This one is addressed to everyone:

Guys, I think we all find this discussion more pleasant and productive if we all will tone down the adversarial overtones. I want to remind as much to myself as to every single one of you that there's no competition or battle taking place here. We are all on the same team and we share our common passion and interest in physics. Let's celebrate it with collaborative communication. All objections, different views and rigour stays the same. I ask only to reconsider the emotional tone. Just a pinch of kindness and collaboration might have very surprising effect on overall productivity of this engagment.

5 hours ago, TheVat said:

What ontological claims do you then think mathematics is making? Just to clarify this tragedy you speak of.

Mine or anybody else thoughts or opinions are irrelevant here. What we have here is a different operational understanding of mathematical language between us. And I would like to understand your position clearly. Lets take this simple example where 2 equations are solving for the same value but, as I see it, having radically different ontological meanings:

\( v_{a} = \sqrt{\frac{GM}{r}} \qquad\text{vs.}\qquad v_{b} = \frac{2\pi r}{P} \)

Can you see the ontological difference?

13 minutes ago, Anton Rize said:

va=GMr−−−√vs.vb=2πrP

Can you see the ontological difference?

Not every algebraic manipulation deserves an brand-new ontological coinage.

4 hours ago, MigL said:

Not sure if anyone else has noted that whenever @Time Traveler is asked a particularly 'difficult' question, his answer always includes highlighted text, and it begins with "Thank you for the sharp and critical counterarguments" or "I appreciate you holding my feet to the fire".
Almost as if he poses your questions to an AI, then copies and pasts the AI's reply here.

@exchemist is a pretty good early-warning system for this kind of thing. He's clued us all in a while ago.

12 minutes ago, joigus said:

Not every algebraic manipulation deserves an brand-new ontological coinage.

You making it very hard for me not to sound adversarial right now hahaha!
If you will look at this two equations as an algorithms one has to preform in order to obtain the values of v_a and v_b - you will find that this are categorically different algorithms. They lead to radically different physical actions that lead to different measurements of different phenomenon. Is it reasonable to call it "algebraic manipulation"?
Maybe if you would actually engage with the argument and spend just few minutes thinking about it before writing your comment - we could better understand each other? Would you agree?

1 hour ago, Anton Rize said:

This one is addressed to everyone:

Guys, I think we all find this discussion more pleasant and productive if we all will tone down the adversarial overtones. I want to remind as much to myself as to every single one of you that there's no competition or battle taking place here. We are all on the same team and we share our common passion and interest in physics. Let's celebrate it with collaborative communication. All objections, different views and rigour stays the same. I ask only to reconsider the emotional tone. Just a pinch of kindness and collaboration might have very surprising effect on overall productivity of this engagment.

Which do you want to discuss - ontology, or physics?

1 hour ago, Anton Rize said:

Mine or anybody else thoughts or opinions are irrelevant here. What we have here is a different operational understanding of mathematical language between us. And I would like to understand your position clearly. Lets take this simple example where 2 equations are solving for the same value but, as I see it, having radically different ontological meanings:

va=GMr−−−√vs.vb=2πrP

Can you see the ontological difference?

But is there ontology of the math, or does ontology only come into play when you add the context of physics to it?

Isn't Ontology a question for Epistemologists ?

Seems to me that Mathematics, unlike Language, needs clearly stated definitions for everything, so as to avoid issues like the above mentioned. But sometimes those definitions can only 'dig down' so far before they start getting circular.

But I'm a simple Physicist ( ? ) and out of my depth here.

I would be interested in @Eise 's take on it.

Edited 29 minutes ago29 min by MigL