Proofs as Spatio-Temporal Processes

Stefaneas, Petros; Vandoulakis, Ioannis M.

doi:10.4000/philosophiascientiae.1010

Cited by 8 publications

(5 citation statements)

References 9 publications

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“…1. The theory of proof-events, initially exposed in (Stefaneas, Vandoulakis, 2014) and formalised in the calculus of proof-events (Stefaneas, Vandoulakis, 2015).…”

Section: Methodsmentioning

confidence: 99%

On The Significance Of Argumentation In Searching For Mathematical Proof

Vandoulakis¹

2018

The European Proceedings of Social and Behavioural Sciences

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In this paper, we argue that argumentation theory can be used to explore certain aspects of the development of discovery proof-events in time. Since argumentation is inseparable from the process of searching for a mathematical proof, a modified model of proof-events calculus, based on certain versions of argumentation theories primarily advanced by Toulmin and Pollock, can be used to this effect. We claim that the exchange of arguments and counterarguments set forward to clarify eventual gaps or implicit assumptions occurring in the course of a proof-event can be represented by appealing to argumentation theories. In this paper, a comparative analysis was carried out between the theory of proof-events and the theory of argumentation. The combination of these two theories enables us to represent controversial points in the process of searching for proof. By expanding the calculus of proof-events with the theory of argumentation we can take into consideration such moments as incomplete or even false purported proofs, intuitive ideas, correct or incorrect steps of reasoning, commentaries, etc. and represent them formally at the appropriate stages that take place during the evolution of a sequence of proof-events.

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“…1. The theory of proof-events, initially exposed in (Stefaneas, Vandoulakis, 2014) and formalised in the calculus of proof-events (Stefaneas, Vandoulakis, 2015).…”

Section: Methodsmentioning

confidence: 99%

On The Significance Of Argumentation In Searching For Mathematical Proof

Vandoulakis¹

2018

The European Proceedings of Social and Behavioural Sciences

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“…Future research should examine the SMC with respect to different practices using both neuronal correlates of the different states they produce, as well as some physiological markers, such as heart rate variability and other parasympathetic measures ( Travis and Wallace, 1999 ; Travis and Pearson, 2000 ), as well as in relation to augmented and virtual reality ( Kiourexidou et al, 2015 ). In addition, similarly to sensory deprivation, which has been found to be beneficial for memory functions, creativity, perception and signal detection, social cognition, and the readiness to change one’s attitudes on social phenomena inducing increased motivation to change critical and maladaptive behavior patterns (for a review, see Vaitl et al, 2005 ); the importance of voluntarily entering into a state of silence, as an educational conceptual space, can and should be studied also in educational settings, in relation to the functions mentions above, as well as logics and mathematics ( Stefaneas and Vandoulakis, 2014 ).…”

Section: Concluding Remarks and Future Perspectivesmentioning

confidence: 99%

Reflections on Inner and Outer Silence and Consciousness Without Contents According to the Sphere Model of Consciousness

Paoletti¹,

Ben‐Soussan²

2020

Front. Psychol.

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In the current hypothesis paper, we propose that focusing attention on silence can be used as a paradigm conceptually similar to sensory deprivation, to study consciousness without content. We briefly overview recent influential models of consciousness and consider how they assess the relationship between consciousness and contents. After discussing the strengths and weaknesses of current models, we suggest an extension based on the Sphere Model of Consciousness (SMC) and introduce new definitions for identification and self-awareness as states of consciousness. We further compare Paoletti’s theoretical model for the development of self with other influential models, highlighting similarities and differences. We conclude with a discussion of how attentional focus on silence can be empirically tested.

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“…An attempt has been undertaken (Vandoulakis and Stefaneas forthcoming b; Stefaneas and Vandoulakis ) to transform this concept into a theoretical framework for the understanding of the mathematical proving activity as an interaction that involves two principal agents—a prover and an interpreter—and requires validation by an appropriate social group. We have distinguished seven essential components of the concept of proof‐event and described some types of it.…”

Section: Web Proving As a Particular Type Of Proof‐eventmentioning

confidence: 99%

“…Nevertheless, the traditional approaches to the concept of proof are not adequate for capturing Web‐based proving activity, with its new and uncommon features. We claim that these new features can be incorporated in an ideal fashion inside a broader theoretical framework for the understanding of the proving activity initially based on the concept of proof‐event introduced by Joseph Goguen () and further developed by us (in Vandoulakis and Stefaneas forthcoming a and b; Stefaneas and Vandoulakis ).…”

Section: Introductionmentioning

confidence: 99%

The Web as A Tool For Proving

Stefaneas

Vandoulakis

2012

Metaphilosophy

Self Cite

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The Web may critically transform the way we understand the activity of proving. The Web as a collaborative medium allows the active participation of people with different backgrounds, interests, viewpoints, and styles. Mathematical formal proofs are inadequate for capturing Web‐based proofs. This article claims that Web provings can be studied as a particular type of Goguen's proof‐events. Web‐based proof‐events have a social component, communication medium, prover‐interpreter interaction, interpretation process, understanding and validation, historical component, and styles. To demonstrate its claim, the article discusses the Kumo and Polymath projects, both of which employ Web‐based communication as part of proving. Web proving is a novel type of proving activity that may have a serious impact on the change in mathematical practices, despite the fact that it is not currently a universally acceptable methodology.

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Proofs as Spatio-Temporal Processes

Cited by 8 publications

References 9 publications

On The Significance Of Argumentation In Searching For Mathematical Proof

On The Significance Of Argumentation In Searching For Mathematical Proof

Reflections on Inner and Outer Silence and Consciousness Without Contents According to the Sphere Model of Consciousness

The Web as A Tool For Proving

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