You’ve redefined ‘x exists’ to mean ‘x is described by a map that has been tested and so far has seemed reliable to us’, and ‘x is true’ correspondingly.
I disagree that this is a redefinition. You believe that elephants exists because you can go and see them, or talk to someone you trust who saw them, etc. You believe that live T-Rex (almost surely) does not exist because it went extinct some 60 odd million years ago. Both beliefs can be updated based on new information.
’Newtonian physics used to be true, but these days it’s false
That’s not at all what I am saying. Consider resisting your tendency to strawman. Newtonian physics is still true in its domain of applicability, it has never been true where it’s not been applicable, though people didn’t know this until 1905.
‘Phlogiston used to exist, but then it stopped existing because someone overturned phlogiston theory’
Again, a belief at the time was that it existed, a more accurate belief (map) superseded the old one and now we know that phlogiston never existed. Maps thought of as being reliable can be found wanting all the time, so the territory they describe is no longer believed to exist, not stopped existing. This is pretty uncontroversial, I would think. Science didn’t kill gnomes and fairies, and such. At least this is the experiment-bounded realist position, as far as I understand it.
You can simply note that things like Abstract Numbers, being causally inert, couldn’t be responsible for the ‘unreasonable efficacy of mathematics’; so that efficacy can’t count as evidence for such Numbers.
I can’t even parse that, sorry. Numbers don’t physically exist because they are ideas, and as such belong in the realm of logic, not physics. (Again, I’m wearing a realist hat here.) I don’t think parsimony is required here. It’s a postulate, not a conclusion.
Perhaps a few mathematicians are deluded into thinking that ‘exists’ means exactly the same thing in both contexts, but it is more charitable to interpret mathematics in general in the less ontologically committing way
Then I don’t understand why you reply to questions of physical existence with some mathematical expressions...
You see, we aren’t so different, you and I. Not once we bracket whether unexperienced cucumbers exist out there, anyway!
I disagree that this is a redefinition. You believe that elephants exists because you can go and see them, or talk to someone you trust who saw them, etc.
Sure, but ‘you believe in X because of Y’ does not as a rule let us conclude ‘X = Y’. I believe in elephants because of how they’ve causally impacted my experience, but I don’t believe that elephants are experiences of mine, or logical constructs out of my experiences and predictions. I believe elephants are animals.
Indeed, a large part of the reason I believe in elephants is that I think elephants would still exist even had you severed the causal links between me and them and I’d never learned about them. The territory doesn’t go away when you stop knowing about it, or even when you stop being able to ever know about it. If you shot an elephant in a rocket out of the observable universe, it wouldn’t stop existing, and I wouldn’t believe it had blinked out of existence or that questions regarding its existence were meaningless, once its future state ceased to be knowable to me.
Elephants don’t live in my map. But they also don’t live in my map-territory relation. Nor do they live in a function from observational data to hypotheses-that-help-us-build-rockets-and-iPhones-and-vaccines. They simply and purely live in the territory.
That’s not at all what I am saying. Consider resisting your tendency to strawman.
I’m not trying to strawman you, I’m suggesting a problem for how you stated you view so that you can reformulate your view in a way that I’ll better understand. I’m sorry if I wasn’t clear about that!
Newtonian physics is still true in its domain of applicability, it has never been true where it’s not been applicable, though people didn’t know this until 1905.
Right. But you said “‘accurate map’, a.k.a. ‘true map’ is a map that has been tested against the territory and found reliable enough to use as a guide for further travels”. My objection is that wide-applicability Newtonian Physics used to meet your criterion for truth (i.e., for a long time it passed all experimental tests and remained reliable for further research), but eventually stopped meeting it. Which suggests that it was true until it failed a test, or until it ceased to be a useful guide to further research; after that it became false. If you didn’t mean to suggest that, then I’m not sure I understand “map that has been tested against the territory and found reliable enough to use as a guide for further travels” anymore, which means I don’t know what you mean by “truth” and “accuracy” at this point.
Perhaps instead of defining “true” as “has been tested against the territory and found reliable enough to use as a guide for further travels”, what you meant to say was “has been tested against the territory and will always be found reliable enough to use as a guide for further travels”? That way various theories that had passed all tests at the time but are going to eventually fail them won’t count as ever having been ‘true’.
Numbers don’t physically exist because they are ideas, and as such belong in the realm of logic, not physics. (Again, I’m wearing a realist hat here.) I don’t think parsimony is required here. It’s a postulate, not a conclusion.
Postulates like ‘1 is nonphysical’, ‘2 is nonphysical’, etc. aren’t needed here; that would make our axiom set extraordinarily cluttered! The very idea that ‘ideas’ aren’t a part of the physical world is in no way obvious at the outset, much less axiomatic. There was a time when lightning seemed supernatural, a violation of the natural order; conceivably, we could have discovered that there isn’t really lightning (it’s some sort of illusion), but instead we discovered that it reduced to a physical process. Mental contents are like lightning. There may be another version of ‘idea’ or ‘thought’ or ‘abstraction’ that we can treat as a formalist symbol game or a useful fiction, but we still have to also either reduce or eliminate the natural-phenomenon-concept of abstract objects if we wish to advance the Great Reductionist Project.
It sounds like you want to eliminate them, and indeed stop even talking about them because they’re silly. I can get behind that, but only if we’re careful not to forget that not all mathematicians (etc.) agree on this point, and don’t equivocate between the two notions of ‘abstract’ (formal/fictive vs. spooky and metaphysical and Tegmarkish).
Then I don’t understand why you reply to questions of physical existence with some mathematical expressions...
Only because the apples are behaving like numbers whether you believe in numbers or not. You might not think our world does resemble the formalism in this respect, but that’s not obvious to everyone before we’ve talked the question over. A logic can be treated as a regimentation of natural language, or as an independent mathematical structure that happens to structurally resemble a lot of our informal reasoning and natural-language rules. Either way, information we get from logical analysis and deduction can tell us plenty about the physical world.
I disagree that this is a redefinition. You believe that elephants exists because you can go and see them, or talk to someone you trust who saw them, etc. You believe that live T-Rex (almost surely) does not exist because it went extinct some 60 odd million years ago. Both beliefs can be updated based on new information.
That’s not at all what I am saying. Consider resisting your tendency to strawman. Newtonian physics is still true in its domain of applicability, it has never been true where it’s not been applicable, though people didn’t know this until 1905.
Again, a belief at the time was that it existed, a more accurate belief (map) superseded the old one and now we know that phlogiston never existed. Maps thought of as being reliable can be found wanting all the time, so the territory they describe is no longer believed to exist, not stopped existing. This is pretty uncontroversial, I would think. Science didn’t kill gnomes and fairies, and such. At least this is the experiment-bounded realist position, as far as I understand it.
I can’t even parse that, sorry. Numbers don’t physically exist because they are ideas, and as such belong in the realm of logic, not physics. (Again, I’m wearing a realist hat here.) I don’t think parsimony is required here. It’s a postulate, not a conclusion.
Then I don’t understand why you reply to questions of physical existence with some mathematical expressions...
I’m not nearly as optimistic.
Sure, but ‘you believe in X because of Y’ does not as a rule let us conclude ‘X = Y’. I believe in elephants because of how they’ve causally impacted my experience, but I don’t believe that elephants are experiences of mine, or logical constructs out of my experiences and predictions. I believe elephants are animals.
Indeed, a large part of the reason I believe in elephants is that I think elephants would still exist even had you severed the causal links between me and them and I’d never learned about them. The territory doesn’t go away when you stop knowing about it, or even when you stop being able to ever know about it. If you shot an elephant in a rocket out of the observable universe, it wouldn’t stop existing, and I wouldn’t believe it had blinked out of existence or that questions regarding its existence were meaningless, once its future state ceased to be knowable to me.
Elephants don’t live in my map. But they also don’t live in my map-territory relation. Nor do they live in a function from observational data to hypotheses-that-help-us-build-rockets-and-iPhones-and-vaccines. They simply and purely live in the territory.
I’m not trying to strawman you, I’m suggesting a problem for how you stated you view so that you can reformulate your view in a way that I’ll better understand. I’m sorry if I wasn’t clear about that!
Right. But you said “‘accurate map’, a.k.a. ‘true map’ is a map that has been tested against the territory and found reliable enough to use as a guide for further travels”. My objection is that wide-applicability Newtonian Physics used to meet your criterion for truth (i.e., for a long time it passed all experimental tests and remained reliable for further research), but eventually stopped meeting it. Which suggests that it was true until it failed a test, or until it ceased to be a useful guide to further research; after that it became false. If you didn’t mean to suggest that, then I’m not sure I understand “map that has been tested against the territory and found reliable enough to use as a guide for further travels” anymore, which means I don’t know what you mean by “truth” and “accuracy” at this point.
Perhaps instead of defining “true” as “has been tested against the territory and found reliable enough to use as a guide for further travels”, what you meant to say was “has been tested against the territory and will always be found reliable enough to use as a guide for further travels”? That way various theories that had passed all tests at the time but are going to eventually fail them won’t count as ever having been ‘true’.
Postulates like ‘1 is nonphysical’, ‘2 is nonphysical’, etc. aren’t needed here; that would make our axiom set extraordinarily cluttered! The very idea that ‘ideas’ aren’t a part of the physical world is in no way obvious at the outset, much less axiomatic. There was a time when lightning seemed supernatural, a violation of the natural order; conceivably, we could have discovered that there isn’t really lightning (it’s some sort of illusion), but instead we discovered that it reduced to a physical process. Mental contents are like lightning. There may be another version of ‘idea’ or ‘thought’ or ‘abstraction’ that we can treat as a formalist symbol game or a useful fiction, but we still have to also either reduce or eliminate the natural-phenomenon-concept of abstract objects if we wish to advance the Great Reductionist Project.
It sounds like you want to eliminate them, and indeed stop even talking about them because they’re silly. I can get behind that, but only if we’re careful not to forget that not all mathematicians (etc.) agree on this point, and don’t equivocate between the two notions of ‘abstract’ (formal/fictive vs. spooky and metaphysical and Tegmarkish).
Only because the apples are behaving like numbers whether you believe in numbers or not. You might not think our world does resemble the formalism in this respect, but that’s not obvious to everyone before we’ve talked the question over. A logic can be treated as a regimentation of natural language, or as an independent mathematical structure that happens to structurally resemble a lot of our informal reasoning and natural-language rules. Either way, information we get from logical analysis and deduction can tell us plenty about the physical world.