This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of theoretical economics. This analysis is substantially expanded through a dynamic approach, where the truth of a valuation results in an updated interpretation or changes in the agent's subjective belief regarding the effectiveness of the selected action as well as the objective reality of the effectiveness of all other (...) possible actions (i.e. consequence realization). Complications arise when the economic agent is presented with a set of actions that render ambiguous preference, or when the effectiveness of an action cannot be perceived upon its selection, thereby necessitating a different theory of choice and consequence realization. (shrink)

In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson’s nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius and Russell, which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors (...) suggested. Unlike Arntzenius’s proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell’s proposal and does not retreat to mere finite additivity. (shrink)

I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry based on certain algebraic objects, which regiments a mode of reasoning heuristically used by geometricists and physicists. I argue that SIG has the following utilities. It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. It generalizes a standard implementation of spacetime algebraicism called Einstein algebras. It solves the long-standing problem of (...) interpreting smooth infinitesimal analysis realistically, an alternative foundation of spacetime theories to real analysis, 277–392, 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations. Against this, I argue that SIG is such a reformulation. But SIG has an unorthodox mereology, in which the principle of supplementation fails. (shrink)

I visited Professor Hintikka and discussed with him about ten times during my visit to Harvard University from 2000 to 2001. I can still vividly remember my first visit to him in his office and then Jaakko inviting me for lunch in the BU faculty club, including how I tried my best to ‘show’ my knowledge of Aristotle and Frege, with a hope that it was my first but not the last talk with him and how really excited I was (...) when he kindly said to me after lunch: “You are welcome to visit me again at the same time in two weeks”. In my view Hintikka was a brilliant philosopher and logician, and also a very kind and engaging person from and with whom one can constantly learn new ideas without limitations. (shrink)

I visited Professor Hintikka and discussed with him about ten times during my visit to Harvard University from 2000 to 2001. I can still vividly remember my first visit to him in his office and then Jaakko inviting me for lunch in the BU faculty club, including how I tried my best to ‘show’ my knowledge of Aristotle and Frege, with a hope that it was my first but not the last talk with him and how really excited I was (...) when he kindly said to me after lunch: “You are welcome to visit me again at the same time in two weeks”. In my view Hintikka was a brilliant philosopher and logician, and also a very kind and engaging person from and with whom one can constantly learn new ideas without limitations. (shrink)

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions. (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If (...) logic is a necessary instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s official answer to these questions centers on three distinctions: general versus particular logic; pure versus applied logic; pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, I argue, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined ‘transcendental logic’ while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, I reassess the place of Kant’s theory in the history of philosophy of logic and highlight certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism. In Chapter 1, “Kant and a Philosophical History of Logic – Methodological Reflections,” I discuss certain exegetical challenges posed by Kant’s logic corpus and argue for a “history of philosophical problems” method by which to reconstruct a Kantian theory of logic. In Chapter 2, “The Nature and Place of Logic – A History of Controversies,” I construct a partial history of philosophy of logic that revolves around the (supposedly) scientific status of logic on the one hand and its value or utility on the other. In Chapter 3, “The Making of a Scientific Logic from Bacon to Wolff,” I examine how four representative early modern philosophers – Francis Bacon, John Locke, G.W. Leibniz, and Christian Wolff – approached the four questions mentioned above. In Chapter 4, “Kant on the Way to His Own Philosophy of Logic,” I consider how Kant, in the decade between around mid-1760s and mid-1770s, navigated between existing accounts of logic until he finally found his own voice. I highlight the breakthroughs that would mark his critical departures from previous views and pave the way for the final articulation of his own view. In Chapter 5, “Logic and the Demands of Kantian ‘Science’,” I zero in on Kant’s official theory of logic in his monumental publication, Critique of Pure Reason. I foreground both what makes the theory original and what leaves it vulnerable to criticisms from post-Kantian thinkers. (shrink)

Mit seiner Summa Logicae, einer umfangreichen und systematischen Darstellung der aristotelischen Logik, gilt Ockham als einer der größten Logiker des Mittelalters. Dort entwickelt Ockham seine Modallogik zu einer systematischen Größe, die nicht zuletzt mittelalterliche Innovationen und Entdeckungen enthält, wie z.B. Gesetze modaler Aussagenlogik, die Aristoteles nicht kennt. In der vorliegenden Arbeit wird bemüht, solche Aspekte systematisch darzustellen. Der formale Teil der vorliegenden Untersuchung wird durch eine ausführliche semantische Analyse der Modalbegriffe bei Ockham ergänzt, die zeigen soll, wie Ockhams Modallogik mit (...) seiner Ontologie zusammenhängt. Dabei wird für die These argumentiert, daß hinsichtlich der Bedeutung der Modalbegriffe bei Ockham ein Pluralismus vorzufinden ist, der den Schlüssel zur Interpretation von Ockhams Lösung zu dem sogenannten Seeschlacht-Problem bietet, das seit Aristoteles Generationen von Philosophen und Interpreten beschäftigt und zu neuen Entwicklungen der Logik angeregt hat. (shrink)

At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)

There is an exegetical quandary when it comes to interpreting Locke's relation to logic.On the one hand, over the last few decades a substantive amount of literature has been dedicated to explaining Locke's crucial role in the development of a new logic in the seventeenth and eighteenth centuries. John Yolton names this new logic the "logic of ideas," while James Buickerood calls it "facultative logic."1 Either way, Locke's Essay is supposedly its "most outspoken specimen" or (...) "culmination."2 Call this reading the 'New Logic interpretation.'On the other hand, from the typical standpoint of a philosopher accustomed to the modern conception of logic, whatever Locke—indeed, whatever most of the... (shrink)

John Venn has the “uneasy suspicion” that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kant’s “disastrous effect on logical method,” namely the “strictest preservation [of logic] from mathematical encroachment.” Kant’s actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Euler’s circles and comparing it with Euler’s own use. I do so in light of the developments in logical calculus from (...) G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion (...) of logical extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

Kant claims that Aristotles logic as complete, explain the historical and philosophical considerations that commit him to proving the completeness claim and sketch the proof based on materials from his logic corpus. The proof will turn out to be an integral part of Kant’s larger reform of formal logic in response to a foundational crisis facing it.

In this chapter, I discuss some problems of Kant’s logic corpus while recognizing its richness and potential value. I propose and explain a methodic way to approach it. I then test the proposal by showing how we may use various mate- rials from the corpus to construct a Kantian demonstration of the formal rules of thinking (or judging) that lie at the base of Kant’s Metaphysical Deduction. The same proposal can be iterated with respect to other topics. The said (...) demonstration will have cleared the path for such iterations. (shrink)

How "red", "green" were defined? Through analyzing how two children with congenitally inverted color sensations corresponding to red flags and green grass accept their grand mothers’ teaching about colors, the paper get opposite conclusions against logical empiricism. The “red” and “green” and other names of properties of objects were defined by objective physical properties (or together with behavior, such as in defining “beauty”), instead our sensations. So language directly points to things in themselves passing through sensations and presentative world. It (...) is not that things in themselves are unknowable, but that sensations and presentative world cannot be exactly described by daily language. (shrink)

Abstract:In classical Greek philosophy, the pursuit of Truth was done primarily through logical argumentation using language as “Truth tool.” The major thinkers in classical China, on the other hand, were famously suspicious of language, with Confucius declaring, “I wish to be wordless.” They turned instead to music to express the philosophically ineffable. In this paper, we use the example of the Chinese guqin to show how music serves as “Truth tool” in the Chinese philosophical tradition; in fact, music may be (...) Truth itself. Through a quartet of interrelated themes–namely, the “Search for Truth,” the “Search for Harmony,” the “Search for Ethical Awakening,” and the “Search for Sagehood”–we show how playing the guqin constitutes the doing of philosophy in this musical tradition. Through the guqin, performers and listeners experience Confucian, Daoist, and Buddhist philosophical insights; no words are needed. We conclude by proffering implications for contemporary music education. (shrink)

How to make sense of Kant's theory of radical evil is a controversial problem, for the solution of which three approaches have been attempted: (1) the anthropological, (2) the transcendental, and (3) the quasi‐transcendental. This article aims at developing a new quasi‐transcendental approach to radical evil, and its main innovation consists in reinterpreting the propensity to evil as a potential for moral evil, whose nuanced modality (i.e., potentiality) lies between full actuality and logical (empty) possibility. This evil potential inherent to (...) our species' nature can be actualized by individual Willkür in one's evil Gesinnung. Thanks to this reinterpretation, not only the compatibility of radical evil with individual freedom will be convincingly demonstrated, because the potential for evil only strongly pushes rather than necessitating individuals to do evil, but also Kant's bold statement “the human being is by nature evil” becomes easily confirmable, because even a single individual's illegal action provides sufficient empirical evidence to a regressive argument for the transcendental precondition for evil in his species' nature. (shrink)

Kant describes logic as “the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking”. (Bviii-ix) But what is the source of our cognition of such rules (“logical cognition” for short)? He makes no concerted effort to address this question. It will nonetheless become clear that the question is a philosophically significant one for him, to which he can see three possible answers: those representations are innate, derived from experience, or originally acquired a priori. (...) Although he gives no explicit argument for the third answer, he seems committed to it—especially given his views on the source of pure concepts of the understanding and on the nature of logic. It takes careful preparatory work to gather all the essential materials for motivating and reconstructing Kant’s “original acquisition” account of logical cognition. I shall proceed in two sections. In section 1, I analyze Kant’s argument that pure concepts of the understanding (or intellectual concepts)—as one kind of pure cognition—must be acquired originally and a priori. My analysis partly concerns his varied attitudes toward Crusius’s and Leibniz’s versions of the nativist account of such concepts. I give special attention to how Kant characterizes the nativist account and his own “original acquisition” account in terms of “preformation” and “epigenesis”. My goal is, firstly, to tease out the sense in which Kant grants that there must be an innate ground (or preformation) for the derivation of pure concepts and, secondly, to introduce—and pave the way for answering—the question about the source of logical cognition. In section 2, in light of Kant’s reference to Locke and Leibniz as the greatest reformers of philosophy (including logic) in their times (Log, AA 9: 32), I examine the Lockean and Leibnizian approaches to logic, respectively. Both approaches are “physiological” by Kant’s standard and are directly opposed to his own strictly critical method. I explain how this methodological move shapes Kant’s view that representations of logical rules must be originally acquired a priori. This acquisition involves a kind of radical epigenesis of pure reason: unlike the acquisition of pure concepts, it presupposes no further innate ground (or preformation). This view will have important consequences for issues such as the ground of the normativity of logical rules and the boundaries of their rightful use. (shrink)

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address these (...) challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)

ABSTRACT We are concerned with the theorem proving in annotated logics. By using annotated polynomials to express knowledge, we develop an inference rule superposition. A proof procedure is thus presented, and an improvement named M- strategy is mainly described. This proof procedure uses single overlaps instead of multiple overlaps, and above all, both the proof procedure and M-strategy are refutationally complete.

This paper examines Du Châtelet’s and Kant’s responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742) and Kant in his debut, the Thoughts on the True Estimation of Living Forces (1746–49). The Institutions was not only a highly influential contribution to the vis viva controversy, but also a pioneering attempt to integrate Leibnizian metaphysics and Newtonian physics. The young Kant’s evident knowledge of this work has led some to speculate about his indebtedness to her (...) philosophy. My study corrects such speculations as well as misunderstandings of the Living Forces. This corrective result has implications for how to investigate Kant’s relation to the ever-evolving landscape of Leibniz exegeses. (shrink)

Research into logical syntax provides us the knowledge of the structure of sentences, while logical semantics provides a window into uncovering the truth of sentences. Therefore, it is natural to make sentences and truth the central concern when one deals with the theory of meaning logically. Although their theories of meaning differ greatly, both Michael Dummett’s theory and Donald Davidson’s theory are concerned with sentences and truth and developed in terms of truth. Logical theories and methods first introduced by G. (...) Frege underwent great developments during the past century and have played an important role in expanding these two scholars’ theories of meaning. (shrink)

Events have beginnings, ends, and often overlap in time. A major question is how perceivers come to parse a stream of multimodal information into meaningful units and how different event boundaries may vary event processing. This work investigates the roles of these three types of event boundaries in constructing event temporal relations. Predictions were made based on how people would err according to the beginning state, end state, and overlap heuristic hypotheses. Participants viewed animated events that include all the logical (...) possibilities of event temporal relations, and then made temporal relation judgments. The results showed that people make use of the overlap between events and take into account the ends and beginnings, but they weight ends more than beginnings. Neural network simulations showed a self‐organized distinction when learning temporal relations between events with overlap versus those without. (shrink)

With the rapid development of the Internet, political culture plays an increasingly prominent role in ethical guidance and value orientation, and the intergenerational inheritance of political culture in various countries needs to be carried out in a sophisticated way. From the perspective of empathic narrative, this study applies the network text analysis method to detect the cultural communication regularities to the contemporary young adults in online political communication and explores contemporary young adults’ perception of online political culture through empirical analysis. (...) Moreover, it proposes the empathic narrative logic of online political communication by comparing the existing communication elements and the urgently needed communication elements. Our findings suggest that we need to deepen the cognitive empathy, stabilize the emotional empathy, and adjust the emotional bias in online political communication. (shrink)

本书分析了因明发展中自身的逻辑线索,对因明中所包含的知识论、逻辑学、论辩学的内容作分别的研究。.

Based on the text Zhong Yong 中庸, this article clarifies the phenomenological experience of genuineness. The Introduction presents the discussion of genuineness-substance from Zhou Dunyi 周敦頤 and Mou Zongsan 牟宗三, pointing out their omission of the concrete activity of genuineness. Section 2 explains concepts such as ti 體, the endowment of Heaven, the original nature, right, norm, with an indication that genuineness denotes keeping and developing an original status. Section 3 then shows that the original status of human nature is (...) the endowment of emotion, reason, will, and so on, and the original status of the Heavenly way is the tendency of [ceaseless] growing. Under a holistic view, Section 4 expounds in detail the meaning of the statements “from genuineness to illumination” and “from illumination to genuineness” by making use of the distinction between nascent genuineness and refined genuineness. Section 5 reveals the creativity of genuineness in terms of the activating effect, which is caused by human beings’ exertion of their potentials. From the perspective of Zhong Yong, this section also demonstrates the inner logic by which Neo-Confucianism is developed and differentiated into the learning of the heart-mind and the learning of pattern. This section also examines whether or not Zhu Xi’s 朱熹 doctrine is unorthodox, as Mou Zongsan proposes. (shrink)

The Linguistic Turn had a great impact and brought about global changes in the objects, methods, and styles of many twentieth-century philosophical works. However, a considerable number of Chinese scholars and philosophers nowadays think that the Linguistic Turn has already passed. Some of them are even of the opinion that the immediate products of the Linguistic Turn, such as analytic philosophy and the philosophy of language, are by now outdated. In their view, this is an inevitable consequence of the Linguistic (...) Turn, as this revolutionary change in philosophy was based on the inherently limited methods of mathematical logic: structural methods and greatly restricted methods of language analysis. Therefore, analytic philosophy and the philosophy of language could never resolve basic philosophical and, especially, metaphysical questions. (shrink)

The thin set theorem for n-tuples and k colors states that every k-coloring of $[\mathbb {N}]^n$ admits an infinite set of integers H such that $[H]^n$ avoids at least one color. In this paper, we study the combinatorial weakness of the thin set theorem in reverse mathematics by proving neither $\operatorname {\mathrm {\sf {TS}}}^n_k$, nor the free set theorem imply the Erdős–Moser theorem whenever k is sufficiently large. Given a problem $\mathsf {P}$, a computable instance of $\mathsf {P}$ is universal (...) iff its solution computes a solution of any other computable $\mathsf {P}$ -instance. It has been established that most of Ramsey-type problems do not have a universal instance, but the case of Erdős–Moser theorem remained open so far. We prove that Erdős–Moser theorem does not admit a universal instance. (shrink)

By the Riesz representation theorem for the dual of C [0; 1], if F: C [0; 1] → ℝ is a continuous linear operator, then there is a function g: [0;1] → ℝ of bounded variation such that F = ∫ f dg . The function g can be normalized such that V = ‖F ‖. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows (...) to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S ′ mapping F and its norm to some appropriate g. (shrink)

Let $\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\Gamma$ that preserve sides. We classify the closed permutation subgroups containing the group $\operatorname {Aut}(\Gamma)^{\ast}$ , where $\operatorname {Aut}(\Gamma)^{\ast}$ is the group of all isomorphisms and anti-isomorphisms of $\Gamma$ preserving the two sides. Our results rely on a combinatorial theorem of Nešetřil and Rödl and a strong (...) finite submodel property for $\Gamma$. (shrink)

The concept of fuzzy Galois connections is defined on fuzzy posets with Bělohlávek's fuzzy Galois connections as a special case. The properties of fuzzy Galois connections are investigated. Then the relations between fuzzy Galois connections and fuzzy closure operators, fuzzy interior operators are studied.

Theorists, historians, and artists address the precarious futurity of the notion of the future. Not long ago, a melancholic left and a manic neoliberalism seemed to arrive at an awkward consensus: the foreclosure of futurity. Whereas the former mourned the failure of its utopian project, the latter celebrated the triumph of a global marketplace. The radical hope of realizing a singularly different, more equitable future displaced by a belief that the future had already come to pass, limiting post-historical society to (...) an uneventful life of endless accumulation. Today, amidst an abundance of neofuturisms, posthumanisms, futurologies, speculative philosophies and accelerationist scenarios, there is as well an expanding awareness of a looming planetary catastrophe driven by the extractionist logic of capitalism. Despite this return to the future, the temporal horizon of our present moment is perhaps more aptly characterized by the “shrinking future” of just-in-time production, risk management, high-frequency trading, and the futures market. In Futurity Report, theorists, historians, and artists address the precarious futurity of the notion of the future itself. Contributors McKenzie Wark, China Miéville, Kerstin Stakemeier, Diedrich Diederichsen, Natascha Sadr Haghighian, Marina Vishmidt, Johannes Paul Raether, Felicity D. Scott, Silvia Maglioni, Graeme Thomson, Doreen Mende, Pedro Neves Marques, Achille Mbembe, Kodwo Eshun, Haytham El-Wardany, T. J. Demos, Ana Teixeira Pinto. (shrink)

This book is a masterpiece on Kant's theory of analyticity. It culminates in a new story of how Kant arrived at his mature view. Here is the chief lesson of this story: "the logical conception of the analytic/synthetic distinction is the fundamental idea of analyticity involved in Kant's distinctive, critical project. … [H]is critique of metaphysics crucially depends on the logical conception and cannot be supported by its merely methodological and epistemological ancestors". This passage consolidates two leading theses of the (...) book: Kant has three versions of the analytic/synthetic distinction: a methodological distinction between two ways of knowing, an epistemological one between two kinds of concept... (shrink)

The generalized Brans–Dicke theory (GBD), as one of the modified gravitational theories, was proposed previously and some interesting properties were found in this theory. Here we investigate the traversable-wormhole physics for GBD theory. Firstly, we derive the gravitational field equation in the framework of GBD wormhole geometry. The traversable wormhole could be gained in this theory. Secondly, using the classical reconstruction technique we originally derive an Lagrangian function for describing gravity in GBD theory. And the derived Lagrangian function for gravity (...) could be satisfied with the requirement of the viable conditions, such as the local gravity tests and the cosmological constraints, etc. Thus, the viable model for cosmology, local gravity and traversable WH can be unified in a uniform Lagrangian quantity within the framework of GBD theory. Thirdly, given that the violation of the energy conditions (ECs) often induce some problems in theory, we explore the ECs of matter in the traversable wormhole. It is shown that the null EC, the weak EC and the dominated EC for the matter can be satisfied in the traversable-wormhole physics of GBD theory, which are different from the results given in GR. It seems that the theory of GBD owns the more logic technically and consistency formally than the theory of GR. Fourthly, some other properties of GBD traversable WH are explored, such as the total gravitational energy, the volume integral quantifier, the dynamical stability of the anisotropic matter, and the difference of the propagation of sound within the matter configuration. The results support the GBD to provide an interesting candidate for traversable WH. (shrink)

Understanding a proposition for an intelligent agent is an important epistemic concept. We first discuss intuitively general logic characteristics of understanding, and give a language and a semantics containing understanding as a modal operator. Secondly, we develop the system LU for the operator, give some results of its proof theory, and then we prove the frame soundness and frame completeness of LU.

A critical discussion of Lu-Adler's chapter on Kant's mature view of pure general logic. I sketch an alternative interpretation of its formality on which Kant would hold no deduction is possible of this logic's laws.

Understanding a proposition for an intelligent agent is an important epistemic concept. We first discuss intuitively general logic characteristics of understanding, and give a language and a semantics containing understanding as a modal operator. Secondly, we develop the system LU for the operator, give some results of its proof theory, and then we prove the frame soundness and frame completeness of LU.