4 ms·

right, axioms are logically antecedent to theory.

lisper 6y ago
Actually, they are not. The whole idea of an axiom is part of a theory (formal logic) and that theory has no axioms. Even within the framework of formal logic, there are logics with no axioms, only rules of inference. https://en.wikipedia.org/wiki/Hilbert_system https://en.wikipedia.org/wiki/Hilbert_system
- chordalkeyboard 6y ago
  Fascinating! Can you share how this can be used to develop a physical theory with no axioms?
  - lisper 6y ago
    Sure. Go look at yourself in a mirror. Observe that the thing you see in the mirror looks very similar to other things around you that you call "people" or "humans". Observe further that the thing in the mirror behaves differently from other humans. You can control the behavior of the thing in the mirror in ways that you cannot control the behavior of other humans. Observe that when you try to touch the thing in the mirror it feels different than when you touch one of these other humans. It will feel cold, smooth, and hard, like glass, not soft and warm like flesh. Now, go find another human and ask them to look in the mirror with you. Observe that you can now see a second human-looking thing in the mirror, but this second human-looking thing has yet another set of properties. For starters, this second human-looking-thing in the mirror doesn't look like you, it looks like the other human whose assistance you have solicited. If you try to touch the second human-looking-thing-in-the-mirror you will find that you will not be able to. The first human-looking-thing, the one whose behavior you have direct control over, will thwart your efforts and get in your way. You will find that the control you exercise over the first human-looking-thing-in-the-mirror is constrained in a way that makes it impossible to touch anything in the mirror other than it. Now ask the other human whose help your have solicited what they see. You will find that their perceptions are similar to yours. They will (almost certainly) tell you that they also see two human-looking-things in the mirror, and that one of them, the first one, looks and acts just like you. You will find that your assistant will agree with you on many other observations as well. They will agree on the location of the mirror, the fact that it feels smooth and hard. If there are other objects nearby they will agree on the location and appearance of those objects. Now turn out the lights. Observe that you can no longer see the mirror or any of the objects in it that you could see before. From this and a whole lot of other similar observations you can construct the following theory: you are a thing that exists in space which has three dimensions. In this space there is this stuff called "light" which moves in straight lines (more or less) from sources and ultimately enters part of the space that you occupy that you call "eyes". When this happens, you obtain information about other things that occupy the same three-dimensional space that you do. Some of these things are very similar to you. They also have eyes and other body parts, all of which are things that exist in the same 3-D space and occupy particular subsets of that space. The particular subset of the space occupied by things changes, and this is an indication of the existence of something called "time", which is a radically different kind of thing from the kind of thing you are and the kind of thing light it. You and light exist in space. Time does not. Time is some seriously weird shit. Do you need me to elaborate further, or are you getting the idea?
    - chordalkeyboard 6y ago
      No, because I feel like there are a lot of background assumptions involved in that process, many of which are either unexamined or necessary for the theory-making process. These background assumptions are reinforced every time the theory allows me to make correct predictions and challenged every time I make incorrect predictions. Incorrect predictions allow me to update the theory or the assumptions. When scientists do the a formal version of the same process as you have described, they make similar background assumptions. Perhaps you can explain how this whole process transpires without assuming anything?
      - lisper 6y ago
        > I feel like there are a lot of background assumptions involved in that process Like what?
        chordalkeyboard 6y ago
        In your informal example, I’m assuming that the person I’m speaking to is an honest interlocutor. In the scientist’s formal counterpart, he is assuming that the phenomena he observes correspond to the representation he assigns in the formal model. For a specific example, in order to infer the composition of a star, one must assume that the spectra emitted by a star are products of the same emission process as observed in a laboratory here on Earth.
        lisper 6y ago
        > I’m assuming that the person I’m speaking to is an honest interlocutor. OK, but you have taken it upon yourself to assume that. I never asked you to assume it. It is entirely possible that the person you are talking to is not being honest. They could be gaslighting you. It is even possible that they are not a person. They could be a shape-shifting space alien disguising themselves as a person as part of a grand conspiracy to prevent you from discovering the fact that you are a 13-dimensional being with super-powers who would take over the universe if you became aware of your true nature. So... among these two theories which I have now proposed to explain your observations, which do you think is more likely?
- deleted 6y ago
  [deleted]

Actually, they are not. The whole idea of an axiom is part of a theory (formal logic) and that theory has no axioms. Even within the framework of formal logic, there are logics with no axioms, only rules of inference. https://en.wikipedia.org/wiki/Hilbert_system https://en.wikipedia.org/wiki/Hilbert_system

chordalkeyboard 6y ago
Fascinating! Can you share how this can be used to develop a physical theory with no axioms?
- lisper 6y ago
  Sure. Go look at yourself in a mirror. Observe that the thing you see in the mirror looks very similar to other things around you that you call "people" or "humans". Observe further that the thing in the mirror behaves differently from other humans. You can control the behavior of the thing in the mirror in ways that you cannot control the behavior of other humans. Observe that when you try to touch the thing in the mirror it feels different than when you touch one of these other humans. It will feel cold, smooth, and hard, like glass, not soft and warm like flesh. Now, go find another human and ask them to look in the mirror with you. Observe that you can now see a second human-looking thing in the mirror, but this second human-looking thing has yet another set of properties. For starters, this second human-looking-thing in the mirror doesn't look like you, it looks like the other human whose assistance you have solicited. If you try to touch the second human-looking-thing-in-the-mirror you will find that you will not be able to. The first human-looking-thing, the one whose behavior you have direct control over, will thwart your efforts and get in your way. You will find that the control you exercise over the first human-looking-thing-in-the-mirror is constrained in a way that makes it impossible to touch anything in the mirror other than it. Now ask the other human whose help your have solicited what they see. You will find that their perceptions are similar to yours. They will (almost certainly) tell you that they also see two human-looking-things in the mirror, and that one of them, the first one, looks and acts just like you. You will find that your assistant will agree with you on many other observations as well. They will agree on the location of the mirror, the fact that it feels smooth and hard. If there are other objects nearby they will agree on the location and appearance of those objects. Now turn out the lights. Observe that you can no longer see the mirror or any of the objects in it that you could see before. From this and a whole lot of other similar observations you can construct the following theory: you are a thing that exists in space which has three dimensions. In this space there is this stuff called "light" which moves in straight lines (more or less) from sources and ultimately enters part of the space that you occupy that you call "eyes". When this happens, you obtain information about other things that occupy the same three-dimensional space that you do. Some of these things are very similar to you. They also have eyes and other body parts, all of which are things that exist in the same 3-D space and occupy particular subsets of that space. The particular subset of the space occupied by things changes, and this is an indication of the existence of something called "time", which is a radically different kind of thing from the kind of thing you are and the kind of thing light it. You and light exist in space. Time does not. Time is some seriously weird shit. Do you need me to elaborate further, or are you getting the idea?
  - chordalkeyboard 6y ago
    No, because I feel like there are a lot of background assumptions involved in that process, many of which are either unexamined or necessary for the theory-making process. These background assumptions are reinforced every time the theory allows me to make correct predictions and challenged every time I make incorrect predictions. Incorrect predictions allow me to update the theory or the assumptions. When scientists do the a formal version of the same process as you have described, they make similar background assumptions. Perhaps you can explain how this whole process transpires without assuming anything?
    - lisper 6y ago
      > I feel like there are a lot of background assumptions involved in that process Like what?
      - chordalkeyboard 6y ago
        In your informal example, I’m assuming that the person I’m speaking to is an honest interlocutor. In the scientist’s formal counterpart, he is assuming that the phenomena he observes correspond to the representation he assigns in the formal model. For a specific example, in order to infer the composition of a star, one must assume that the spectra emitted by a star are products of the same emission process as observed in a laboratory here on Earth.
        lisper 6y ago
        > I’m assuming that the person I’m speaking to is an honest interlocutor. OK, but you have taken it upon yourself to assume that. I never asked you to assume it. It is entirely possible that the person you are talking to is not being honest. They could be gaslighting you. It is even possible that they are not a person. They could be a shape-shifting space alien disguising themselves as a person as part of a grand conspiracy to prevent you from discovering the fact that you are a 13-dimensional being with super-powers who would take over the universe if you became aware of your true nature. So... among these two theories which I have now proposed to explain your observations, which do you think is more likely?
deleted 6y ago
[deleted]