By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'' or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such (...) facts to hold. Also, EVM is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent, publicly available, and contains theorems both from formal and constructive mathematics. Any theorem of any mathematician from past or present forever belongs to K. Mathematical statements with known constructive proofs exist in K separately and form the set K_c⊆K. We assume that mathematical sets are atemporal entities. They exist formally in ZFC theory (...) although their properties can be time-dependent (when they depend on K) or informal. The true statement "K is non-empty" is outside K forever because K is not a formal set. Paul Cohen proved in 1963 that the equality 2^{\aleph_0}=\aleph_1 is independent of ZFC. Before 1963, the statement "There is a known constructively defined integer n⩾1 such that 2^{\aleph_0}=\aleph_n" was outside K. Since 1963, this statement is outside K forever. The true statement "There exists a set X⊆{1,...,49} such that card(X)=6 and X never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside K forever. In Martin-Löf's terminology, every currently known theorem is actually true whereas every theorem (known or unknown) is potentially true. Actual truth is knowledge dependent and tensed. Potential truth is knowledge independent and tenseless. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. For every such statement, its truth concerning the current mathematical knowledge is implied by a true statement of the form: (the conjunction of i conditions of the form α∈K)∧(the conjunction of j conditions of the form β∉K)∧(the conjunction of k conditions of the form γ∈K_c)∧(the conjunction of l conditions of the form δ∉K_c), where i,j,k,l∈N and α,β,γ,δ are mathematical statements. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a mathematical statement depends on time, where the statement is formally stated in the classical mathematics without the predicate K. In this article, mathematical statements on decidable sets X⊆N refer to time because they refer to the current mathematical knowledge on X. They cannot be formally stated in the classical mathematics without the predicate K and their logical values may change in time. For a set X⊆N whose infiniteness is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(X)=ω" is outside K. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove the assumption of the above statement. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧(Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. We prove that there exists a naturally defined set C⊆N which satisfies the following conditions (6)-(11). (6) A known and simple algorithm for every k∈N decides whether or not k∈C. (7) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(C)=ω" is outside K. (8) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(N\C)=ω" is outside K. (9) It is conjectured, though so far unproven, that C is infinite. (10) For every known algorithm A with no input, the statement "A returns an integer n satisfying card(C)<ω ⇒ C⊆(-∞,n]" is outside K. (11) For every known algorithm A with no input, the statement "A returns an integer m satisfying card(N\C)<ω ⇒ N\C⊆(-∞,m]" is outside K. The set C={k∈N: 2^{2^k}+1 is composite} is naturally defined and satisfies conditions (6)-(11). (shrink)

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to the former is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways of suppressing within-collective variation in fitness, and moreover to evaluate (...) their biological interest. I distinguish four such ways: increasing retaliatory capacity, homogenising assortment, and collapsing either fitness structure or character distribution to a mean value. The second task is to discover whether the third term of the Price decomposition measures the effect of any of these hypothetical interventions. On this basis I argue that the multi-level Price decomposition has explanatory value primarily when the sharing-out of collective resources is `subtractable'. Thus its value is more circumscribed than its champions Sober and Wilson (1998) suppose. (shrink)

Several authors have recently argued that intelligibility, rather than value, constitutes life’s meaning. In this paper I criticize the intelligibility view by offering examples of cases in which i...

According to subjectivist views about a meaningful life, one's life is meaningful in virtue of desire satisfaction or feelings of fulfilment. Standard counterexamples consist of satisfaction found through trivial or immoral tasks. In response to such examples, many philosophers require that the tasks one is devoted to are objectively valuable, or have objectively valuable consequences. I argue that the counterexamples to subjectivism do not require objective value for meaning in life. I also consider other reasons for thinking that meaning (...) in life requires objective value and raise doubts about their strength. Finally, I argue that beauty is not plausibly objective, but that it seems important for meaning. This puts pressure on the objectivist to explain why objectivity matters in the case of other values. (shrink)

In this article, I reply to a critical notice of my book, Meaning in Life: An Analytic Study, that Stephen Kershnar has published elsewhere in this issue of Science, Religion & Culture. Beyond expounding the central conclusions of the book, Kershnar advances two major criticisms of it, namely, first, that I did not provide enough evidence that meaning in life is a genuine value-theoretic category as something distinct from and competing with, say, objective well-being, and, second, that, even if (...) there were a value of meaning in life, my fundamentality theory of it would not capture it well. Here I respond to both of these criticisms, aiming to probe these underexplored issues still more deeply. I also contend that these two criticisms are in tension with each other; in order to contend that my theory of meaning is incorrect, Kershnar must draw on intuitions about the existence of meaning that undercut his suggestion that there is no such thing. (shrink)

The problem of value disagreement and contextualist, relativist and metalinguistic attempts of solving it are laid out. Although the metalinguistic account seems to be on the right track, it is argued that it does not sufficiently explain why and how disagreements about the meaning of evaluative terms are based on and can be decided by appeal to existing social practices. As a remedy, it is argued that original suggestions from Putnam's 'The Meaning of "Meaning"' ought to be taken seriously. (...) The resulting dual aspect theory of meaning can explain value disagreement in much the same way as it deals with disagreement about general terms. However, the account goes beyond Putnam's by not just defending a version of social externalism, but also defending the thesis that the truth conditional meaning of many evaluative terms is not fixed by experts either and instead constantly contested as part of a normal function of language. (shrink)

This essay considers the theoretical disagreement between Isaiah Berlin and Hannah Arendt on the meaning and value of freedom. Berlin thinks that negative liberty as non-interference is commendable because it is attuned to the implication of value pluralism that man is a choice-making creature and cannot be otherwise. By contrast, the political freedom to act is in Arendt’s view a more fulfilling ideal because it is only in political action that man’s potentiality is actualised, his unique identity manifested (...) and his being-in-the-world-with-others reaffirmed. What lies beneath the two thinkers’ dispute over the most satisfactory meaning of freedom, I argue, is a deeper disagreement over human nature itself. The implication of this analysis for the contemporary debate between pluralist liberals and their agonistic critics is briefly discussed in conclusion. (shrink)

In this article, part of a special issue on meaning in life and medical ethics, I argue that several issues encountered in a bioethical context are not adequately addressed only with values such as morality and welfare. I maintain, more specifically, that the value of what makes a life meaningful is essential to being able to provide conclusive judgements about which decisions to make. After briefly indicating how meaningfulness differs from rightness and happiness, I point out how it is (...) plausibly central to making decisions in six ‘life and death’ matters. My aim is not to draw any firm conclusions about what to do when it comes to these topics, but rather to show that in order to arrive at any, one cannot plausibly ignore the category of life’s meaning that has, until recently, been nearly absent from Western bioethics since its inception. (shrink)

This paper expands on another which focussed on Socrates’s question: ‘How should one live?’. The present paper also focusses on the ‘meaning of life’ and ‘meaning in life’ issues, and more on rights. To fully rationally answer Socrates’s question, we need to answer the epistemic question: ‘How can one know how one should live?’. This paper attempts to answer both. And knowing how one should live fundamentally involves knowing what values one should live by. This includes which rights one should (...) have and which rights others should have. So one’s values include how one should treat all persons (and (other) animals, the environment and so on.) All this relates to what one finds meaningful in life and the meaning or point of one’s life. In sum, all the notions in this paper’s title are interrelated. The issue of rationality is crucial here. Just one example here (qualified later) is that our rationality gives us cognitively meaningful notions. ‘Rationality’ here only concerns knowledge, e.g., ways to acquire scientific knowledge, and meta-knowledge concerning values. No values or rights as such are rational or knowledge. However:- Many factors are required for human rationality to exist and develop, e.g., life, mental health and evidence-based education. Human rationality’s need for those factors, hence their value to rationality, is rationally-unquestionable – and that applies to the practised values prescribing the prescribable factors. With this, there are rationally-unquestionable rights to those factors. Those prescribable factors require certain interrelated epistemic, moral, social, political, legal, educational and other values/rights to be practised. This implies a pro-rationality values-theory with one obligatory, general end – a uniquely rationally-unquestionable end. This end provides the basis for answering Socrates’s question as rationally (correctly) as is possible for values/rights. That end is fundamentally epistemic, namely ‘Be pro-rationality’, yet the theory has deeply-humanly-meaningful, universal applications. It has implications for current and all possible moral, social, political, legal, educational, environmental etc issues. E.g., the theory shows that human rationality crucially requires love and certain other emotions, health-care, education and upbringing. These require certain right to be respected and practised. With this, the paper discusses affection, free speech, journalism, psychotherapy, political and sexual consent, responsibilities, freedom and government. The theory’s general sub-values prescribe much prescribed by some other theories, e.g., broad and deep knowledge-acquisition (in certain areas), rationally-critical thinking, non-sexism, non-racism, general types of liberalism, holistic flourishing, happiness, unselfishness and fairness. However, all other values-theories lack pro-rationality theory’s maximum possible rational-unquestionability, internal coherence and coherence with rationality. The theory encourages (the right to) total freedom in a-rationality areas, areas irrelevant to its obligatory end. The theory inherently requires its advocates to be (self )critical, rationally viewing the theory’s necessarily human-suggested specifics as often fallible or unavoidably approximate. So the theory is a work-in-progress. (shrink)

The purpose of this paper is to inquire into the relationship between persuasive definition and common knowledge (propositions generally accepted and not subject to dispute in a discussion). We interpret the gap between common knowledge and persuasive definition (PD) in terms of potential disagreements: PDs are conceived as implicit arguments to win a potential conflict. Persuasive definitions are analyzed as arguments instantiating two argumentation schemes, argument from classification and argument from values, and presupposing a potential disagreement. The argumentative structure of (...) PDs reveals different levels of disagreement, and different pos-sibilities of resolving the conflict or causing dialogical deadlock. (shrink)

This document presents a Gentzen-style deductive calculus and proves that it is complete with respect to a 3-valued semantics for a language with quantifiers. The semantics resembles the strong Kleene semantics with respect to conjunction, disjunction and negation. The completeness proof for the sentential fragment fills in the details of a proof sketched in Arnon Avron (2003). The extension to quantifiers is original but uses standard techniques.

The thesis that there is a reciprocal relationship between human beings and work—i.e., although man controls work, he may find in it either fulfillment or degradation—has its roots in the Marxist theory of alienation. This paper, therefore, tackles this problem from a Marxist perspective. It examines Marx and Engels’s analysis of the history and causes of human alienation by presenting their views on human nature and how work is related to the individual’s search for meaning and fulfillment. The two—man and (...) work—cannot be separated, for doing so leads to alienated work (production alienation) and alienated worker (self-alienation). Hence, the problem of employee satisfaction has to be dealt with from the perspective of how employees experience their relation to their work. (shrink)

Several researchers have recently argued that p values lose their meaning in exploratory analyses due to an unknown inflation of the alpha level (e.g., Nosek & Lakens, 2014; Wagenmakers, 2016). For this argument to be tenable, the familywise error rate must be defined in relation to the number of hypotheses that are tested in the same study or article. Under this conceptualization, the familywise error rate is usually unknowable in exploratory analyses because it is usually unclear how many hypotheses have (...) been tested on a spontaneous basis and then omitted from the final research report. In the present article, I argue that it is inappropriate to conceptualize the familywise error rate in relation to the number of hypotheses that are tested. Instead, it is more appropriate to conceptualize familywise error in relation to the number of different tests that are conducted on the same null hypothesis in the same study. Under this conceptualization, alpha level adjustments in exploratory analyses are (a) less necessary and (b) objectively verifiable. As a result, p values do not lose their meaning in exploratory analyses. (shrink)

In her impressive book, looking at the philosophy and science of well-being, Anna Alexandrova argues for the strong claim that we possess no stable, unified concept of well-being. Instead, she thinks the word “well-being” only comes to have a specific meaning in particular contexts, and has a quite different meaning in different contexts. I take issue with (1) her claim that we do not possess a unified, all-things-considered concept of well-being as well as with (2) her failure to consider why (...) we might want a unified concept. I grant that Alexandrova is probably correct that the word “well-being” is used differently in different contexts. But this only shows that one word can come to be used to express different concepts. Moreover, noting that several concepts exist that are picked out by “well-being” doesn’t establish that we lack altogether a notion of all-things-considered well-being. I believe we have such a concept, even though it is not always the concept in play. Moreover, I think we need such a concept. The conceptual muddles Alexandrova highlights—muddles that result from a single word being used to express multiple ideas—remind us how important it is to be able to distinguish different concepts from one another, as well as how important it is to periodically remind ourselves of how various forms of specialist dialogue relate back to the broader, more general notion of “well-being.”. (shrink)

This paper argues that the Value Sensitive Design (VSD) methodology provides a principled approach to embedding common values in to AI systems both early and throughout the design process. To do so, it draws on an important case study: the evidence and final report of the UK Select Committee on Artificial Intelligence. This empirical investigation shows that the different and often disparate stakeholder groups that are implicated in AI design and use share some common values that can be used (...) to further strengthen design coordination efforts. VSD is shown to be both able to distill these common values as well as provide a framework for stakeholder coordination. (shrink)

Desire comes in two kinds: attraction and aversion. But contemporary theories of desire have paid little attention to the distinction, and some philosophers doubt that it is psychologically real. I argue that one reason to think there is a difference between the attitudes, and to care about it, is that attractions and aversions contribute in radically different ways to our well-being. Attraction-motivated activity adds to the good life in a way that aversion-driven activity doesn’t. I argue further that the (...) class='Hi'>value of attraction-motivated activity is irreducible to the prudential value of pleasure or desire-satisfaction. Rather it contributes in a distinctive way to the felt meaningfulness of life. In the end I offer a hypothesis: when we are attracted to something, we see it as (non-comparatively) good; and it is only when we pursue the apparent good that we see ourselves as engaged with value that makes our lives and the universe worth maintaining. -/- . (shrink)

Abstract In this paper I argue that to understand the ethics of belief we need to put it in a context of what we care about. Epistemic values always arise from something we care about and they arise only from something we care about. It is caring that gives rise to the demand to be epistemically conscientious. The reason morality puts epistemic demands on us is that we care about morality. But there may be a (small) class of beliefs which (...) it is not wrong to hold unconscientiously. I also argue that epistemic values enjoy a privileged place in the panorama of what we care about because they are entailed by anything we care about. That means that when there is a conflict between caring about knowledge or true belief and caring about something else, that conflict cannot be resolved simply by following the one we care about the most because caring about knowledge in any domain is entailed by caring about that domain. Finally, I argue that whereas caring demands different degrees of conscientiousness in different contexts, contextualism about knowledge is less plausible. (shrink)

From time involved in pair production process, in the photon-photon collision, we consider energy and then mass uncertainty. Taking the latter as the mass of a particle, we repeat pair production process obtaining another mass uncertainty, then another particle mass, and so on. Starting with the heaviest charged elementary particle that is possible using Planck length for electromagnetic mass, we obtain a mass value close to electron mass. It is supposed exactly electron mass, considering the presence of uncertainties in (...) the process. Then plausible neutrino mass and other particles masses are obtained. (shrink)

Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...) - and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor’s proof that there is no greatest cardinal number in the variation of (...) the functional theory holding that only some but not all complexes can be analyzed into function and argument. The final manuscript, “Meaning and Denotation”, examines how his pre-1905 dis­tinction between meaning and denotation is to be understood with respect to functions and their arguments. In them, Russell seems to endorse an extensional view of functions not endorsed in other works prior to the 1920s. All three manuscripts illustrate the close connection between his work on the logical paradoxes and his work on the theory of meaning. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...) of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

Often, when one faces a choice between alternative actions, there are reasons both for and against each alternative. On one way of understanding these words, what one “ought to do all things considered (ATC)” is determined by the totality of these reasons. So, these reasons can somehow be “combined” or “aggregated” to yield an ATC verdict on these alternatives. First, various assumptions about this sort of aggregation of reasons are articulated. Then it is shown that these assumptions allow for the (...) proof of a “Reasons Aggregation Theorem” – parallel to John Harsanyi’s 1955 “Social Aggregation Theorem”. All reasons for action are grounded in reason-providing values; and, for every such reason-providing value, there is in principle a way of measuring how strongly this value counts against each alternative. The theorem tells us that the appropriate measure of how much reason ATC there is against each alternative is simply a weighted sum of the strengths with which these values count against that alternative; the agent ought not ATC to perform an action iff there is ATC more reason against it than against some available alternative. (shrink)

Fitting Attitudes accounts of value analogize or equate being good with being desirable, on the premise that ‘desirable’ means not, ‘able to be desired’, as Mill has been accused of mistakenly assuming, but ‘ought to be desired’, or something similar. The appeal of this idea is visible in the critical reaction to Mill, which generally goes along with his equation of ‘good’ with ‘desirable’ and only balks at the second step, and it crosses broad boundaries in terms of philosophers’ (...) other commitments. For example, Fitting Attitudes accounts play a central role both in T.M. Scanlon’s [1998] case against teleology, and in Michael Smith [2003], [unpublished] and Doug Portmore’s [2007] cases for it. And of course they have a long and distinguished history. (shrink)

Two competing accounts of value incomparability have been put forward in the recent literature. According to the standard account, developed most famously by Joseph Raz, ‘incomparability’ means determinate failure of the three classic value relations ( better than , worse than , and equally good ): two value-bearers are incomparable with respect to a value V if and only if (i) it is false that x is better than y with respect to V , (ii) it (...) is false that x is worse than y with respect to V and (iii) it is false that x and y are equally good with respect to V . Most philosophers have followed Raz in adopting this account of incomparability. Recently, however, John Broome has advocated an alternative view, on which value incomparability is explained in terms of vagueness or indeterminacy . In this paper I aim to further Broome’s view in two ways. Firstly, I want to supply independent reasons for thinking that the phenomenon of value incomparability is indeed a matter of the indeterminacy inherent in our comparative predicates. Secondly, I attempt to defend Broome’s account by warding off several objections that worry him, due mainly to Erik Carlson and Ruth Chang. (shrink)

Safe-by-Design (SBD) frameworks for the development of emerging technologies have become an ever more popular means by which scholars argue that transformative emerging technologies can safely incorporate human values. One such popular SBD methodology is called Value Sensitive Design (VSD). A central tenet of this design methodology is to investigate stakeholder values and design those values into technologies during early stage research and development (R&D). To accomplish this, the VSD framework mandates that designers consult the philosophical and ethical literature (...) to best determine how to weigh moral trade-offs. However, the VSD framework also concedes the universalism of moral values, particularly the values of freedom, autonomy, equality trust and privacy justice. This paper argues that the VSD methodology, particularly applied to nano-bio-info-cogno (NBIC) technologies, has an insufficient grounding for the determination of moral values. As such, an exploration of the value-investigations of VSD are deconstructed to illustrate both its strengths and weaknesses. This paper also provides possible modalities for the strengthening of the VSD methodology, particularly through the application of moral imagination and how moral imagination exceed the boundaries of moral intuitions in the development of novel technologies. (shrink)

In this work we consider the problem of the approximate hedging of a contingent claim in the minimum mean square deviation criterion. A theorem on martingale representation in case of discrete time and an application of the result for semi-continuous market model are also given.

Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undeter- mined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third (...) value could be seen as a step beyond the Aristotelian dichotomy of Being and non-Being. According to Suszko, Łukasiewicz’s ideas rested on a confusion between algebraic values (what sentences describe/denote) and log- ical values (truth and falsity). Thus, Łukasiewicz’s third undetermined value is no more than an algebraic value, a possible denotation for a sentence, but not a genuine logical value. Suszko’s Thesis is endorsed by a formal result baptized as Suszko’s Reduction, a theorem that states every Tarskian logic may be characterized by a two-valued semantics. The present study is intended as a thorough investigation of Suszko’s thesis and its implications. The first part is devoted to the historical roots of many-valuedness and introduce Suszko’s main motivations in formulating the double character of truth-values by drawing the distinction in between algebraic and logical values. The second part explores Suszko’s Reduction and presents the developments achieved from it; the properties of two-valued semantics in comparison to many-valued semantics are also explored and discussed. Last but not least, the third part investigates the notion of logical values in the context of non-Tarskian notions of entailment; the meaning of Suszko’s thesis within such frameworks is also discussed. Moreover, the philosophical foundations for non-Tarskian notions of entailment are explored in the light of recent debates concerning logical pluralism. (shrink)

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument (...) by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. (shrink)

In this paper I shall defend the idea that there is an abstract and general core meaning of objectivity, and what is seen as a variety of concepts or conceptions of objectivity are in fact criteria of, or means to achieve, objectivity. I shall then discuss the ideal of value-free science and its relation to the objectivity of science; its status can be at best a criterion of, or means for, objectivity. Given this analysis, we can then turn to (...) the problem of inductive risk. Do the value judgements regarding inductive risk really pose a threat to the objectivity of science? I claim that this is not the case because they do not lower the thresholds scientifically postulated for objectivity. I shall conclude the paper with a discussion of under-appreciated influences of values on science, which indeed pose a serious threat to the objectivity of some scientific disciplines. (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued (...) trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

In this article I argue that the value of epistemic justification cannot be adequately explained as being instrumental to truth. I intend to show that false belief, which is no means to truth, can nevertheless still be of epistemic value. This in turn will make a good prima facie case that justification is valuable for its own sake. If this is right, we will have also found reason to think that truth value monism is false: assuming that (...) true belief does have value, there is more of final epistemic value than mere true belief. (shrink)

Value pluralists see themselves as philosophical grown-ups. They profess to face reality as it is and accept resultant pessimism, while criticising their monist rivals for holding on to the naïve idea that the right, the good and the beautiful are ultimately harmonisable with each other. The aim of this essay is to challenge this self-image of value pluralists. Notwithstanding its usefulness as a means of subverting monist dominance, I argue that the self-image has the downside of obscuring various (...) theoretical positions that do not fall into either the pluralist or monist camp. Yet such positions do exist, as shown by my discussion of Albert Camus and Hannah Arendt. Near contemporaries of the pioneering value pluralist Isaiah Berlin, the pair, just like him, sought to be realistic about the lived experiences of political disasters and moral disorientation in the twentieth century. Moreover, they shared with Berlin a keen interest in real-world moral dilemmas, which seemed to them to have made traditional morality obsolete. But the three thinkers’ perspectives on ‘reality’ hardly converged, and neither Camus nor Arendt became a value pluralist as a result of their reflections on moral dilemmas. This, however, by no means indicates the pair’s immaturity. Rather, it shows that there is more than one way of observing fidelity to our actual experience and that value pluralists’ commitment to realism and resultant pessimism is not as uniquely mature as they would have us believe. (shrink)

Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. (...) A popular reply to Lewis's results is to claim that conditional claims, or claims about subjective value, lack truth conditions. For this strategy to have a chance of success, it needs to give up basic structural principles about how epistemic states can be updated—in a way that is strikingly parallel to the commitments of the project of dynamic semantics. (shrink)

Value pluralists believe in multiple dimensions of value. What does betterness along a dimension have to do with being better overall? Any systematic answer begins with the Strong Pareto principle: one thing is overall better than another if it is better along one dimension and at least as good along all others. We defend Strong Pareto from recent counterexamples and use our discussion to develop a novel view of dimensions of value, one which puts Strong Pareto on (...) firmer footing. We conclude by defending Dimensionalism, the hypothesis that overall value relations are determined solely by how things compare along value dimensions. These are first steps towards a more systematic value pluralism. (shrink)

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

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

The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics (...) proposes that all quantum systems be interpreted as dissipative ones and that the theorem be thus derstood. The conclusion is that the continual representation, by force or (gravitational) field between parts interacting by means of it, of a system is equivalent to their mutual entanglement if representation is discrete. Gravity (force field) and entanglement are two different, correspondingly continual and discrete, images of a single common essence. General relativity can be interpreted as a superluminal generalization of special relativity. The postulate exists of an alleged obligatory difference between a model and reality in science and philosophy. It can also be deduced by interpreting a corollary of the heorem. On the other hand, quantum mechanics, on the basis of this theorem and of V on Neumann's (1932), introduces the option that a model be entirely identified as the modeled reality and, therefore, that absolutely reality be recognized: this is a non-standard hypothesis in the epistemology of science. Thus, the true reality begins to be understood mathematically, i.e. in a Pythagorean manner, for its identification with its mathematical model. A few linked problems are highlighted: the role of the axiom of choice forcorrectly interpreting the theorem; whether the theorem can be considered an axiom; whether the theorem can be considered equivalent to the negation of the axiom. (shrink)

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly certain preliminary goal, and the choice is only the mean, by which it can be achieved or not by the one who determines the goal. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, (...) the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. The choice is usually linked to very complicated systems such as human brain or society and even often associated with consciousness. In its background, the material world is deterministic and absolutely devoid of choice. However, quantum mechanics introduces the choice in the fundament of physical world, in the only way, in which it can exist: All exists in the “phase transition” of the present between the uncertain future and the well-ordered past. Thus the present is forced to choose in order to be able to transform the coherent state of future into the well-ordering of past. The concept of choice as if suggests that there is one who chooses. However quantum mechanics involves a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors, Conway and Kochen, and according to them: “Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We don’t know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity” “The import of the free will theorem is that it is not only current quantum theory, but the world itself that is non-deterministic, so that no future theory can return us to a clockwork universe”. Those theorems can be considered as a continuation of the so-called theorems about the absence of “hidden variables” in quantum mechanics. (shrink)

The profound changes in personality, mood, and other features of the self that neural interventions can induce can be disconcerting to patients, their families, and caregivers. In the neuroethical debate, these concerns are often addressed in the context of possible threats to the narrative self. In this paper, I argue that it is necessary to consider a dimension of impacts on the narrative self which has so far been neglected: neural interventions can lead to a loss of meaning of actions, (...) feelings, beliefs, and other intentional elements of our self-narratives. To uphold the coherence of the self-narrative, the changes induced by neural interventions need to be accounted for through explanations in intentional or biochemical terms. However, only an explanation including intentional states delivers the content to directly ascribe personal meaning, i.e., subjective value to events. Neural interventions can deprive events of meaning because they may favor a predominantly biochemical account. A loss of meaning is not inherently negative but it can be problematic, particularly if events are affected one was not prepared or willing to have stripped of meaning. The paper further examines what it is about neural interventions that impacts meaning by analyzing different methods. To which degree the pull towards a biochemical view occurs depends on the characteristics of the neural intervention. By comparing Deep Brain Stimulation, Prozac, Ritalin, psychedelics, and psychotherapy, the paper identifies some main factors: the rate of change, the transparency of the causal chain, the involvement of the patient, and the presence of an acute phenomenological experience. (shrink)

As things currently stand, our deaths are unavoidable and our lifespans short. It might be thought that these qualities leave room for improvement. According to a prominent line of argument in philosophy, however, this thought is mistaken. Against the idea that a longer life would be better, it is claimed that negative psychological states, such as boredom, would be unavoidable if our lives were significantly longer. Against the idea that a deathless life would be better, it is claimed that such (...) a life would be lacking in important sources of value, because death is a precondition for many of our valuing attitudes. I argue that these problems are avoided by very long lives that incorporate fading memory, limited ignorance of future events, and temporal scarcity. I conclude that very long lives are, in principle, desirable, and that death does not play an essential role in our valuing attitudes. (shrink)

An e-book devoted to 13 critical discussions of Thaddeus Metz's book "Meaning in Life: An Analytic Study", with a lengthy reply from the author. -/- Preface Masahiro Morioka i -/- Précis of Meaning in Life: An Analytic Study Thaddeus Metz ii-vi -/- Source and Bearer: Metz on the Pure Part-Life View of Meaning Hasko von Kriegstein 1-18 -/- Fundamentality and Extradimensional Final Value David Matheson 19-32 -/- Meaningful and More Meaningful: A Modest Measure Peter Baumann 33-49 -/- Is Meaning (...) in Life Comparable?: From the Viewpoint of ‘The Heart of Meaning in Life’ Masahiro Morioka 50-65 -/- Agreement and Sympathy: On Metz’s Meaning in Life Sho Yamaguchi 66-89 -/- Metz’s Quest for the Holy Grail James Tartaglia 90-111 -/- Meaning without Ego Christopher Ketcham 112-133 -/- Death and the Meaning of Life: A Critical Study of Metz’s Meaning in Life Fumitake Yoshizawa 134-149 -/- Metz’ Incoherence Objection: Some Epistemological Considerations Nicholas Waghorn 150-168 -/- Meaning in Consequences Mark Wells 169-179 -/- Defending the Purpose Theory of Meaning in Life Jason Poettcker 180-207 -/- Review of Thaddeus Metz’s Meaning in Life Minao Kukita 208-214 -/- A Psychological Model to Determine Meaning in Life and Meaning of Life Yu Urata 215-227 -/- Assessing Lives, Giving Supernaturalism Its Due, and Capturing Naturalism: Reply to 13 Critics of Meaning in Life Thaddeus Metz 228-278 . (shrink)

This book is a collection of all the papers published in the special issue “Philosophy and Meaning in Life Vol.4: Selected Papers from the Pretoria Conference,” Journal of Philosophy of Life, Vol.12, No.1, 2022, pp.1-115. -/- Theorizing About Meaning in Life Cheshire Calhoun -/- Is It Possible to Say ‘Yes’ to Traumatic Experiences?: A Philosophical Approach to Human Suffering Masahiro Morioka -/- Why Beauvoir Is Not a Subjectivist about Meaning in Life Kiki Berk -/- Axiological Values Grounded in Basic Motivational (...) Dispositions: How to Be a Subjectivist about Meaning in Life Frank Martela -/- Pessimism, Political Critique, and the Contingently Bad Life Patrick O’Donnell -/- Reason, Luck, and Meaning: A Critique of the Moralist View of Meaning in Life Kazuki Watanabe. (shrink)

The aim of this paper is to propose a new approach to the question of meaning in life by criticizing Thaddeus Metz’s objectivist theory in his book Meaning in Life: An Analytic Study. I propose the concept of “the heart of meaning in life,” which alone can answer the question, “Alas, does my life like this have any meaning at all?” and I demonstrate that “the heart of meaning in life” cannot be compared, in principle, with other people’s meaning in (...) life. The answer to the question of “the heart of meaning in life” ought to have two values, yes-or-no, and there is no ambiguous gray zone between them. I believe that this concept constitutes the very central content of meaning in life. (shrink)

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by (...) environmental factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

Safe-by-Design (SBD) frameworks for the development of emerging technologies have become an ever more popular means by which scholars argue that transformative emerging technologies can safely incorporate human values. One such popular SBD methodology is called Value Sensitive Design (VSD). A central tenet of this design methodology is to investigate stakeholder values and design those values into technologies during early stage research and development (R&D). To accomplish this, the VSD framework mandates that designers consult the philosophical and ethical literature (...) to best determine how to weigh moral trade-offs. However, the VSD framework also concedes the universalism of moral values, particularly the values of freedom, autonomy, equality trust and privacy justice. This paper argues that the VSD methodology, particularly applied to nano-bio-info-cogno (NBIC) technologies, has an insufficient grounding for the determination of moral values. As such, an exploration of the value-investigations of VSD are deconstructed to illustrate both its strengths and weaknesses. This paper also provides possible modalities for the strengthening of the VSD methodology, particularly through the application of moral imagination and how moral imagination exceed the boundaries of moral intuitions in the development of novel technologies. (shrink)

Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the (...) relation of set theory and arithmetic are demonstrated. (shrink)