Mathematical Epistemology from a Peircean Semiotic Point of View

Learning is better than knowing, generalization is more illuminating than abstract generality or universality because we perceive and thus become conscious of change or development only. Signs and representations establish the dialectic of fixation on the one hand and transformation on the other, which is so essential to learning and cognition. Mathematical epistemology from a semiotic point of view therefore is above all a genetical epistemology. All real mathematical activity is concerned with representations of mathematical entities rather than with things in themselves and with the processes of continuous transformation of a given representation into others. This paper tries to give an overview of the essential relationships between activity theory, epistemology and mathematical education, using the semiotics of Charles S. Peirce as a unifying reference. It is certainly beyond the scope of such a paper to spell out all the questions involved in every detail. Much of what is said in the four short sections to follow is calling for further concretization and research.     

Critical Thinking about Truth in Teaching: The epistemic ethos

This paper discusses the most persistent controversial issue that occurred in Western educational philosophy ever since Socrates questioned the Sophists: the role of truth in teaching. Ways of teaching these kinds of controversy issues are briefly considered to isolate their epistemic characteristics, which will enable the interpretation of Plato and Dewey as exemplars of rationalism and empiricism regarding the role of knowledge in the curriculum and thus include their partial truths in the epistemic ethos of teaching. The consideration of pedagogy will then include the partial truths of rationalism and empiricism in the epistemic ethos of teaching by following Kant's 'Concepts without percepts are empty; perceptions without conceptions are blind'.
This claim, however, is narrowed down in two ways compatible with postmodernism and the heavy emphasis on constructionism in faculties of education. After quoting Harry Broudy's statement that the educational epistemic ethos should be domain-specific, guided by the experts' inquiry protocols in each curricular area, it is narrowed down further with Maxine Greene's explication that it should be pluralistic and lesson-specific. This epistemic ethos is not argued as a synthesis but as an aggregate of the partial truths of various epistemologies in the spirit of the postmodern doubt in any one theory of knowledge without throwing out the baby with the dirty bath water.
Finally, the streams of consciousness involved in teaching and learning good knowledge are described phenomenologically to disclose how truth can be disclosed in teaching, thereby grounding propositional knowledge, for example, ontologically in the being of the student and in the being of the world.     

皮尔士与量词

量词是逻辑学尤其是现代逻辑中的一个核心概念，在逻辑分析和语言分析中有着特别的重要性，不少人认为是弗雷格首次给出了量词的现代逻辑意义，但事实上皮尔士对于量词有着更为清晰、深刻的理解和表述。他提出了代数和图表的两种表现形式、而且还给出了量词的深刻的指号学语境。     

现代西方哲学家论模糊性的本质

伴随现代西方哲学的“语言的转向”, “语言的模糊性”得到深入探讨。皮尔斯是西方哲学史上确认“语言本身的模糊性”的第一位哲学家; 维特根斯坦强调语言确定性与模糊性的并存关系, 并试图将二者统一; 罗素从符号逻辑的水平上首次打破了古典逻辑的排中律, 开辟了形式化模糊逻辑或多值逻辑的研究道路。     

皮尔士心中的逻辑学：从科学分类法来看

皮尔士试图从科学分类法阐明逻辑学与其他科学之间的诸种关联,从而让我们看到一个既有所主张又有所保留、既充分包容又严格限定的逻辑科学：1.逻辑学作为实证科学,被归在哲学分部中,位居数学这一非实证科学之后;2.即便在哲学内部,逻辑学作为规范科学也不是处在第一位,形而上学倒是排在逻辑学之后,但在逻辑学之前存在着现象学这一哲学分支,而且在规范科学内部还有伦理学、美学位居逻辑学之前;3.逻辑学自身也是一个复杂的学科体系,其不仅关注论证有效性的批判论即今天通常意义上的逻辑,而且把理论意义上的语法和修辞也包括在内。     

信息时代符号幻象性断想

在高度信息化社会里 ,符号的幻象性已引起了人们的广泛关注。符号之所以能够建构幻象世界 ,是由其本身特点——移位性和任意性决定的 ,同时也离不开人的认识参与。符合的幻象性所带来的效应是正反两方面的 ,关键在于我们人类怎么利用它。     

皮尔士对康托连续统的哲学批判

皮尔士对于康托连续统给予高度评价,同时又从概念层面上予以批判。他从逻辑学考察出发,指出康托连续统并非几何直观意义上的连续统,因而是＂伪连续统＂。皮尔士依据无穷小理论所界定的非度量性的连续统观念,为现代数学的基础批判提供了有益启示。     

论皮尔士与索绪尔符号学观中的相通之处

国内符号学研究往往把皮尔士和索绪尔分别当作现代符号学的两支源头．认为二者观点互不相干,然而经仔细研究．二者的符号学观中却有惊人的相似之处,具体体现在其反对的对象,符号及符号学界定,符号意义,作用,分类,发展及符号的依赖关系上．了解这些相似点,有助于国际符号学交流,统一认识,推动符号学的发展。     

Semiotics,edusemiotics and the culture of education

Semiotics is the study of signs addressing their action, usage, communication and signification (meaning). Edusemiotics—educational semiotics—is a recently developed direction in educational theory that takes semiotics as its foundational philosophy and explores the philosophical specifics of semiotics in educational contexts. As a novel theoretical field of inquiry, it is complemented by research known under the banner ‘semiotics in education’, which is largely an applied enterprise. In this respect edusemiotics is a new conceptual framework for both theoretical and empirical studies. Edusemiotics has also been given the status of being a new branch of theoretical semiotics and it was launched as such at the 12th World Congress of the International Association for Semiotic Studies in September 2014 at the New Bulgarian University in Sofia. The article presents ‘semiosis’ as the action of signs across culture AND nature and posits ‘learning’ in terms of developing semiotic consciousness and semiotic competence. Semiosis is a process and as such it defies the Cartesian philosophy of substance-dualism that still informs the culture of education. The paper focuses specifically on university education permeated by disciplinary boundaries and the fragmentation of knowledge grounded in objective science inherited from modernity. Where is semiotics as the science of signs (or relations) in the context of academic culture? The authors conclude by affirming the transdisciplinary character of semiotics and edusemiotics and specify the distinctive focal points of transdisciplinary knowledge afforded by edusemiotics.