world dynamics provides stagnating problem solutions and reconstitution of the intrinsic causality and unity of science desperately missing in its artificially limited unitary framework. Painful stagnation of the latter should be replaced now by the unlimited new progress of the extended, causally complete knowledge of the universal science of complexity, which provides the urgently needed issue from the current impasse of the global civilisation development. (shrink)

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multivalued function Sep and a natural notion of reducibility for multivalued functions, we obtain a computational counterpart of the subsystem of second-order arithmetic WKL0. We study analogies and differences between (...) WKL0 and the class of Sep-computable multivalued functions. Extending work of Brattka, we show that a natural multivalued function associated with the Hahn-Banach Extension Theorem is Sep-complete. (shrink)

A problem is a multivalued function from a set of instances to a set of solutions. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness property if every computable instance of the problem admits a solution relative to which the property holds. For example, cone avoidance is the ability, given a noncomputable set A and a computable instance of a problem ${\mathsf {P}}$, to find a solution relative to which (...) A is still noncomputable.In this article, we compare relativized versions of computability-theoretic notions of preservation which have been studied in reverse mathematics, and prove that the ones which were not already separated by natural statements in the literature actually coincide. In particular, we prove that it is equivalent to admit avoidance of one cone, of $\omega $ cones, of one hyperimmunity or of one non- $\Sigma ^{0}_1$ definition. We also prove that the hierarchies of preservation of hyperimmunity and non- $\Sigma ^{0}_1$ definitions coincide. On the other hand, none of these notions coincide in a nonrelativized setting. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

In this article, we develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous “multivalued functions.” This generalizes known statements about weakly o-minimal, C-minimal, and P-minimal theories.

We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions (...) turns out to be strictly stronger than any previously studied multivalued functions arising from statements around $\mathrm {ATR}_0$. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of (...) the paper is devoted to four-valued Nmatrices, including Kearns’s and Ivlev’s. Besides proving with full details Kearns’s results for T, S4 and S5, we also obtain a characterisation of the system B by four-valued Nmatrices with level valuations. Concerning Ivlev’s results, two new modal systems are introduced and char.. (shrink)

The urgent drive for vaccine development in the midst of the current COVID-19 pandemic has prompted public and private organisations to invest heavily in research and development of a COVID-19 vaccine. Organisations globally have affirmed the commitment of fair global access, but the means by which a successful vaccine can be mass produced and equitably distributed remains notably unanswered. Barriers for low-income countries include the inability to afford vaccines as well as inadequate resources to vaccinate, barriers that are exacerbated during (...) a pandemic. Fair distribution of a pandemic vaccine is unlikely without a solid ethical framework for allocation. This piece analyses four allocation paradigms: ability to develop or purchase; reciprocity; ability to implement; and distributive justice, and synthesises their ethical considerations to develop an allocation model to fit the COVID-19 pandemic. (shrink)

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U -contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equations.

This is a short overview of the biological functions debate in philosophy. While it was fairly comprehensive when it was written, my short book ​A Critical Overview of Biological Functions has largely supplanted it as a definitive and up-to-date overview of the debate, both because the book takes into account new developments since then, and because the length of the book allowed me to go into substantially more detail about existing views.

In the foundations of Fechner's psychophysics, the concept of “functional relation” plays a highly relevant role in three different respects: (1) in respect to the principles of measurement, (2) in respect to the mind-body problem, and (3) in respect to the concept of a law of nature. In all three cases, it is important to explain the difference between a functional dependency of a variable upon another and a causal relationship between two (or more) variables. In all three respects, Ernst (...) Mach developed Fechner's ideas further and tried to extend the lessons he had learned from using the concept of a functional relation in psychophysics to the whole of science. For all three cases, I explain why they are still relevant for psychophysics and philosophy today. (shrink)

ABSTRACT A modal logic interpretation of Dempster-Shafer theory is developed in the framework of multivalued models of modal logic, i.e. models in which in any possible world an arbitrary number (possibly zero) of atomic propositions can be true. Several approaches to conditioning in multivalued models of modal logic are presented.

We define the notion of “potential existence” by starting from the fact that in multi-valued logic the existential quantifier is interpreted by the least upper bound operator. Besides, we try to define in a general way how to pass from potential into actual existence.

This study examined the relationship between individual differences in executive functions (EF; assessed by measures of working memory, Stroop, trail making, and verbal fluency) and ability to down-regulate and up-regulate responses to emotionally evocative film clips. To ensure a wide range of EF, 48 participants with diverse neurodegenerative disorders and 21 older neurologically normal ageing participants were included. Participants were exposed to three different movie clips that were designed to elicit a mix of disgust and amusement. While watching the (...) films they were either instructed to watch, down-regulate, and up-regulate their visible emotional responses. Heart rate and facial behaviours were monitored throughout. Emotion regulatory ability was operationalised as changes in heart rate and facial behaviour in the down- and up-regulation conditions, controlling for responses in the watch condition. Results indicated that higher verbal fluency scores were related to greater ability to regulate emotion in both the down-regulation and up-regulation conditions. This finding remained significant even after controlling for age and general cognitive functioning. No relationships were found between emotion regulation and the other EF measures. We believe these results derive from differences among EF measures, with verbal-fluency performance best capturing the complex sequence of controlled planning, activation, and monitoring required for successful emotion regulation. These findings contribute to our understanding of emotion–cognition interaction, suggesting a link between emotion-regulatory abilities and individual differences in complex executive functions. (shrink)

In the debate over the moral status of nonsentient organisms, biocentrists argue that all living things, including nonsentient ones, have interests of their own. They often defend this claim by arguing that living organisms are goal-directed, functionally organized systems. This argument for ascribing interests has faced a serious challenge that is sometimes called the Problem of Scope. Critics have argued that ascribing interests on the basis of functional organization would have implausible implications regarding the scope of the argument, such as (...) ascribing interests to inanimate artifacts and machines. In this paper, I argue that much of the recent discussion on the Problem of Scope is based on an uncharitable interpretation of the argument for ascribing interests, which presupposes a reductionist account of functions. I assess this version of the argument, and explain why it cannot succeed. I then consider an alternative interpretation of the argument, which starts from a non-reductionist account of functions. I argue that this version of the argument avoids the Problem of Scope, while acknowledging that it has limitations of its own. (shrink)

Justin Garson has recently argued that proper functions are proximal activities of traits selected by phylogenetic or ontogenetic selection processes, and that traits are dysfunctional only if they cannot perform their proper functions for constitutional reasons. We partially agree with Garson, but reject the view that functions are proximal activities, as well as his account of dysfunctions. Instead, we propose our own theory that biological functions are selected dispositions and that a trait is dysfunctional in virtue (...) of not having the dispositions for which it was selected. This account can explain both defects (or dysfunctions in Garson’s sense) and dysfunctions due to environmental factors. Moreover, it offers a neat way to explain the graduality of dysfunction. (shrink)

The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by the disjunction of the equations ∃E = 1 and ∃E = 0. We also define a weaker notion (...) of "relatively functional" algebra, and show that every member of MBA is isomorphic to a relatively functional one. (shrink)

Our perceptual systems are not stagnant but can learn from experience. Why is this so? That is, what is the function of perceptual learning? I consider two answers to this question: The Offloading View, which says that the function of perceptual learning is to offload tasks from cognition onto perception, thereby freeing up cognitive resources (Connolly, 2019) and the Perceptual View, which says that the function of perceptual learning is to improve the functioning of perception. I argue that the Perceptual (...) View better explains data from infants and animals, and better accounts for learned tasks that only perception could perform. (shrink)

This paper discusses whether rationality, morality or prudence impose process-requirements upon us. It has been argued that process-requirements fulfil two essential functions within a system of rational, moral or prudential requirements. These functions are considered to prove the existence of process-requirements. First, process-requirements are deemed necessary to ensure that rationality, morality or prudence can guide our deliberations and actions. Second, their existence is regarded as essential for the correctness of our ordinary explanations of why a person possesses a (...) certain degree of morality, rationality or prudence. However, I argue that these two functions are unable to show the existence of process-requirements. Instead, I propose a different essential function for process-requirements: they are necessary for attributing the correct degree of rationality, morality or prudence to a subject who is not entirely rational, moral or prudent. This function, I argue, necessitates the existence of process-requirements. (shrink)

In this companion volume to Warrant: The Current Debate, Plantinga develops an original approach to the question of epistemic warrant; that is what turns true belief into knowledge. He argues that what is crucial to warrant is the proper functioning of one's cognitive faculties in the right kind of cognitive environment.

This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, i.e. Dialectica and Diller-Nahm interpretation as well as Kreisel's modified realization, together with their Troelstra-style hybrids, are applied to constructive as well as classical (...) systems of arithmetic, analysis, and set theory. They yield relative consistency and conservativity results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations. Prerequisites are: familiarity with classical and intuitionistic predicate logic, basics of computability theory, Gödel's incompleteness theorems. (shrink)

The present paper revisits the debate between realists about gravitational energy in GR and anti-realists/eliminativists. I re-assess the arguments underpinning Hoefer’s seminal eliminativist stance, and those of their realist detractors’ responses. A more circumspect reading of the former is proffered that discloses where the so far not fully appreciated, real challenges lie for realism about gravitational energy. I subsequently turn to Lam and Read’s recent proposals for such a realism. Their arguments are critically examined. Special attention is devoted to the (...) adequacy of Read’s appeals to functionalism, imported from the philosophy of mind. (shrink)

Objective Manic and depressive phases of bipolar disorder (BD) show opposite psychomotor symptoms. Neuronally, these may depend on altered relationships between sensorimotor network (SMN) and subcortical structures. The study aimed to investigate the functional relationships of SMN with substantia nigra (SN) and raphe nuclei (RN) via subcortical-cortical loops, and their alteration in bipolar mania and depression, as characterized by psychomotor excitation and inhibition. -/- Method In this resting-state functional magnetic resonance imaging (fMRI) study on healthy (n = 67) and BD (...) patients (n = 100), (1) functional connectivity (FC) between thalamus and SMN was calculated and correlated with FC from SN or RN to basal ganglia (BG)/thalamus in healthy; (2) using an a-priori-driven approach, thalamus-SMN FC, SN-BG/thalamus FC, and RN-BG/thalamus FC were compared between healthy and BD, focusing on manic (n = 34) and inhibited depressed (n = 21) patients. -/- Results (1) In healthy, the thalamus-SMN FC showed a quadratic correlation with SN-BG/thalamus FC and a linear negative correlation with RN-BG/thalamus FC. Accordingly, the SN-related FC appears to enable the thalamus-SMN coupling, while the RN-related FC affects it favoring anti-correlation. (2) In BD, mania showed an increase in thalamus-SMN FC toward positive values (ie, thalamus-SMN abnormal coupling) paralleled by reduction of RN-BG/thalamus FC. By contrast, inhibited depression showed a decrease in thalamus-SMN FC toward around-zero values (ie, thalamus-SMN disconnection) paralleled by reduction of SN-BG/thalamus FC (and RN-BG/thalamus FC). The results were replicated in independent HC and BD datasets. -/- Conclusions These findings suggest an abnormal relationship of SMN with neurotransmitters-related areas via subcortical-cortical loops in mania and inhibited depression, finally resulting in psychomotor alterations. (shrink)

The evolutionary theory of artefact proper function holds that an artefact’s proper function is that effect which explains the reproduction of past instances of the artefact type. This theory has many sources but received its clearest presentation in Beth Preston’s essay “Why Is a Wing Like a Spoon?”. More recently, Preston has raised an objection to the theory, based on the phenomenon of ‘phantom functions’: these are functions that an artefact type is unable to perform, but which nonetheless (...) apparently constitute its proper function. Deflecting qi energy, for example, is the proper function of feng shui mirrors, even though no feng shui mirror is able to do this. Preston concludes that the existence of phantom functions refutes the evolutionary theory of artefact proper function. In this paper, the evolutionary theory is defended, by arguing that it can adequately account for phantom function cases. (shrink)

Effective domain theory is applied to fuzzy logic. The aim is to give suitable notions of semi-decidable and decidable L-subset and to investigate about the effectiveness of the fuzzy deduction apparatus.

We characterize a type of functional explanation that addresses why a homologous trait originating deep in the evolutionary history of a group remains widespread and largely unchanged across the group’s lineages. We argue that biologists regularly provide this type of explanation when they attribute conserved functions to phenotypic and genetic traits. The concept of conserved function applies broadly to many biological domains, and we illustrate its importance using examples of molecular sequence alignments at the intersection of evolution and cell (...) biology. We use these examples to show how the study of conserved functions can integrate knowledge of a trait’s causal effects on fitness and its history of natural selection without invoking adaptation. We also show how conserved function provides a novel basis for addressing objections against evolutionary functions raised by Robert Cummins. (shrink)

A study of what Descartes calls émotions in his Passions of the Soul suggests that, rather than just a theory of passions—as Descartes himself explicitly claims to be proposing—he was in practice putting forward a more comprehensive theory of passions-émotions, a unified theory which would be closer to what today should properly be called Descartes’ theory of emotions. I try here to make explicit the grounds of this unity by showing that émotions both fit within the functional account Descartes attributes (...) to what he calls passions; and complement the intentionality of passions by expanding it to new objects. In order to show this I offer also a tentative distinction, functionally and intentionally, between passions and émotions in general, on one hand, and, on the other, between the two apparent types of émotions Descartes refers to in the treatise—interior or internal [intérieure] and intellectual [intellectuelle] émotions. (shrink)

This is an exploratory paper whose aim is to investigate the potentialities of bilattice theory for an adequate definition of the deduction apparatus for multi-valued logic. We argue that bilattice theory enables us to obtain a nice extension of the graded approach to fuzzy logic. To give an example, a completeness theorem for a logic based on Boolean algebras is proved.

In this paper, I identify a central problem for conceptual engineering: the problem of showing concept-users why they should recognise the authority of the concepts advocated by engineers. I argue that this authority problem cannot generally be solved by appealing to the increased precision, consistency, or other theoretical virtues of engineered concepts. Outside contexts in which we anyway already aim to realise theoretical virtues, solving the authority problem requires engineering to take a functional turn and attend to the functions (...) of concepts. But this then presents us with the problem of how to specify a concept’s function. I argue that extant solutions to this function specification problem are unsatisfactory for engineering purposes, because the functions they identify fail to reliably bestow authority on concepts, and hence fail to solve the authority problem. What is required is an authoritative notion of conceptual function: an account of the functions of concepts which simultaneously shows why concepts fulfilling such functions should be recognised as having authority. I offer an account that meets this combination of demands by specifying the functions of concepts in terms of how they tie in with our present concerns. (shrink)

This book, originally published in French, examines the philosophical debates on functions over the last forty years and proposes new ways of analysis. Pervasive throughout the life sciences, the concept of function has the air of an epistemological scandal: ascribing a function to a biological structure or process amounts to suggesting that it is explained by its effects. This book confronts the debates on function with the use of the notion in a wide range of disciplines, such as biology, (...) psychology, and medicine. It also raises the question of whether this notion, which is as old in the history of technology as it is in the life sciences, has the same meaning in these two domains. (shrink)

Wave function realism is an interpretative framework for quantum theories which recommends taking the central ontology of these theories to consist of the quantum wave function, understood as a field on a high-dimensional space. This paper presents and evaluates three standard arguments for wave function realism, and clarifies the sort of ontological framework these arguments support.

“Functional finance” is an economic theory within the Post Keynesian school of thought. Especially in the form of Modern Monetary Theory (MMT), it has begun to have two big but opposite effects on the debate over Universal Basic Income (UBI). Some people state MMT in an exaggerated way that implies the government can spend all it wants on UBI or anything else without ever raising taxes or borrowing money as if government spending had no limits of any kind. Other people (...) refer to MMT while arguing that any effort to maintain a livable level of UBI is unsustainable. This article discusses the functional finance implications for the cost and sustainability of UBI, arguing that neither of those exaggerated implications are correct. MMT doesn’t free us for the concern for how to support UBI with taxes, but neither does it give reason to believe UBI is any less sustainable. (shrink)

This chapter contains sections titled: Introduction Function and Malfunction Function and Evolution Function Based on Past Origins Biological Functions Based on the Distant Past: Natural Selection Fitness and Goal‐Contribution Accounts Neo‐Teleology Looking at the Present: Causal Roles and Functions Evolution Bites Back: Vindication of the Selectionist Approach Postscript: Counterpoint Acknowledgments Notes References.

Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position (...) was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

As well known, the exact sciences served Kant as a model of metaphysical cognition. There is also an opposite relation between science and metaphysics, however, namely the teleology of reason, as expressed at the end of the Critique of Pure Reason. There, Kant claims that the sciences are ultimately subordinate to the essential ends of humanity “through the mediation of a rational cognition from mere concepts”, i. e., metaphysical cognition.

In this paper I defend an etiological theory of biological functions (according to which the proper function of a trait is the effect for which it was selected by natural selection) against three objections which have been influential. I argue, contrary to Millikan, that it is wrong to base our defense of the theory on a rejection of conceptual analysis, for conceptual analysis does have an important role in philosophy of science. I also argue that biology requires a normative (...) notion of a "proper function", and that a normative notion is not ahistorical. (shrink)

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

This 2001 book offers an examination of functional explanation as it is used in biology and the social sciences, and focuses on the kinds of philosophical presuppositions that such explanations carry with them. It tackles such questions as: why are some things explained functionally while others are not? What do the functional explanations tell us about how these objects are conceptualized? What do we commit ourselves to when we give and take functional explanations in the life sciences and the social (...) sciences? McLaughlin gives a critical review of the debate on functional explanation in the philosophy of science. He discusses the history of the philosophical question of teleology, and provides a comprehensive review of the post-war literature on functional explanation. What Functions Explain provides a sophisticated and detailed Aristotelian analysis of our concept of natural functions, and offers a positive contribution to the ongoing debate on the topic. (shrink)

In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration.