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Cartography can also model any consistent universe, and I fail to see how that changes anything for the “it’s just a model” argument. We can permutate and enum
by wmal 3y ago
Cartography can also model any consistent universe, and I fail to see how that changes anything for the “it’s just a model” argument.
We can permutate and enumerate symbols for mountains, rivers and roads on a piece of paper. Maybe we would even get some “interesting” results like a map of the Lords of the Rings universe. How would that change anything?
- naasking 3y agoShow me a cartographic map of a 5-dimensional universe.
- jplusequalt 3y agoI think you are both getting lost in the weeds trying to make this metaphor work, or not work. Math is simply the logical conclusion of a set of conditions someone accepts as inherently true. If this, then that. Follow this logic far enough and you end up where we are today.
- naasking 3y agoI think this conflates logic and mathematics. Some would dispute that logic underpins mathematics. Counting can be analyzed logically, but it does not in any meaningful sense seem to depend on logic.
- jplusequalt 3y agoSure it does. How else would you prove that one number follows or precedes another? I think you are conflating the act of physically counting with the logical foundation of our number systems.
- naasking 3y agoIt doesn't seem correct to equate mathematics with proof. If I express a mathematical construction like the whole numbers (let Whole = Zero | Succ Whole), and I build further constructions on that foundation, am I doing mathematics? If so, then it seems mathematics does not depend on logic, as logic depends on propositions and there are no propositions to be seen. Certainly you can analyze such constructions using logic, but that's again conflating logic with mathematics. There's overlap, but they aren't strictly the same.
- jplusequalt 3y agoI would say that a mathematical construction is based in logic, maybe not in the traditional sense, but there is definitely logic behind the construction itself. I think we are talking past one another, what I mean by logic here is more nebulous than predicate calculus. There is an innate logic behind the philosophy of mathematics and I believe you cannot divorce mathematics from logic.