scholarly journals Studentsr Proof Schemes for Disproving Mathematical Proposition

2018 ◽  
Author(s):  
Mochammad Amirudin ◽  
Yusuf Fuad ◽  
Pradnyo Wijayanti
Keyword(s):  
Proof Schemes ◽  
Mathematical Proposition

The Cartesian Doubt Experiment and Mathematics

1998 ◽  
pp. 35-40
Author(s):  
Halil Turan
Keyword(s):  
Common Sense ◽  
Mathematical Proposition ◽  
Logical Operations ◽  
Substantial Problem ◽  
And Mathematics ◽  
Mathematical Operations ◽  
Cartesian Doubt ◽  
Positive Results

The view that Descartes called mathematical propositions into doubt as he impugned all beliefs concerning common-sense ontology by assuming that all beliefs derive from perception seems to rest on the presupposition that the Cartesian problem of doubt concerning mathematics is an instance of the problem of doubt concerning existence of substances. I argue that the problem is not 'whether I am counting actual objects or empty images,' but 'whether I am counting what I count correctly.' Considering Descartes's early works, it is possible to see that for him, the proposition '2+3=5' and the argument 'I think, therefore I am,' were equally evident. But Descartes does not found his epistemology upon the evidence of mathematical propositions. The doubt experiment does not seem to give positive results for mathematical operations. Consciousness of carrying out a mathematical proposition, however, unlike putting forth a result of an operation, is immune to doubt. Statements of consciousness of mathematical or logical operations are instances of 'I think' and hence the argument 'I count, therefore I am' is equivalent to 'I think, therefore I am.' If impugning the veridicality of mathematical propositions could not pose a difficulty for Descartes's epistemology which he thought to establish on consciousness of thinking alone, then he cannot be seen to avoid the question. Discarding mathematical propositions themselves on the grounds that they are not immune to doubt evoked by a powerful agent does not generate a substantial problem for Descartes provided that he believes that he can justify them by appeal to God's benevolence.

The Zero-Knowledge Proof Schemes Based on Williams Public-Key Cryptosystem

2012 ◽  
Vol 546-547 ◽  
pp. 526-530
Author(s):  
Qian Zhang ◽  
De Han
Keyword(s):  
Proof Theory ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Zero Knowledge ◽  
Proof Schemes ◽  
Proof Scheme ◽  
Set Up ◽  
Zero Knowledge Proof

In this paper, through introducing the Williams public-key cryptosystem in detail, the analysis of the characteristics of the system, and the combination with zero knowledge proof, we set up a zero-knowledge proof scheme based on Williams public-key cryptosystem. The scheme will enrich the theory of cryptography, and particularly zero-knowledge proof theory.

Knowing Involves Deciding

Philosophy ◽  
1957 ◽  
Vol 32 (120) ◽  
pp. 39-57
Author(s):  
John Hartland-Swann
Keyword(s):  
Mathematical Proposition ◽  
Knowing That ◽  
Pure Mathematics ◽  
Ordinary Conversation

SUMMARYEvery case of knowing that S is, was or will be P involves, when analysed, some decision or the acceptance of some decision. This applies equally when you are discussing the so-called tautological propositions of logic and pure mathematics; for you can only claim to “know” that some logical or mathematical proposition is true because you have previously decided to accept that certain meanings shall be attached to certain words, or that certain symbols shall function in a certain way. When we examine what philosophers are doing who demand that we prefix “we know” to this or that part of their analyses of perceptual situations, we find that they are often using “know” in a question-begging manner in order to buttress some particular, and usually contentious, analysis. Nor is any philosopher in a position to lay down rigid and precise rules for the proper use of “know” in ordinary conversation; although he can usefully debate the nature and cogency of the grounds on which decisions, issuing in “know”-statements, are generally made. Lastly, Austin is quite right in claiming that when I say “I know” I give my authority and pledge my word, which I do not do when I merely say “I believe”; but I give my authority and pledge my word only because I have decided, or accepted a decision, that so and so is the case.

scholarly journals Registros em língua natural das superfícies quádricas: análise semiótica e possibilidades de uso de novos registrosRecords in natural language of quadric surfaces: semiotic analysis and possibilities of using new records

2018 ◽  
Vol 20 (1) ◽  
Author(s):  
Sérgio Florentino Da Silva ◽  
Méricles Thadeu Moretti
Keyword(s):  
Natural Language ◽  
New Records ◽  
Semiotic Analysis ◽  
Quadric Surfaces ◽  
Mathematical Proposition ◽  
Visual Variables ◽  
Global Properties ◽  
Semiotic Representations ◽  
Conversion Operation ◽  
Higher Education Books

Levando em conta a teoria dos registros de representações semióticas de Raymond Duval, sobretudo em relação a abordagem de interpretação global de propriedades figurais, as funções discursivas da linguagem e a operação semiótica e cognitiva de conversão, neste trabalho, proporemos analisar os registros em língua natural das superfícies quádricas (não cilíndricas e não degeneradas) presentes em livros do Ensino Superior. Tais análises evidenciaram que esses registros pesquisados recorrem, mesmo que nem sempre de forma explícita, a variáveis visuais e a propriedades globais das figuras e que apresentam potencial para contemplar diversas funções discursivas, tais como, a apofântica que reflete a capacidade de designação de algo sob a forma de uma proposição matemática, a expansão discursiva que permite ligações entre proposições matemáticas de forma coerente além da operação de conversão. Ao adicionarmos a essa discussão o Princípio de Extensão de Bento de Jesus Caraça, indicaremos possibilidades do uso de novos registros para as cônicas.Taking into consideration Raymond Duval's theory of the records of semiotic representations, especially in relation to the global interpretation approach of figurative properties, the discursive functions of language and the semiotic and cognitive operation of conversion, we propose to analyze the records in natural language of the quadric (non-cylindrical and non-degenerated) surfaces present in Higher Education books. Such analyzes have evidenced that these researched records recur, although not always explicitly, to visual variables and to the global properties of the figures and that present the potential to contemplate several discursive functions, such as the apophantic, which reflects the capacity to designate something under the form of a mathematical proposition, the discursive expansion that allows connections between mathematical propositions in a coherent way, in addition to the conversion operation. When we add to this discussion Bento de Jesus Caraça’s Principle of Extension, we indicate possibilities of using new records for the conics.  

scholarly journals Proclus’ division of the mathematical proposition into parts: how and why was it formulated?

1999 ◽  
Vol 49 (1) ◽  
pp. 282-303 ◽  
Author(s):  
Reviel Netz
Keyword(s):  
Logical Form ◽  
Conic Sections ◽  
Mathematical Proposition ◽  
Single Author ◽  
Communication Situation ◽  
Greek Mathematics

There are a number of ways in which Greek mathematics can be seen to be radically original. First, at the level of mathematical contents: many objects and results were first discovered by Greek mathematicians (e.g. the theory of conic sections). Second, Greek mathematics was original at the level of logical form: it is arguable that no form of mathematics was ever axiomatic independently of the influence of Greek mathematics. Finally, third, Greek mathematics was original at the level of form, of presentation: Greek mathematics is written in its own specific, original style. This style may vary from author to author, as well as within the works of a single author, but it is still always recognizable as the Greek mathematical style. This style is characterized (to mention a few outstanding features) by (i) the use of the lettered diagram, (ii) a specific technical terminology, and (iii) a system of short phrases (‘formulae’). I believe this third aspect of the originality—the style—was responsible, indirectly, for the two other aspects of the originality. The style was a tool, with which Greek mathematicians were able to produce results of a given kind (the first aspect of the originality), and to produce them in a special, compelling way (the second aspect of the originality). This tool, I claim, emerged organically, and reflected the communication-situation in which Greek mathematics was conducted. For all this I have argued elsewhere.

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