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> But the problem for .. anyone who tries to ground moral truth in the natural world, is that moral truths, like mathematical truths, are necessarily true, whic

> But the problem for .. anyone who tries to ground moral truth in the natural world, is that moral truths, like mathematical truths, are necessarily true, which means that it’s impossible for them to be false. What a bizarre argument. Mathematical truths are defined to be true -- entirely the opposite of what the author is trying to claim about moral truths, so this is about as absurd a comparison as one could make. I'm no expert but this article reads to me like hand-waving psychobabble.

konjin 6y ago
Maths is what happens when you take nonsense very seriously. For some odd reason a subset of all the possible non-sense maps really well to the real world.
- Ste_Evans 6y ago
  I think the terms used in Mathematics are a tad more precise than those in natural language e.g. 1 is fairly clear, "moral" is not as clear. The reason Maths works is because it is based on intuitions (counting, space) that are presumably shadows of the physical world cast on the evolving brain via coarse perception. The effectiveness of Mathematics in Physics is probably not unreasonable at all.
  - ukj 6y ago
    Clear to whom? The meaning of "1" is conventional/socially constructed. For the sake of argument I can conveniently forget what "1" means, and then you can try and explain it to me like I am from another planet. Semantics are a non-trivial matter.
    - Kednicma 6y ago
      To be extremely precise: 1 is the successor of 0. Anywhere that there is a natural numbers object, there's a semantics for this statement. What is socially constructed here is the choice of topos which hosts the natural numbers object!
      - ukj 6y ago
        SUCC(0) is no explanation of 1, until you explain 0. Note how you are reaching for complex/abstract ideas (like a "topos" and "natural numbers") to explain simple/intuitive ones (like 0 and 1). "toposes" and "sets" (of "natural numbers") are socially constructed in the subculture of Mathematicians. Outside of that shared experience, they are pretty meaningless. I guess you are on the "discovered" side, and I am on the "invented" side of Mathematics ;)
        Kednicma 6y ago
        Humans are what, about 99.9% similar to each other on average? So that gives me 3 nines belief that yes, if I can understand, then you can understand; we're just humans after all. I think that you're being sarcastic; once we define categories, Cartesian closed categories, and elementary topoi, then categorical set theory is a straightforward sequence of diagram schemata. But I understand your point! You're super-close to a deep realization: all words are only sensical to certain subcultures. IOW there's no absolute meaning to any word. In that perspective, we're both right; "1" is meaningless and 1 is categorical, and it's just a question of pointers vs. names. Another quick and deep corollary is that reality is socially constructed; whenever a quorum of humans is mutually intelligible during a conversation, then they are agreeing on the local nature of reality. Humans can't construct global maps of reality, though, since they can't observe the Universe all at once. Indeed global maps of reality are forbidden by the Kochen-Specker Theorem. Edit: To clarify for the audience, I have no appeal to higher categories here, and the definitions of category theory are not some sort of categorization or classification process, but axiomatic definitions akin to set theory.
        ukj 6y ago
        Heh, how did I know you are going to appeal to infinity-categories at some point? "defining categories" and their respective categorisation rules is the process of classification. They don't account for the classifiers themselves. You are super-close to a deeper realisation even. If any notation is meaningful (even one that uses symbols like ∞), then it's Turing-recognisable. Type-0 Chomsky grammar. In formal languages syntax is semantics. In so far as understanding (comprehension?) goes, you could say that I subscribe to the axiom of unrestricted comprehension. It's rather un-Mathematical doing so.
    - Ste_Evans 6y ago
      Clear to everyone but you. Maths has clear and precise concepts so logic can be successfully applied in Mathematical proofs with the validity remaining stable line after line. Attempts to do this in natural language, as Wittgenstein pointed out, tend to fail except in toy examples, as can be seen by this nonsense written by Goff. After the first 3 words of the title, "The universe knows..", we have no idea what he is on about and know we are dealing with a crank. The universe, like Philip Goff, doesn't know anything.
Ste_Evans 6y ago
You are nearly there. It is hand-waving psychobabble paid for with taxes. This fraud and narcissist, Goff, is employed by a UK university. This is the tw*t that wrote "Galileo's Error". Presumably, he'll be bringing out a sequel, "Einstein's hopeless confusion".
MaxBarraclough 6y ago
> Mathematical truths are defined to be true Perhaps a nitpick, but: axioms are defined to be true. Mathematics, roughly speaking, is the business of exploring the consequences of chosen sets of axioms. Sometimes published mathematical theorems turn out to be wrong.
- jjgreen 6y ago
  Do you think? I'd say that axioms were just taken; there's no commitment to their truth (since there is no need for it, and mathematics likes economy).
  - qznc 6y ago
    Axiom are just taken but over time we picked the most useful ones. This is why they map well to the physical world. The baffling thing is how few and simple axioms we need for them to be useful.
  - amelius 6y ago
    It also doesn't make sense to define axioms as true. What if later it turns out that the axioms were a mutual contradiction?
    - jjgreen 6y ago
      Truth is tricky. If I state "The sky is blue", I can look out of the window, the sky is blue, my statement corresponds to the state of the world, my statement is true, right? But in mathematics there is no window, everything is internal, abstract, so what does "truth" mean when there is no state of the world with which to compare? More importantly, would the mathematics be any different if the axioms are declared to be true? No, it wouldn't make any difference at all. So let's leave "truth" to the physicists and philosophers.
      - chousuke 6y ago
        This is perhaps not all that relevant to your point, but "the sky is blue" so often being used as an example of an obvious truth is amusing to me, because very often the sky is not all that blue at all. If I look outside right now, the sky is probably better described as cyan; quite obviously a different colour from the blue exercise mat that happens to be on my floor. The sky can also be described by many of the other colours depending on weather or the time of day.
deleted 6y ago
[deleted]
brudgers 6y ago
The argument echos Kant...which is too big a sea to boil in a comment. So at geostationary orbit, Kant's metaphysics says we cannot have absolute knowledge of the empirical world, only knowledge mediated by the a priori conditions of human experience, space and time. However, we can have absolute knowledge of morals because such knowledge is not dependent on the aforementioned a priori conditions of human experience. Going further, in Critique of Pure Reason Kant uses mathematics as an example of synthetic a priori knowledge. This is the lever he uses to overturn the traditional halving of all knowledge into either analytic and a priori or synthetic and a posteriori (empirical). The halving was the basis for Hume's radical skepticism and it's predecessors.

konjin 6y ago

Maths is what happens when you take nonsense very seriously. For some odd reason a subset of all the possible non-sense maps really well to the real world.

Ste_Evans 6y ago
I think the terms used in Mathematics are a tad more precise than those in natural language e.g. 1 is fairly clear, "moral" is not as clear. The reason Maths works is because it is based on intuitions (counting, space) that are presumably shadows of the physical world cast on the evolving brain via coarse perception. The effectiveness of Mathematics in Physics is probably not unreasonable at all.
- ukj 6y ago
  Clear to whom? The meaning of "1" is conventional/socially constructed. For the sake of argument I can conveniently forget what "1" means, and then you can try and explain it to me like I am from another planet. Semantics are a non-trivial matter.
  - Kednicma 6y ago
    To be extremely precise: 1 is the successor of 0. Anywhere that there is a natural numbers object, there's a semantics for this statement. What is socially constructed here is the choice of topos which hosts the natural numbers object!
    - ukj 6y ago
      SUCC(0) is no explanation of 1, until you explain 0. Note how you are reaching for complex/abstract ideas (like a "topos" and "natural numbers") to explain simple/intuitive ones (like 0 and 1). "toposes" and "sets" (of "natural numbers") are socially constructed in the subculture of Mathematicians. Outside of that shared experience, they are pretty meaningless. I guess you are on the "discovered" side, and I am on the "invented" side of Mathematics ;)
      - Kednicma 6y ago
        Humans are what, about 99.9% similar to each other on average? So that gives me 3 nines belief that yes, if I can understand, then you can understand; we're just humans after all. I think that you're being sarcastic; once we define categories, Cartesian closed categories, and elementary topoi, then categorical set theory is a straightforward sequence of diagram schemata. But I understand your point! You're super-close to a deep realization: all words are only sensical to certain subcultures. IOW there's no absolute meaning to any word. In that perspective, we're both right; "1" is meaningless and 1 is categorical, and it's just a question of pointers vs. names. Another quick and deep corollary is that reality is socially constructed; whenever a quorum of humans is mutually intelligible during a conversation, then they are agreeing on the local nature of reality. Humans can't construct global maps of reality, though, since they can't observe the Universe all at once. Indeed global maps of reality are forbidden by the Kochen-Specker Theorem. Edit: To clarify for the audience, I have no appeal to higher categories here, and the definitions of category theory are not some sort of categorization or classification process, but axiomatic definitions akin to set theory.
        ukj 6y ago
        Heh, how did I know you are going to appeal to infinity-categories at some point? "defining categories" and their respective categorisation rules is the process of classification. They don't account for the classifiers themselves. You are super-close to a deeper realisation even. If any notation is meaningful (even one that uses symbols like ∞), then it's Turing-recognisable. Type-0 Chomsky grammar. In formal languages syntax is semantics. In so far as understanding (comprehension?) goes, you could say that I subscribe to the axiom of unrestricted comprehension. It's rather un-Mathematical doing so.
  - Ste_Evans 6y ago
    Clear to everyone but you. Maths has clear and precise concepts so logic can be successfully applied in Mathematical proofs with the validity remaining stable line after line. Attempts to do this in natural language, as Wittgenstein pointed out, tend to fail except in toy examples, as can be seen by this nonsense written by Goff. After the first 3 words of the title, "The universe knows..", we have no idea what he is on about and know we are dealing with a crank. The universe, like Philip Goff, doesn't know anything.

Ste_Evans 6y ago

You are nearly there. It is hand-waving psychobabble paid for with taxes. This fraud and narcissist, Goff, is employed by a UK university. This is the tw*t that wrote "Galileo's Error". Presumably, he'll be bringing out a sequel, "Einstein's hopeless confusion".

MaxBarraclough 6y ago

> Mathematical truths are defined to be true Perhaps a nitpick, but: axioms are defined to be true. Mathematics, roughly speaking, is the business of exploring the consequences of chosen sets of axioms. Sometimes published mathematical theorems turn out to be wrong.

jjgreen 6y ago
Do you think? I'd say that axioms were just taken; there's no commitment to their truth (since there is no need for it, and mathematics likes economy).
- qznc 6y ago
  Axiom are just taken but over time we picked the most useful ones. This is why they map well to the physical world. The baffling thing is how few and simple axioms we need for them to be useful.
- amelius 6y ago
  It also doesn't make sense to define axioms as true. What if later it turns out that the axioms were a mutual contradiction?
  - jjgreen 6y ago
    Truth is tricky. If I state "The sky is blue", I can look out of the window, the sky is blue, my statement corresponds to the state of the world, my statement is true, right? But in mathematics there is no window, everything is internal, abstract, so what does "truth" mean when there is no state of the world with which to compare? More importantly, would the mathematics be any different if the axioms are declared to be true? No, it wouldn't make any difference at all. So let's leave "truth" to the physicists and philosophers.
    - chousuke 6y ago
      This is perhaps not all that relevant to your point, but "the sky is blue" so often being used as an example of an obvious truth is amusing to me, because very often the sky is not all that blue at all. If I look outside right now, the sky is probably better described as cyan; quite obviously a different colour from the blue exercise mat that happens to be on my floor. The sky can also be described by many of the other colours depending on weather or the time of day.

deleted 6y ago

[deleted]

brudgers 6y ago

The argument echos Kant...which is too big a sea to boil in a comment. So at geostationary orbit, Kant's metaphysics says we cannot have absolute knowledge of the empirical world, only knowledge mediated by the a priori conditions of human experience, space and time. However, we can have absolute knowledge of morals because such knowledge is not dependent on the aforementioned a priori conditions of human experience. Going further, in Critique of Pure Reason Kant uses mathematics as an example of synthetic a priori knowledge. This is the lever he uses to overturn the traditional halving of all knowledge into either analytic and a priori or synthetic and a posteriori (empirical). The halving was the basis for Hume's radical skepticism and it's predecessors.