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Session Track 1
Duration 1 hour
Date/Time 05 Feb 2025 17:00 GMT
9:00am PST/12:00pm EST
5:00pm GMT/6:00pm CET
Convener Gary Berg-Cross

Ontology Summit 2025 Track 1

Agenda

Michael Gruninger

  • Title: The Heirs of Hilbert's Sixth Problem
  • Abstract: In an address to the International Congress on Mathematicians in 1900, David Hilbert posed twenty-three challenge problems, in areas ranging from logic to number theory and partial differential equations. These problems have had a profound impact on research in mathematics. However, the sixth problem posed by Hilbert has never been adequately addressed: "Mathematical treatment of the axioms of physics: The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which mathematics plays an important part." This talk will explore the ways in which ontologies are the axiomatic theories required by Hilbert as a solution to his Sixth Problem. It will also consider how the methodology for evaluating scientific theories can be applied to the problem of empirical evaluation of ontologies.
  • Video Recording

Conference Call Information

Discussion

Modern Physics

12:20:30 Ravi Sharma: Michael the second one is favorable even though the former is easy in ref to two views on ontologies, namely physics and also as ontology defining the logic of all attributes?
12:21:45 Ravi Sharma: scalar, vector, tensor and eventually multidimensional and topological descriptions are required for Physical theories.
12:28:04 Ravi Sharma: time duration and intervals in continuous or discrete math is a challenge for physics today.
12:30:36 Ravi Sharma: classical description would require one type of ontology while QFT would need another kind including topologies?
12:33:48 Ravi Sharma: Granularity and accuracy are related and so how would that manifest in ontologies as physics?
12:38:06 Ravi Sharma: every model of ontology is a molecule is likely to be mostly incorrect because those depicted may not exist or be not stable!
however some and likely sparse may match a molecule!
12:50:09 Ravi Sharma: kindly expand on geometries and multigeometries in relation to Hilbert's sixth?

Use Cases

12:29:02 Mark Underwood: The units of measure use cases are central in thinking about how to support traditional data interoperability with ontologies
12:32:39 Bobbin Teegarden: Use cases, etc, are a specification of context of subject matter (perspective)

  • Mike Bennett: This is an important point. Use case is in a context but what it means to be a given kind of thing is itself context independent. So context = use cse specifies an extract from the intended reality.
    • Bobbin Teegarden: 👍
    • Stephen Powley: I like this way of understanding context, similar to how I've come to understand it.. Do you know of any theories of context that formalise this particular idea?
    • Stephen Powley: 👍
    • Jim Logan (Ontogenesis): 👍
  • janet singer: Is the idea of having no context a misdirection? Would it be better to think of generic use cases that have the context of being context invariant?
    • Bobbin Teegarden: no context is a context in itself ... ;0)
      • janet singer: 👌
    • Bobbin Teegarden: Ontologies are always 'true' in some context ... and when you change/modify the context (and time is an element of context), couldn't you create parallaxes in the 'true' ontology?

Semantic Errors

12:41:28 ToddSchneider: What is a ‘semantic error’?

COLORE

12:42:51 Mark Underwood: FYI https://github.com/gruninger/colore

  • Stephen Powley: 👍

Reduction

13:07:58 Greg Sharp: The reduction of ontological models to mathematical theories reminds me of the recent critique in "The Blind Spot" by Frank, Gleiser and Thompson. They caution against mistaking the map (i.e., theories) for the territory (i.e., experience) in scientific practice. The risk being the exclusion of emergent properties when moving in the reductive direction. What if measurement, time, space are meant to be emergent from an understanding of extension developed within the ontology, rather than being given to the ontology by a God's-eye view of the system?

  • janet singer: Systems theorist and mathematical biologist Robert Rosen’s work on measurement and modeling relations in science takes the ideas from the talk in the other direction (showing limitations of reductionism)
    • janet singer: Rosen realized in the 1950s that category theory provided a general theory of modeling in how entailment structures are put into correspondence. In science one puts inferential entailment into correspondence with causal entailment is a natural system. See his modeling relations

Our Mathematical Universe

13:09:50 Michael Gruninger: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Max Tegmark

Appreciation

13:25:30 janet singer: Excellent talk that derives the ideas anew
13:26:13 Giancarlo Guizzardi: It was great! Thanks!
13:26:14 Ravi Sharma: Thanks Michael

Resources

Previous Meetings

 Session
ConferenceCall 2025 01 29Track 1
ConferenceCall 2025 01 22Keynote
ConferenceCall 2025 01 15Overview

Next Meetings

 Session
ConferenceCall 2025 02 12Track 1
ConferenceCall 2025 02 19Track 1
ConferenceCall 2025 02 26Track 2
... further results
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