In physics, the objects of study are mass, velocity, energy, etc. It’s natural to quantify them, and as soon as you’ve done that you’ve taken the first step in applying math to physics. There are a couple reasons that this is a productive thing to do:
You already derive benefit from a very simple starting point.
There are strong feedback loops. You can make experimental predictions, test them, and refine your theories.
Together this means that you benefit from even very simple math and can scale up smoothly to more sophisticated. From simply adding masses to F=ma to Lagrangian mechanics and beyond.
It’s not clear to me that those virtues apply here:
I don’t see the easy starting point, the equivalent of adding two masses.
It’s not obvious that the objects of study are quantifiable. It’s not even clear what the objects of study are.
Formal statements about religion must be unfathomably complex?
I don’t see feedback loops. It must be hard to run experiments, make predictions, etc.
Perhaps these concerns would be addressed by examples of the kind of statement you have in mind.
It could also help for zhukeepa to give any single instance of such a ‘Rosetta Stone’ between different ideologies or narratives or (informal) worldviews. I do not currently know what to imagine, other than a series of loose analogies, which can be helpful, but are a bit of a difficult target to point at and I don’t expect to find with a mathematical framework.
It’s relevant that I think of the type signature of religious metaphysical claims as being more like “informal descriptions of the principles of consciousnes / the inner world” (analogously to informal descriptions of the principles of the natural world) than like “ideology or narrative”. Lots of cultures independently made observations about the natural world, and Newton’s Laws in some sense could be thought of as a “Rosetta Stone” for these informal observations about the natural world.
It is my belief that in the next decade and in the next century the technical advances forged by category theorists will be of value to dialectical philosophy, lending precise form with disputable mathematical models to ancient philosophical distinctions such as general vs. particular, objective vs. subjective, being vs. becoming, space vs. quantity, equality vs. difference, quantitative vs. qualitative etc. In turn the explicit attention by mathematicians to such philosophical questions is necessary to achieve the goal of making mathematics (and hence other sciences) more widely learnable and useable. Of course this will require that philosophers learn mathematics and that mathematicians learn philosophy.
I think getting technical precision on philosophical concepts like these will play a crucial role in the kind of math I’m envisioning.
In physics, the objects of study are mass, velocity, energy, etc. It’s natural to quantify them, and as soon as you’ve done that you’ve taken the first step in applying math to physics. There are a couple reasons that this is a productive thing to do:
You already derive benefit from a very simple starting point.
There are strong feedback loops. You can make experimental predictions, test them, and refine your theories.
Together this means that you benefit from even very simple math and can scale up smoothly to more sophisticated. From simply adding masses to F=ma to Lagrangian mechanics and beyond.
It’s not clear to me that those virtues apply here:
I don’t see the easy starting point, the equivalent of adding two masses.
It’s not obvious that the objects of study are quantifiable. It’s not even clear what the objects of study are.
Formal statements about religion must be unfathomably complex?
I don’t see feedback loops. It must be hard to run experiments, make predictions, etc.
Perhaps these concerns would be addressed by examples of the kind of statement you have in mind.
It could also help for zhukeepa to give any single instance of such a ‘Rosetta Stone’ between different ideologies or narratives or (informal) worldviews. I do not currently know what to imagine, other than a series of loose analogies, which can be helpful, but are a bit of a difficult target to point at and I don’t expect to find with a mathematical framework.
It’s relevant that I think of the type signature of religious metaphysical claims as being more like “informal descriptions of the principles of consciousnes / the inner world” (analogously to informal descriptions of the principles of the natural world) than like “ideology or narrative”. Lots of cultures independently made observations about the natural world, and Newton’s Laws in some sense could be thought of as a “Rosetta Stone” for these informal observations about the natural world.
I’m not sure exactly what you’re asking—I wonder how much my reply to Adam Shai addresses your concerns?
I will also mention this quote from the category theorist Lawvere, whose line of thinking I feel pretty aligned with:
I think getting technical precision on philosophical concepts like these will play a crucial role in the kind of math I’m envisioning.
Very helpful, thank you.