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Probably one of the few people that read the whole thing, but the argument is, in my opinion, pretty weak. It basically boils down to making some kind of equiva

by dvt 8y ago

Probably one of the few people that read the whole thing, but the argument is, in my opinion, pretty weak. It basically boils down to making some kind of equivalence between metaphysics and pure mathematics. Of course, it ignores the main force of mathematical progress: theorem-building. Metaphysics might be "interconnected in much the same way" as Dr. Baron argues, but let's not kid ourselves. To argue that metaphysics is as "conceptually interrelated" as mathematics is is a real stretch. Just consider volume: it's estimated that around a quarter of a million theorems are proved every year. That's real, measurable, progress; what's the metaphysics equivalent? The distinction between "internally applied metaphysics" and "externally applied metaphysics" on page 14 is a shameless red herring. The only thing we ought to care about, given the preceding section on applications of pure mathematics is "externally applied metaphysics," but in typical philosopher fashion, Dr. Baron equivocates for a few unnecessary pages. Finally, let me leave you with this gem: "All three cases are examples in which scientists appear to be doing metaphysics. Computer scientists build models of objects and categories in order to provide the resources for artificial intelligence to successfully navigate the world, or make judgements [sic] about it." Yeah, that's not metaphysics; it's pretty much just regular taxonomy (and, by the way, the term of art is labeling). TensorFlow models have nothing to do with metaphysical models, and this is exactly why philosophers get such a bad rap. They extend far beyond the reaches of their knowledge base and don't even have the courtesy to look up "machine learning model" on Wikipedia.

NotAnEconomist 8y ago
Isn't the equivalent metaphysics all those moments we have a theory of how to examine the world, so as to come to an accurate conclusion? Metaphysics is required to make an inference -- it's the philosophical underpinning of things like science. Hence "meta-" "physics": the study of the study of physics. Metaphysics is the glue that takes the language of mathematics to ontologies of physics. Mathematics is the modern rigorous language of metaphysics. Assorted marketing campaigns have made the topic murky. > Yeah, that's not metaphysics; it's pretty much just regular taxonomy (and, by the way, the term of art is labeling). That literally is metaphysics. It's okay there's another word (or two?), but words are not exclusive in the way your logic implies.
- dvt 8y ago
  > That literally is metaphysics. The claim that toddlers figuring out what shapes fit in what wooden holes are doing metaphysics is seriously off-base. Metaphysics deals with first causes, ontology, modality, free will, and so on. Let's not mince words. Taxonomy is not metaphysics. > No, they do. I think the burden of proof is on you. You're making fantastical claims but I don't see any connection between a TensorFlow model and any metaphysical model whatsoever. > This is why people get frustrated: you don't seem to understand the link, squawk about how it doesn't exist, and then insist philosophy must be useless because you never took the time to understand where you do it naturally. I studied philosophy.
  - NotAnEconomist 8y ago
    > what shapes fit in what wooden holes > ontology We must be talking past each other, or something. For context, for other readers -- > Traditionally listed as the core of metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences. https://en.wikipedia.org/wiki/Metaphysics#Ontology_(Being) https://en.wikipedia.org/wiki/Metaphysics#Ontology_(Being)
    - dvt 8y ago
      > We must be talking past each other, or something. I guess we are. According to you, when my cousins go to Six Flags, they're doing fluid mechanics. Forgive me if I don't buy that.
      - NotAnEconomist 8y ago
        It's literally ontology -- they're discovering the idea of shape as a concept, which is an equivalence of structural forms, which is an ontological concept. I mean, I get that you don't like that because it proves my point, and that's why you're making really silly comparisons. But to answer -- yes, most children at water parks also are figuring out fluid mechanics at a simple level, eg drag or interference.
ubernostrum 8y ago
The general idea you're missing here is that it's very hard -- perhaps impossible -- to develop a clear, bright-line method for distinguishing between fields that deal with concepts we can't empirically test, in such a way that it will put mathematics into the "good, useful, keep doing it" side and metaphysics into the "bad, silly, stop doing it" side. And in fact mathematics is a great place to dive in, because one very important question -- namely, whether mathematical realism is true¹ -- is really a metaphysical question, and one which can never be answered by empirical observations about the world. I'd also caution against too much scorn on philosophers going "beyond the reaches of their knowledge base"; historically, philosophy's successes have spun off into entire fields whose origins we now like to forget or at least overlook. (and, well, I've had a successful career in programming, and also hold a degree in philosophy, and I think the basic observation that lots of people do metaphysics who we don't normally think of as doing metaphysics is a sound one, regardless of how you feel about the paper's specific examples) --- ¹"Mathematical realism" asserts that truths of mathematics are necessary and discovered, rather than contingent and created, and thus have some sort of existence independently of human minds and human culture. The exact sense in which these mathematical truth-entities would exist is, of course, a metaphysical question, as is the question of what mathematics really is, if mathematical realism is false.
- hackinthebochs 8y ago
  >And in fact mathematics is a great place to dive in, because one very important question -- namely, whether mathematical realism is true¹ -- is really a metaphysical question, and one which can never be answered by empirical observations about the world. The important distinction between math and metaphysics is that the substantive content of the field of mathematics does not turn on whether mathematical realism is true. Mathematics tells us something about the world by telling us what can be true about the world. We know that there are prime numbers because we know that no such world exists where prime numbers are finite. But this is just saying that a system with certain axioms have certain relationships, or necessarily exclude certain relationships (e.g. whatever axioms of arithmetic you take). On the other hand, there is no substantive content in metaphysics (at least as far as ontology goes) if the statements do not pick out real entities.
man-and-laptop 8y ago
It boils down to the fact that Pure Mathematics has a well-tested (if sometimes rigid) methodology. Metaphysics may lack an adequate methodology. The role of methodologies in general is to determine what's true and what's false, and what's outright nonsense. Pure Mathematics may well be defined by its methodology.
- whatshisface 8y ago
  I think that's close to hitting it on the head. The author makes it sound like metaphysics is distrusted because there is no clear way for it to put bread on the table, while in reality it is distrusted because there is no way to tell if it is true.
jules 8y ago
It wouldn't change much even if there were 10 metaphysics papers for every mathematics paper. The main difference is that math is rigorous: there is an agreed upon standard for correctness that is falsifiable in two ways. Firstly, a proof of a theorem can be falsified by finding a mistake, and what is a mistake is agreed upon. Second, and more importantly, the system of proof itself is falsifiable. If a theorem says that an equation p(x,y,z) = 0 has no solutions, and a proof without mistakes is found, then it better have no solutions. If somebody comes along and demonstrates that x=43,y=23,z=809 is a solution, then the system is in trouble. This ensures that math is not a formal game of arbitrary axioms that is internally consistent but ultimately meaningless. That is important, because metaphysics could develop internal correctness criteria that everybody agrees upon, but it could still be meaningless.
- rntz 8y ago
  > Second, and more importantly, the system of proof itself is falsifiable. If a theorem says that an equation p(x,y,z) = 0 has no solutions, and a proof without mistakes is found, then it better have no solutions. If somebody comes along and demonstrates that x=43,y=23,z=809 is a solution, then the system is in trouble. This ensures that math is not a formal game of arbitrary axioms that is internally consistent but ultimately meaningless. I don't see how what you've said is anything other than the criterion of formal consistency - that a thing and its negation are not both provable. And a system may certainly be consistent, yet not particularly useful. It should be noted that mathematics has not always been as rigorous as people assume. Attempts to ground math in formal logic didn't really get off the ground until the late 1800s. And this isn't a trivial point; the "rules of the game" were up for debate, and often debated, before then (and, to a lesser extent, since). People disagreed about which numbers exist; people disagree about which proof methods are acceptable; and for example, calculus - a highly practical branch of mathematics - was invented before its formal justifications were found.
  - jules 8y ago
    It is more than formal consistency because to show a whole number solution to a^n + b^n = c^n and n > 2, one doesn't need to use a high powered formal framework like ZFC. Thus Wiles' proof of Fermat's last theorem, which uses all kinds of infinite sets and other features of ZFC, can be falsified by a simple manipulation of finite numbers. You just need the numbers a,b,c,n of the counterexample and a calculator. Mathematics thus makes predictions about the world (in this case about the behaviour of calculators, human or electronic) in a somewhat similar way that physics makes predictions about the world. Or as Arnold famously said: "Mathematics is the part of physics where experiments are cheap". You wouldn't have that if math was an arbitrary symbol pushing game with arbitrary axioms, with the only requirement that they be consistent. [If a counterexample to Fermat's last theorem is found it probably isn't because ZFC is inconsistent, but because Wiles' proof has a mistake, which would show that the checking of the proof was inadequate and that mathematics needs to use a higher standard for what is considered a valid proof. So the system of proof is falsifiable in a very broad sense: it can expose a bad proof checking culture within mathematics as well as inconsistencies in the formal system. I don't think that metaphysics has anything equivalent. If somebody comes up with a counterexample a,b,c,n then Wiles would immediately admit that his proof has a mistake, even though he wouldn't even know where in the proof the mistake is. Try convincing a metaphysicist that their argument is wrong or meaningless... That said, there are certainly also stubborn mathematicians who insist that their proof is right even though other mathematicians have pointed out that a particular step isn't clear. However, if the mathematician who came up with the proof cannot clarify that step, ultimately down to the axioms of ZFC, then the proof isn't accepted.]
myWindoonn 8y ago
Mathematics is metaphysics. I'd like your refutation to center on any nuance which might separate the two disciplines other than the sad fact that many philosophers don't learn much maths. Logic is metaphysics: https://philpapers.org/archive/ALVLIM-3.pdf https://philpapers.org/archive/ALVLIM-3.pdf Logic is mathematical, logic is categorical (structured in a deep way amenable to category theory), maths is categorical: http://math.ucr.edu/home/baez/rosetta.pdf http://math.ucr.edu/home/baez/rosetta.pdf https://ncatlab.org/nlab/show/internal+logic https://ncatlab.org/nlab/show/internal+logic https://ncatlab.org/nlab/show/topos https://ncatlab.org/nlab/show/topos Ontology is categorical: https://arxiv.org/abs/1102.1889v2 https://arxiv.org/abs/1102.1889v2 https://arxiv.org/abs/1706.00526 https://arxiv.org/abs/1706.00526 The working programmer is an ontologist and a taxonomist, but this fact isn't well-understood.
- vinceguidry 8y ago
  I'd like to draw a distinction between non-physical and metaphysical. The opposite of a thing is not the same thing as the meta of that same thing. The meta attempts to unify the topic and it's reverse. Metaphysics wants to kill the distinction between physical reality and non-physical reality. Non-physical disciplines such as mathematics wants to distill the non-physical essence of things
  - myWindoonn 8y ago
    This is a really nifty insight. Mathematical objects aren't physical, but that doesn't mean that there aren't objects that are neither physical nor mathematical. I wonder what those objects might be like!
- hackinthebochs 8y ago
  This kind of response really grinds my gears about these discussions of philosophy (more often than not related to metaphysics). You're referencing the mostly unobjectionable features of the field to defend the objectionable features, when there is very little similarity between the two. You can't defend ontology language games by appealing to the truth of logic or mathematics, as they share nothing of relevance in common. If you want to give an actual defense of the things people find objectionable about metaphysics, you have to defend the features being attacked, not tangentially related things that happen to be categorized under the same broad label. >Logic is metaphysics: Maybe this is true, but doing logic isn't doing metaphysics. One does not need to take a stance on the metaphysics of logic to study and create formal systems. >The working programmer is an ontologist and a taxonomist, but this fact isn't well-understood. Not in any substantive sense. There is a surface-level connection between what a programmer does and a metaphysician does, but this is the extent of the connection. The ontologies studied in metaphysics attempt to make true substantive statements about what exists in the actual world. The programmer is merely stipulating the basic objects and relationships in a fully contingent domain of inquiry. The programmer is doing metaphysics only if you remove anything of substance from what we take the metaphysician to be doing.
rntz 8y ago
> Just consider volume: it's estimated that around a quarter of a million theorems are proved every year. That's real, measurable, progress; what's the metaphysics equivalent? I'm not sure I disagree with your overall argument, but this point here is silly. First, I'd like to know where you got that number. (I must admit it sounds rather high to me, but I'm sure it depends how you count.) But more importantly, measuring mathematical progress by number of theorems proved is absurd. I can write a computer program to prove theorems; it will almost surely prove more than a quarter-million a day (though eventually it will have to slow down). But they will not be _useful_ theorems. Nobody will read them, nobody will use them, nobody will build on them, nobody will find them beautiful, nobody will apply them to any practical problem. "Number of theorems proven" may be measurable, but it is not "real progress".

by dvt 8y ago

NotAnEconomist 8y ago

Isn't the equivalent metaphysics all those moments we have a theory of how to examine the world, so as to come to an accurate conclusion? Metaphysics is required to make an inference -- it's the philosophical underpinning of things like science. Hence "meta-" "physics": the study of the study of physics. Metaphysics is the glue that takes the language of mathematics to ontologies of physics. Mathematics is the modern rigorous language of metaphysics. Assorted marketing campaigns have made the topic murky. > Yeah, that's not metaphysics; it's pretty much just regular taxonomy (and, by the way, the term of art is labeling). That literally is metaphysics. It's okay there's another word (or two?), but words are not exclusive in the way your logic implies.

dvt 8y ago
> That literally is metaphysics. The claim that toddlers figuring out what shapes fit in what wooden holes are doing metaphysics is seriously off-base. Metaphysics deals with first causes, ontology, modality, free will, and so on. Let's not mince words. Taxonomy is not metaphysics. > No, they do. I think the burden of proof is on you. You're making fantastical claims but I don't see any connection between a TensorFlow model and any metaphysical model whatsoever. > This is why people get frustrated: you don't seem to understand the link, squawk about how it doesn't exist, and then insist philosophy must be useless because you never took the time to understand where you do it naturally. I studied philosophy.
- NotAnEconomist 8y ago
  > what shapes fit in what wooden holes > ontology We must be talking past each other, or something. For context, for other readers -- > Traditionally listed as the core of metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences. https://en.wikipedia.org/wiki/Metaphysics#Ontology_(Being) https://en.wikipedia.org/wiki/Metaphysics#Ontology_(Being)
  - dvt 8y ago
    > We must be talking past each other, or something. I guess we are. According to you, when my cousins go to Six Flags, they're doing fluid mechanics. Forgive me if I don't buy that.
    - NotAnEconomist 8y ago
      It's literally ontology -- they're discovering the idea of shape as a concept, which is an equivalence of structural forms, which is an ontological concept. I mean, I get that you don't like that because it proves my point, and that's why you're making really silly comparisons. But to answer -- yes, most children at water parks also are figuring out fluid mechanics at a simple level, eg drag or interference.

ubernostrum 8y ago

The general idea you're missing here is that it's very hard -- perhaps impossible -- to develop a clear, bright-line method for distinguishing between fields that deal with concepts we can't empirically test, in such a way that it will put mathematics into the "good, useful, keep doing it" side and metaphysics into the "bad, silly, stop doing it" side. And in fact mathematics is a great place to dive in, because one very important question -- namely, whether mathematical realism is true¹ -- is really a metaphysical question, and one which can never be answered by empirical observations about the world. I'd also caution against too much scorn on philosophers going "beyond the reaches of their knowledge base"; historically, philosophy's successes have spun off into entire fields whose origins we now like to forget or at least overlook. (and, well, I've had a successful career in programming, and also hold a degree in philosophy, and I think the basic observation that lots of people do metaphysics who we don't normally think of as doing metaphysics is a sound one, regardless of how you feel about the paper's specific examples) --- ¹"Mathematical realism" asserts that truths of mathematics are necessary and discovered, rather than contingent and created, and thus have some sort of existence independently of human minds and human culture. The exact sense in which these mathematical truth-entities would exist is, of course, a metaphysical question, as is the question of what mathematics really is, if mathematical realism is false.

hackinthebochs 8y ago
>And in fact mathematics is a great place to dive in, because one very important question -- namely, whether mathematical realism is true¹ -- is really a metaphysical question, and one which can never be answered by empirical observations about the world. The important distinction between math and metaphysics is that the substantive content of the field of mathematics does not turn on whether mathematical realism is true. Mathematics tells us something about the world by telling us what can be true about the world. We know that there are prime numbers because we know that no such world exists where prime numbers are finite. But this is just saying that a system with certain axioms have certain relationships, or necessarily exclude certain relationships (e.g. whatever axioms of arithmetic you take). On the other hand, there is no substantive content in metaphysics (at least as far as ontology goes) if the statements do not pick out real entities.

man-and-laptop 8y ago

It boils down to the fact that Pure Mathematics has a well-tested (if sometimes rigid) methodology. Metaphysics may lack an adequate methodology. The role of methodologies in general is to determine what's true and what's false, and what's outright nonsense. Pure Mathematics may well be defined by its methodology.

whatshisface 8y ago
I think that's close to hitting it on the head. The author makes it sound like metaphysics is distrusted because there is no clear way for it to put bread on the table, while in reality it is distrusted because there is no way to tell if it is true.

jules 8y ago

It wouldn't change much even if there were 10 metaphysics papers for every mathematics paper. The main difference is that math is rigorous: there is an agreed upon standard for correctness that is falsifiable in two ways. Firstly, a proof of a theorem can be falsified by finding a mistake, and what is a mistake is agreed upon. Second, and more importantly, the system of proof itself is falsifiable. If a theorem says that an equation p(x,y,z) = 0 has no solutions, and a proof without mistakes is found, then it better have no solutions. If somebody comes along and demonstrates that x=43,y=23,z=809 is a solution, then the system is in trouble. This ensures that math is not a formal game of arbitrary axioms that is internally consistent but ultimately meaningless. That is important, because metaphysics could develop internal correctness criteria that everybody agrees upon, but it could still be meaningless.

rntz 8y ago
> Second, and more importantly, the system of proof itself is falsifiable. If a theorem says that an equation p(x,y,z) = 0 has no solutions, and a proof without mistakes is found, then it better have no solutions. If somebody comes along and demonstrates that x=43,y=23,z=809 is a solution, then the system is in trouble. This ensures that math is not a formal game of arbitrary axioms that is internally consistent but ultimately meaningless. I don't see how what you've said is anything other than the criterion of formal consistency - that a thing and its negation are not both provable. And a system may certainly be consistent, yet not particularly useful. It should be noted that mathematics has not always been as rigorous as people assume. Attempts to ground math in formal logic didn't really get off the ground until the late 1800s. And this isn't a trivial point; the "rules of the game" were up for debate, and often debated, before then (and, to a lesser extent, since). People disagreed about which numbers exist; people disagree about which proof methods are acceptable; and for example, calculus - a highly practical branch of mathematics - was invented before its formal justifications were found.
- jules 8y ago
  It is more than formal consistency because to show a whole number solution to a^n + b^n = c^n and n > 2, one doesn't need to use a high powered formal framework like ZFC. Thus Wiles' proof of Fermat's last theorem, which uses all kinds of infinite sets and other features of ZFC, can be falsified by a simple manipulation of finite numbers. You just need the numbers a,b,c,n of the counterexample and a calculator. Mathematics thus makes predictions about the world (in this case about the behaviour of calculators, human or electronic) in a somewhat similar way that physics makes predictions about the world. Or as Arnold famously said: "Mathematics is the part of physics where experiments are cheap". You wouldn't have that if math was an arbitrary symbol pushing game with arbitrary axioms, with the only requirement that they be consistent. [If a counterexample to Fermat's last theorem is found it probably isn't because ZFC is inconsistent, but because Wiles' proof has a mistake, which would show that the checking of the proof was inadequate and that mathematics needs to use a higher standard for what is considered a valid proof. So the system of proof is falsifiable in a very broad sense: it can expose a bad proof checking culture within mathematics as well as inconsistencies in the formal system. I don't think that metaphysics has anything equivalent. If somebody comes up with a counterexample a,b,c,n then Wiles would immediately admit that his proof has a mistake, even though he wouldn't even know where in the proof the mistake is. Try convincing a metaphysicist that their argument is wrong or meaningless... That said, there are certainly also stubborn mathematicians who insist that their proof is right even though other mathematicians have pointed out that a particular step isn't clear. However, if the mathematician who came up with the proof cannot clarify that step, ultimately down to the axioms of ZFC, then the proof isn't accepted.]

myWindoonn 8y ago

Mathematics is metaphysics. I'd like your refutation to center on any nuance which might separate the two disciplines other than the sad fact that many philosophers don't learn much maths. Logic is metaphysics: https://philpapers.org/archive/ALVLIM-3.pdf https://philpapers.org/archive/ALVLIM-3.pdf Logic is mathematical, logic is categorical (structured in a deep way amenable to category theory), maths is categorical: http://math.ucr.edu/home/baez/rosetta.pdf http://math.ucr.edu/home/baez/rosetta.pdf https://ncatlab.org/nlab/show/internal+logic https://ncatlab.org/nlab/show/internal+logic https://ncatlab.org/nlab/show/topos https://ncatlab.org/nlab/show/topos Ontology is categorical: https://arxiv.org/abs/1102.1889v2 https://arxiv.org/abs/1102.1889v2 https://arxiv.org/abs/1706.00526 https://arxiv.org/abs/1706.00526 The working programmer is an ontologist and a taxonomist, but this fact isn't well-understood.

vinceguidry 8y ago
I'd like to draw a distinction between non-physical and metaphysical. The opposite of a thing is not the same thing as the meta of that same thing. The meta attempts to unify the topic and it's reverse. Metaphysics wants to kill the distinction between physical reality and non-physical reality. Non-physical disciplines such as mathematics wants to distill the non-physical essence of things
- myWindoonn 8y ago
  This is a really nifty insight. Mathematical objects aren't physical, but that doesn't mean that there aren't objects that are neither physical nor mathematical. I wonder what those objects might be like!
hackinthebochs 8y ago
This kind of response really grinds my gears about these discussions of philosophy (more often than not related to metaphysics). You're referencing the mostly unobjectionable features of the field to defend the objectionable features, when there is very little similarity between the two. You can't defend ontology language games by appealing to the truth of logic or mathematics, as they share nothing of relevance in common. If you want to give an actual defense of the things people find objectionable about metaphysics, you have to defend the features being attacked, not tangentially related things that happen to be categorized under the same broad label. >Logic is metaphysics: Maybe this is true, but doing logic isn't doing metaphysics. One does not need to take a stance on the metaphysics of logic to study and create formal systems. >The working programmer is an ontologist and a taxonomist, but this fact isn't well-understood. Not in any substantive sense. There is a surface-level connection between what a programmer does and a metaphysician does, but this is the extent of the connection. The ontologies studied in metaphysics attempt to make true substantive statements about what exists in the actual world. The programmer is merely stipulating the basic objects and relationships in a fully contingent domain of inquiry. The programmer is doing metaphysics only if you remove anything of substance from what we take the metaphysician to be doing.

rntz 8y ago

> Just consider volume: it's estimated that around a quarter of a million theorems are proved every year. That's real, measurable, progress; what's the metaphysics equivalent? I'm not sure I disagree with your overall argument, but this point here is silly. First, I'd like to know where you got that number. (I must admit it sounds rather high to me, but I'm sure it depends how you count.) But more importantly, measuring mathematical progress by number of theorems proved is absurd. I can write a computer program to prove theorems; it will almost surely prove more than a quarter-million a day (though eventually it will have to slow down). But they will not be _useful_ theorems. Nobody will read them, nobody will use them, nobody will build on them, nobody will find them beautiful, nobody will apply them to any practical problem. "Number of theorems proven" may be measurable, but it is not "real progress".