SEMF | Andrea Sereni | Counting Numbers, Counting Things | NUMEROUS NUMEROSITY 2021 @SEMF | Uploaded September 2021 | Updated October 2024, 3 hours ago.
Plenary session kindly contributed by Andrea Sereni in SEMF's 2021 Numerous Numerosity: semf.org.es/numerosity
SESSION ABSTRACT
Any philosophical theory of mathematical knowledge needs to provide a suitable account of natural numbers. Despite their central role in our theoretical and practical life, definitions have varied significantly, depending on whether philosophers have conceived of naturals as ordinal or cardinal numbers, emphasized the role of pure or applied mathematics, conceived of the subject-matter of mathematics in terms of objects or structures (or nothing at all). Disconcerting as it may seem, such disagreement points to some crucial philosophical issues. We'll survey some of the major philosophies of arithmetic and their core definitions, and we'll try to understand why "What are (natural) numbers?" is still an open question in philosophy.
SESSION MATERIALS
· The Conceptual Basis of Numerical Abilities: One-to-one Correspondence versus the Successor Relation (tandfonline.com/doi/abs/10.1080/09515080802285255)
· Real Numbers, Quantities, and Measurement (philpapers.org/rec/HALRNQ)
· Definitions of numbers and their applications (Abstractionism, pp. 333–348) (oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780199645268.001.0001/acprof-9780199645268)
· Frege’s Constraint and the Nature of Frege’s Foundational Program (cambridge.org/core/journals/review-of-symbolic-logic/article/abs/freges-constraint-and-the-nature-of-freges-foundational-program/61A5E7A9D8E30DAB2708B3377DACF0B1)
· Neologicism, Frege’s Constraint, and the Frege-Heck Condition (ashoka.edu.in/static/doc_uploads/file_1593631249.pdf)
· Sereni, A. On the Philosophical Significance of Frege’s Constraint (academic.oup.com/philmat/article-abstract/27/2/244/5522900)
· Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege’s Constraint (semanticscholar.org/paper/Neo-Fregean-Foundations-for-Real-Analysis%3A-Some-on-Wright/19524dc5201ec93c12b5b82b66601b9d0f3e5f1c)
ANDREA SERENI
Scuola Universitaria Superiore Pavia (IUSS): http://www.iusspavia.it/home
IUSS Profile: http://www.iusspavia.it/en/-/facullty-andrea-sereni
ResearchGate: researchgate.net/scientific-contributions/Andrea-Sereni-21768644
Academia.edu: https://unisr.academia.edu/AndreaSereni
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
Plenary session kindly contributed by Andrea Sereni in SEMF's 2021 Numerous Numerosity: semf.org.es/numerosity
SESSION ABSTRACT
Any philosophical theory of mathematical knowledge needs to provide a suitable account of natural numbers. Despite their central role in our theoretical and practical life, definitions have varied significantly, depending on whether philosophers have conceived of naturals as ordinal or cardinal numbers, emphasized the role of pure or applied mathematics, conceived of the subject-matter of mathematics in terms of objects or structures (or nothing at all). Disconcerting as it may seem, such disagreement points to some crucial philosophical issues. We'll survey some of the major philosophies of arithmetic and their core definitions, and we'll try to understand why "What are (natural) numbers?" is still an open question in philosophy.
SESSION MATERIALS
· The Conceptual Basis of Numerical Abilities: One-to-one Correspondence versus the Successor Relation (tandfonline.com/doi/abs/10.1080/09515080802285255)
· Real Numbers, Quantities, and Measurement (philpapers.org/rec/HALRNQ)
· Definitions of numbers and their applications (Abstractionism, pp. 333–348) (oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780199645268.001.0001/acprof-9780199645268)
· Frege’s Constraint and the Nature of Frege’s Foundational Program (cambridge.org/core/journals/review-of-symbolic-logic/article/abs/freges-constraint-and-the-nature-of-freges-foundational-program/61A5E7A9D8E30DAB2708B3377DACF0B1)
· Neologicism, Frege’s Constraint, and the Frege-Heck Condition (ashoka.edu.in/static/doc_uploads/file_1593631249.pdf)
· Sereni, A. On the Philosophical Significance of Frege’s Constraint (academic.oup.com/philmat/article-abstract/27/2/244/5522900)
· Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege’s Constraint (semanticscholar.org/paper/Neo-Fregean-Foundations-for-Real-Analysis%3A-Some-on-Wright/19524dc5201ec93c12b5b82b66601b9d0f3e5f1c)
ANDREA SERENI
Scuola Universitaria Superiore Pavia (IUSS): http://www.iusspavia.it/home
IUSS Profile: http://www.iusspavia.it/en/-/facullty-andrea-sereni
ResearchGate: researchgate.net/scientific-contributions/Andrea-Sereni-21768644
Academia.edu: https://unisr.academia.edu/AndreaSereni
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
![[Bad Audio] David Spivak | Applied Category Theory: Toward a Hard Science of Interdisciplinarity](https://i.ytimg.com/vi/hz58zG-W3qE/hqdefault.jpg "[Bad Audio] David Spivak | Applied Category Theory: Toward a Hard Science of Interdisciplinarity
Talk kindly contributed by David Spivak in SEMFs 2023 Interdisciplinary Summer School (https://semf.org.es/school2023)
Full session: https://www.youtube.com/watch?v sVFZv9tYdA
TALK ABSTRACT
Effective interoperation between multiple scientific disciplines is crucial to systems engineering. Can the study of interoperability the working negotiations and hand-offs between theories and models itself be made into a hard science? Hard sciences are based on mathematics, so this would require a mathematics of interoperability, a mathematics whose subject consists of the bridges and analogies that make data- and model-integration actually work. I propose that category theory serves this purpose exceptionally well.
In this talk, I will give evidence for the above claim, and without assuming the audience has seen any category theory before. I will focus on operads, which offer a framework for various forms of compositionality. In particular, I will discuss how operads model the interconnection of dynamical systems, provide a new method for solving systems of nonlinear equations, and explain how these two issues are connected category-theoretically. Finally, Ill explain how all this fits into a larger mathematical approach to interdisciplinarity.
DAVID SPIVAK
Personal Site: http://www.dspivak.net/
Topos Institute Profile: https://topos.site/people/owen-lynch/
SEMF NETWORKS
Website: https://semf.org.es
Twitter: https://twitter.com/semf_nexus
LinkedIn: https://www.linkedin.com/company/semf-nexus
Instagram: https://www.instagram.com/semf.nexus
Facebook: https://www.facebook.com/semf.nexus")
