The strong continuity principle reads “every pointwise continuous function from a complete separable metric space to a metric space is uniformly continuous near each compact image.” We show that this principle is equivalent to the fan theorem for monotone \ bars. We work in the context of constructive reverse mathematics.

In the context of constructive reverse mathematics, we show that weak Kőnig's lemma () implies that every pointwise continuous function is induced by a code in the sense of reverse mathematics. This, combined with the fact that implies the Fan theorem, shows that implies the uniform continuity theorem: every pointwise continuous function has a modulus of uniform continuity. Our results are obtained in Heyting arithmetic in all finite types with quantifier‐free axiom of choice.

A function from Baire space to the natural numbers is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer‐operation (i.e., inductively defined neighbourhood function); the other is a function uniformly continuous near every compact image. We show that formal continuity is equivalent to the former while it is strictly (...) stronger than the latter. The equivalence of formally continuous functions and those induced by Brouwer‐operations requires Countable Choice. (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)

We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion (...) of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID. (shrink)

We characterize the category of Sambin’s positive topologies as the result of the Grothendieck construction applied to a doctrine over the category Loc of locales. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the constructed adjunction.

We identify bar recursion on moduli of continuity as a fundamental notion of constructive mathematics. We show that continuous functions from the Baire space \ to the natural numbers \ which have moduli of continuity with bar recursors are exactly those functions induced by Brouwer operations. The connection between Brouwer operations and bar induction allows us to formulate several continuity principles on the Baire space stated in terms of bar recursion on continuous moduli which naturally characterise some variants of bar (...) induction. These principles state that a certain kind of continuous function from \ to \ admits a modulus of continuity with a bar recursor. The results for the Baire space are recast in the setting of the Cantor space \ using the notion of fan recursor, a bar recursor for binary trees. This yields characterisations of uniformly continuous functions on the Cantor space and fan theorem in terms of fan recursors. The results for the Cantor space hold over the extensional version of intuitionistic arithmetic in all finite types ), and those for the Baire space hold over \ extended with the type for Brouwer operations. Our work places Spector’s bar recursion in a proper context of Brouwer’s intuitionistic mathematics and clarifies the connection between bar recursion and bar induction. (shrink)

We characterize the category of Sambin’s positive topologies as the result of the Grothendieck construction applied to a doctrine over the category Loc of locales. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the constructed adjunction.

This study investigates metaphoric gestures in face-to-face conversation. It is found that gestures of this kind are mainly performed in the central gesture space with noticeable and discernable configurations, providing visible evidence for cross-domain cognitive mappings and the grounding of conceptual metaphors in people's recurrent bodily experiences and in what people habitually do in social and cultural practices. Moreover, whether metaphorical thinking is conveyed by gesture exclusively or along with metaphoric speech, the manual enactment of even conventional metaphors manifests dynamism (...) in communicating metaphors. Metaphoric gestures can provide salient, additional information about the aspect of the conceptualization which is the speaker's focus of attention in real-time multimodal communication. (shrink)

Many systems of thoughts have migrated to Japan from abroad - Buddhism, Taoism, Confucianism, natural science, Marxism; all were transmitted to Japan and stopped there. It is said that Japan has been the terminus for imported thoughts. However, during the process of taking root in Japan almost every idea has been transformed within the Japanese mind. I would like to discuss a typical example of how Christianity has been changed within the Japanese mind.

The present study claims that the use of spontaneous gestures can contribute to accomplishing coherence in sequential conversational exchanges. Three types of speech-accompanying gestures were analyzed in Chinese conversation. Based on the syntactic-semantic relation with the co-occurring utterance, the first type is associated with words that do not convey explicit meaning; the second type is associated with covert constituents; the third type does not have any linguistic affiliates. They suggest different ways in which gesture adds information to the propositional content (...) of the associated utterance or to the content of the speech event under discussion. They also play a role in achieving conversational coherence: on the part of the speaker, it is only by using the various types of gesture that a current speaker can make the message to be conveyed in the utterance complete. On the part of the next speaker, the recognition and negotiation with the former speaker of the gestured information is a way to acknowledge or confirm mutual knowledge. The collaborative efforts contribute to the coherence of the talk in the subsequent interaction. (shrink)

The study investigates the manifestation of the “IDEA-IS-AN-ENTITY” metaphor across the linguistic and manual modalities by the use of the object gesture in daily conversation, to understand the relationship between metaphorical conceptualization and the context of use. Two types of the entity metaphor were distinguished: “cross-modal entity metaphor” and “gesture-only entity metaphor.” For the former, the metaphor was expressed by metaphorical speech and the object gesture simultaneously. Among all of the 67 cross-modal instances, a wide variety of idea was represented (...) as referring, characterizing, and quantifying referents in speech. Manually, the object gesture was configured in numerous ways. The way the object gesture was configured reveals the facet of the metaphorical conceptualization the speaker focuses on during speaking, and the details about the real-time thinking of a metaphorical object in discourse. For the gesture-only entity metaphor, it was manifested in the single modality of gesture. Among all of the 73 gesture-only instances, the object gesture depicted a stretch of talk as discrete object mainly by configuring a spatial boundary with curled fingers. Metaphor of this type attests that the thinking of phrasal-clausal ideas as entities is as common as that of lexical ideas as entities in conversation. Importantly, the object gesture bears out the emergence of a phrasal or clausal idea being conceptualized as object in natural discourse. Together, the findings demonstrate the inseparability of metaphorical conceptualization from cognition and the context of use. (shrink)

Background One of the biggest challenges of practicing medicine in the age of informational technology is how to conciliate the overwhelming amount of medical-scientific information with the multiple patients’ values of modern pluralistic societies. To organize and optimize the the Decision-Making Process of seriously ill patient care, we present a framework to be used by Healthcare Providers. The objective is to align Bioethics, Evidence-based Practice and Person-centered Care. Main body The framework divides the DMP into four steps, each with a (...) different but complementary focus, goal and ethical principle. Step 1 focuses exclusively on the disease, having accuracy is its ethical principle. It aims at an accurate and probabilistic estimation of prognosis, absolute risk reduction, relative risk reduction and treatments’ burdens. Step 2 focuses on the person, using empathic communication to learn about patient values and what suffering means for the patient. Emphasis is given to learning and active listening, not taking action. Thus, instead beneficence, we trust comprehension and understanding with the suffering of others and respect for others as autonomous moral agents as the ethical principles of Step 2. Step 3 focuses on the healthcare team, having the ethics of situational awareness guiding this step. The goal is, through effective teamwork, to contextualize and link rates and probabilities related to the disease to the learned patient’s values, presenting a summary of which treatments the team considers as acceptable, recommended, potentially inappropriate and futile. Finally, Step 4 focuses on provider-patient relationship, seeking shared Goals of Care, for the best and worst scenario. Through an ethics of deliberation, it aims for a consensus that could ensure that the patient’s values will be respected as well as a scientifically acceptable medical practice will be provided. In summary: accuracy, comprehension, understanding, situational awareness and deliberation would be the ethical principles guiding each step. Conclusion Hopefully, by highlighting and naming the different perspectives of knowledge needed in clinical practice, this framework will be valuable as a practical and educational tool, guiding modern medical professionals through the many challenges of providing high quality person-centered care that is both ethical and evidence based. (shrink)

立法・法改正論争が盛んな現代日本の法理論の背後にあるものを理解するため、幕末から新憲法までの法思想の道筋を辿る。.

dai 1-kan. Sandō heikō hen -- dai 3-kan. Shintō soku kokutai mon -- dai 4-kan. Judō soku keisei mon -- dai 5-6-kan. Butsudō soku gedatsu mon -- dai 7-kan. Shoshi soku hyakka mon -- dai 8-9-kan. Keisei jiron hen -- dai 10-kan. Shisō oyobi shukan hen.

西洋近代を経験した東アジア各国はいかに固有の哲学を生み出しそして今どんな〈世界哲学〉の構想が可能なのか。国際共同研究の成果。.

20世紀日本を代表する哲学者の今日的意味とは?求真会主催のもと気鋭の執筆者が集ったシンポの記録。本邦初訳フッサール書簡収録。.

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

Transvertebral magnetic stimulation (TVMS) of the human lumbar spinal cord can evoke bilateral rhythmic leg movements, as in walking, supposedly through the activation of spinal locomotor neural circuitry. However, an appropriate stimulus intensity that can effectively drive the human spinal locomotor circuitry to evoke walking-like movements has not been determined. To address this issue, TVMS was delivered over an intervertebral space of the lumbar cord (L1–L3) at different stimulus intensities (10–70% of maximum stimulator output) in healthy human adults. In a (...) stimulus intensity-dependent manner, TVMS evoked two major patterns of rhythmic leg movements in which the left-right movement cycles were coordinated with different phase relationships: hopping-like movements, in which both legs moved in the same direction in phase, and walking-like movements, in which both legs moved alternatively in anti-phase; uncategorized movements were also observed which could not be categorized as either movement type. Even at the same stimulation site, the stimulus-evoked rhythmic movements changed from hopping-like movements to walking-like movements as stimulus intensity was increased. Different leg muscle activation patterns were engaged in the induction of the hopping- and walking-like movements. The magnitude of the evoked hopping- and walking-like movements was positively correlated with stimulus intensity. The human spinal neural circuitry required a higher intensity of magnetic stimulation to produce walking-like leg movements than to produce hopping-like movements. These results suggest that TVMS activates distinct neural modules in the human spinal cord to generate hopping- and walking-like movements. (shrink)

Studies with primates in sequence production tasks reveal that chimpanzees make action plans before initiating responses and making on-line adjustments to spatially exchanged stimuli, whereas such planning isn't evident in monkeys. Although planning may rely on phylogenetically newer regions in the inferior parietal lobe – along with the frontal lobes and basal ganglia – it dates back to as far as five million years ago.

Following Dirac's generalized canonical formalism, we develop a quantization scheme for theN-dimensional system described by the Lagrangian $L_0 (\dot y,y) = \frac{1}{2}h_{ij} (y)\dot y^i \dot y^j + b_i (y)\dot y^i - w(y)$ which is supposed to be invariant under the gauge transformation $y^i \to y\prime ^i = y^i + (\rho ^i _\alpha + \sigma ^i _{\alpha j} \dot y^j )\delta \Lambda ^\alpha + \tau ^i _\alpha \delta \dot \Lambda ^\alpha$ . The gauge invariance necessarily implies that the Lagrangian is singular. (...) The identities imposed by the gauge invariance are enumerated and reduced to simpler forms. There are primary and secondary constraints, both of which are of first class. The reduced identities are solved explicitly for the case where the secondary constraints constitute the generators of the groupSO(M), and thus an explicit expression for the manifestly gauge-invariant Lagrangian is obtained. By fixing the gauge appropriately, the unphysical variables are eliminated and a quantization is achieved using only physical variables. Our formulation is covariant under an arbitrary point transformation of physical variables. The problem of formulating a quantum action principle is also commented on briefly. (shrink)

ABSTRACTThreat detection is crucial to survival. Studies using unnatural visual scene settings have shown that humans and primates are able to identify snakes more quickl...

One of our recent studies has revealed that a numerically trained chimpanzee can memorize a correct sequence of five numbers shown on a monitor. Comparative investigations with humans show very similar patterns of errors in the two species, suggesting humans and chimpanzee share homologous memory processes. Whether or not 5 is a pure capacity limit for the chimpanzee remains an empirical question.

Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL c( $\dot x$ , x)=(M/2)gij(x) $\dot x$ i $\dot x$ j−v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point (...) transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian. (shrink)