It seems like there is a real phenomenon in computers and proofs (and some other brittle systems), where they are predicated on long sequences of precise relationships and so quickly break down as the relationships become slightly less true. But this situation seems rare in most domains.
If there’s a single exception to conservation of energy, then a high percentage of modern physics theories completely break. The single exception may be sufficient to, for example, create perpetual motion machines. Physics, then, makes a very high-precision claim that energy is conserved, and a refuter of this claim need not supply an alternative physics.
I don’t know what “break” means, these theories still give good predictions in everyday cases and it would be a silly reason to throw them out unless weird cases became common enough. You’d end up with something like “well we think these theories work in the places we are using them, and will keep doing so until we get a theory that works better in practice” rather than “this is a candidate for the laws governing nature.” But that’s just what most people have already done with nearly everything they call a “theory.”
Physics is weird example because it’s one of the only domains where we could hope to have a theory in the precise sense you are talking about. But even e.g. the standard model isn’t such a theory! Maybe in practice “theories” are restricted to mathematics and computer science? (Not coincidentally, these are domains where the word “theory” isn’t traditionally used.)
In particular, theories are also responsible for a negligible fraction of high-precision knowledge. My claim that there’s an apple because I’m looking at an apple is fairly high-precision. Most people get there without having anything like an exceptionless “theory” explaining the relationship between the appearance of an apple and the actual presence of an apple. You could try and build up some exceptionless theories that can yield these kinds of judgments, but it will take you quite some time.
I’m personally happy never using the word “theory,” not knowing what it means. But my broader concern is that there are a bunch of ways that people (including you) arrive at truth, that in the context of those mechanisms it’s very frequently correct to say things like “well it’s the best we have” of an explicit model that makes predictions, and that there are relatively few cases of “well it’s the best we have” where the kind of reasoning in this post would move you from “incorrectly accept” to “correctly reject.” (I don’t know if you have an example in mind.)
(ETA: maybe by “theory” you mean something just like “energy is conserved”? But in these cases the alternative is obvious, namely “energy is often conserved,” and it doesn’t seem like that’s a move anyone would question after having exhibited a counterexample. E.g. most people don’t question “people often choose the option they prefer” as an improvement over “people always choose the option they prefer.” Likewise, I think most people would accept “there isn’t an apple on the table” as a reasonable alternative to “there is an apple on the table,” though they might reasonably ask for a different explanation for their observations.)
*Another way of visualizing if then statements is flowcharts.
Theorists may be interested in being able to make all the flowcharts
Non-theorists may be interested in the flowcharts they use continuing to work, but not too fussed about everything else.
Long:
It seems like there is a real phenomenon in computers and proofs (and some other brittle systems), where they are predicated on long sequences of precise relationships and so quickly break down as the relationships become slightly less true. But this situation seems rare in most domains.
Types of reasoning:
If x = 2, x^2 = 4. (Single/multi-case. Claims/if then statements.*)
For all x >= 0, x^2 is monotonic. (For every case. Universal quantification.)
Either can be wrong: the incorrect statement “If x =2, x^2 =3” and “For all real x, x^2 is monotonic.”
A claim about a single case probably isn’t a theory. Theories tend to be big.
We can think of there being “absolute theories” (correct in every case, or wrong), or “mostly correct theories” (correct more than some threshold, 50%, 75%, 90%, etc.).
Or we can think of “absolute”, “mostly correct”, “good enough”, etc. as properties. One error has been found in a previously spotless theory? It’s been moved from “absolute” to “mostly correct”. Theorists may want ‘the perfect theory’ and work on coming up with a new, better theory and ‘reject’ the old one. Other people may say ‘it’s good enough.’ (Though sometimes a flaw reveals a deep underlying issue that may be a big deal—consider the replication crisis.)
This post is about “absolute theories” or “theories which are absolute”. As paulfchristiano points out, a theory may be good enough even if it isn’t absolute. The post seems to be about: a) Critics need not replace the theory, and b) once we see that a theory is flawed, more caution may be required when using it, and c) pretending the theory is infallible and ignoring its flaws as they pile up will lead to problems. ‘If you see a crack in an aquarium, fix it, don’t let it grow into a hole that lets all the water out.’
The post might be about a specific context, where the author thinks people are ‘ignoring cracks in the aquarium and letting water out.’ Some posts do a bad job of being a continuation of one or more IRL conversations, but I found this to be a fairly good one.
Perhaps different types of theories should be handled differently, particularly based on how important the consequences are, and the difference between theories which are “absolute” and theories which are not, may matter a lot. If cars could run on any fuel except water, which would make them explode, but otherwise would be fine with anything...people wouldn’t just put anything in their fuel tank—they’d be careful to only put things that they knew didn’t have any water in them.
Or the difference mostly matters to theorists, and non-theorists are more interested in specifics (things that pertaining to the specific theories they care about/use), rather than the abstract (theories in general), and this post won’t be very useful to them.*
I don’t know what “break” means, these theories still give good predictions in everyday cases and it would be a silly reason to throw them out unless weird cases became common enough.
If perpetual motion machines are possible that changes quite a lot. It would mean searching for perpetual motion machines might be a good idea, and the typical ways people try to rule them out ultimately fail. Once perpetual motion machines are invented, they can become common.
But even e.g. the standard model isn’t such a theory!
Not totally exceptionless due to anomalies but it makes lots of claims at very high levels of precision (e.g. results of chemical experiments) and is precise at that level, not at a higher level than that. Similarly with the apple case. (Also, my guess is that there are precise possibly-true claims such as “anomalies to the standard model never cohere into particles that last more than 1 second”)
I don’t want to create a binary between “totally 100% exceptionless theory” and “not high precision at all”, there are intermediate levels even in computing. The point is that the theory needs to have precision corresponding to the brittleness of the inference chains it uses, or else the inference chain probably breaks somewhere.
It seems like there is a real phenomenon in computers and proofs (and some other brittle systems), where they are predicated on long sequences of precise relationships and so quickly break down as the relationships become slightly less true. But this situation seems rare in most domains.
I don’t know what “break” means, these theories still give good predictions in everyday cases and it would be a silly reason to throw them out unless weird cases became common enough. You’d end up with something like “well we think these theories work in the places we are using them, and will keep doing so until we get a theory that works better in practice” rather than “this is a candidate for the laws governing nature.” But that’s just what most people have already done with nearly everything they call a “theory.”
Physics is weird example because it’s one of the only domains where we could hope to have a theory in the precise sense you are talking about. But even e.g. the standard model isn’t such a theory! Maybe in practice “theories” are restricted to mathematics and computer science? (Not coincidentally, these are domains where the word “theory” isn’t traditionally used.)
In particular, theories are also responsible for a negligible fraction of high-precision knowledge. My claim that there’s an apple because I’m looking at an apple is fairly high-precision. Most people get there without having anything like an exceptionless “theory” explaining the relationship between the appearance of an apple and the actual presence of an apple. You could try and build up some exceptionless theories that can yield these kinds of judgments, but it will take you quite some time.
I’m personally happy never using the word “theory,” not knowing what it means. But my broader concern is that there are a bunch of ways that people (including you) arrive at truth, that in the context of those mechanisms it’s very frequently correct to say things like “well it’s the best we have” of an explicit model that makes predictions, and that there are relatively few cases of “well it’s the best we have” where the kind of reasoning in this post would move you from “incorrectly accept” to “correctly reject.” (I don’t know if you have an example in mind.)
(ETA: maybe by “theory” you mean something just like “energy is conserved”? But in these cases the alternative is obvious, namely “energy is often conserved,” and it doesn’t seem like that’s a move anyone would question after having exhibited a counterexample. E.g. most people don’t question “people often choose the option they prefer” as an improvement over “people always choose the option they prefer.” Likewise, I think most people would accept “there isn’t an apple on the table” as a reasonable alternative to “there is an apple on the table,” though they might reasonably ask for a different explanation for their observations.)
TLDR:
*Another way of visualizing if then statements is flowcharts.
Theorists may be interested in being able to make all the flowcharts
Non-theorists may be interested in the flowcharts they use continuing to work, but not too fussed about everything else.
Long:
Types of reasoning:
If x = 2, x^2 = 4. (Single/multi-case. Claims/if then statements.*)
For all x >= 0, x^2 is monotonic. (For every case. Universal quantification.)
Either can be wrong: the incorrect statement “If x =2, x^2 =3” and “For all real x, x^2 is monotonic.”
A claim about a single case probably isn’t a theory. Theories tend to be big.
We can think of there being “absolute theories” (correct in every case, or wrong), or “mostly correct theories” (correct more than some threshold, 50%, 75%, 90%, etc.).
Or we can think of “absolute”, “mostly correct”, “good enough”, etc. as properties. One error has been found in a previously spotless theory? It’s been moved from “absolute” to “mostly correct”. Theorists may want ‘the perfect theory’ and work on coming up with a new, better theory and ‘reject’ the old one. Other people may say ‘it’s good enough.’ (Though sometimes a flaw reveals a deep underlying issue that may be a big deal—consider the replication crisis.)
This post is about “absolute theories” or “theories which are absolute”. As paulfchristiano points out, a theory may be good enough even if it isn’t absolute. The post seems to be about: a) Critics need not replace the theory, and b) once we see that a theory is flawed, more caution may be required when using it, and c) pretending the theory is infallible and ignoring its flaws as they pile up will lead to problems. ‘If you see a crack in an aquarium, fix it, don’t let it grow into a hole that lets all the water out.’
The post might be about a specific context, where the author thinks people are ‘ignoring cracks in the aquarium and letting water out.’ Some posts do a bad job of being a continuation of one or more IRL conversations, but I found this to be a fairly good one.
Perhaps different types of theories should be handled differently, particularly based on how important the consequences are, and the difference between theories which are “absolute” and theories which are not, may matter a lot. If cars could run on any fuel except water, which would make them explode, but otherwise would be fine with anything...people wouldn’t just put anything in their fuel tank—they’d be careful to only put things that they knew didn’t have any water in them.
Or the difference mostly matters to theorists, and non-theorists are more interested in specifics (things that pertaining to the specific theories they care about/use), rather than the abstract (theories in general), and this post won’t be very useful to them.*
If perpetual motion machines are possible that changes quite a lot. It would mean searching for perpetual motion machines might be a good idea, and the typical ways people try to rule them out ultimately fail. Once perpetual motion machines are invented, they can become common.
Not totally exceptionless due to anomalies but it makes lots of claims at very high levels of precision (e.g. results of chemical experiments) and is precise at that level, not at a higher level than that. Similarly with the apple case. (Also, my guess is that there are precise possibly-true claims such as “anomalies to the standard model never cohere into particles that last more than 1 second”)
I don’t want to create a binary between “totally 100% exceptionless theory” and “not high precision at all”, there are intermediate levels even in computing. The point is that the theory needs to have precision corresponding to the brittleness of the inference chains it uses, or else the inference chain probably breaks somewhere.