Comments by "" (@ToriKo_) on "How to Count" video.

  1.  @orisegel4055  wow what a fantastic answer. I appreciated how you responded on both the surface level and a more foundational level. I don’t know anything about mathematics but this reminds me of Sellar’s Myth of the Given in philosophy, which says something like: ‘you can either have pure unquestionable experience, or a foundation to build your arguments of truth upon, but not both’. We have to start somewhere, and so we start with assumptions (axioms of Logic, and axioms of set theory), but we can’t start with axioms that can’t be questioned. And so logic and set theory are co-constructed precariously in that way
    3
  2.  @MuffinsAPlenty  wow I really really appreciate you taking the time out of your day to try to help me with some of those problems. Those questions seemed to be the result of trying to articulate unarticulated notions noticed over extended periods of time; and so I feel like I’ll have to subject (your) answers to the same treatment. I’m very grateful. In a sense, I’ll be trying to see if or when your answers apply to specific situations, see if or when there are counter examples, and try to build up an intuition (notion) through that. I also appreciate that your a mathematician, since it gives your answer credence, compared to a YT commenter who’s just as lost as me lol. Btw I’d like to ask what part of mathematics you work with, but I may not understand Also I appreciate you saying that “I don’t think it’s actually as clear cut as people make it out to be”. I guess a follow up question could be; so why do so many smart people make it out to be that way, consistently?
    2
  3. Wow you’re really amazing. You have a real knack for knowing what questions or objections someone learning this stuff if about to ask, and then answer it, which is a very difficult skill to have. Noticing how the function of even numbers was injective to the set of integers was okay, but then figuring out that the set of even numbers was bijective to the integers before you said it was so satisfying, realizing the implication that the two sets were equal in size under these assumptions. I have a question that I have trouble articulating but it’s long so you can ignore it. It has to do with how people talk about mathematics. And I think it has to do with the philosophy of mathematics. People definitively talk about mathematics like it is the ‘language of the universe’. People also talk about it being the ‘languages of languages’ (-Joshua Bach). People also talk about, and moreover interact with mathematics like it is objective and invariant, and that it transcends culture and language. I have a really really hard time understanding those claims that are made so frequently by smart people. To illustrate my point I’ll talk about science. I understand the philosophy of science in four parts: -that it delivers statistical knowledge of falsifiable claims -it seems to give knowledge around mechanisms and not necessarily ontology -that there are stages of science where there is a consensus on foundational assumptions, and so piecemeal progress is made -there comes a point where things don’t make sense anymore, and so a new paradigm is needed, and so foundational assumptions are updated and re-instantiated, and then you go back to step three. People don’t seem to talk about mathematics this way. And it seems really weird to me that people see equations and symbols that could mean a billion different things, and somehow all have this similar intuitive knowledge about how to do maths, and what maths is saying. How do people learn about things like tensors, (or matrixes, or vectors, integration, differentiation), from listening to lectures and practice questions, that take place with no oversight, from all over the world, and then come away from that experience sharing an understanding of those mathematical objects, and understand how they can and can’t be implemented, and intuiting the same implicit strikingly-nuanced assumptions??? I feel like I kind of get Western philosophy, I kind of get science, I kind of get Eastern philosophy, but I’m never ever going to ‘get’ mathematics
    1
  4.  @AnotherRoof  that would be fantastic
    1
  5. Another comment I would like to make is about the guy in the yellow shirt counting. You portray him as ridiculous, but there’s some really really interesting stuff he’s pointing out. In cognitive science there is an amazingly powerful idea called ‘relevance realization’, and all the ‘problems’ that the yellow guy portrayed are all actually relevance realization problems in disguise (it’s no disguise at all really). If your interested a guy called John Vervaeke has a lot of free lectures on YT that go into more detail. I find relevance realization endlessly fascinating, and it might be why I’m suspect of everyone seeming to agree on the foundations of mathematics
    1
  6. You watching this in 2x???
    1
  7. I thought it was fine
    1
  8. 100% agree with this
    1