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The statement that "the truths of mathematics would be the same, because they are true by definition" is correct. Mathematics exist independently of biology or

The statement that "the truths of mathematics would be the same, because they are true by definition" is correct. Mathematics exist independently of biology or perception of reality. It is just a collection of arbitrary abstract definitions and what follows from them. The alien species may come up with different base definitions that they find more useful or interesting. But they would derive the same conclusions as we would if they were starting from the same definitions and applying the same abstract rules.

bmitc 4y ago
> Mathematics exist independently of biology or perception of reality. Is there a “proof” of that? How could a proof exist? You’d probably win several awards if you had one. > It is just a collection of arbitrary abstract definitions and what follows from them. … created by humans.
- dagw 4y ago
  Is there a “proof” of that? It's how we define the concept "mathematics". If a result was dependant on "biology or perception of reality" or anything else outside its defining axioms, it wouldn't be mathematics.
  - bmitc 4y ago
    I'm sorry, but I just disagree that that's how mathematics is defined and that it doesn't depend on our biology and perception, because we are making those definitions. A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted, but this is not a totally novel or off the rails idea. It is basically accepted in robotics that embodied cognition is how you get a robot to understand and perceive its environment. Where do you think that idea came from?
    - dagw 4y ago
      A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being I haven't read that book, but I did just read the wikipedia page for it, for what it's worth. Based on that I feel it's more that they're arguing that the path we've taken and the metaphors we've used while exploring our way to our current understanding of mathematics is based on our biology. Our biology has greatly affected the order we've discovered things and how we understand those thing and how we actually 'do' math day to day, and all that I agree with. It's also very likely that aliens will have taken a very different path and have very different metaphors and proofs for understanding and doing their version of what we call mathematics. Because of this it might very well be very difficult for us to initially understand each others mathematics. Indeed looking through human history our philosophical understanding of mathematics fundamentally 'is' has changed many times. Yet mathematical truth's we've found along the way have always remained constant (barring errors in calculation or reasoning) even as our understanding of mathematics has changed. I believe that once we gotten passed all that both us and the aliens will find that, at the core, we both agree on what is "mathematically" true. I will however also concede that some of the arguments in this thread has made me slightly less sure than I was before, so that is something I guess.
rendall 4y ago
> Mathematics exist independently of biology or perception of reality. Even the concept of "number" itself is almost certainly an artifact of perception that enabled our ancestors to survive our niche, planetary environment, and not an inherent feature of objective reality. Aliens, evolved to survive in another environment entirely with a different set of initial conditions, almost certainly would not have the same, nor even any, understanding of "number". Would we consider such aliens a civilization or some kind of insensate "process"?
- DontchaKnowit 4y ago
  Um no. I'm so over this deconstructionist "reality is your perception" line. Numbers are a thing. In fact they're one of the most basic observable things about the universe. And the concept if a number holds up all the way down to the quantum level. I.e. space and time are discrete and therefore space and time can both be COUNTED. Counting is literally one of the most basic and early achievements of human cognition and were gonna act like we just made it up? Absolute silliness.
  - bmitc 4y ago
    > I'm so over this deconstructionist "reality is your perception" line. What makes you completely reject that? I don't think it has as much to do with deconstructionism as it does embodied cognition. We keep learning more and more about how biology and physiology and evolutionary pressures affect and inform cognition and thus perception. I was recently reading about how there have been scientific studies that seem to suggest that certain animals seem to experience time differently that we do. So you could say "time is a thing", but yet, it appears that it is not the same thing across lifeforms. There are animals that sense gravitational and electromagnetic fields, something we cannot do. Would it make sense to them to say "all beings can read these fields because we do"? I think the problem is that it is all too easy to fall into the trap in thinking that alien lifeforms would be like us. There's a multitude of evidence of that here on Earth in the variety of life, despite even coming from the same origin.
    - 4y ago

bmitc 4y ago

> Mathematics exist independently of biology or perception of reality. Is there a “proof” of that? How could a proof exist? You’d probably win several awards if you had one. > It is just a collection of arbitrary abstract definitions and what follows from them. … created by humans.

dagw 4y ago
Is there a “proof” of that? It's how we define the concept "mathematics". If a result was dependant on "biology or perception of reality" or anything else outside its defining axioms, it wouldn't be mathematics.
- bmitc 4y ago
  I'm sorry, but I just disagree that that's how mathematics is defined and that it doesn't depend on our biology and perception, because we are making those definitions. A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted, but this is not a totally novel or off the rails idea. It is basically accepted in robotics that embodied cognition is how you get a robot to understand and perceive its environment. Where do you think that idea came from?
  - dagw 4y ago
    A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being I haven't read that book, but I did just read the wikipedia page for it, for what it's worth. Based on that I feel it's more that they're arguing that the path we've taken and the metaphors we've used while exploring our way to our current understanding of mathematics is based on our biology. Our biology has greatly affected the order we've discovered things and how we understand those thing and how we actually 'do' math day to day, and all that I agree with. It's also very likely that aliens will have taken a very different path and have very different metaphors and proofs for understanding and doing their version of what we call mathematics. Because of this it might very well be very difficult for us to initially understand each others mathematics. Indeed looking through human history our philosophical understanding of mathematics fundamentally 'is' has changed many times. Yet mathematical truth's we've found along the way have always remained constant (barring errors in calculation or reasoning) even as our understanding of mathematics has changed. I believe that once we gotten passed all that both us and the aliens will find that, at the core, we both agree on what is "mathematically" true. I will however also concede that some of the arguments in this thread has made me slightly less sure than I was before, so that is something I guess.

rendall 4y ago

> Mathematics exist independently of biology or perception of reality. Even the concept of "number" itself is almost certainly an artifact of perception that enabled our ancestors to survive our niche, planetary environment, and not an inherent feature of objective reality. Aliens, evolved to survive in another environment entirely with a different set of initial conditions, almost certainly would not have the same, nor even any, understanding of "number". Would we consider such aliens a civilization or some kind of insensate "process"?

DontchaKnowit 4y ago
Um no. I'm so over this deconstructionist "reality is your perception" line. Numbers are a thing. In fact they're one of the most basic observable things about the universe. And the concept if a number holds up all the way down to the quantum level. I.e. space and time are discrete and therefore space and time can both be COUNTED. Counting is literally one of the most basic and early achievements of human cognition and were gonna act like we just made it up? Absolute silliness.
- bmitc 4y ago
  > I'm so over this deconstructionist "reality is your perception" line. What makes you completely reject that? I don't think it has as much to do with deconstructionism as it does embodied cognition. We keep learning more and more about how biology and physiology and evolutionary pressures affect and inform cognition and thus perception. I was recently reading about how there have been scientific studies that seem to suggest that certain animals seem to experience time differently that we do. So you could say "time is a thing", but yet, it appears that it is not the same thing across lifeforms. There are animals that sense gravitational and electromagnetic fields, something we cannot do. Would it make sense to them to say "all beings can read these fields because we do"? I think the problem is that it is all too easy to fall into the trap in thinking that alien lifeforms would be like us. There's a multitude of evidence of that here on Earth in the variety of life, despite even coming from the same origin.
  - 4y ago