And this kind of response really grinds my gears; I am relatively certain, given the time scales involved and the nature of your response, that you didn't read my links, and you haven't provided any of your own. Nonetheless!
Doing logic is doing metaphysics. Suppose 1+1=2 for addable numbers, that you have oranges and can add more oranges, and also that the number of oranges you have is an addable number. Now you know, as a matter of plain old philosophical handwavey logic, that if you have 1 orange, and you add 1 more orange, then you'll have 2 oranges. Easy, right? This generalizes to any topos and it's known as "internal logic". The slogan we have is, "a topos is a place for doing logic".
Doing metaphysics is doing logic. Want to know what's impossible? If it can be characterized purely by mathematical structures, and those structures' existence leads to contradiction, then it's impossible. Thus, "models" in the first sense of the original article, free unconstrained unicorn metaphysics models, are actually logically (and thus mathematically) constrained by "models" in the second sense, in the mathematical sense. A powerful example of this is M-theory, borne from string theory; right now, the "swampland" cleanup is sweeping through string theory and helping refine our sense of which particle physics are possible.
An ontologist in today's postmodern world surely knows that the (inherently mathematical!) structures that they are building and studying are created, not discovered; subjective, not objective; narratives, not truths. Mathematicians know this formally, via Tarski's Undefinability. Just like an ontologist tries to find models, a programmer tries to find models, searching for the database schemata and the class hierarchy that will match their problem.
(Indeed, what is "anything of substance"? Is it physical?)
>I am relatively certain, given the time scales involved and the nature of your response, that you didn't read my links, and you haven't provided any of your own
The content of the links didn't seem relevant to the objection I offered. Perhaps that's incorrect, but you didn't make the case.
>Doing logic is doing metaphysics. Suppose 1+1=2 for addable numbers... that if you have 1 orange, and you add 1 more orange, then you'll have 2 oranges.
I could object to doing math being an instance of metaphysics, but setting that aside, the issue is that the connection between logic and metaphysics is the "mostly unobjectionable" subset of metaphysics that I mentioned previously. So again, you can't substantiate the objectionable parts with arguments that only apply to the unobjectionable parts.
>An ontologist in today's postmodern world surely knows that the (inherently mathematical!) structures that they are building and studying are created, not discovered; subjective, not objective; narratives, not truths.
Here you seem to be admitting that metaphysics is unsubstantive! Metaphysics purports to discover what exists, not subjective notions of preferred taxonomies. But it is precisely the charge that nothing objective is being discovered that underpins the argument against metaphysics.
Now I understand why you see a close connection between what a programmer does and what the metaphysician does: they're both theorizing about contingent domains of inquiry, with no external objective facts at stake. But now I don't get why you object to saying metaphysics is unsubstantive.
Doing logic is doing metaphysics. Suppose 1+1=2 for addable numbers, that you have oranges and can add more oranges, and also that the number of oranges you have is an addable number. Now you know, as a matter of plain old philosophical handwavey logic, that if you have 1 orange, and you add 1 more orange, then you'll have 2 oranges. Easy, right? This generalizes to any topos and it's known as "internal logic". The slogan we have is, "a topos is a place for doing logic".
Doing metaphysics is doing logic. Want to know what's impossible? If it can be characterized purely by mathematical structures, and those structures' existence leads to contradiction, then it's impossible. Thus, "models" in the first sense of the original article, free unconstrained unicorn metaphysics models, are actually logically (and thus mathematically) constrained by "models" in the second sense, in the mathematical sense. A powerful example of this is M-theory, borne from string theory; right now, the "swampland" cleanup is sweeping through string theory and helping refine our sense of which particle physics are possible.
An ontologist in today's postmodern world surely knows that the (inherently mathematical!) structures that they are building and studying are created, not discovered; subjective, not objective; narratives, not truths. Mathematicians know this formally, via Tarski's Undefinability. Just like an ontologist tries to find models, a programmer tries to find models, searching for the database schemata and the class hierarchy that will match their problem.
(Indeed, what is "anything of substance"? Is it physical?)