Dear Tejinder,
thank you very much for reading and appreciating my essay, I'm very glad of it.
I truly can't find an absolute [not relative] sense in which reductionism is fundamental, since everything we can deal with, "is what it is" due a complex net of relations. Laptops, chairs, atoms, nucleons, electrons... they are always defined by relations with other things. When we talk about stuff like chairs and tables, we have a perceptive bias that since we can "feel", "use", "see" them etc, they are somewhat more concrete. But, as you write in your essay (a quote which I loved):
> if we investigate into deeper and deeper reductionist layers of physical reality [the vertical fundamental], laws come 'closer and closer' to things, until there comes the lowermost layer, where laws are not distinguishable from things at all.
When we investigate these real but intangible relations it seems that we are just playing with abstractions - but then these relations (laws) "works" with chairs and tables as well, and concreteness comes back to us. But, again, they are always relations, just more tangible in our phenomenal world; I would say, "at our level of reality".That's why I enjoyed your conclusion that,
> the mathematical world and the physical world are one and the same.
Because mathematic looks like a discipline that traces the most common relations of our world - maybe the only relations that we can ever perceive or imagine.
Thank you again and all the best,
Francesco