I’d say both since it’s only an application or play with logic.
Well, the rules found within maths do concur with those in the natural world. It’s still based on the logic that if a equals b and a equals z, then z equals b. To describe is also true but modern maths is much more fluid than to just be used for the description of the world around us. You can see this with things like imaginary numbers which had no use in the 1600s but only began to find practical importance a couple of centuries after. Obviously, earlier formulations (particularly amongst Greeks) were largely practical, but then you also have abstract concepts.Mathematics is not a play with logic. It is a language humans invented to describe the natural/physical phenomena we discover around us.
The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. It is a product of the human mind and we make mathematics up as we go along to suit our purposes.
If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it's invented.
Well, the rules found within maths do concur with those in the natural world. It’s still based on the logic that if a equals b and a equals z, then z equals b. To describe is also true but modern maths is much more fluid than to just be used for the description of the world around us. You can see this with things like imaginary numbers which had no use in the 1600s but only began to find practical importance a couple of centuries after. Obviously, earlier formulations (particularly amongst Greeks) were largely practical, but then you also have abstract concepts.
But your right that the loss of the universe and therefore any of the reasoning required will render it useless.
So all together, I’d still say it’s both. You have the real world occurrences which follow logick and exert influence on our human reasoning, then you have mathematicks which doesn’t solely seek an explanation, but builds itself up through gradual abstraction all deriving from those same natural phenomena.
Well I meant axioms. All axioms are based on logical truths that apply in the real world. But as it gets more abstract, it does only ‘fits in’ or stays ‘accurate’. But then there always must be a ‘better’ substitution for physical descriptions. It Could just be a fault in observation and a wrong mathematical association than a fault in the whole system. A famous example being Einsteinian and Newtonian gravity which are both ‘true’ but the former is ‘better’ suited for physical descriptions as it incorporates a better definition of the phenomenon.Not quite.
Mathematics are not as accurate and successful as the ubiquity of mathematical applications has led us to believe. Analytical mathematical equations only ''approximately'' describe the real world, and even then only describe a limited subset of all the phenomena around us. We tend to focus on those physical problems for which we find a way to apply mathematics, so overemphasis on these successes is a form of "cherry picking."
This is the realist position.
Well I meant axioms. All axioms are based on logical truths that apply in the real world. But as it gets more abstract, it does only ‘fits in’ or stays ‘accurate’. But then there always must be a ‘better’ substitution for physical descriptions. It Could just be a fault in observation and a wrong mathematical association than a fault in the whole system. A famous example being Einsteinian and Newtonian gravity which are both ‘true’ but the former is ‘better’ suited for physical descriptions as it incorporates a better definition of the phenomenon.
I’d say the answer is the way God shaped our understanding to have an innate sense of logic. I’d also say a metaphysical analysis is suitable for an alternate reality in which our current understandings of reason are inaplicable.That's a bit of a problem. Logic, as humans understand it and as it relates to mathematics, is a set of artifacts like , Venn diagrams, syllogisms, rules, proofs and algorithms etc
These are definitely things that humans created. Logic that forms the foundation of mathematics itself is based on human reasoning, i can't concieve how logic can exist independently without a subject to think it.
Anyway, From the gist of what Penrose says in the video, Math exists independent of us and we discover it.
Yes, I think whoever says otherwise is a lunatic attacking objective truth.
The curlicue on that 9 though lolWorth mentioning in this thread is how the Arabic numerals the world uses today came about. They were designed by Muḥammad ibn Mūsā al-Khwārizmī (780–850). Each digit represented number of angles.
View attachment 217648
Dont we discover maths through observations of the real worldIncorrect answer.
Mathematics is not a play with logic. It is a language humans invented to describe the natural/physical phenomena we discover around us.
The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. It is a product of the human mind and we make mathematics up as we go along to suit our purposes.
If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it's invented.