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Yes, it's not the apparent logic in the operations that counts but the choice of definitions (and these include the definitions of the operations). I wrote a pa

Yes, it's not the apparent logic in the operations that counts but the choice of definitions (and these include the definitions of the operations). I wrote a paper for the "Mind-Body Conference" in 1975 that discussed this. The idea is that "reasonable things" are done within "stable neighborhoods of 'truth' " that can be thought of as regions whose boundaries are the definitions. Inside we pretend the definitions are true, while the larger view from above knows the neighborhood is arbitrary. This is an old idea (e.g. Euclid). The "modern" part of it is that the definitions are not assumed to be true outside the neighborhood. This is simple and powerful because the results are larger worlds that can be compared to others and to phenomena and experiment (and without setting up dogmas and religions). Because of the way human minds work, there will be tendencies to think the definitions are "actually true" (and so the logic inside the boundaries) if they and the conclusions are appealing. But the form of this knowledge helps keep us saner if we are diligent about drawing the maps and boundaries correctly. Much of science has this character, and the model helps to understand what it means to "know" something scientifically. Science is a negotiation between "what's out there?" and what we can represent inside our heads via phenomena on the one hand and the "boundaries and neighborhoods" on the other. Einstein's nice line about "math vs. reality" hits it perfectly ("As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."). Newton's Principia was a huge step along these (and many other lines). He completely separates out the math part in the first large parts of the work. And only then does he start looking to see how the math models map onto observed phenomena. To say it again, Science is partly about being very careful about how the definitions map to "out there". In terms of context, if you are aware that you are in contexts -- the first step! -- and aware and careful about the ones you are using -- the next steps! -- there is a chance that "reasonable thinking" might happen.

da02 9y ago
> Science is partly about being very careful about how the definitions map to "out there". I keep tripping on this part. Definition as in understanding the boundary? As in trying to find the boundaries between better, perfect, and the impossible (ie sweet spot)? > Because of the way human minds work, there will be tendencies to think the definitions are "actually true" (and so the logic inside the boundaries) if they and the conclusions are appealing. Does this mean?: Humans are pre-disposed to a model of how the Universe works: Zeus's thunderbolts, witches, Saturn/Satan/Santa, Geo-centric, etc. Science is a set of guidelines to help prevent us from shoehorning the Universe into the inaccurate mental models we are pre-disposed to believing? > while the larger view from above knows the neighborhood is arbitrary Can the leap from Geocentric model to Kepler's work be an example of this? As in: Geocentric model becomes irrelevant with Kepler's discoveries and p.o.v.?
- alankay1 9y ago
  1. The definitions are the boundary -- these are what are used to make the interior. The analogy is to definitions (used to be called axioms) in math. Simple for math (because it is only about itself). Difficult for science because we can't just make up the definitions, we have to try to find ones that have some mappings to "out there". A boundary for chemistry is the physics standard model. Within physics the model is pretty accurate but unsatisfying as far as knowledge. They would like to have a better boundary, and get the standard model (and the key constants) from it. But it makes a good boundary for chemistry to make excellent chemical models. Similarly (oversimplifying here) chemistry makes a good boundary of definitions for molecular biology. Note that in this scheme of thinking, the "knowledge and meanings" exist inside the boundary, but don't include the boundary. One of the issues addressed in this approach is how to make progress in "knowing" without infinite regresses. Philosophically, it is a kind of pragmatism. As I mentioned elsewhere, science is a negotiation between two different kinds of things not a set of truths. It has many things in common with mapping (and making good maps is a branch of science, and one of the real starts of real science). 2. We are predisposed to believe things. Bacon's notion of why we needed to invent a "new science" is to create a set of processes and heuristics that would help us deal with and get around to some extent "what's wrong with our brains". As a young scientist, I got the warning that is given to most young scientists "Beware, you always find what you are looking for!" Some of the interesting examples of good science turning into belief revolve around Newton and both Maxwell's Equations and the orbit of Mercury (neither are "Newtonian"). And if you look at the history you'll see that Newton was a lot less Newtonian than many of his followers. And yes, we also seem to have some things that are easier to imagine than others -- gods, demons, witches, etc seem easy, but future floods etc seem hard. 3. Sure. E.g. if you think things have to be circles, then this will be part of your implicit context for thinking about orbits. Geocentric used circular orbits and then epicycles to correct them and save the theory (and some great metaphors there for lots of human thinking). But it's important to realize that Copernicus also used circular orbits, and they also used epicycles to save that theory. Kepler worked with Brahe and admired him, so decided to trust his measurements. This led to a different model. The planets themselves didn't care about any of the models. The definitions are still not -true- and the neighborhood is still not the phenomena. It's just better. You only get Newton from Kepler, not Maxwell or the orbit of Mercury and then Einstein for both.

da02 9y ago

> Science is partly about being very careful about how the definitions map to "out there". I keep tripping on this part. Definition as in understanding the boundary? As in trying to find the boundaries between better, perfect, and the impossible (ie sweet spot)? > Because of the way human minds work, there will be tendencies to think the definitions are "actually true" (and so the logic inside the boundaries) if they and the conclusions are appealing. Does this mean?: Humans are pre-disposed to a model of how the Universe works: Zeus's thunderbolts, witches, Saturn/Satan/Santa, Geo-centric, etc. Science is a set of guidelines to help prevent us from shoehorning the Universe into the inaccurate mental models we are pre-disposed to believing? > while the larger view from above knows the neighborhood is arbitrary Can the leap from Geocentric model to Kepler's work be an example of this? As in: Geocentric model becomes irrelevant with Kepler's discoveries and p.o.v.?

alankay1 9y ago
1. The definitions are the boundary -- these are what are used to make the interior. The analogy is to definitions (used to be called axioms) in math. Simple for math (because it is only about itself). Difficult for science because we can't just make up the definitions, we have to try to find ones that have some mappings to "out there". A boundary for chemistry is the physics standard model. Within physics the model is pretty accurate but unsatisfying as far as knowledge. They would like to have a better boundary, and get the standard model (and the key constants) from it. But it makes a good boundary for chemistry to make excellent chemical models. Similarly (oversimplifying here) chemistry makes a good boundary of definitions for molecular biology. Note that in this scheme of thinking, the "knowledge and meanings" exist inside the boundary, but don't include the boundary. One of the issues addressed in this approach is how to make progress in "knowing" without infinite regresses. Philosophically, it is a kind of pragmatism. As I mentioned elsewhere, science is a negotiation between two different kinds of things not a set of truths. It has many things in common with mapping (and making good maps is a branch of science, and one of the real starts of real science). 2. We are predisposed to believe things. Bacon's notion of why we needed to invent a "new science" is to create a set of processes and heuristics that would help us deal with and get around to some extent "what's wrong with our brains". As a young scientist, I got the warning that is given to most young scientists "Beware, you always find what you are looking for!" Some of the interesting examples of good science turning into belief revolve around Newton and both Maxwell's Equations and the orbit of Mercury (neither are "Newtonian"). And if you look at the history you'll see that Newton was a lot less Newtonian than many of his followers. And yes, we also seem to have some things that are easier to imagine than others -- gods, demons, witches, etc seem easy, but future floods etc seem hard. 3. Sure. E.g. if you think things have to be circles, then this will be part of your implicit context for thinking about orbits. Geocentric used circular orbits and then epicycles to correct them and save the theory (and some great metaphors there for lots of human thinking). But it's important to realize that Copernicus also used circular orbits, and they also used epicycles to save that theory. Kepler worked with Brahe and admired him, so decided to trust his measurements. This led to a different model. The planets themselves didn't care about any of the models. The definitions are still not -true- and the neighborhood is still not the phenomena. It's just better. You only get Newton from Kepler, not Maxwell or the orbit of Mercury and then Einstein for both.