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I have a great respect for this author, but I do have to note that the debate of "constructivism" vs. "platonism" doesn't really exist in Philosophy per se, bec

I have a great respect for this author, but I do have to note that the debate of "constructivism" vs. "platonism" doesn't really exist in Philosophy per se, because it relies on a kind of basic misunderstanding of Plato in general. At least since Kant, the general consensus in Philosophy about Plato's "forms" or ideal objects is that they are conceptual objects, famously Kant argued that while reality in-itself is inscrutable, the means of judgement whereby we organize the world into concepts (beginning with the intuitions of time and space) are not, and by analysis of judgement we can begin to better understand the process of reasoning and therefore more rigorously understand the means by which empirical judgements are made (and thus further our understanding of empirical reality). Of course, many have attempted to answer the question of the psychological/biological explanation for how humans have shared concepts like this and shared, intelligible language. The most prominent thinkers of the 20th century, on both "sides" if you will, were Lacan on the "continental" end, and Chomsky on the "analytic" side. (Even though most Anglo-American--i.e. Analytic--philosophers would not accept Chomsky's logic as valid, and Lacan often referenced Anglo-American philosophy in his work...the categories are basically meaningless at this point.) But there are many other names, many people asking the above question, and I will not say who's thought attracts me the most, but I will say that most people I meet who study math are not familiar with them or the intellectual trends they are a part of, and they do not have a rigorous enough understanding of what philosophy is, really, to make claims about the usefulness of philosophy for their work--or even debate it, for that matter.

techno_tsar 4y ago
I believe that "platonism" in this article refers to mathematical platonism, i.e. the view that mathematical entities actually exist, as opposed to mathematical formalism, i.e. the view that mathematical entities are made up. https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Platonism https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Plat... https://iep.utm.edu/mathplat/ https://iep.utm.edu/mathplat/ This view is only called platonism because it parallels Plato's thoughts, but it is not an explicit reference to Plato's original philosophy. Modern platonism (after Kant) exists as an attitude about a kind of non-mental realism of abstract objects, and so it is with mathematical platonism. These days, there are very few Platonists (those who subscribe to the philosophy of Plato), but many platonists. As for the second point: A PhilPapers survey showed that most professional philosophers of mathematics are platonists, and most mathematicians who are familiar with the debate lean towards platonism. It is much more intuitive to understand how mathematical claims are true if you believe that numbers are real objects in the fist place, which in turn allows us to use the same accounts of truth we would normally use for non-abstract objects. At least prima facie, mathematical truths like 2+2=4 do not seem like they are different types of truth than empirical truths like "Biden is currently president". If mathematical objects like 2 and 4 weren't real, we would have to come up with a new account of truth that applies specifically to mathematics to explain what makes its statements true, which while possible, is a lot less elegant. Obviously, that doesn't refute platonism's alternatives, but in the words of a friend, it would really suck if he spent his career studying something that was entirely fictional, so he better be a platonist.
- dr_dshiv 4y ago
  Plato is worth reading in the original because of the way it makes one think. But we might call it Pythagorean if we want to claim that the world is made of Math. Roger Penrose has a very nice “3 worlds theory” about mathematics, the physical world and the world of mental experience. He describes theories for how these worlds encompass each other and overlap. In “The Road to Reality.”
  - techno_tsar 4y ago
    In addition to this, Plato is worth reading because he is still relevant and his work outlined the agenda of huge swathes of western philosophy, which undeniably influences our scientific paradigm and political worldviews. I have not yet read The Road to Reality. At 1094 pages, I hope it is not extremely complicated.
    - dr_dshiv 4y ago
      Plato gets summarized — and that mostly doesn’t work. Need to read it. The Parmenides is supposed to be the hardest to understand—pah, I’d start with that. Cut to Zeno arguing conclusively that all is one. He then conclusively argues that everything can’t be one. Then… Don’t be put off by the size of Penrose’s road to reality! The introduction and first chapter already made the book worth it. I’ve not gotten much further myself (but that’s how I read)
      - DiscourseFan 4y ago
        Plato can't be summarized, there are no conclusions to any of the arguments, just endless arguments. That's why he's so great, he always leaves the question open, there is always room for greater understanding.
- DiscourseFan 4y ago
  >Obviously, that doesn't refute platonism's alternatives, but in the words of a friend, it would really suck if he spent his career studying something that was entirely fictional, so he better be a platonist. Remember, fiction is real: it takes time to be written, its distributed to its audiences, it has a definite cultural impact and often changes how people view the world. Entirely fictional plays have spawned political revolutions--there are many forces at play in a fictional work that are certainly objective and real. There isn't anything that isn't "real", the question is not "is math real" (it definitely is), the question is "where does math exist?", and on account of its location (inside or outside the head), how we should be approaching it and where it should be applied. Nobody would say math isn't useful, but we might say it could be more useful if its basis is more rigorously examined.
mjh2539 4y ago
> At least since Kant, the general consensus in Philosophy about Plato's "forms" or ideal objects is that they are conceptual objects. ...you just made this up. Kantianism is not the predominant view among working metaphysicians today. It's a large plurality, at best.
- dmarchand90 4y ago
  ... but he doesn't say a majority of philosophers believe in Kant. He just says the view of the forms has been different since Kant's time
  - mjh2539 4y ago
    > At least since Kant, the general consensus in Philosophy about Plato's "forms" or ideal objects is that they are conceptual objects.
    - eouwt 4y ago
      Repasting the quote without addressing the response does not do much to bolster your position - perhaps the opposite!
- atoav 4y ago
  > Kantianism is not the predominant view among working metaphysicians today Which gladly nobody claimed to be the case. "At least since Kant" gives us a time frame not a causal link — and even if it did pretend there was a causal link, any philosopher wouldn't have to be a Kantian in order to agree to a thing Kant said about Plato's concept. Or phrased differently: A Non-Kantian can agree with Kant on a thing Kant said about Plato without suddenly becoming a Kantian. What the poster said here is to my knowledge correct (I studied philosophy).
bmitc 4y ago
Being stirred by your last sentence, I have a lot of trouble reading some philosophy. I have read your comment several times, and I am still not sure what it is saying. > I do have to note that the debate of "constructivism" vs. "platonism" doesn't really exist in Philosophy per se, because it relies on a kind of basic misunderstanding of Plato in general. What is the misunderstanding, exactly? Did you end up addressing this? The next sentence is a long run-on, and I'm getting lost in what you're saying Plato actually said versus what you think people think he said. And I think I agree with another commenter that you are confusing Platonic and platonic. And what does philosophy say about constructivism? If it doesn't address it versus some notion of idealized objects existing, then why does that matter to mathematics? It is a legitimate line of thinking and isn't an exclusively philosophical subject. > Of course, many have attempted to answer the question of the psychological/biological explanation for how humans have shared concepts like this and shared, intelligible language. The most prominent thinkers of the 20th century, on both "sides" if you will, were Lacan on the "continental" end, and Chomsky on the "analytic" side. (Even though most Anglo-American--i.e. Analytic--philosophers would not accept Chomsky's logic as valid, and Lacan often referenced Anglo-American philosophy in his work...the categories are basically meaningless at this point.) There are just names and labels here. What are you saying here?
beezlebroxxxxxx 4y ago
It's very weird that you would reach for Lacan and Chomsky. Neither of them are really seen as credible in the field of philosophy, nor have they had really large impacts in philosophy. Cultural criticism and linguistics? Sure, I guess. But not in philosophy. Even in the 20th century "continental" tradition of cultural criticism, Lacan is not very high in the eyes of many. Heidegger (controversially, of course) or Maurice Merleau-Ponty or Paul Ricoeur have been much more influential. For whatever reason, Lacanian analysis did burn bright in the 70s and 80s, but man has it fallen hard. Arguably all modern philosophy of language in the 20th century was influenced by Ludwig Wittgenstein. Wittgenstein is, for many philosophers, the most influential philosopher of the 20the century. Wittgenstein's "method" and work in Philosophical Investigations also offers the most far reaching and consequential criticisms of platonism, cartesian mind-body dualism, and philosophical skepticism, in the philosophical canon. I do agree with your closing comments though. Most people aren't very well versed in philosophy and operate on a sort of pop understanding of it. They simply lack the framework to make credible claims on the usefulness of it in general. It's especially hilarious when they try to say one of the longest and most fruitful intellectual disciplines in human civilization is "not very useful." Sure, bud.
- AnimalMuppet 4y ago
  > It's especially hilarious when they try to say one of the longest and most fruitful intellectual disciplines in human civilization is "not very useful." Sure, bud. One of the longest? Sure. One of the most fruitful? I'm not so sure. What are the concrete, usable conclusions of philosophy, and what are the fruit of those conclusions? How do they compare to the fruit of the usable conclusions of Newtonian mechanics or Maxwell's Electrodynamics?
Koshkin 4y ago
“Philosophy tries to answer questions that do not have answers; theology studies that which does not exist.’
voxl 4y ago
Unfortunately much of philosophy is very easily ignored. The philosopher will get very defensive about this, as perhaps they should, since their work was the "initial" work leading to the development of a rigorous field (physics, mathematics, psychology, etc). However, much of philosophy is intentionally vague because the philosopher is grasping at straws, is speculating. Philosophy is a discipline whose success is desperately trying to reclassify itself from its own subject. In that regard, when you say that mathematicians do not care and cannot argue philosophy, you are merely being defensive. There is nothing in the philosophy of math that a Mathematician could not grapple with at your level of expertise or better in a simple conversation with no preparation. The issue is that what you have to say is not rigorous, it is not grounded in anything, it is vague. This is your problem, not the mathematicians.

techno_tsar 4y ago

I believe that "platonism" in this article refers to mathematical platonism, i.e. the view that mathematical entities actually exist, as opposed to mathematical formalism, i.e. the view that mathematical entities are made up. https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Platonism https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Plat... https://iep.utm.edu/mathplat/ https://iep.utm.edu/mathplat/ This view is only called platonism because it parallels Plato's thoughts, but it is not an explicit reference to Plato's original philosophy. Modern platonism (after Kant) exists as an attitude about a kind of non-mental realism of abstract objects, and so it is with mathematical platonism. These days, there are very few Platonists (those who subscribe to the philosophy of Plato), but many platonists. As for the second point: A PhilPapers survey showed that most professional philosophers of mathematics are platonists, and most mathematicians who are familiar with the debate lean towards platonism. It is much more intuitive to understand how mathematical claims are true if you believe that numbers are real objects in the fist place, which in turn allows us to use the same accounts of truth we would normally use for non-abstract objects. At least prima facie, mathematical truths like 2+2=4 do not seem like they are different types of truth than empirical truths like "Biden is currently president". If mathematical objects like 2 and 4 weren't real, we would have to come up with a new account of truth that applies specifically to mathematics to explain what makes its statements true, which while possible, is a lot less elegant. Obviously, that doesn't refute platonism's alternatives, but in the words of a friend, it would really suck if he spent his career studying something that was entirely fictional, so he better be a platonist.

dr_dshiv 4y ago
Plato is worth reading in the original because of the way it makes one think. But we might call it Pythagorean if we want to claim that the world is made of Math. Roger Penrose has a very nice “3 worlds theory” about mathematics, the physical world and the world of mental experience. He describes theories for how these worlds encompass each other and overlap. In “The Road to Reality.”
- techno_tsar 4y ago
  In addition to this, Plato is worth reading because he is still relevant and his work outlined the agenda of huge swathes of western philosophy, which undeniably influences our scientific paradigm and political worldviews. I have not yet read The Road to Reality. At 1094 pages, I hope it is not extremely complicated.
  - dr_dshiv 4y ago
    Plato gets summarized — and that mostly doesn’t work. Need to read it. The Parmenides is supposed to be the hardest to understand—pah, I’d start with that. Cut to Zeno arguing conclusively that all is one. He then conclusively argues that everything can’t be one. Then… Don’t be put off by the size of Penrose’s road to reality! The introduction and first chapter already made the book worth it. I’ve not gotten much further myself (but that’s how I read)
    - DiscourseFan 4y ago
      Plato can't be summarized, there are no conclusions to any of the arguments, just endless arguments. That's why he's so great, he always leaves the question open, there is always room for greater understanding.
DiscourseFan 4y ago
>Obviously, that doesn't refute platonism's alternatives, but in the words of a friend, it would really suck if he spent his career studying something that was entirely fictional, so he better be a platonist. Remember, fiction is real: it takes time to be written, its distributed to its audiences, it has a definite cultural impact and often changes how people view the world. Entirely fictional plays have spawned political revolutions--there are many forces at play in a fictional work that are certainly objective and real. There isn't anything that isn't "real", the question is not "is math real" (it definitely is), the question is "where does math exist?", and on account of its location (inside or outside the head), how we should be approaching it and where it should be applied. Nobody would say math isn't useful, but we might say it could be more useful if its basis is more rigorously examined.

mjh2539 4y ago

> At least since Kant, the general consensus in Philosophy about Plato's "forms" or ideal objects is that they are conceptual objects. ...you just made this up. Kantianism is not the predominant view among working metaphysicians today. It's a large plurality, at best.

dmarchand90 4y ago
... but he doesn't say a majority of philosophers believe in Kant. He just says the view of the forms has been different since Kant's time
- mjh2539 4y ago
  > At least since Kant, the general consensus in Philosophy about Plato's "forms" or ideal objects is that they are conceptual objects.
  - eouwt 4y ago
    Repasting the quote without addressing the response does not do much to bolster your position - perhaps the opposite!
atoav 4y ago
> Kantianism is not the predominant view among working metaphysicians today Which gladly nobody claimed to be the case. "At least since Kant" gives us a time frame not a causal link — and even if it did pretend there was a causal link, any philosopher wouldn't have to be a Kantian in order to agree to a thing Kant said about Plato's concept. Or phrased differently: A Non-Kantian can agree with Kant on a thing Kant said about Plato without suddenly becoming a Kantian. What the poster said here is to my knowledge correct (I studied philosophy).

bmitc 4y ago

Being stirred by your last sentence, I have a lot of trouble reading some philosophy. I have read your comment several times, and I am still not sure what it is saying. > I do have to note that the debate of "constructivism" vs. "platonism" doesn't really exist in Philosophy per se, because it relies on a kind of basic misunderstanding of Plato in general. What is the misunderstanding, exactly? Did you end up addressing this? The next sentence is a long run-on, and I'm getting lost in what you're saying Plato actually said versus what you think people think he said. And I think I agree with another commenter that you are confusing Platonic and platonic. And what does philosophy say about constructivism? If it doesn't address it versus some notion of idealized objects existing, then why does that matter to mathematics? It is a legitimate line of thinking and isn't an exclusively philosophical subject. > Of course, many have attempted to answer the question of the psychological/biological explanation for how humans have shared concepts like this and shared, intelligible language. The most prominent thinkers of the 20th century, on both "sides" if you will, were Lacan on the "continental" end, and Chomsky on the "analytic" side. (Even though most Anglo-American--i.e. Analytic--philosophers would not accept Chomsky's logic as valid, and Lacan often referenced Anglo-American philosophy in his work...the categories are basically meaningless at this point.) There are just names and labels here. What are you saying here?

beezlebroxxxxxx 4y ago

It's very weird that you would reach for Lacan and Chomsky. Neither of them are really seen as credible in the field of philosophy, nor have they had really large impacts in philosophy. Cultural criticism and linguistics? Sure, I guess. But not in philosophy. Even in the 20th century "continental" tradition of cultural criticism, Lacan is not very high in the eyes of many. Heidegger (controversially, of course) or Maurice Merleau-Ponty or Paul Ricoeur have been much more influential. For whatever reason, Lacanian analysis did burn bright in the 70s and 80s, but man has it fallen hard. Arguably all modern philosophy of language in the 20th century was influenced by Ludwig Wittgenstein. Wittgenstein is, for many philosophers, the most influential philosopher of the 20the century. Wittgenstein's "method" and work in Philosophical Investigations also offers the most far reaching and consequential criticisms of platonism, cartesian mind-body dualism, and philosophical skepticism, in the philosophical canon. I do agree with your closing comments though. Most people aren't very well versed in philosophy and operate on a sort of pop understanding of it. They simply lack the framework to make credible claims on the usefulness of it in general. It's especially hilarious when they try to say one of the longest and most fruitful intellectual disciplines in human civilization is "not very useful." Sure, bud.

AnimalMuppet 4y ago
> It's especially hilarious when they try to say one of the longest and most fruitful intellectual disciplines in human civilization is "not very useful." Sure, bud. One of the longest? Sure. One of the most fruitful? I'm not so sure. What are the concrete, usable conclusions of philosophy, and what are the fruit of those conclusions? How do they compare to the fruit of the usable conclusions of Newtonian mechanics or Maxwell's Electrodynamics?

Koshkin 4y ago

“Philosophy tries to answer questions that do not have answers; theology studies that which does not exist.’

voxl 4y ago

Unfortunately much of philosophy is very easily ignored. The philosopher will get very defensive about this, as perhaps they should, since their work was the "initial" work leading to the development of a rigorous field (physics, mathematics, psychology, etc). However, much of philosophy is intentionally vague because the philosopher is grasping at straws, is speculating. Philosophy is a discipline whose success is desperately trying to reclassify itself from its own subject. In that regard, when you say that mathematicians do not care and cannot argue philosophy, you are merely being defensive. There is nothing in the philosophy of math that a Mathematician could not grapple with at your level of expertise or better in a simple conversation with no preparation. The issue is that what you have to say is not rigorous, it is not grounded in anything, it is vague. This is your problem, not the mathematicians.