scholarly journals Logic of Relations and Diagrammatic Reasoning: Structuralist Elements in the Work of Charles Sanders Peirce

2020 ◽  
pp. 241-272
Author(s):  
Jessica Carter
Keyword(s):  
Mathematical Reasoning ◽  
Charles Sanders Peirce ◽  
Diagrammatic Reasoning ◽  
Structuralist View

This chapter presents aspects of the work of Charles Sanders Peirce showing that he adhered to a number of pre-structuralist themes. Further, it indicates that Peirce’s position is similar in spirit to the category theoretical structuralist view of Steve Awodey (2004). The first part documents Peirce’s extensive knowledge of, and contribution to, the mathematics of his time, illustrating that relations played a fundamental role. The second part addresses Peirce’s characterization of mathematical reasoning as diagrammatic reasoning, that is, as reasoning done by constructing and observing rational relations in diagrams.

Mathematics Based on Fuzzy Logic

2017 ◽  
Author(s):  
Radim Bělohlávek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Mathematical Analysis ◽  
Classical Logic ◽  
Mathematical Reasoning ◽  
Narrow Sense ◽  
And Mathematics ◽  
Truth Degrees

Mathematical reasoning is governed by the laws of classical logic, based on the principle of bivalence. With the acceptance of intermediate truth degrees, the situation changed substantially. This chapter begins with a characterization of mathematics based on fuzzy logic, an identification of principal issues of its development, and an outline of this development. It then examines the role of fuzzy logic in the narrow sense for developing mathematics based on fuzzy logic and the main approaches developed toward its foundations. Next, some selected areas of mathematics based on fuzzy logic are presented, such as the theory of sets and relations, algebra, topology, quantities and mathematical analysis, probability, and geometry. The chapter concludes by examining various semantic questions regarding fuzzy logic and mathematics based on it.

scholarly journals Aspectos erotéticos del «hibridismo» de Mendel

2013 ◽  
Author(s):  
Pablo Lorenzano
Keyword(s):  
Problem Solving ◽  
Theory Approach ◽  
Theoretical Context ◽  
Semantic Conception ◽  
Precise Characterization ◽  
Structuralist View ◽  
Semantic Conception Of Theories

RESUMENEl objetivo de este trabajo es mostrar, en la línea sugerida por Nickles (1980, 1981) y desarrollada por Sintonen (1985, 1996), no sólo que el «enfoque de resolución de problemas» y el «enfoque de teorías» no son contrapuestos, sino que este último, mediante la versión de la concepción semántica de las teorías conocida bajo el nombre de «estructuralismo metateórico», puede ser utilizado para aportar precisión al enfoque de resolución de problemas, a través de la caracterización más precisa del contexto teórico en el que se plantean los problemas y, de este modo, de su individuación e historia, pudiéndose así distinguir dos tipos de «cambio problemático»: «cambio en un problema» y «cambio de problema». Para ello, se presentará dicha propuesta y luego será aplicada al caso del «hibridismo» de Mendel.PALABRAS CLAVEPROBLEMA CIENTÍFICO, ENFOQUE DE RESOLUCIÓN DE PROBLEMAS, ESTRUCTURALISMO METATEÓRICO, HIBRIDISMOABSTRACTThe aim of this paper is to show, in the line suggested by Nickles (1980, 1981) and developed by Sintonen (1985, 1996), not just that the «problem-solving approach» and the «theory approach» are not incompatible, but also that the latter, in the version of the semantic conception of theories known as «structuralist view», can be used to give precision to the problem-solving approach, by a more precise characterization of the theoretical context in which problems arise and, in this way, to their individuation and history, distinguishing two types of «problem change»: «change in a problem» and «change of a problem». In order to do this, it will be presented a proposal that will be applied to Mendel’s «hybridism».KEYWORDSSCIENTIFIC PROBLEM, PROBLEM-SOLVING APPROACH, METATHEORETICAL STRUCTURALISM, HYBRIDISM

Charles Peirce and Bertrand Russell on Euclid

2020 ◽  
Vol 19 (37) ◽  
pp. 79-94
Author(s):  
Irving Anellis
Keyword(s):  
Deductive Reasoning ◽  
Charles Sanders Peirce ◽  
Diagrammatic Reasoning ◽  
Bertrand Russell ◽  
Mathematical Intuition ◽  
Existential Graphs ◽  
Charles Peirce ◽  
The Mind ◽  
Graphical System

Both Charles Sanders Peirce (1839–1914) and Bertrand Russell (1872–1970) held that Euclid’s proofs in geometry were fundamentally flawed, and based largely on mathematical intuition rather than on sound deductive reasoning. They differed, however, as to the role which diagramming played in Euclid’s emonstrations. Specifically, whereas Russell attributed the failures on Euclid’s proofs to his reasoning from diagrams, Peirce held that diagrammatic reasoning could be rendered as logically rigorous and formal. In 1906, in his manuscript “Phaneroscopy” of 1906, he described his existential graphs, his highly iconic, graphical system of logic, as a moving picture of thought, “rendering literally visible before one’s very eyes the operation of thinking in actu”, and as a “generalized diagram of the Mind” (Peirce 1906; 1933, 4.582). More generally, Peirce personally found it more natural for him to reason diagrammatically, rather than algebraically. Rather, his concern with Euclid’s demonstrations was with its absence of explicit explanations, based upon the laws of logic, of how to proceed from one line of the “proof” to the next. This is the aspect of his criticism of Euclid that he shared with Russell; that Euclid’s demonstrations drew from mathematical intuition, rather than from strict formal deduction.

scholarly journals Toward an Integrated History and Philosophy of Diagrammatic Practices

2020 ◽  
Vol 14 (2) ◽  
pp. 347-376
Author(s):  
Chiara Ambrosio
Keyword(s):  
Nineteenth Century ◽  
Scientific Knowledge ◽  
Charles Sanders Peirce ◽  
Diagrammatic Reasoning ◽  
Late Nineteenth Century ◽  
Diagrammatic Representation ◽  
Object Based ◽  
False Dichotomy ◽  
Nineteenth And Twentieth Centuries ◽  
Late Nineteenth

Abstract This article offers an overview of current approaches to the study of diagrams and their roles in scientific knowledge making. The discussion develops in three parts. The first investigates and questions historical and philosophical analyses of the suppression of diagrams in the nineteenth and twentieth centuries. It attempts to sketch an alternative historiography of diagrammatic practices in which the insights of advocates of diagrammatic reasoning in a time of “objectivity without images” take center stage. The second part turns to the American philosopher, scientist, and logician Charles Sanders Peirce as a representative defender of diagrammatic reasoning and diagrammatic representation in the late nineteenth century, and it investigates his legacy on current approaches to diagrams. The final part exposes a puzzling paradox in the literature, characterizing it as a false dichotomy between “the representational view” and the “object-based view” of diagrams. The article concludes that this dichotomy reveals more about the identities of scholars embracing particular disciplinary traditions than about diagrams themselves, and it suggests that this can be overcome by attending to diagramming as a practice at the intersections of representation, manipulation, and experimentation.

Translation and other acts of meaning: In between cognitive semiotics and semiotics of culture

2014 ◽  
Vol 7 (2) ◽  
Author(s):  
Göran Sonesson
Keyword(s):  
Charles Sanders Peirce ◽  
Cultural Translation ◽  
Semiotic Resources ◽  
Roman Jakobson ◽  
Definition Of

AbstractIf translation is an act of meaning transaction, semiotics should be able to define its specificity in relation to other semiotic acts. Instead, following upon suggestions by Roman Jakobson, the Tartu school, and, more implicitly, Charles Sanders Peirce, the notion of translation has been generalized to cover more or less everything that can be done within and between semiotic resources. In this paper, we start out from a definition of communication elaborated by the author in an earlier text, characterizing translation as a double act of meaning. This characterization takes into account the instances of sending and receiving of both acts involved: the first one at the level of cognition and the second one at the level of communication. Given this definition, we show that Jakobson’s “intralinguistic translation” is, in a sense, the opposite of translation and that his “intersemiotic translation” has important differences and well as similarities to real translation. We also suggest that “cultural translation” has very little to do with translation proper except, in some cases, at the end of its operation. Peirce’s idea of exchanging signs for other signs is better understood as a characterization of tradition.

Peirce’s Pragmatic Maxim: Realist or Nominalist?

1996 ◽  
pp. 91-102 ◽  
Author(s):  
Vincent G. Potter
Keyword(s):  
Charles Sanders Peirce ◽  
American Pragmatism ◽  
Extreme Form ◽  
Pragmatic Maxim ◽  
Philosophical Doctrine

This chapter argues that American pragmatism is not to be simply identified with positivism. Positivism refers to a rather extreme form of nominalism that developed along the lines of classical empiricism. Nominalism refers to any philosophical doctrine that denies the reality of general ideas as part of the ontological structure of things. While this is an incomplete characterization of positivism, it is sufficient in the sense that these essential notes of nominalism are what the chapter denies of pragmaticism as developed by Charles Sanders Peirce. It should also be said at the outset that certain forms of classical rationalism are likewise nominalistic and have developed into a type of positivism all their own.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

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