Operationally defined, no infinite sets can exist, and the idea of infinite sets of different sizes is also impossible. However, what is possible, is that in the generation of positional names, some sets of names must be produced faster and some slower, so that at any given moment the size of the sets will differ. A number is the name of a position. A position can be applied to any dimension, and any number of dimensions. We can create mathematics using triangulation (the greek model) beginning with sizes, and using ratios of sizes, or we can create mathematics of positions and apply them to lengths in any dimension. This property defines the reciprocity of measurement. So we can start with the mathematics of triangulation, then apply it to scale (just as we apply money to prices as a standard unit), and then we can scale the unit reciprocally.
If we taught mathematics operationally then all this fictionalism that makes math nonsense to so many people would disappear.
So for example, we can measure art by triangulation but we cannot measure it by numbers. We can measure distances by either triangulation or numbers. There are phenomenon we cannot measure by numbers other than probability (causal density is too high).
Category: Epistemology and Method
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(from elsewhere) Prof Wildberger: I love that you’re trying to de-platonize math
(from elsewhere) Prof Wildberger: I love that you’re trying to de-platonize mathematics, and return it to the sciences. Mathematical platonism uses a grammar and semantics of fiction (it’s technically a ‘Fictionalism’). And I can understand why some people have a natural tendency, out of historical bias, and out of the influence of hermeneutics (religious and scriptural interpretation) to fictionalize mathematics. In doing so they convert it from a science of measurement of constant relations in increasing dimensions into a linguistic ANALOGY – thereby obscuring (losing) the causal properties of mathematics (measurement of constant relations in increasing dimensions using positional naming). And that is the reason it’s both difficult to teach people (when it should be trivial), and forces us to rely on memorization rather than ‘understanding’. Where “understanding” means ‘in the context of existential reality, and therefore an extension of existential reality. -
(from elsewhere) Prof Wildberger: I love that you’re trying to de-platonize math
(from elsewhere) Prof Wildberger: I love that you’re trying to de-platonize mathematics, and return it to the sciences. Mathematical platonism uses a grammar and semantics of fiction (it’s technically a ‘Fictionalism’). And I can understand why some people have a natural tendency, out of historical bias, and out of the influence of hermeneutics (religious and scriptural interpretation) to fictionalize mathematics. In doing so they convert it from a science of measurement of constant relations in increasing dimensions into a linguistic ANALOGY – thereby obscuring (losing) the causal properties of mathematics (measurement of constant relations in increasing dimensions using positional naming). And that is the reason it’s both difficult to teach people (when it should be trivial), and forces us to rely on memorization rather than ‘understanding’. Where “understanding” means ‘in the context of existential reality, and therefore an extension of existential reality. -
(from elsewhere) Prof Wildberger: I love that you’re trying to de-platonize math
(from elsewhere)
Prof Wildberger:
I love that you’re trying to de-platonize mathematics, and return it to the sciences.
Mathematical platonism uses a grammar and semantics of fiction (it’s technically a ‘Fictionalism’). And I can understand why some people have a natural tendency, out of historical bias, and out of the influence of hermeneutics (religious and scriptural interpretation) to fictionalize mathematics.
In doing so they convert it from a science of measurement of constant relations in increasing dimensions into a linguistic ANALOGY – thereby obscuring (losing) the causal properties of mathematics (measurement of constant relations in increasing dimensions using positional naming).
And that is the reason it’s both difficult to teach people (when it should be trivial), and forces us to rely on memorization rather than ‘understanding’. Where “understanding” means ‘in the context of existential reality, and therefore an extension of existential reality.
Source date (UTC): 2017-11-21 11:03:00 UTC
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For Americans, any foreign language you would recommend for study?
For Americans, any foreign language you would recommend for study? -
For Americans, any foreign language you would recommend for study?
For Americans, any foreign language you would recommend for study? -
How Do You Define Philosophy?
Philosophy. Mindfulness. Dominance over the mind in the face of the unknown. Using grammar of technology. Tech(philio) vs Fiction(religion). Deflation vs Inflation. Mindfulness was necessary at ‘worry’ post-human-scales. All civ’s encountered demand for mindfulness as scale increased – and trust decreased. All about the same time. Probably due to trade. Westerners used competing (class) variants of mindfulness. Science can in fact provide mindfulness for those with the ‘ability’. Sport, Family, Work, Ritual, Wealth, Science Philosophy/Reason, Fiction, Religion. All can provide mindfulness (Disciplined thought in the face of the unknown/complexity). The principle problem of scale was creating mindfulness through trust. The only question is whether one’s form of mindfulness encouraged adaptation (philosophy > reason > science) or discouraged it (religion > abrahamism). -
How Do You Define Philosophy?
Philosophy. Mindfulness. Dominance over the mind in the face of the unknown. Using grammar of technology. Tech(philio) vs Fiction(religion). Deflation vs Inflation. Mindfulness was necessary at ‘worry’ post-human-scales. All civ’s encountered demand for mindfulness as scale increased – and trust decreased. All about the same time. Probably due to trade. Westerners used competing (class) variants of mindfulness. Science can in fact provide mindfulness for those with the ‘ability’. Sport, Family, Work, Ritual, Wealth, Science Philosophy/Reason, Fiction, Religion. All can provide mindfulness (Disciplined thought in the face of the unknown/complexity). The principle problem of scale was creating mindfulness through trust. The only question is whether one’s form of mindfulness encouraged adaptation (philosophy > reason > science) or discouraged it (religion > abrahamism). -
HOW DO YOU DEFINE PHILOSOPHY? Philosophy. Mindfulness. Dominance over the mind i
HOW DO YOU DEFINE PHILOSOPHY?
Philosophy. Mindfulness. Dominance over the mind in the face of the unknown. Using grammar of technology. Tech(philio) vs Fiction(religion). Deflation vs Inflation. Mindfulness was necessary at ‘worry’ post-human-scales. All civ’s encountered demand for mindfulness as scale increased – and trust decreased. All about the same time. Probably due to trade. Westerners used competing (class) variants of mindfulness. Science can in fact provide mindfulness for those with the ‘ability’. Sport, Family, Work, Ritual, Wealth, Science Philosophy/Reason, Fiction, Religion. All can provide mindfulness (Disciplined thought in the face of the unknown/complexity). The principle problem of scale was creating mindfulness through trust. The only question is whether one’s form of mindfulness encouraged adaptation (philosophy > reason > science) or discouraged it (religion > abrahamism).
Source date (UTC): 2017-11-21 08:25:00 UTC
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Every increase in explanatory power has been the result of a counter intuitive d
Every increase in explanatory power has been the result of a counter intuitive discovery that caused a costly revision of existing categories, relations and values. Just how it is. Your simple sacred cows die. New generations of superior sacred cows evolve. The slaughter continues anew. And in this stepwise fashion evolution leaves behind the detritus of past utility. 😉