I come into this with an open mind, but I find several things here that leave me unpersuaded. First, there are some dubious assertions in the text above:
> "Mathematicians are the ultimate scientists, discovering absolute truths not just about this physical universe but about any possible universe."
I don't know anyone in the science community who would vouch for this. Math is a *tool* in science but not science itself. (If it were, then string theory would be the TOE and physics would be over.)
> "If it’s all just Stories and Math, and we are eliminating Math, then doesn’t that just make everything a Story? The answer is Yes."
Lakoff does not assert this in the video you linked. If that's *your* contention, you have a long way to go in grounding it. Lakoff starts off by stating that the dichotomy between invented or discovered math is false. He goes on to argue that patterns exist in nature (Nature's language?) and that we have emergent metaphors that align with those patterns. I'm not convinced, because in the video, at least, Lakoff implies, without evidence, that finding neural functions that are extendable into higher mathematics rules out the possibility that math exists independent of brains.
I have high regard for Lakoff and would not want to dismiss his case without reading his book, but on the face of it the argument seems trivial. Regardless of whether math is invented or discovered, human brains *must* have the capacity to model it, or we wouldn't be having a debate on its ontology.
I usually have more quotes I'd like to include in these posts than I have time and space for - I do try mightily to keep posts short while not sacrificing content. In this case, I seem to have failed.
On your first point, you are probably correct in that a lot of working scientists do not subscribe to the Romance of Mathematics; however, a lot of scientists and mathematicians do (Donald Hoffman for example). When I finally get around to writing a 'Critique of Scientism', I will draw heavily on Sabine Hossenfelder's book, Lost in Math: How Beauty Leads Physics astray. In there I will elaborate more on how silly it can be to say such things as 'Mathematics is the Language of Nature.'
On your second point, the evidence is in the book, Where Mathematics Comes From. Specifically, there are four grounding domains that humans use to derive higher mathematics from: Forming Collections, Putting Objects Together, Using Measuring Sticks, and Moving Through Space. Each one is grounded in our conceptual systems and bodily movements.
The whole idea to be grasped is that the, "Out There" or, "External Reality" or, whatever you want to call it, is not built of mathematics. Mathematics does not exist in the "Out There" or in Nature.
"Mathematics is a mental creation that evolved to study objects in the world. Given that objects in the world have these properties, it is no surprise that mathematical entities should inherit them. Thus, mathematics, too, is universal, precise, consistent within each subject matter, stable over time, generalizable, and discoverable. The view that mathematics is a product of embodied cognition - mind as it arises through interaction with the world - explains why mathematics has these properties." (Page 350)
I hope this helps, but if it doesn't, let me know. I'll try to make it clearer in a future post.
I come into this with an open mind, but I find several things here that leave me unpersuaded. First, there are some dubious assertions in the text above:
> "Mathematicians are the ultimate scientists, discovering absolute truths not just about this physical universe but about any possible universe."
I don't know anyone in the science community who would vouch for this. Math is a *tool* in science but not science itself. (If it were, then string theory would be the TOE and physics would be over.)
> "If it’s all just Stories and Math, and we are eliminating Math, then doesn’t that just make everything a Story? The answer is Yes."
Lakoff does not assert this in the video you linked. If that's *your* contention, you have a long way to go in grounding it. Lakoff starts off by stating that the dichotomy between invented or discovered math is false. He goes on to argue that patterns exist in nature (Nature's language?) and that we have emergent metaphors that align with those patterns. I'm not convinced, because in the video, at least, Lakoff implies, without evidence, that finding neural functions that are extendable into higher mathematics rules out the possibility that math exists independent of brains.
I have high regard for Lakoff and would not want to dismiss his case without reading his book, but on the face of it the argument seems trivial. Regardless of whether math is invented or discovered, human brains *must* have the capacity to model it, or we wouldn't be having a debate on its ontology.
Hello Clay. I always appreciate your feedback.
I usually have more quotes I'd like to include in these posts than I have time and space for - I do try mightily to keep posts short while not sacrificing content. In this case, I seem to have failed.
On your first point, you are probably correct in that a lot of working scientists do not subscribe to the Romance of Mathematics; however, a lot of scientists and mathematicians do (Donald Hoffman for example). When I finally get around to writing a 'Critique of Scientism', I will draw heavily on Sabine Hossenfelder's book, Lost in Math: How Beauty Leads Physics astray. In there I will elaborate more on how silly it can be to say such things as 'Mathematics is the Language of Nature.'
On your second point, the evidence is in the book, Where Mathematics Comes From. Specifically, there are four grounding domains that humans use to derive higher mathematics from: Forming Collections, Putting Objects Together, Using Measuring Sticks, and Moving Through Space. Each one is grounded in our conceptual systems and bodily movements.
The whole idea to be grasped is that the, "Out There" or, "External Reality" or, whatever you want to call it, is not built of mathematics. Mathematics does not exist in the "Out There" or in Nature.
"Mathematics is a mental creation that evolved to study objects in the world. Given that objects in the world have these properties, it is no surprise that mathematical entities should inherit them. Thus, mathematics, too, is universal, precise, consistent within each subject matter, stable over time, generalizable, and discoverable. The view that mathematics is a product of embodied cognition - mind as it arises through interaction with the world - explains why mathematics has these properties." (Page 350)
I hope this helps, but if it doesn't, let me know. I'll try to make it clearer in a future post.