Informal Proofs and Mathematical Rigour

Marfori, Marianna Antonutti

doi:10.1007/s11225-010-9280-4

Cited by 33 publications

(12 citation statements)

References 14 publications

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“…The worries of Rav (1999) and Weir (2016) about whether the process of filling in intermediate authors, I do not think an account like Hamami's can ultimately be successful, though I do not have space to discuss it in detail here. 3 As illustrations of the objections, and the calls for improvement, see for instance Rav (1999), Rav (2007), Celluci (2009), Detlefsen (2009), Leitgeb (2009), Pelc (2009), Goethe & Friend (2010), Antonutti Marfori (2010), Larvor (2012), Weir (2016), De Toffoli & Giardino (2016, and Larvor (2019). 4 The account developed here is a fuller version of that sketched in Tatton- Brown (2019).…”

Section: §1 Introductionmentioning

confidence: 93%

Rigour and Proof

Tatton-Brown¹

2020

The Review of Symbolic Logic

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This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to. The account is used to address two current questions in the literature: that of how mathematicians are so good at resolving disputes about validity, and that of whether rigorous proofs are necessarily formalizable.

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Section: §1 Introductionmentioning

confidence: 93%

Rigour and Proof

Tatton-Brown¹

2020

The Review of Symbolic Logic

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“…We will not assume that proofs need to be formalisable, for discussion, see Avigad (2008), Antonutti Marfori (2010) and Tanswell (2015). 9 Wittgenstein discusses surveyability throughout the Remarks on the Foundations of Mathematics (1956).…”

Section: From Individual To Social Features Of Proofsmentioning

confidence: 99%

“… 8 We will not assume that proofs need to be formalisable, for discussion, see Avigad (2008), Antonutti Marfori (2010) and Tanswell (2015). …”

mentioning

confidence: 99%

Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups

Habgood‐Coote¹,

Tanswell²

2021

Episteme

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In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects.

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“…Informal arguments typically depend on their logical form as well as on their content and contexts. Informal proves cannot be expressed in a general logical language (i.e., by explicitly defined well-formed formulae), and cannot be applied successively on explicitly specified logical inference rules or axioms [41].…”

Section: Achieving System-level Holism In Reasoning and Decision Makingmentioning

confidence: 99%

A Computational Framework for Procedural Abduction Done by Smart Cyber-Physical Systems

Horváth

2018

Designs

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To be able to provide appropriate services in social and human application contexts, smart cyber-physical systems (S-CPSs) need ampliative reasoning and decision-making (ARDM) mechanisms. As one option, procedural abduction (PA) is suggested for self-managing S-CPSs. PA is a knowledge-based computation and learning mechanism. The objective of this article is to provide a comprehensive description of the computational framework proposed for PA. Towards this end, first the essence of smart cyber-physical systems is discussed. Then, the main recent research results related to computational abduction and ampliative reasoning are discussed. PA facilitates beliefs-driven contemplation of the momentary performance of S-CPSs, including a ‘best option’-based setting of the servicing objective and realization of any demanded adaptation. The computational framework of PA includes eight clusters of computational activities: (i) run-time extraction of signals and data by sensing, (ii) recognition of events, (iii) inferring about existing situations, (iv) building awareness of the state and circumstances of operation, (v) devising alternative performance enhancement strategies, (vi) deciding on the best system adaptation, (vii) devising and scheduling the implied interventions, and (viii) actuating effectors and controls. Several cognitive algorithms and computational actions are used to implement PA in a compositional manner. PA necessitates not only a synergic interoperation of the algorithms, but also an objective-dependent fusion of the pre-programmed and the run time acquired chunks of knowledge. A fully fledged implementation of PA is underway, which will make verification and validation possible in the context of various smart CPSs.

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Informal Proofs and Mathematical Rigour

Cited by 33 publications

References 14 publications

Rigour and Proof

Rigour and Proof

Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups

A Computational Framework for Procedural Abduction Done by Smart Cyber-Physical Systems

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