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Thread: The last and final argument about reality.

  1. #13681
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    Quote Originally Posted by Len Moran View Post
    Yet if the model passes all it's tests it then appears to be the case that the maths has a direct connection with experience, so does that mean the a priori elements of the maths are a priori elements of experience?
    I see the situation with "a priori" aspects of physical theories to be similar to their "deterministic" elements. People who notice that deterministic equations often predict results quite well (but also have their limits, like weather or human behavior) often make the jump to concluding that the future is actually determined by the past, but no tested physical theory claims that or requires that (because that's not what theories do). It's mistaking tested successes of a model for untested constraints on reality, a constant problem in how we frame physics (akin to MIR belief in scientific contexts). Similarly, when we notice that mathematics works so well, we see an a priori element in our surroundings, but that's once again mistaking the model for the reality. Determinism, and a priori, are attributes of models, and what we call "reality" is a kind of uber-model that amalgamates all those individual models in a more sophisticated (and logically fuzzier) way than simply carrying over all those model attributes, because model attributes are always contextual, idealized, and subject to change. This is obvious any time a teacher says something like "when UV light is shined on an atom, the electron in the atom can be knocked free," and isn't immediately faced with a bright student who says "wait a minute, all electrons are indistinguishable so you cannot talk about the individual electron that is in the atom." Because we don't wish to face that, we are admitting that the attributes of reality are not simply inherited from attributes of models, they are modes of thinking about our circumstances, and those modes of thinking benefit from contextually convenient notions like determinism and causation-- and a priori.

    On that last point, I recall some physicist had said words to the effect that reducing a physical law to a symmetry is the best way to expose its a priori character. I responded that even a physical theory reduced to a symmetry cannot be regarded as a priori, because the symmetry is probably broken at some level. Thus the issue is not whether the symmetry is really true in some absolute sense, it suffices that it be true enough for us to simplify, predict, and understand. I think the resolution is that the act of understanding something involves creating a sense of an a priori aspect, like we are trying to make some phenomenon seem a prior to us, moreso than that we are trying to prove it really is. In that way, if it not a necessary axiom of science to assume anything is a priori, just as it is not a necessary axiom of shoe shopping to assume we will find shoes that fit our feet. We only need to have reason to expect it will be worth the effort.

    All this is more or less what we can observe just by watching the process, but it doesn't answer the deep mystery of why does math work so well in science? Is it because, as some have said, "god is a mathematician," which has the a priori character you are wondering about? Or is mathematics just our chosen angle of attack based on our brain function, and it works for some more anthropic reason (if it didn't, there would never have been a survival advantage to high intelligence, so it wouldn't have evolved and no one would be around to wonder why it works so well)? That latter answer is related also to the answer that perhaps we are very good at restricting the topics we analyze to those that our mathematics happens to work well with, but I admit that solving differential equations shows no immediate connection to escaping from a sabre-toothed tiger's den!
    Last edited by Ken G; 2020-Feb-29 at 04:46 PM.

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    Quote Originally Posted by Selfsim View Post
    Whilst Heaviside's techniques must have had their basis well and truly referenced to classical mathematical axioms and theorems, I don't think I would say in this case, the 'a priori' components were 'discarded as far as the the physical workings of the theory are concerned' .. More like: they were embraced in order to make Maxwell's equations workable for the electrical sciences, (theoretical), I think.
    Yes, I think the way to look at is that our goal is to give our theories as much of an a priori character as we can, we say a theory is well formulated if it sounds maximally a priori. Note that our theories can often be formulated in completely differently sounding ways, yet still make all the same testable predictions. Just look at how different the interpretations of quantum mechanics seem, but we already had this issue with Newtonian mechanics (if you think that forces are real things that actually push on objects and cause acceleration, you have bought off on one interpretation of Newtonian mechanics, and it is an interpretation that is never tested against other interpretations that "action" is what exists and is minimized, for example). The tendency to imagine that reality simply inherits its attributes from our model interpretations creates a significant problem when combined with the tendency to think reality can simply inherit those model attributes in the first place. Wrong algebra of models, yet again.

    The situation with vectors in Maxwell's equations is particularly enlightening here. Many people associate vectors with arrows, but the deeper mathematical purpose of a vector is to be an abstract object that retains its meaning and purpose in any coordinate system. You can think of it as being like a common word, like "love", that appears in all languages-- the meaning of the word is intended to be the same regardless of which language it is translated into (and of course this is easier to actually make work in science, with its emphasis on that which is objective). The reason the mathematical notion of "vector" works so well in science is the need for objectivity, we want to build science from objective objects that have the same core meaning to all observers, even if they appear superficially different (like a different language, or a different frame of reference). So by translating the experimental results into the mathematical structure of vectors, Heaviside was able to put Maxwell's equations into a form that is independent of coordinates and can be used the same way for all observers in all inertial reference frames (and of course Einstein extended that to all observers in all reference frames). So we can add to the list of the qualities we are seeking to formulate our theories to be-- deterministic, a priori, and objective for all observers.

    So this answers why Heaviside did it, but it doesn't answer why it worked. And of course, the scientist must also ask the next question-- when will it be found to not work?

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    Quote Originally Posted by Ken G View Post
    ... So this answers why Heaviside did it, but it doesn't answer why it worked.
    Comes back to yet more evidence underpinning the MDR interpretation of Occam's Razor, (for consistency's sake), I think(?):

    Quote Originally Posted by Ken G
    The MDR thinker can understand what Occam's Razor is-- since the goal is to understand, and the simplest theory that agrees with data is the best path to understanding, then that's clearly the best theory. That's it, that's the Razor, nothing more. The MIR thinker actually believes that the Razor leads to How Things Actually Work, as if the universe was a simulation made by a fairly inexpert programmer who therefore had to "keep it simple."
    Quote Originally Posted by Ken G
    And of course, the scientist must also ask the next question-- when will it be found to not work?
    .. and when/if that happens, for a general population of MIR only thinkers, who simply would never accept MDR thinking, the feeling of being betrayed by what they think science is about (which of course it isn't) .. Which is a rather bleak inevitability, I think.

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    Quote Originally Posted by Selfsim View Post
    and when/if that happens, for a general population of MIR only thinkers, who simply would never accept MDR thinking, the feeling of being betrayed by what they think science is about (which of course it isn't) .. Which is a rather bleak inevitability, I think.
    Who are these MIR only thinkers who never accept MDR thinking? Can you name one poster here who doesn't accept MDR thinking but doesn't write off MIR entirely either?

    Your arguments are insulting and self serving to everybody who has contributed to this thread but doesn't agree with your position.

    That's the real problem with MDR alone thinking at the exclusion of everything else, either you state all of your respective caveats (which you never do) and only describe a minor portion of what could be called 'your universe' or you state no caveats whatsoever so that the old Stromatolite is the lowest common denominator solution to your basic model.

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    Quote Originally Posted by Selfsim View Post
    .. and when/if that happens, for a general population of MIR only thinkers, who simply would never accept MDR thinking, the feeling of being betrayed by what they think science is about (which of course it isn't) .. Which is a rather bleak inevitability, I think.
    PS: I am of course, referring to the vast majority of folk with whom I have interacted thus far on the MIR/MDR distinctions, from beyond this thread (and this site) .. referred to above, as 'a general population of MIR only thinkers'.

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    Quote Originally Posted by Selfsim View Post
    .. and when/if that happens, for a general population of MIR only thinkers, who simply would never accept MDR thinking, the feeling of being betrayed by what they think science is about (which of course it isn't) .. Which is a rather bleak inevitability, I think.
    Yes, this is one of the purposes of showing how well the MDR hypothesis tests out-- to get a better understanding of what science is and how it works, so that there is not constant "egg" in the face of the science-theory believer. Without this, not only does the science-theory believer tend to think that the current science understanding is correct, they also tend to think that their own current understanding is what is correct-- even if they have not advanced beyond college physics!

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    Quote Originally Posted by LaurieAG View Post
    Who are these MIR only thinkers who never accept MDR thinking? Can you name one poster here who doesn't accept MDR thinking but doesn't write off MIR entirely either?
    You'd have to go back to the early pages of the thread to see this, those posters tended to simply exit when they found their arguments could not be supported with evidence but they wished to hold to them all the same. Those that stuck around, like yourself and gzhpcu, came to a better understanding of what the MDR hypothesis is actually saying. Many early posters mistook it for solipsism, but solipsism says one can only know one's own mind, MDR observes that all knowledge requires modeling, even modeling of one's own mind, so one does not know one's own mind any better than anything else. Others mistook it for claiming that we can fantasize anything we want into our working concept of reality, but of course MDR says no such thing. So yes, there were plenty of posters who expressed strong personal MIR beliefs that they could not connect with scientific thinking, and who also had a deep misunderstanding of what is meant by MDR thinking, and the easily testable MDR hypothesis.
    That's the real problem with MDR alone thinking at the exclusion of everything else
    That statement is coming entirely from you, no one else on this thread has ever said anything of the kind. Need I repeat the MDR hypothesis so you can see what you just said ain't in it? So you should ask yourself, why do you insist on inserting these false interpretations just so you can object to them? Your argument is just like when an anti-evolutionist claims that evolutionary biologists embrace evolution at the exclusion of everything else, as if a good testable model for how humanity arose is some kind of claim that nothing else matters about humanity. That's a complete failure to understand what scientific theories actually do!
    Last edited by Ken G; 2020-Mar-01 at 12:21 PM.

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    Quote Originally Posted by Ken G View Post
    I see the situation with "a priori" aspects of physical theories to be similar to their "deterministic" elements. People who notice that deterministic equations often predict results quite well (but also have their limits, like weather or human behavior) often make the jump to concluding that the future is actually determined by the past, but no tested physical theory claims that or requires that (because that's not what theories do). It's mistaking tested successes of a model for untested constraints on reality, a constant problem in how we frame physics (akin to MIR belief in scientific contexts). Similarly, when we notice that mathematics works so well, we see an a priori element in our surroundings, but that's once again mistaking the model for the reality. Determinism, and a priori, are attributes of models, and what we call "reality" is a kind of uber-model that amalgamates all those individual models in a more sophisticated (and logically fuzzier) way than simply carrying over all those model attributes, because model attributes are always contextual, idealized, and subject to change. This is obvious any time a teacher says something like "when UV light is shined on an atom, the electron in the atom can be knocked free," and isn't immediately faced with a bright student who says "wait a minute, all electrons are indistinguishable so you cannot talk about the individual electron that is in the atom." Because we don't wish to face that, we are admitting that the attributes of reality are not simply inherited from attributes of models, they are modes of thinking about our circumstances, and those modes of thinking benefit from contextually convenient notions like determinism and causation-- and a priori.

    On that last point, I recall some physicist had said words to the effect that reducing a physical law to a symmetry is the best way to expose its a priori character. I responded that even a physical theory reduced to a symmetry cannot be regarded as a priori, because the symmetry is probably broken at some level. Thus the issue is not whether the symmetry is really true in some absolute sense, it suffices that it be true enough for us to simplify, predict, and understand. I think the resolution is that the act of understanding something involves creating a sense of an a priori aspect, like we are trying to make some phenomenon seem a prior to us, moreso than that we are trying to prove it really is. In that way, if it not a necessary axiom of science to assume anything is a priori, just as it is not a necessary axiom of shoe shopping to assume we will find shoes that fit our feet. We only need to have reason to expect it will be worth the effort.

    All this is more or less what we can observe just by watching the process, but it doesn't answer the deep mystery of why does math work so well in science? Is it because, as some have said, "god is a mathematician," which has the a priori character you are wondering about? Or is mathematics just our chosen angle of attack based on our brain function, and it works for some more anthropic reason (if it didn't, there would never have been a survival advantage to high intelligence, so it wouldn't have evolved and no one would be around to wonder why it works so well)? That latter answer is related also to the answer that perhaps we are very good at restricting the topics we analyze to those that our mathematics happens to work well with, but I admit that solving differential equations shows no immediate connection to escaping from a sabre-toothed tiger's den!
    I thought I understood the term a priori, but now I’m not so sure. I tended to think of the term in relation to Kant and his claim that by pure philosophical reasoning he could demonstrate that the concept of space is a priori - that it in no way derives from observed relationships between external phenomena. In other words the concept is in no way an empirical one derived from our experience of some external space. (I use this just as an example, not to suggest that Kant is correct).

    In terms of logic (and hence I assume all of mathematics) the a priori notion seems to be essential since logic does not require empirical experience in order to be tested.

    In both these cases a priori seems to denote an intrinsic “something” that facilitates a working structure that transcends empiricism. In terms of Kant, it allows the mind to model things as being organised in terms of their locations with respect to each other - they fall into this model via the a priori notion of space. And presumably in terms of logic it allows us to say that 2 + 2 = 4 without having to empirically show that this is the case.

    But a search on Google shows a complete spectrum of views regarding the term a priori. They range from that alluded by me above (a priori being independent of empirical experience) to a claim that all empirical science has a priori as its foundation. A long piece goes into an analysis of what “independent of experience” really refers to and another piece claims that a priori is totally about causation.

    You seems to link it with the way determinism is used problematically in science, but I am left wondering if the term provides any benefit over other language when discussing physical theories. All models seem to have at their bottom layer assumptions that lead to empirical findings – the effect of one particle interfering with itself shows up as an interference pattern, the underlying level of such an observed effect could be called a priori I suppose – we don’t have any experience of how one particle could interfere with itself, we just treat it as a given that “just is”. But some day we might get down to a lower level and then the term a priori would shift down to that level and so on. So if this is how science uses the term, I just don’t see any distinction between using “a priori” and “assumption” – does science really need this term in the way that logic uses it and Kant used it?

    It seems better reserved for specific areas of knowledge that would not be increased at all by experience. For example, a mountain range through experience will be known to have peaks of different heights. But a priori we can know that within that range there will be a highest peak, we can know this without recourse to having any knowledge over which peak that is or its actual height. Empirically finding out which one of the mountains is the highest and what height it actually rises to adds nothing of value to the original intent of the a priori statement.

    It’s use in logic and mathematics seems to be quite different to its use in science – maths doesn’t seem to work in terms of predicting the future from the past in the way F =MA does (as you pointed out). It’s as if the a priori element underlying logic and maths allows all possible outcomes to be correct all of the time whereas F=MA makes an assumption that the prediction will work from past to future, but all we have to rely on with such predictive models is a confidence factor (experience). It could be that one day the prediction may suddenly not work, but with logic and maths, the a priori gives us a 100% confidence that 2+2 will always equal 4. So when we transfer the maths to an empirical model, it doesn’t seem to me we are transferring the a priori element, if we were then we could have a 100% confidence that F=MA will always work from past to future just as we can be 100% sure that 2+2 will always equal 4. And then that really would be a distinguishing feature of a priori – it would be an a priori element that gives the model the same kind of status that logic and maths has. But clearly that isn’t the case, any a priori element included in a model seems to be no more than a bottom level descriptive assumption that serves to descriptively prop up the predictive model.

    So I am left wondering and confused over what really a priori is all about in terms of empirical models. I’m not at all sure the term serves any useful purpose within such models - perhaps this is what you are suggesting.

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    In my view, a prori stands in maths or abstract logic where you can start with a postulate. There is no link from postulate to experience except in the words we use. The mountain peaks hide arithmetic where there can be no infinity. Any postulate such as "something cannot come from nothing" can be used to argue a physics but we cannot subject it to an experience test even if it works as a predictive model. Obviously modern physics, from experience, has to grapple with that one.

    A priori postulate 1: "Only humans have agency in this universe" 2 "Humans only have the illusion of agency in this universe" You can build an argument on either but they are mind models. But if A=B and B=C then A=C works in the arbitrary rules we have invented.

    The a priori MIR that got expressed as "self evident" is the central example for this thread because in common parlance reality is thought of as "a given", and the weakness of that a prori thought has been hammered out over thousands of posts.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    So I think you are saying that a priori as a notion serves no distinguishing purpose when used within empirical models.

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    Quote Originally Posted by Ken G View Post
    You'd have to go back to the early pages of the thread to see this, those posters tended to simply exit when they found their arguments could not be supported with evidence but they wished to hold to them all the same. Those that stuck around, like yourself and gzhpcu, came to a better understanding of what the MDR hypothesis is actually saying.
    So why make untruthful statements and build obvious straw men from over 13,000 posts ago if you think you are so correct?

    You don't have an explanation that is rigorous enough to counter all the doubts about your assertions, while keeping a consistent set of caveats, so is this bluff intended to brace your position(s) or is it just general trolling? If you ask me it's all 3.

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    Quote Originally Posted by LaurieAG View Post
    So why make untruthful statements and build obvious straw men from over 13,000 posts ago if you think you are so correct?

    You don't have an explanation that is rigorous enough to counter all the doubts about your assertions, while keeping a consistent set of caveats, so is this bluff intended to brace your position(s) or is it just general trolling? If you ask me it's all 3.
    Such nonsense ..

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    Quote Originally Posted by Len Moran View Post
    So I think you are saying that a priori as a notion serves no distinguishing purpose when used within empirical models.
    yes I think so. In Bayesian prediction we talk of a prior assumption or prediction but it does not survive a rigorous rationalisation, the experience comes first, then the model. After that the superstition where the model is challenged.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by LaurieAG View Post
    So why make untruthful statements and build obvious straw men from over 13,000 posts ago if you think you are so correct?
    Unfortunately I have no idea what you are talking about. Do you have any actual evidence?
    You don't have an explanation that is rigorous enough to counter all the doubts about your assertions, while keeping a consistent set of caveats, so is this bluff intended to brace your position(s) or is it just general trolling? If you ask me it's all 3.
    Again, no idea, you are just spewing opinion, I don't see any argument there and certainly no evidence.

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    Quote Originally Posted by Len Moran View Post
    I thought I understood the term a priori, but now I’m not so sure. I tended to think of the term in relation to Kant and his claim that by pure philosophical reasoning he could demonstrate that the concept of space is a priori - that it in no way derives from observed relationships between external phenomena. In other words the concept is in no way an empirical one derived from our experience of some external space. (I use this just as an example, not to suggest that Kant is correct).
    Yes, that is how I take the meaning of the phrase as well, something that can be known to be true by virtue of it having to be true. But I don't think Kant's argument can hold.
    In terms of logic (and hence I assume all of mathematics) the a priori notion seems to be essential since logic does not require empirical experience in order to be tested.
    But even in pure mathematics, we do not have an a priori character as soon as we choose a set of axioms to base the structure on. And without said axioms, mathematics is completely empty. So I see no a priori character, even in any example of pure mathematics. Take for example Euclidean vs. non-Euclidean geometry-- which one of those is "a priori"?
    We must be careful not to confuse "true", which mathematics cannot say and is never a priori, with "inherits the truth value of the axioms it relies on," which mathematics can say and can be a priori, but doesn't have going for it what Kant wishes. If Kant tries to say "space is a priori", he faces the logical contradiction that he can be asked what axioms he is using to assert that, and then he can be asked why he thinks those axioms are "a priori." Then he can be told about spacetime, and poof, it's all gone.
    In both these cases a priori seems to denote an intrinsic “something” that facilitates a working structure that transcends empiricism. In terms of Kant, it allows the mind to model things as being organised in terms of their locations with respect to each other - they fall into this model via the a priori notion of space.
    But is that argument not clearly circular? It asserts, without proof, that space is an "a priori notion", and then uses that assertion as an argument that whenever we manipulate the space concept we are taking advantage of a priori aspects. If I simply reject the claim that space is an a priori notion, I don't see that any part of Kants argument survives.

    And presumably in terms of logic it allows us to say that 2 + 2 = 4 without having to empirically show that this is the case.
    But this is an excellent example of exactly what I'm talking about. In order to assert that 2 + 2 = 4, one requires a set of axioms. Do you know how long mathematicians labored to find such a set? All you have to do is look at the history of that endeavor, and you see how not "a priori" it was! And if you extend those axioms to the real numbers, the axioms we use to this day suffer problems that many tried to correct, until Godel proved it would be impossible to know if the axioms are self-consistent. Thus is it always impossible to know if any statement about the real numbers is true, and the only reason we use proofs in the reals is because they seem to give good results. That's empirical, not a priori! A priori knowledge about the reals is impossible.
    But a search on Google shows a complete spectrum of views regarding the term a priori. They range from that alluded by me above (a priori being independent of empirical experience) to a claim that all empirical science has a priori as its foundation.
    I would tend to regard that latter position as pure nonsense. There is a lot of nonsense said about science, including that it requires MIR as an assumption-- a claim soundly thrashed in this thread.

    A long piece goes into an analysis of what “independent of experience” really refers to and another piece claims that a priori is totally about causation.
    And now we get right to the heart of the issue that keeps cropping up-- so many people treat our words (like "a priori") as if they were just handed to us from the outside, and our only job is to decide if science or mathematics or whatever is actually "a priori" or not. But of course that attitude completely overlooks all the hard work that first has to go into giving our words their meaning. So if one would talk about "a priori" anything, one must begin by saying what you want those words to mean, and by what process you are breathing meaning into the words. This realization is the fundamental basis of MDR thinking. The way you framed those arguments makes it sound like there was not a recognition that there's no such thing as what independent of experience "really means", or that a priori has to be "totally about causation", but there is great value in the effort of analyzing what "independent of experience" could usefully mean, or what useful connections we could draw between some "a priori" concept and some "causation" concept. I just wish people would frame these claims in a manner that is consistent with the process of reaching their conclusions, avoiding language that makes it sound like a concept like "experience" is itself "a priori."

    Indeed, any time anyone wants to argue such-and-such a thing is "a priori", while some other thing is based on experience, I will want them to tell me which of "a priori" and "experience" is an a priori concept. Then I'll sit back and watch them wallow in the paradoxes they suffer, when they try to decide! (It might go like this. They might say the a priori concept is itself an a priori concept because it doesn't require any experience. I say, if it doesn't require any experience, then I don't have to even know what "experience" is, or what the word "experience" even means, otherwise it isn't independent of experience. So if I don't even know what experience means, then the word for me could be "grumblesnuff," for all the difference it could make. Then their argument becomes, "a priori is an a priori notion because it doesn't require any grumblesnuff." See the problem? Their argument is nothing more than saying it is a priori because it isn't saying anything at all, but if it isn't saying anything, it can be neither a priori nor not a priori! Or, if they say the a priori concept requires experience to understand, but each a priori notion requires no experience to know it is true, then they are holding that it is possible to know something is true without understanding it. Then it is purely a symbolic truth, like positions in a logic table, but the words don't mean anything, and we're right back to grumblesnuff.)

    In short, I would argue that the only way one can hold that any statement is "a priori", one must either not know what the statement means, or one must hold that meaning can exist independent of experience. If I say 2 + 2 = 4 but have no experience, then it is saying that grumblesnuff + grumblesnuff = blargleheap. All meaning is a process of experience, or arguments like Kant's should be restricted to symbols that have no experiential meaning for us. If he didn't need meaning, why does he use terms that we do associate experiential meaning with, instead of inventing a new language with no such baggage to make his case?

    And for anyone who still thinks there exists "a priori" notions, say those encountered in purely abstract math, then let them consider the experience of thought. We certainly can distinguish the experience of a walk in the park from the experience of closing one's eyes and imagining a park, but those are both experiences. If one holds that "a priori" restricts to experiences one can have inside one's mind without ever having experienced anything similar in the world around them, that's fine, but it's still just two types of experiences, and we certainly cannot hold that the mental experience does not depend on the mind. Imagine the logical problems of claiming that a purely mental experience is a priori in the sense of not depending on the functionings of that mind! So even "a priori" meant as "internal mental experience" carries no independence of the mind doing it, and let's face it, also the experiences that conditioned that mind to function as it does. And even if the mind is programmed like a computer, with no experiences of its own, then look to the experiences of the programmer instead. At the end of the day, "experience" can mean little more than "that which had to come before to reach the state in question." No examples of "a priori" reasoning escape that meaning of "experience," and the tiger is still chasing its tail around and around.

    You seems to link it with the way determinism is used problematically in science, but I am left wondering if the term provides any benefit over other language when discussing physical theories.
    It's value is in the sense of understanding it conveys. We like to imagine "things happen for a reason", we like to imagine "it had to be this way," but in act those only test out successfully as being convenient modes of thinking moreso than absolute truths. Just like the axioms of the real numbers.
    So if this is how science uses the term, I just don’t see any distinction between using “a priori” and “assumption” – does science really need this term in the way that logic uses it and Kant used it?
    "Need" is a strong word, let's instead say "benefits from," in terms of the goals we put out for science. This is the sense that it can be said once something is reduced to a symmetry, we can feel like we understand why it is true, or why it "had to be" true (though we have learned that latter is itself not likely to be true in any absolute sense). For example, Noether proved that the postulates of Newton's laws connect the mysterious principle of conservation of energy with the seemingly more natural concept of time symmetry (meaning that times in the past are more or less the same as times in the future, the laws of physics don't evolve with time). Once we understand this, we say "aha, now I understand why energy is conserved." But of course we don't really, because we don't know why Newton's postulates hold (or when they won't), and we don't know why (or if) the laws of physics don't evolve with time. So I would say that Noether's theorem only seems to provide an "a priori" aspect to conservation of energy, but that's the only way "a priori" really appears in science-- at the level of appearance, like the way the goal of Occam's Razor is to provide the appearance that the laws of physics can be made simple.
    Last edited by Ken G; 2020-Mar-02 at 12:34 PM.

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    Quote Originally Posted by Len Moran
    It could be that one day the prediction may suddenly not work, but with logic and maths, the a priori gives us a 100% confidence that 2+2 will always equal 4. So when we transfer the maths to an empirical model, it doesn’t seem to me we are transferring the a priori element, if we were then we could have a 100% confidence that F=MA will always work from past to future just as we can be 100% sure that 2+2 will always equal 4.
    Beware of confusing a proof that a statement like 2+2=4 inherits the truth value of a set of axioms, with a claim that we can be "100% sure" it will always hold true. If we are talking about holding true in our experience, then of course that has already crossed out of pure mathematics, and if we are talking about what can be proven, then we still can never be "100% sure" the axioms are true, or even consistent with each other. So all we can say about 2+2=4 is that it is just as "a priori" as the axioms used to prove it. I see no requirement to regard those axioms as "a priori," just as there is no requirement to see conservation of energy as that, or time symmetry as that, but we want for our own purposes that we have the sense that they are. We put "a priori" elements into our mathematics, and into our physics, for the same basic reason-- we want it to be there. But we never know that it actually is, and it is certainly not impossible to imagine that someday a new way to axiomatize the integers might be suggested as an improvement. If so, we will then have to regard 2+2=4 as being true because of those axioms, rather than for the reasons we used to say it was true, mathematically speaking.

    So I'm saying that there is a place for a sense of "a priori" aspects to both math and science, but neither are "a priori" endeavors. So I do agree that science is more likely to be harmed by the idea that it involves truths that are actually a priori (including space), but good models can make us feel like we are getting away with imagining that (just as there are good models of electrons in many contexts that get away with imagining that electrons can be distinguished from each other, like this electron or that electron, when we know that more sophisticated models require us to remove that property). And most physics models respect the concept of local realism, to the point that Einstein made the mistake of thinking those principles were "a priori"-- but they are not.

  17. #13697
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    Getting back to mind models, I was listening to a talk recently on colour constancy as a tool for investigating the brain model. Our brain can allocate a colour in very varied lighting conditions, even adjusting for reflected colours off other coloured objects. This is part of how we enhance our 3D perception and can be fooled by clever illusions. I used to do conservation lighting of pictures and demonstrated that adjusting colour temperature changed the perception of brightness distribution. In particular lower temperature lighting akin to candle light can make a top lit picture appear uniformly lit as well as emotionally "warmer" This little example illustrates how we make sophisticated models of our reality and relate to these models even when they are pigments on canvas. We tend to make the very natural step that the model implies independent reality. We say "seeing is believing" but in this thread we can imbue a deeper meaning to that proverb.
    Last edited by profloater; 2020-Mar-02 at 12:43 PM. Reason: typo
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Yes, when we say "seeing is believing," we naturally imagine the claim is that we believe to be true what we see to be true. But actually, what we see must be what we believe we have seen, so "seeing is believing" is better interpreted as "seeing requires that we be able to believe." This time by "believe" I don't mean choose to have faith in without testing, I mean "make sense." Notice that the very phrase "what we see to be true" requires a kind of mind-dependent judgement on our part-- there is no such thing as "seeing to be true" without a mind to make sense of that judgement.

  19. #13699
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    Quote Originally Posted by Ken G
    Beware of confusing a proof that a statement like 2+2=4 inherits the truth value of a set of axioms, with a claim that we can be "100% sure" it will always hold true. If we are talking about holding true in our experience, then of course that has already crossed out of pure mathematics, and if we are talking about what can be proven, then we still can never be "100% sure" the axioms are true, or even consistent with each other. So all we can say about 2+2=4 is that it is just as "a priori" as the axioms used to prove it. I see no requirement to regard those axioms as "a priori," just as there is no requirement to see conservation of energy as that, or time symmetry as that, but we want for our own purposes that we have the sense that they are. We put "a priori" elements into our mathematics, and into our physics, for the same basic reason-- we want it to be there. But we never know that it actually is, and it is certainly not impossible to imagine that someday a new way to axiomatize the integers might be suggested as an improvement. If so, we will then have to regard 2+2=4 as being true because of those axioms, rather than for the reasons we used to say it was true, mathematically speaking.

    So I'm saying that there is a place for a sense of "a priori" aspects to both math and science, but neither are "a priori" endeavors. So I do agree that science is more likely to be harmed by the idea that it involves truths that are actually a priori (including space), but good models can make us feel like we are getting away with imagining that (just as there are good models of electrons in many contexts that get away with imagining that electrons can be distinguished from each other, like this electron or that electron, when we know that more sophisticated models require us to remove that property). And most physics models respect the concept of local realism, to the point that Einstein made the mistake of thinking those principles were "a priori"-- but they are not.
    Well, I've gotta say the idea of drawing close parallels between how we arrive at meanings for 'a priori', 'axiom' and 'objective', is certainly consistent with the notion that a single type of mind is continually at work in doing all of that (ie: a very human (mind's) work). This argument is also consistent with the notion we discussed previously, ie: that 'truth' is assignable (and yet, is also subject to change with new information).

    Just recapping my understanding of what is presented here: there seem to be three main ways we arrive at a meaning for truth - believing, referencing axioms and objectively testing.
    Reality then flows on from the respective meanings we derive from those distinct ways. In making sense of reality, we also make use of the wild cards of determinism/causality, randomness and free choice. These are 'wild' because they stem from asking different, philosophically formed questions. In science we may, (or may not), notice 'connections' amongst these, which help in achieving science's overall purpose of making useful predictions.

    Also, (come to think of it), forming conclusions in science, always involves logical inferences, so its not only math logic which is firmly embedded in the scientific method.
    Science makes use of many complex philosophical concepts which go way beyond its own simplified, widely published and taught method .. but improvements in its efficiency are demonstrably achievable by ignoring the mind's natural tendency of believing in those concepts. .. (?) ..

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    Quote Originally Posted by Ken G View Post
    ... Notice that the very phrase "what we see to be true" requires a kind of mind-dependent judgement on our part-- there is no such thing as "seeing to be true" without a mind to make sense of that judgement.
    .. (or other minds in order to concur on that judgement, conditionally).

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    Isn't that our mental models of other minds?

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    Quote Originally Posted by Selfsim View Post
    Just recapping my understanding of what is presented here: there seem to be three main ways we arrive at a meaning for truth - believing, referencing axioms and objectively testing.
    Yeah that makes sense to me. It's a shame we use the same word "truth" for all three, it helps us forget that we own our truths based on the choices we make to arrive at them. And just look at all the problems forgetting that causes!
    Reality then flows on from the respective meanings we derive from those distinct ways. In making sense of reality, we also make use of the wild cards of determinism/causality, randomness and free choice. These are 'wild' because they stem from asking different, philosophically formed questions. In science we may, (or may not), notice 'connections' amongst these, which help in achieving science's overall purpose of making useful predictions.
    Yes, the scientific toolkit often borrows from philosophy, but only in a conditional and contextual way, and always with a mind to testing.
    Also, (come to think of it), forming conclusions in science, always involves logical inferences, so its not only math logic which is firmly embedded in the scientific method.
    Science makes use of many complex philosophical concepts which go way beyond its own simplified, widely published and taught method .. but improvements in its efficiency are demonstrably achievable by ignoring the mind's natural tendency of believing in those concepts. .. (?) ..
    I'd say the individual scientist has an uneasy relationship with their capacity to believe. They take advantage of that capacity to help them frame the purpose of what they are doing (to inform their beliefs, which they will have one way or another), but they must also maintain a distance from their beliefs or it can compromise their effectiveness.

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    Quote Originally Posted by Chuck View Post
    Isn't that our mental models of other minds?
    It sounds like you are making the mistake of bad algebra of models here. By that I mean, claiming that realizing "other minds" is a model requires that we refer to them as "mental models of other minds", which would be like calling them mental models of mental models. If you already know that anything we talk about is going to be a testable mental model, you do not need to preface the models with the adjective, or you may fall into the erroneous claim that saying Neil Armstrong walked on the Moon is a claim that a model can walk on another model.

  24. #13704
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    Quote Originally Posted by Selfsim View Post
    Well, ...
    Also, (come to think of it), forming conclusions in science, always involves logical inferences, so its not only math logic which is firmly embedded in the scientific method.
    Science makes use of many complex philosophical concepts which go way beyond its own simplified, widely published and taught method .. but improvements in its efficiency are demonstrably achievable by ignoring the mind's natural tendency of believing in those concepts. .. (?) ..
    It seems right that maths, which is logical, is involved in science models but the basis of science, observation, hypothesis, predict, test is more of a process than any logic based on assumptions.

    Maybe we can say logic enables us to predict from an hypothesis but it's much more like "last time this happened, so next time we predict what happens"

    There is an assumed cause and effect logical premise but we have discussed that and modern physics challenges cause and effect.

    Is model making logical or just effective for prediction.? Our decisions are emotional then acted out by rational thinking. We cannot pretend there are no emotions in science, science investigates what is interesting and that comes from emotion.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

  25. #13705
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    Quote Originally Posted by Ken G View Post
    It sounds like you are making the mistake of bad algebra of models here. By that I mean, claiming that realizing "other minds" is a model requires that we refer to them as "mental models of other minds", which would be like calling them mental models of mental models. If you already know that anything we talk about is going to be a testable mental model, you do not need to preface the models with the adjective, or you may fall into the erroneous claim that saying Neil Armstrong walked on the Moon is a claim that a model can walk on another model.
    I thought that my mental model of Neil Armstrong did my mental model of walking on my mental model of the moon. That's all I can say about it.

    Is someone else's mind the same thing as my mental model of it? I can't even be sure that other minds exist but I'm aware of my mental models of them. They seem to be different things. And what's wrong with having a mental model of a mental model? If someone tells me about his mental model of a tree don't I then become aware of a model of a model?

  26. #13706
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    Quote Originally Posted by profloater View Post
    It seems right that maths, which is logical, is involved in science models but the basis of science, observation, hypothesis, predict, test is more of a process than any logic based on assumptions.

    Maybe we can say logic enables us to predict from an hypothesis but it's much more like "last time this happened, so next time we predict what happens"

    There is an assumed cause and effect logical premise but we have discussed that and modern physics challenges cause and effect.
    Ya .. I suppose there's a delicate balance there .. I mean physics, I think, recognises causality and even recognises the conditions where an effect might possibly precede a cause (ie: outside a light cone) ... even though cause and effect never explicitly appears in the relationships between the parameters of its various mathematically expressed models.

    Quote Originally Posted by profloater
    Is model making logical or just effective for prediction.? Our decisions are emotional then acted out by rational thinking. We cannot pretend there are no emotions in science, science investigates what is interesting and that comes from emotion.
    I think curiosity can be both a behavior and an emotion .. its also a way of thinking (or a mindset) too, IMO .. Either way, I accept that its certainly a motivator for initiating the scientific method .. as well as yet another way of getting into serious trouble, irrespective of science!

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    Quote Originally Posted by Selfsim View Post
    Such nonsense ..
    Name one person on this thread who only believes in MIR? Yes that statement of yours is nonsense.

  28. #13708
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    Quote Originally Posted by Selfsim View Post
    Ya .. I suppose there's a delicate balance there .. I mean physics, I think, recognises causality and even recognises the conditions where an effect might possibly precede a cause (ie: outside a light cone) ... even though cause and effect never explicitly appears in the relationships between the parameters of its various mathematically expressed models.

    I think curiosity can be both a behavior and an emotion .. its also a way of thinking (or a mindset) too, IMO .. Either way, I accept that its certainly a motivator for initiating the scientific method .. as well as yet another way of getting into serious trouble, irrespective of science!
    I think causality creeps in very early in our infant models but then so does stuff that just seems to happen. Put those together and we grow up thinking there's a cause and if we cannot see it, there is an external agency such as Karma or a god. The trouble is we got better at science and we have to challenge those naiive assumptions.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

  29. #13709
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    Quote Originally Posted by Ken G View Post
    Beware of confusing a proof that a statement like 2+2=4 inherits the truth value of a set of axioms, with a claim that we can be "100% sure" it will always hold true. If we are talking about holding true in our experience, then of course that has already crossed out of pure mathematics, and if we are talking about what can be proven, then we still can never be "100% sure" the axioms are true, or even consistent with each other. So all we can say about 2+2=4 is that it is just as "a priori" as the axioms used to prove it. I see no requirement to regard those axioms as "a priori," just as there is no requirement to see conservation of energy as that, or time symmetry as that, but we want for our own purposes that we have the sense that they are. We put "a priori" elements into our mathematics, and into our physics, for the same basic reason-- we want it to be there. But we never know that it actually is, and it is certainly not impossible to imagine that someday a new way to axiomatize the integers might be suggested as an improvement. If so, we will then have to regard 2+2=4 as being true because of those axioms, rather than for the reasons we used to say it was true, mathematically speaking.

    So I'm saying that there is a place for a sense of "a priori" aspects to both math and science, but neither are "a priori" endeavors. So I do agree that science is more likely to be harmed by the idea that it involves truths that are actually a priori (including space), but good models can make us feel like we are getting away with imagining that (just as there are good models of electrons in many contexts that get away with imagining that electrons can be distinguished from each other, like this electron or that electron, when we know that more sophisticated models require us to remove that property). And most physics models respect the concept of local realism, to the point that Einstein made the mistake of thinking those principles were "a priori"-- but they are not.
    Well perhaps the way to play safe with any account of a priori is not to view that account as being set in stone but rather being subject to change at the hands of minds. Certainly the examples you give in your replies would indicate that, especially the not so obvious one involving the axioms of integers where 2+2=4 has the potential to be true when derived from two different axioms.

    Just as an interesting, but probably very simplistic question, if I was able to build up a mathematical structure from my own axioms such that 1+1=3, presumably it would be the case that my mathematical structure would not map onto physics in the manner our current use of maths does - no matter how hard I tried, I would not be able to weigh one molecule of water as "a" and two molecules of water as "3a", I would be stuck with the two molecules weighing "2a".

    As I said I'm sure this is way too simplistic in approach, but it does lead me to think about the axioms that do provide a mathematical structure that successfully maps onto physics - it seems too great a coincidence to think that the current axioms just happen to be such that our maths does map so well onto the material world.

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    Quote Originally Posted by Len Moran View Post
    .. As I said I'm sure this is way too simplistic in approach, but it does lead me to think about the axioms that do provide a mathematical structure that successfully maps onto physics - it seems too great a coincidence to think that the current axioms just happen to be such that our maths does map so well onto the material world.
    Its the same type of (like-thinking) mind which conceived both math and physics though .. all whilst trying to make sense of its situation.

    I'm reminded of the story of zero and how long it took for humanity to come up with that concept .. There's some evidence from history that even the humble zero wasn't 'apriori'!

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