SEMF | Flexible Foundations of Mathematics | Ciarán Dunne | Numerosity Workshop 2021 @SEMF | Uploaded February 2022 | Updated October 2024, 50 minutes ago.
Session kindly contributed by Ciarán Dunne in SEMF's 2021 Numerous Numerosity Workshop: semf.org.es/numerosity
ABSTRACT
What are numbers anyway? How do they fit in to the foundations of mathematics? Different groups of people have different answers to these question for different reasons. We propose the perspective that all of these answers are correct in their own ways, and that communication of these different perspectives and the ability to reason about the different representations of numbers is necessary for progress in mathematics.
Our current research begins to build a formal notion of this perspective
– for numbers and other mathematical objects – by putting layers of abstraction on top of the universe of sets characterised by foundational set theories like Zermelo-Fraenkel Set Theory. Doing so allows us to create formal foundations of mathematics in which the objects of study can be free of unexpected representation details, only having the properties that the user desires.
In our talk, we will present some intuition behind how these foundations are created, and discuss their potential applications in computer-assisted theorem proving software.
CIARÁN DUNNE
Heriot-Watt University
Heriot-Watt University profile: macs.hw.ac.uk/~cmd1
SEMF NETWORKS
Website: semf.org.es
Twitter: twitter.com/semf_nexus
LinkedIn: linkedin.com/company/semf-nexus
Instagram: instagram.com/semf.nexus
Facebook: facebook.com/semf.nexus
Session kindly contributed by Ciarán Dunne in SEMF's 2021 Numerous Numerosity Workshop: semf.org.es/numerosity
ABSTRACT
What are numbers anyway? How do they fit in to the foundations of mathematics? Different groups of people have different answers to these question for different reasons. We propose the perspective that all of these answers are correct in their own ways, and that communication of these different perspectives and the ability to reason about the different representations of numbers is necessary for progress in mathematics.
Our current research begins to build a formal notion of this perspective
– for numbers and other mathematical objects – by putting layers of abstraction on top of the universe of sets characterised by foundational set theories like Zermelo-Fraenkel Set Theory. Doing so allows us to create formal foundations of mathematics in which the objects of study can be free of unexpected representation details, only having the properties that the user desires.
In our talk, we will present some intuition behind how these foundations are created, and discuss their potential applications in computer-assisted theorem proving software.
CIARÁN DUNNE
Heriot-Watt University
Heriot-Watt University profile: macs.hw.ac.uk/~cmd1
SEMF NETWORKS
Website: semf.org.es
Twitter: twitter.com/semf_nexus
LinkedIn: linkedin.com/company/semf-nexus
Instagram: instagram.com/semf.nexus
Facebook: facebook.com/semf.nexus
