Frank Arntzenius - Are There Really Instantaneous Velocities?

In this 2000 paper from the journal The Monist, Frank Arntzenius discusses the notion of instantaneous velocity, that is, velocity at an instant. Should we reduce this to positions at times? Should we accept it as a fundamental property of objects? Or should we drop the idea of instants altogether? According to Arntzenius, none of the options looks good.
Victor Gijsbers teaches philosophy at Leiden University in the Netherlands. This video is part of an ongoing look at various philosophical papers: • Philosophical Papers

[@Abren_]

Hi - really interesting video, thanks for sharing your insight outside of your academic institution. Intuitively, speaking of instantaneous velocity feels paradoxical to me.

[@CjqNslXUcM]

It seems to me that, definitionally, you need instantaneous velocities for a markovian world with instants to exist. An instant without velocities would have more than one possible past and future. I'm entirely comfortable with the idea of using chunks of time with length epsilon instead of actual infinitesimals (instants) existing. Actual points cause a lot of headaches, such as the banach-tarski paradox. Thank you for the video!

[@MELUTONIN]

I think it's easier to start with momentum then and use that to define velocity. Conversation of momentum follows from the laws of physics being constant over spacetime (Noether's theorem) and momentum is already treated like an intrensic property in physics.

[@jamesb46]

The principle that if an object does not have a property at every instant of an interval, then on the interval in does have the property is not the whole story.
A better statement would be: if it is possible at every instant for an object to have a property, then if for every instant it does not have the property, then on any interval that contains only those instant, it lacks the property.
Otherwise it is akin to the fallacy of composition.

[@tesafilm8447]

Really interesting topic! Have you also been thinking about making a video on (contradictory) accounts of change?:)

[@VictorGijsbers]

I'm not exactly planning it, but it might certainly happen. I believe one of my colleagues, Martin Lipman, has written about that in his work on fragmentalism; could be a good way to approach it.

[@das.gegenmittel]

Has the Epistemology Series been finished? 🤔

[@VictorGijsbers]

Nope, not at all. We're only slightly past the halfway point, I think.

[@jamesb46]

@@VictorGijsberscurrently watching episode 18 trying to figure out if I should trust you or not 🤔