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Platonists don't need to renounce empiricism. Assuming that I am real, if I can think about what mathematics is and arrive at answers, then logic exists and rea

by yholio 6y ago

Platonists don't need to renounce empiricism. Assuming that I am real, if I can think about what mathematics is and arrive at answers, then logic exists and reality is non-uniform, it has some form of structure that permits non-uniformity of answers, allows questions, logic. So the first thought I formulate is an empirical proof that reality has structure. Mathematics is nothing but a description of that structure of reality. We may describe it in human-centric terms and models, but the structure must by necessity pre-exist the mind and is empirically discovered by the action rational tought, not created by the mind. No similar conclusion can be drawn for other non-empirical hypothesis, such as the existence of God. My ability to think does not imply the existence of anything else beside myself, so other empirical proofs must be considered.

chongli 6y ago
What’s an empirical proof? I’m not being facetious, I’m genuinely interested because I’ve never heard the term before. To me, a proof is a deductive mathematical argument that takes a claim of the form “if P then Q” and shows how Q is necessarily true when we assume P. I don’t know how to translate from reality into that formalism. All of modern mathematics does not attempt to do so. Instead, it is built up from the axioms of set theory, which take the form of rules for manipulating symbols on paper (or on a computer or even in our minds) without saying anything specific about what those symbols really mean.
vlovich123 6y ago
I like that. The way I like to think of it is that mathematics is the language of the Universe. All parts of the universe can be described by this language but not all things described by the language may occur within the universe. While it can be used to describe the reality we experience about our universe, it can also create imagined universes that have only the most tenuous grasp (if any). Like any language it supports fiction and non-fiction applications. There are also rules about how the language evolves that are more strict and defined than human language and the evolution often is more akin to discovery. It’s like the exercise to try to write every single possible English language novel to find Shakespeare. Except instead of stories about human experience we’re trying to identify which random storyline we’re following maps to some fundamental truth about how the universe works. You can sometimes also map fiction to our experience of the world so that it becomes more tangible (eg playing with 4d objects in a 3d video game viewed through a 2d plane). This is no different from reading a fiction book to learn about concepts like compassion even though the story itself is made up. So it’s not either or to me. Both empiricism and Platonism interpretations coexist. Empiricism is what we use to understand what story reality is telling us and how to confirm our comprehension of that story is correct. Platonism is that mathematics itself as a concept is something humans can explore and try to master but exists outside of us and the rules of the language are predefined outside of humanity. Note that just like any language it even has really significant gaps you can’t do anything about (which ironically the language gave us the ability to prove that about itself). That being said the original question this article references indicates a lack of curiosity, which is where my problem with it stems from. And it’s not even like it’s hard to find (although it may require more than a superficial query). “What are practical applications of algebra” is answered in the first few hits. “Who discovered/invented algebra” can be similarly answered. These questions only sound deep if you are actively avoid actually trying to find answers to these questions. There are legitimate philosophical discussions to be had but the original question was not an attempt to have that discussion.
- jackcosgrove 6y ago
  > While it can be used to describe the reality we experience about our universe, it can also create imagined universes that have only the most tenuous grasp (if any). Like any language it supports fiction and non-fiction applications. Maybe I am wading into well-charted waters and thinking of something others have already hashed out, but if our universe only applies a subset of math, could that also mean there is another universe where a different subset of math is applicable? And the multiverse in sum encompasses all math? Platonism would then be true at the most global scope, but empiricism is necessary to discover what part of math our particular universe encompasses.
  - vlovich123 6y ago
    How are you defining the word “universe”? Is it in a hypothetical imagined virtual universe? If so then yes, that happens regularly in mathematics (eg Carl Sagan’s flatworld). If you’re asking “are there multiple real universes in reality with some kind of relationship between them” we don’t know yet and until we have a falsifiable theory that withstands experiments we won’t know. Mathematics can be used to prove certain properties in the absence of those experiments and to explain how a theory might be falsifiable. An example of this would be string theory. Mathematically self-consistent, all available evidence seems to be against it (can’t recall if it was finally disproven or still just highly unlikely to be true)
colordrops 6y ago
> Assuming that I am real That still leaves the definition of "real" and "exists". And even if a precise definition is given, that leaves the question of whether you are real or not. The answers to these questions are not incidental and are indeed relevant to your subsequent assertions.
skissane 6y ago
> but the structure must by necessity pre-exist the mind Why must the structure by necessity pre-exist the mind? In other words, you are asserting that idealism (all reality is mind-dependent) is necessarily false, but what is your argument to justify that assertion? (Even someone who believes that idealism is false might not agree that it is necessarily false, although the term necessity is ambiguous and can have different meanings – broad vs narrow logical necessity, metaphysical necessity, epistemic necessity, nomic necessity, real necessity, etc.)

by yholio 6y ago

chongli 6y ago

What’s an empirical proof? I’m not being facetious, I’m genuinely interested because I’ve never heard the term before. To me, a proof is a deductive mathematical argument that takes a claim of the form “if P then Q” and shows how Q is necessarily true when we assume P. I don’t know how to translate from reality into that formalism. All of modern mathematics does not attempt to do so. Instead, it is built up from the axioms of set theory, which take the form of rules for manipulating symbols on paper (or on a computer or even in our minds) without saying anything specific about what those symbols really mean.

vlovich123 6y ago

I like that. The way I like to think of it is that mathematics is the language of the Universe. All parts of the universe can be described by this language but not all things described by the language may occur within the universe. While it can be used to describe the reality we experience about our universe, it can also create imagined universes that have only the most tenuous grasp (if any). Like any language it supports fiction and non-fiction applications. There are also rules about how the language evolves that are more strict and defined than human language and the evolution often is more akin to discovery. It’s like the exercise to try to write every single possible English language novel to find Shakespeare. Except instead of stories about human experience we’re trying to identify which random storyline we’re following maps to some fundamental truth about how the universe works. You can sometimes also map fiction to our experience of the world so that it becomes more tangible (eg playing with 4d objects in a 3d video game viewed through a 2d plane). This is no different from reading a fiction book to learn about concepts like compassion even though the story itself is made up. So it’s not either or to me. Both empiricism and Platonism interpretations coexist. Empiricism is what we use to understand what story reality is telling us and how to confirm our comprehension of that story is correct. Platonism is that mathematics itself as a concept is something humans can explore and try to master but exists outside of us and the rules of the language are predefined outside of humanity. Note that just like any language it even has really significant gaps you can’t do anything about (which ironically the language gave us the ability to prove that about itself). That being said the original question this article references indicates a lack of curiosity, which is where my problem with it stems from. And it’s not even like it’s hard to find (although it may require more than a superficial query). “What are practical applications of algebra” is answered in the first few hits. “Who discovered/invented algebra” can be similarly answered. These questions only sound deep if you are actively avoid actually trying to find answers to these questions. There are legitimate philosophical discussions to be had but the original question was not an attempt to have that discussion.

jackcosgrove 6y ago
> While it can be used to describe the reality we experience about our universe, it can also create imagined universes that have only the most tenuous grasp (if any). Like any language it supports fiction and non-fiction applications. Maybe I am wading into well-charted waters and thinking of something others have already hashed out, but if our universe only applies a subset of math, could that also mean there is another universe where a different subset of math is applicable? And the multiverse in sum encompasses all math? Platonism would then be true at the most global scope, but empiricism is necessary to discover what part of math our particular universe encompasses.
- vlovich123 6y ago
  How are you defining the word “universe”? Is it in a hypothetical imagined virtual universe? If so then yes, that happens regularly in mathematics (eg Carl Sagan’s flatworld). If you’re asking “are there multiple real universes in reality with some kind of relationship between them” we don’t know yet and until we have a falsifiable theory that withstands experiments we won’t know. Mathematics can be used to prove certain properties in the absence of those experiments and to explain how a theory might be falsifiable. An example of this would be string theory. Mathematically self-consistent, all available evidence seems to be against it (can’t recall if it was finally disproven or still just highly unlikely to be true)

colordrops 6y ago

> Assuming that I am real That still leaves the definition of "real" and "exists". And even if a precise definition is given, that leaves the question of whether you are real or not. The answers to these questions are not incidental and are indeed relevant to your subsequent assertions.

skissane 6y ago

> but the structure must by necessity pre-exist the mind Why must the structure by necessity pre-exist the mind? In other words, you are asserting that idealism (all reality is mind-dependent) is necessarily false, but what is your argument to justify that assertion? (Even someone who believes that idealism is false might not agree that it is necessarily false, although the term necessity is ambiguous and can have different meanings – broad vs narrow logical necessity, metaphysical necessity, epistemic necessity, nomic necessity, real necessity, etc.)