Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

On Knowledge and Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Cognitive Abilities ◽  
Historical Development ◽  
Mathematical Knowledge ◽  
General Scheme ◽  
Philosophy Of Mathematics ◽  
Scientific Practices ◽  
Advanced Mathematics ◽  
Mathematical Practices ◽  
Everyday Practices ◽  
Different Levels

This book proposes a novel analysis of mathematical knowledge from a practice-oriented standpoint and within the context of the philosophy of mathematics. The approach it is advocating is a cognitive, pragmatist, historical one. It emphasizes a view of mathematics as knowledge produced by human agents, on the basis of their biological and cognitive abilities, the latter being mediated by culture. It also gives importance to the practical roots of mathematics—that is, its roots in everyday practices, technical practices, mathematical practices themselves, and scientific practices. Finally, the approach stresses the importance of analyzing mathematics' historical development, and of accepting the presence of hypothetical elements in advanced mathematics. The book's main thesis is that several different levels of knowledge and practice are coexistent, and that their links and interplay are crucial to mathematical knowledge. This chapter offers some remarks that may help readers locate the book's arguments within a general scheme.

Survey Data Quality in Analyzing Harmonized Indicators of Protest Behavior: A Survey Data Recycling Approach

2021 ◽  
pp. 000276422110216
Author(s):  
Kazimierz M. Slomczynski ◽  
Irina Tomescu-Dubrow ◽  
Ilona Wysmulek
Keyword(s):  
Data Processing ◽  
Data Quality ◽  
Survey Data ◽  
A Priori ◽  
Data Sets ◽  
New Approach ◽  
Survey Quality ◽  
Survey Error ◽  
Ex Post ◽  
The Impact

This article proposes a new approach to analyze protest participation measured in surveys of uneven quality. Because single international survey projects cover only a fraction of the world’s nations in specific periods, researchers increasingly turn to ex-post harmonization of different survey data sets not a priori designed as comparable. However, very few scholars systematically examine the impact of the survey data quality on substantive results. We argue that the variation in source data, especially deviations from standards of survey documentation, data processing, and computer files—proposed by methodologists of Total Survey Error, Survey Quality Monitoring, and Fitness for Intended Use—is important for analyzing protest behavior. In particular, we apply the Survey Data Recycling framework to investigate the extent to which indicators of attending demonstrations and signing petitions in 1,184 national survey projects are associated with measures of data quality, controlling for variability in the questionnaire items. We demonstrate that the null hypothesis of no impact of measures of survey quality on indicators of protest participation must be rejected. Measures of survey documentation, data processing, and computer records, taken together, explain over 5% of the intersurvey variance in the proportions of the populations attending demonstrations or signing petitions.

Necessity, Certainty, and the A Priori

1988 ◽  
Vol 18 (1) ◽  
pp. 43-66 ◽  
Author(s):  
Albert Casullo
Keyword(s):  
Cognitive Processes ◽  
Mathematical Knowledge ◽  
A Priori ◽  
Theory Of Knowledge ◽  
A Posteriori ◽  
Unitary Theory ◽  
Knowledge Based

Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori.

scholarly journals On the security of $\alpha\eta$: response to 'some attacks on quantum-based cryptographic protocols'

2006 ◽  
Vol 6 (7) ◽  
pp. 561-582
Author(s):  
H.P. Yuen ◽  
R. Nair ◽  
E. Corndorf ◽  
G.S. Kanter ◽  
P. Kumar
Keyword(s):  
Coherent State ◽  
Optical Communications ◽  
A Priori ◽  
Key Generation ◽  
Generation System ◽  
New Approach ◽  
Security Proof ◽  
Grover Search ◽  
Channel Loss ◽  
Key Length

Lo and Ko have developed some attacks on the cryptosystem called $\alpha \eta$}, claiming that these attacks undermine the security of $\alpha\eta$ for both direct encryption and key generation. In this paper, we show that their arguments fail in many different ways. In particular, the first attack in [1] requires channel loss or length of known-plaintext that is exponential in the key length and is unrealistic even for moderate key lengths. The second attack is a Grover search attack based on `asymptotic orthogonality' and was not analyzed quantitatively in [1]. We explain why it is not logically possible to "pull back'' an argument valid only at $n=\infty$ into a limit statement, let alone one valid for a finite number of transmissions n. We illustrate this by a `proof' using a similar asymptotic orthogonality argument that coherent-state BB84 is insecure for any value of loss. Even if a limit statement is true, this attack is a priori irrelevant as it requires an indefinitely large amount of known-plaintext, resources and processing. We also explain why the attacks in [1] on $\alpha\eta$ as a key-generation system are based on misinterpretations of [2]. Some misunderstandings in [1] regarding certain issues in cryptography and optical communications are also pointed out. Short of providing a security proof for $\alpha\eta$, we provide a description of relevant results in standard cryptography and in the design of $\alpha\eta$ to put the above issues in the proper framework and to elucidate some security features of this new approach to quantum cryptography.

scholarly journals Towards developing a cyber-physical multi-agent system for managing precise farms with digital twins of plants

2019 ◽  
pp. 257-261
Author(s):  
Vladimir Laryukhin ◽  
Petr Skobelev ◽  
Oleg Lakhin ◽  
Sergey Grachev ◽  
Vladimir Yalovenko ◽  
...  
Keyword(s):  
A Priori ◽  
Knowledge Bases ◽  
Agent Based ◽  
Plant Soil ◽  
Plant Cultivation ◽  
Technical Requirements ◽  
Digital Twins ◽  
History Of ◽  
Multi Agent ◽  
High Uncertainty

The paper presents the multi-agent approach for developing cyber-physical system for managing precise farms with digital twins of plants. It discusses complexity of the problem caused by a priori incompleteness of knowledge about factors of plant growth and development, high uncertainty of crops cultivation, variety of weather, business and technical requirements, etc. The approach proposes knowledge bases and multi-agent technology in combination with machine learning methods for designing considered systems. Digital twin of plant is specified as an agent based on ontology model of objects relevant for plant cultivation (specific sort of plant, soil, etc) associated with history of operations and environment conditions. The architecture and functions of system components are designed. The expected results of system implementation and the benefits for farmers are discussed.

Inventory routing for defense: Moving supplies in adversarial and partially observable environments

2018 ◽  
Vol 17 (1) ◽  
pp. 55-81
Author(s):  
Michelle Blom ◽  
Slava Shekh ◽  
Don Gossink ◽  
Tim Miller ◽  
Adrian R Pearce
Keyword(s):  
Autonomous Vehicles ◽  
Cost Minimization ◽  
A Priori ◽  
Primary Objective ◽  
Inventory Routing ◽  
Agent Based ◽  
Dynamic Events ◽  
Secondary Objective ◽  
Partially Observable ◽  
Item Types

Future defense logistics will be heavily reliant on autonomous vehicles for the transportation of supplies. We consider a dynamic logistics problem in which: multiple supply item types are transported between suppliers and consuming (sink) locations; and autonomous vehicles (road-, sea-, and air-based) make decisions on where to collect and deliver supplies in a decentralized manner. Sink nodes consume dynamically varying demands (whose timing and size are not known a priori). Network arcs, and vehicles, experience failures at times, and for durations, that are not known a priori. These dynamic events are caused by an adversary, seeking to disrupt the network. We design domain-dependent planning algorithms for these vehicles whose primary objective is to minimize the likelihood of stockout events (where insufficient resource is present at a sink to meet demand). Cost minimization is a secondary objective. The performance of these algorithms, across varying scenarios, with and without restrictions on communication between vehicles and network locations, is evaluated using agent-based simulation. We show that stockpiling-based strategies, where quantities of resource are amassed at strategic locations, are most effective on large land-based networks with multiple supply item types, with simpler “shuttling”-based approaches being sufficient otherwise.

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