Within a weak subsystem of second-order arithmetic , that is -conservative over , we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

In this doctoral thesis, I will argue that in his De motu (1721, ‘On motion’), Bishop George Berkeley (c.1684–1753) develops a pragmatist theory of causation regarding mechanical theories outlined previously with Newtonianism. I place chief emphasis on the importance of logic and mathematics in Berkeley’s scientific approach, on which the other levels of semantics, epistemology, and mechanics build up. On my rendering, Berkeley’s pragmatic method to conceive or mathematically imagine causation makes sense in terms of mechanical causes or ‘mathematical hypotheses’. (...) For the mechanist maintains the usefulness and truthfulness of causation by the following definition. Definition. A pragmatist theory of causation is one which holds that: 1 Causal terms are indispensable in scientific deliberation for their usefulness; they cannot be eliminated [contra reductionism]. 2 What a cause is is defined by one’s temporal deliberative practices, independent of a temporal structure that theories hold [contra structuralism]. 3 Causal laws (theories formulated in causal terms) are genuinely true, not fictitious, when one confirms and deduces them [contra instrumentalism]. By justifying this definition, I will object to three rival readings—reductionism, structuralism, and instrumentalism—to my reading of Berkeley as a pragmatist about causation. In particular, my pragmatist reading criticises the most popular instrumentalist reading because, according to the latter, talk of causal terms like forces can be false or merely fictitious inasmuch as one can hold the utility of theories in mechanical practices. The instrumentalist reading is then compatible with mathematical formalism, according to which it is not truth or meaning that counts as formal manipulation or game of meaningless symbols, thereby eschewing a platonist attitude towards mathematical objects. However, I rebut the formalistic instrumentalism from Berkeley’s logical and realist standpoint, maintaining the irreducibility of occult qualities that mathematical objects have in their formulation from hypotheses to propositions. Light shall be shed on the tenet I propose that law-propositions formulated in hypothetical, causal terms must be true, neither false nor fictitious, when we (1) frame, (2) confirm, and (3) express them to the extent of our discursive thinking (in three steps). [339 words]. (shrink)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

As kendo continues to gain in international popularity, there are hopes for its adoption in the Olympic Games as an international competitive event, even while moves to further this aim have not necessarily occurred in Japan or elsewhere. One reason for the efforts to achieve a form of globalization of kendo different from Judo is the attempt to adhere to and preserve the unique concepts kendo, the sport embodies by remaining true to the forms of traditional Japanese culture. This is (...) epitomized by the importance given to zanshin (the combination of posture and fighting spirit after striking), one of the key concepts that constitute yuko-datotsu in kendo. Our purpose in this study is to discuss the intersubjective nature of the decisions regarding the conditions for point-scoring in competitive sports. In particular, we will focus on the aesthetics required for zanshin in kendo, focusing on the theory behind yuko-datotsu (point score), which will also considerably influence its international dissemination. Kendo is characterized from the perspective of western rationalism as an appreciation of form and rules of behavior referred to as formalism and, in this respect, it has unique characteristics differing from those of modern sports that are disseminated internationally. In martial arts, besides refinement and proficiency in the rules of behavior by rigidly adhering to form and rules of behavior and repetition, the aim is to transcend said form and the rules of behavior and embody the spiritual nature dwelling in the background. Kendo should remain traditional path and keep zanshin in the value of point (yuko-datotsu) for its virtue. Kendo has not yet developed into an international competitive sport, but it is in the process of traversing that Geido path as a Do for the purpose of character building through it. Throughout life, one should try to devote oneself to kendo with thought for the value of transcending form and the rules of behaviour, and embodying the spiritual nature of the sport that inheres in its background. That is why one may perceive an evident hesitation or indeed negativity regarding the possible internationalization or development as an Olympic event. (shrink)

A critical examination of Japanese literary and art theories.

Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification for the hierarchical classification in a general context of first-order theories. To this end, we first formalize the standard transformation procedure for prenex normalization. Then we show that the classes $$\textrm{E}_k$$ and $$\textrm{U}_k$$ introduced in [1] are exactly the classes induced by $$\Sigma _k$$ and $$\Pi _k$$ respectively via the transformation procedure in (...) any first-order theory. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

A plausible reading of Berkeley’s view of voluntary motion is occasionalism; this, however, leads to a specious conclusion against his argument of human action. Differing from an unqualified occasionalist reading, I consider the alternative reading that Berkeley is a conservationist regarding bodily motion by the human mind at will. That is, finite minds (spirits) immediately cause motions in their body parts, albeit under the divine conservation. My argument then comports with the conservationist reading from three perspectives: (i) theodicy that the (...) human mind is held liable for sinful actions; (ii) an account of the human mind influencing other minds; and (iii) an improper but necessary directing principle of the human mind. This article is a stepping stone to grasping why the conservationist reading is more coherent than the occasionalist one. (shrink)

Tanabe Hajime, another pole of the so-called Kyoto-School of Philosophy of modern Japan, attempts to construct a dialectical, triadic logic of genus, species and individual as a creative synthesis between Eastern and Western philosophy. Although the formal pattern of his method is influenced by the Hegelian dialectic, the way of his thinking is rather prevailed by Kantian dualism. This makes a sharp contrast to his mentor Nishida Kitaro, whose logic of Topos or Place qua Absolute Nothingness is criticized as all-embracing (...) and static in character by him. The difference between them might be parallel to that of Greek and Latin theology concerning the Trinity. Tanabe never presupposes any preexistent entity as the primordial One in the eternal dimension, but rather maintains the individuality as the free subjective agent in the field of history. The dichotomy between the universal and the individual is overcome in and through the mediation of the third term— the species — as the negatively self-realized, specific form of the genus. The species, however, turns out to be the self-estrangement, when it loses the perpetually negative mediation of the free subjective activity of the individual. (shrink)

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

This article will consider how and why a pragmatist way of thinking is inferred in the Buddhist ethical discourse of curing the sick. This medical analogy, where the Buddha as a medical doctor acts upon the sick, contains a profound implication that the sick need not understand the reason for their sickness, insofar as they are cured or enlightened. What is taken to be pragmatism is critically clarified in this Buddhist context. There being a dissimilarity in terms of the respective (...) ends (ultimate nirvāṇa vs. end as a means to further ends), the two types of moral discourse—Buddhist ethics and American pragmatism—have a common ground. That is, the human is receptive to the utility of a moral end, in which truth works regardless of one’s understanding of its absolute, abstruse reason. (shrink)

We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s (...) Paradox in this framework. Furthermore, we define explicit and implicit self-reference in paradoxes in the incompleteness phenomena. (shrink)

Che 1-pu. Han'guk ŭi kaebyŏk -- 1. Kŭndae Han'guk konggongsŏng ŭi chŏn'gae wa t'aja waŭi yŏndae -- 2. Kŭndae Han'guk siminjŏk konggongsŏng ŭi sŏngnip -- 3. Taejonggyo pŏmt'unggusŭjuŭi wa pop'yŏnjuŭi -- Che 2-pu. Ilbon ŭi kaebyŏk -- 1. Kŭnse Ilbon sasang ŭi Sŏngin'gwan -- 2. Ilbon sinjonggyo ŭi kaebyŏk undong -- 3. Hyŏndae Ilbon ŭi saengmyŏng yŏngsŏng kwa ch'iyu yŏngsŏng -- Che 3-pu. Sirhak ŭi sigak -- 1. 19-segi sirhakcha ŭi Ilbon insik -- 2. Ch'oe Han-gi ŭi chonggyo hoet'ong sasang (...) -- 3. Han'guk, Ilbon, Chungguk e issŏsŏ 'Sinsirhangnon' pigyo -- Che 4-pu. Pigyo ŭi sigak -- 1. Ilbon esŏŭi T'oegye, Yulgok, Tasan yŏn'gu ŭi hŭrŭm -- 2. Ch'oe Han-gi wa Ilbon ŭi konggong sasangga pigyo yŏn'gu -- 3. Tongsŏyang konggongsŏng yŏn'gu wa Han'gukchŏk konggongsŏn. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

This article argues that George Berkeley’s (1685–1753) interpretation of scientific and religious language was significantly received in C.S. Peirce’s (1839–1914) pragmatist semiotic.1 To this end, their similar views against transubstantiation in the Eucharist (Lord’s Supper, Holy Communion) will be considered. Berkeley being an Anglican bishop and Peirce’s life being linked to the Episcopal Church,2 a chief emphasis will be placed upon Peirce’s deriving his pragmatic method from Berkeley’s philosophy of language. At least three times, Peirce reviewed Berkeley’s works, including Manuscript (...) Introduction (to the Principles of Human Knowledge, 1710), in which he identified his version of Berkeleyan nom- inalism. (shrink)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

Detection of genuine altruists could be a solution to the problem of subtle cheating. Brown et al. (Evol Psychol 1:42–69, 2003) found that humans could detect altruists using nonverbal cues. However, their experiments can be improved upon in several ways, and further investigation is needed to determine whether altruist-detection abilities are human universals. In our experiment, we used video clips of natural conversations as the stimulus. We asked a sample of Japanese undergraduates to rate their own level of altruism and (...) then to estimate the videotaped targets’ altruism using the same scale. The perceivers were able to estimate the targets’ altruism levels accurately. Perceivers’ altruism score did not affect their ability to discriminate between altruists and non-altruists. Perceivers’ impressions of the altruist and non-altruist targets were also found to be different. Coding of nonverbal behavior of the targets revealed that altruists exhibited more “felt smiles” than non-altruists, which also supports the results of the previous study. (shrink)

Nobody claims to be a proponent of white feminism, but according to the critique presented in this article, many in fact are. I argue that feminism that does not take multiple axes of oppression into account is bad in three ways: it strategically undermines solidarity between women; it risks inconsistency by advocating justice and equality for some women but not all; and it impedes the ultimate function of feminism function by employing epistemological “master’s tools” that stand in antithesis to feminist (...) emancipatory work. In investigating ethnocentrism in feminism, I develop the idea of latent ethnocentrism, which occupies the space between meaning that is generated from reference to the self and overt racism. I identify an epistemological prong in the ethnocentrism charge against feminism, where I draw on bell hooks’ interlocking axes-model of oppression to answer why the ethnocentrism problem is important for feminism and what its underlying epistemological causes are. I draw on Uma Narayan’s destabilization of cultural dualisms to argue that they do not serve emancipatory agendas. There is a mutually constitutive relation between language that informs our understanding, on the one hand, and the political agendas that produce this language to sustain the male and the western norm as center, on the other hand. I call this circular and reciprocally reinforcing mechanism the episteme-politic. I conclude that the ethnocentrism problem is not merely an issue of strategy or feminist consistency but of shooting oneself in the foot by uncritically accepting patriarchal concepts for feminist politics. (shrink)

The uniform continuity theorem states that every pointwise continuous real‐valued function on the unit interval is uniformly continuous. In constructive mathematics, is strictly stronger than the decidable fan theorem, but Loeb [17] has shown that the two principles become equivalent by encoding continuous real‐valued functions as type‐one functions. However, the precise relation between such type‐one functions and continuous real‐valued functions (usually described as type‐two objects) has been unknown. In this paper, we introduce an appropriate notion of continuity for a modulus (...) of a continuous real‐valued function on [0, 1], and show that real‐valued functions with continuous moduli are exactly those functions induced by Loeb's codes. Our characterisation relies on two assumptions: (1) real numbers are represented by regular sequences (equivalently Cauchy sequences with explicitly given moduli); (2) the continuity of a modulus is defined with respect to the product metric on the regular sequences inherited from the Baire space. Our result implies that is equivalent to the statement that every pointwise continuous real‐valued function on [0, 1] with a continuous modulus is uniformly continuous. We also show that is equivalent to a similar principle for real‐valued functions on the Cantor space. These results extend Berger's [2] characterisation of for integer‐valued functions on and unify some characterisations of in terms of functions having continuous moduli. (shrink)

På mange måter er dette en bok som blir utgitt alt for sent. Det er den første antologien av sitt slag, og retter fokus på kvinnelige metafysikere som virket i den tidlige moderne perioden (16. og tidlig 17. århundre). Redaktør Emily Thomas skriver i introduksjonen at til tross for at flere antologier om moderne metafysikk allerede finnes, er kvinnelige filosofer fortsatt underrepresentert og den filosofiske kanon mannsdominert. De ni filosofene som blir omtalt i totalt 13 kapitler var alle originale og (...) velkjente tenkere i sin samtid, men har blitt glemt i filosofihistoriens løp. (shrink)

The issue of justice after catastrophe is an enormous challenge to contemporary theories of distributive justice. In the past three decades, the controversy over distributive justice has centered on the ideal of equality. One of intensely debated issues concerns what is often called the “equality of what,” on which there are three primary views: welfarism, resourcism, and the capabilities approach. Another major point of dispute can be termed the “equality or another,” about which three positions debate: egalitarianism, prioritarianism, and sufficientarianism. (...) On these topics of distributive justice, authors are concerned with the current difference between the better-off and the worse-off or the present situation of the badly-off. By contrast, it is essential to take account of the past distribution of well-being as well as the present situation in order to explore questions of post-catastrophe justice. Without looking at the pre-disaster distribution of income, preference satisfaction, or basic capabilities among affected people, no present assessment of the damage caused by the disaster could be correct and no proposed remedy adequate. It is true that luck egalitarians assess the current distribution among people by referring to the decision that each individual made. Yet they pay scant attention to the situation in which each one stayed in the past. Therefore, we can legitimately say that most theorists of distributive justice, including luck egalitarians, have failed to give consideration to the past state of each person. -/- To fill this gap in the literature, the present article explores philosophical questions that arise when we take account of each person’s past and present situations in discussing distributive justice regarding public compensation and assistance to survivors and families of victims of natural and industrial disasters. In addressing these novel questions, I develop and refine various concepts, ideas, and arguments that have been presented in the study of distributive justice in normal settings. I tackle two tasks, the first of which is to explore the foundation and scope of luck egalitarianism. Despite the moral appeal it has in many cases, luck egalitarianism has attracted the so-called harshness objection. Some luck egalitarians attempt to avoid this objection in a pragmatic way by combining the luck egalitarian doctrine with the principle of basic needs satisfaction. However, they do not provide any systematic rationale for this combination. In contrast with such pragmatic responses, I seek to offer a principled argument for holding individuals responsible for their choices only when their basic needs are met, by invoking the ideas of respect for human voluntariness and rescue of human vulnerability. Based on this argument, I propose a form of responsibility-sensitive theory, which considers the pre-disaster distribution of well-being as a default position. The second task I take on is to refine sufficientarianism in the context of post-catastrophe justice. Luck egalitarianism with boundaries set by the basic needs principle seems to indicate the potential for sufficientarianism. But major proponents of this view conceive the welfarist assumption, a considerably high standard of well-being, and the controversial treatment of persons staying below the threshold, all of which seem problematic in the post-disaster situation. I try to construct a new version of sufficientarianism by replacing these current features with more robust ones. (shrink)

In the recent debate concerning the boundary of mind, the extended mind thesis (EMT), which states that our mind and cognition are extended into the environment, is influential as an antithesis to the internalist view, according to which mind and cognition are in the head. However, EMT has some serious difficulties. On the contrary to its proponents’ claim, EMT contributes neither to demystifying the mind, nor to promoting our understanding of cognition. Moreover, it leads to an extreme kind of individualism (...) by regarding environmental resources as constituents of individual human minds. After showing this, I explore an alternative anti-Cartesian picture of mind through citing Dewey’s view of the locus of mind. Although the proponents of EMT often invoke Dewey as a pioneer of their view, his view is in fact the one that should be called the ‘unbounded mind’ rather than the ‘extended mind’. Furthermore, I show that Dewey’s view indicates a root to overcome the individualistic dogma that is shared by internalists and the EMT theorists. (shrink)