A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?
B: What do you mean by "why"?
A: Hey, wait a minute, I'm asking the questions here! Um ... I mean ... I want an explanation of what makes the world that way.
B: Really, you do? You didn't like the last three explanations I gave you. What was wrong with them?
A: They didn't go deep enough. They explained things in the world in terms of deeper and deeper levels, but there was always something left to explain.
B: What would it feel like to have a deep-enough explanation? What are some things for which you think you do have a deep-enough explanation?
A: I don't know. Arithmetic, maybe? I don't feel the need to have a deeper explanation of 1 + 1 = 2, I'm happy saying that it just does equal two, and if you set it up to be different you'd just be talking about some operation other than addition on the naturals.
B: I wonder why arithmetic feels adequately explained to you, but electromagnetism doesn't? What would it feel like if arithmetic were as problematic to you as electromagnetism is?
A: ... I'd be asking why ...
This seems to be taking down a straw man, and far from "challenging a central tenet of LW: reductionism", you perfectly describe it and expound on it, if a bit wordily. At least in my mind, it's very obvious that physical 'law' is a map-level concept. Physicists themselves have noticed that for a map-level concept, physical 'law' fits the territory so amazingly well, that they have written articles such as "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
I don't claim that this post in particular challenges the consensus
That would be the bit where you said "This is the first in a planned series of posts challenging a central tenet of the LessWrong consensus". When you say that you're challenging the consensus, it appears to the reader as though you're challenging the consensus.
Hence my parenthetical concession in the grandparent. But you're right, I should edit the post itself. Doing that right now.
A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?
B: BECAUSE IT IS THE LAW.
What do you think of Max Tegmark's answer, that it's because universes with every possible (i.e., non-contradictory) set of laws of physics exist and we happen to be in one with electromagnetic dynamics derived from Maxwell's Lagrangian? (Or alternatively, every mathematical structure exist in a platonic sense and we happen to inhabit one that looks like this from the inside.)
I'm not sure if this can be called a LW consensus, but it has at least a large minority following here. One important reason is that this view seems to make it much easier to do decision theory, because it means that goals/values can be stated in terms of preferences about how mathematical structures turn out or unfold, instead of about "physical stuff". In particular, UDT was heavily influenced by Tegmark's ideas and there seems to be a consensus among people interested in decision theory here that UDT is a step in the right direction. If you're not already familiar with Tegmark's ideas, user ata wrote a post that can serve as an introduction.
LW discussions of anthropics in Tegmark's multiverse:
If you look in the comments of these posts you'll find more links to earlier discussions.
I feel like there's a distinction being made I don't entirely understand. What's the difference between something describing behavior perfectly and determining behavior? If one person says (x-1)(x-2) determines x^2-3x+2, and another person says (x-1)(x-2) perfectly describes x^2-3x+2, do they disagree? Similarly, is there a meaningful way in which "the laws of physics govern reality" is false if the laws of physics perfectly describe reality?
(Our current understanding of the laws of physics is, of course, not complete, and the above paragraph should be assumed to refer a hypothetical set of laws of physics that do describe every phenomenon with perfect accuracy).
"Arguments end where questions begin." How I wish I could remember where I read that sentence. It helped me reduce my use of rhetorical questions. Since then my writing is more clear (sometimes more clearly wrong I'm sure) and more friendly.
Instead of thinking of laws as rules that have an existence above and beyond the objects they govern, think of them as particularly concise and powerful descriptions of regular behavior.
The rest is commentary. I might emphasize the predictive utility of natural laws more than their descriptive utility.
First: upvoted.
On this descriptive conception of laws, the laws do not exist independently in some transcendent realm. They are not prior to the distribution of matter and energy. The laws are just descriptions of salient patterns in that distribution.
I'd also like to point out the flip side of the coin: by the same arguments, it doesn't make sense to talk about matter and energy separate from how it behaves - matter isn't some primordial grey blob, which, by its inaction, forces laws to be separate objects. What we'd call "matter" and "physical law" don't have to exist independently just because we have two words for them.
Note that whether things are separate or not is pretty map-level, but I think the above is necessitated if we accept the foundation of your post.
If the fundamental laws of physics are already lording it over all matter, there is no room for another locus of authority. However, the argument fizzles [...] if we regard laws as descriptive.
I'm confused why you would argue that physical law can't be some separate thing, "lording it over all matter," but still leave room in your picture for a really existing, similarly separate &q...
B: BECAUSE IT IS THE LAW.
I cannot imagine a real physicist saying something like that. Sounds more like a bad physics teacher... or a good judge.
To me, that sounds like just about every physics teacher I've ever spoken to (for cases where I was aware that they were a physics teacher).
I remember once going around to look for them so that one of them could finally tell me where the frak gravity gets its power source. I got so many appeals to authority and confused or borked responses, and a surprisingly high number of password guesses (sometimes more than one guess per teacher - beat that!). One of them just pointed me to the equations and said "Shut up and plug the variables" (in retrospect, that was probably the best response of the lot).
Basically, if you want to study physics, don't come to Canada.
Yeah, that's sad. Here's a positive example from my school, which was in Russia. At some point in our "advanced" math classes we learned the concept of open and closed sets. The idea grew in my young mind and eventually I asked our physics teacher whether actual physical objects were more like closed sets (i.e. include points on their boundary), or more like open sets. That led to an amazingly deep discussion of what happens at the boundary of a physical object. My school was nice =)
If I were an economist, I wouldn't be interested (at least not qua economist) in deductive systems that talked about quarks and leptons. I would be interested in deductive systems that talked about prices and demand. The best system for this coarser-grained vocabulary will give us the laws of economics, distinct from the laws of physics.
There's this difference between economics and physics. The axioms of economics don't come close to completely explaining prices and demand, and we don't expect them to, even in principle. It would be a miracle if they did: finding coarse-grained descriptions at different levels of abstraction that are exceptionless would be miraculous.
We want a complete physics; we know we can't have a complete economics. The expectation that physics can be complete reflects an assumption that we can cut physical reality at its seams, but we have no similar expectation for economics. Physical descriptions are more than mere descriptions because we expect a finite number of them to describe the (physical) universe; we don't expect axiomatized economics to describe the coarse grain of the economics universe, only what's really a small part.
Accusing realists abou...
I haven't put my finger on it exactly, but I am somewhat concerned that this post is leading us to argue about the meanings of words, whilst thinking that we are doing something else.
What can we really say about the world? What we ought to be doing is almost mathematically defined now. We have observations of various kinds, Bayes' theorem, and our prior. The prior ought really to start off as a description of our state of initial ignorance, and Bayes' theorem describes exactly how that initial state of ignorance should be updated as we see further observat...
I'm not sure this dichotomy you've set up is quite so binary. Essentially, I agree with metaphysicist's comment (see also rocurley's) -- a fundamental set of laws is descriptive, but it's also more -- but I'd like to add to it.
It's well accepted that physical laws are descriptive, in the sense that there can be multiple equivalent descriptions (consider all the different descriptions of classical mechanics). On the other hand, we expect that it is possible to find a set of laws which can be called "fundamental", and that these are not just desc...
In a scientific culture immersed in theism, it was unproblematic, even natural, to think of physical laws as rules.
It wasn't just theism that made talk of natural law seem warranted. Many of the pioneers of the scientific revolution (as much as there was such a thing) were, in fact, lawyers.
Posts written by people exercising the thought processes you are exercising are the kind of posts I am most interested in reading on LessWrong, as a category. However, the specific content of this post (possibly in part because it is an introduction) did not make me super interested in this post.
I do think that this is exactly the sort of thing that Main needs more of.
Upvoted; I like where (I think) this is going.
To your distinction between mereological and nomic reductionism, I would add a third kind of reductionism ("ontic reductionism" would be a good name) that goes beyond the mereological claim, to say that the only things that really exist are the entities of fundamental physics. In this view, quarks/strings/wavefunctions or whatever is posited in the ultimate theory are real, but high-level entities like trees and people are only "real": they are certain combinations of fundamental entities t...
A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?
The way I usually answer such questions is “If I knew, I'd have a friggin' Nobel Prize!”
"Here is an accurate map of the city. To get from this location to this location, follow these roads"
"Why those roads and not the highway?"
"Because the highway doesn't go anywhere near the start or end point of the proposed journey."
"Why is that?"
"The highway is located at the place indicated by the blue line. The start point and end point are represented by these symbols. The blue line never gets closer to either of the symbols than they are to each other."
"But why is the blue line there instead of so...
According to Lewis, the laws of nature correspond to the axioms of the deductive system that best balances simplicity and strength. He does not provide a precise algorithm for evaluating this balance, and I don't think his proposal should be read as an attempt at a technically precise decision procedure for lawhood anyway.
This is just minimum message length.
laws of nature do have a privileged role in physical explanation, but that privilege is due to their simplicity and generality, not to some mysterious quasi-causal power they exert over matter. The fact that a certain generalization is a law of nature does not account for the truth and explanatory power of the generalization, any more than the fact that a soldier has won the Medal of Honor accounts for his or her courage in combat.
That's a self-defeating analogy. So long as the process of pinning a medal on someone is epistemically valid, it does indica...
One reason for privileging the laws of physics is revealed to be the product of a confused metaphysical picture.
I have a fix for others' "confused metaphysical pictures." It's another (moving) picture: an updated, more complex, dynamic version of Powers of Ten (that includes info that came out of different humans and at least one non-human animal and a computer -- to convey perspectivism). But it's in my head and I don't have the skills to express it through multimedia production & distribution. Help?
I'm reading an introduction to perspectives on free will for an introductory philosophy course, which contains a lot of discussion of determinism. I found this article immensely clarifying as an accompaniment.
From the free will thing:
...Assuming determinism, the laws of physics completely determine what happens in the universe, including all of your actions. So in principle, everything you do could have been predicted before you were even born. It seems that, if this is true, you are wrong to suppose that you are sometimes able to choose between different o
This is a better explanation than I could have given for my intuition that physicalism (i.e. "the universe is made out of physics") is a category error.
The issue is not whether there are "laws", the issue is whether there are causes. A descriptive approach to physics amounts to saying "wherever you see A, you also see B". But is there a reason why B always accompanies A? If there is no reason, then the regularities of reality are just one big coincidence. If there is a reason, the next question is, is causality the reason? Is B caused to accompany A? If the answer is yes, there are causes, then we have to worry about what a cause is. If the answer is no, there are no causes, then we ha...
The problem with descriptivism in modern physics is that you say physical theory describes something independent, but you end up postulating the things that it describes as part of the description language, you do not provide any additional denotation for them. I.e. you claim that it describes the real stuff, but in fact it only describes the constants of its language. So the descriptive view forces anti-realism. But it seems your mereological reductionism is a form of realism.
Under prescriptivism, the theory postulates reality. So we can remain realists, ...
I think it is good to be somewhat agnostic with regard to metaphysics, acknowledging those metaphysics that work: the realist, the positivist, and the neopragmatist.
One of the main problems with a purely descriptive account of laws is that it renders those laws epistemic. In and of itself, this is not a bad thing. Certainly, our expressions of laws (whether or not there is an underpinning metaphysical reality to them) are entirely epistemic. When I say, "Gravity is a result of the curving of space-time by mass," I am expressing an idea, an epistemic state.
I agree that saying something "Is a Law" can be used as a curiosity-stopper, just as you suggest. Particularly when the speaker is talking with s...
How exactly are abstract, non-physical objects -- laws of nature, living in their "transcendent aerie" -- supposed to interact with physical stuff? What is the mechanism by which the constraint is applied? Could the laws of nature have been different, so that they forced electrons to attract one another?
I feel I should link to my post The Apparent Reality of Physics right now. To summarise: both the "descriptions" and "rules" views are wrong as they suppose there is something to be described or ruled. The (to me, obvious) dissolution is to state that a Universe is its rules.
I propose a following form of reductionism, which I call positivism:
For a theory to count as knowledge, it has to fit into the body of knowledge, there have to be links that can be mathematically traced to the "core theories". The total, firm knowledge postulates a possible reality. There is no claim that the possible reality is real (therefore anti-realism). But for it to count as knowledge it has to be metaphysically possible, there could be reality exactly as described. Where we are not led to believe that a part of our experience or experimen...
Physical laws push matter around in the same sense that decision-theory-implementing algorithm pushes an agent around. In both cases we have an abstract entity that enables coherent behavior of a concrete entity.
Lawhood Is in the Map, not in the Territory
Excellent, you are half way to the basic instrumentalist model: territory is in the map, not in the territory.
The problem is that people ask why about physics.
There is no why of like charges repelling. They just do.
There are two ways I can see your argument going.
In the first case either we can write down the actual rules of the universe inside the universe, or we cannot. Whether the rules can be expressed within the universe as correct natural laws depends on its nature. Given that the rules of a system as simple as arithmetic can be fully described within the system and can be used to prove...
mere correlation is not causation, descriptions can never provide complete explanations of reality since they only summarize relationships between things (correlations) without establishing an actual causal hierarchy (causation)
more complex things are explained by decomposing them into simpler things, so for a full explanation of reality mere data compression is not enough. we also need additional information about how a potentially infinite number of things could be ordered within a causal hierarchy. without this missing information no fully reductioni...
I agree that "Laws" are descriptions. I think it boils down to, we don't 'know' anything we simply assume.
The purpose of a rule is to make or recognize something as regular, or predictable for us as humans. (We even extend this to the physical world, other humans and to ourselves. To the extent that we even use various substances to make our bowel movements "regular") http://file.vintageadbrowser.com/l-ljv90vkqy8nfa4.jpg
regular and rule share similar latin origin
http://www.etymonline.com/index.php?allowed_in_frame=0&search=rule&a...
We speak casually of the laws of nature determining the distribution of matter and energy, or governing the behavior of physical objects. Implicit in this rhetoric is a metaphysical picture: the laws are rules that constrain the temporal evolution of stuff in the universe. In some important sense, the laws are prior to the distribution of stuff. The physicist Paul Davies expresses this idea with a bit more flair: "[W]e have this image of really existing laws of physics ensconced in a transcendent aerie, lording it over lowly matter." The origins of this conception can be traced back to the beginnings of the scientific revolution, when Descartes and Newton established the discovery of laws as the central aim of physical inquiry. In a scientific culture immersed in theism, it was unproblematic, even natural, to think of physical laws as rules. They are rules laid down by God that drive the development of the universe in accord with His divine plan.
Does this prescriptive conception of law make sense in a secular context? Perhaps if we replace the divine creator of traditional religion with a more naturalist-friendly lawgiver, such as an ur-simulator. But what if there is no intentional agent at the root of it all? Ordinarily, when I think of a physical system as constrained by some rule, it is not the rule itself doing the constraining. The rule is just a piece of language; it is an expression of a constraint that is actually enforced by interaction with some other physical system -- a programmer, say, or a physical barrier, or a police force. In the sort of picture Davies presents, however, it is the rules themselves that enforce the constraint. The laws lord it over lowly matter. So on this view, the fact that all electrons repel one another is explained by the existence of some external entity, not an ordinary physical entity but a law of nature, that somehow forces electrons to repel one another, and this isn't just short-hand for God or the simulator forcing the behavior.
I put it to you that this account of natural law is utterly mysterious and borders on the nonsensical. How exactly are abstract, non-physical objects -- laws of nature, living in their "transcendent aerie" -- supposed to interact with physical stuff? What is the mechanism by which the constraint is applied? Could the laws of nature have been different, so that they forced electrons to attract one another? The view should also be anathema to any self-respecting empiricist, since the laws appear to be idle danglers in the metaphysical theory. What is the difference between a universe where all electrons, as a matter of contingent fact, attract one another, and a universe where they attract one another because they are compelled to do so by the really existing laws of physics? Is there any test that could distinguish between these states of affairs?
There are those who take the incoherence of the secular prescriptive conception of laws as reason to reject the whole concept of laws of nature as an anachronistic holdover from a benighted theistic age. I don't think the situation is that dire. Discovering laws of nature is a hugely important activity in physics. It turns out that the behavior of large classes of objects can be given a unified compact mathematical description, and this is crucial to our ability to exercise predictive control over our environment. The significant word in the last sentence is "description". A much more congenial alternative to the prescriptive view is available. Instead of thinking of laws as rules that have an existence above and beyond the objects they govern, think of them as particularly concise and powerful descriptions of regular behavior.
On this descriptive conception of laws, the laws do not exist independently in some transcendent realm. They are not prior to the distribution of matter and energy. The laws are just descriptions of salient patterns in that distribution. Of course, if this is correct, then our talk of the laws governing matter must be understood as metaphorical, but this is a small price to pay for a view that actually makes sense. There may be a concern that we are losing some important explanatory ground here. After all, on the prescriptive view the laws of nature explain why all electrons attract one another, whereas on the descriptive view the laws just restate the fact that all electrons attract one another. But consider the following dialogue:
A: Why are these two metal blocks repelling each other?
B: Because they're both negatively charged, which means they have an excess of electrons, and electrons repel one another.
A: But why do electrons repel one another?
B: Because like charges always repel.
A: But why is that?
B: Because if you do the path integral for the electromagnetic field (using Maxwell's Lagrangian) with source terms corresponding to two spatially separated lumps of identical charge density, you will find that the potential energy of the field is greater the smaller the spatial separation between the lumps, and we know the force points in the opposite direction to the gradient of the potential energy.
A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?
B: BECAUSE IT IS THE LAW.
Is the last link in this chain doing any explanatory work at all? Does it give us any further traction on the problem? B might as well have ended that conversation by saying "Well, that's just the way things are." Now, laws of nature do have a privileged role in physical explanation, but that privilege is due to their simplicity and generality, not to some mysterious quasi-causal power they exert over matter. The fact that a certain generalization is a law of nature does not account for the truth and explanatory power of the generalization, any more than the fact that a soldier has won the Medal of Honor accounts for his or her courage in combat. Lawhood is a recognition of the generalization's truth and explanatory power. It is an honorific; it doesn't confer any further explanatory oomph.
David Lewis offers us a somewhat worked out version of the descriptive conception of law. Consider the set of all truths about the world expressible in a particular language. We can construct deductive systems out of this set of propositions by picking out some of the propositions as axioms. The logical consequences of these axioms are the theorems of the deductive system. These deductive systems compete with one another along (at least) two dimensions: the simplicity of the axioms, and the strength or information content of the system as a whole. We prefer systems that give us more information about the world, but this greater strength often comes at the cost of simplicity. For instance, a system whose axioms comprised the entire set of truths about the world would be maximally strong, but not simple at all. Conversely, a system whose only axiom is something like "Stuff happens" would be pretty simple, but very uninformative. What we are looking for is the appropriate balance of simplicity and strength [1].
According to Lewis, the laws of nature correspond to the axioms of the deductive system that best balances simplicity and strength. He does not provide a precise algorithm for evaluating this balance, and I don't think his proposal should be read as an attempt at a technically precise decision procedure for lawhood anyway. It is more like a heuristic picture of what we are doing when we look for laws. We are looking for simple generalizations that can be used to deduce a large amount of information about the world. Laws are highly compressed descriptions of broad classes of phenomena. This view evidently differs quite substantially from the Davies picture I presented at the beginning of this post. On Lewis's view, the collection of particular facts about the world determines the laws of nature, since the laws are merely compact descriptions of those facts. On Davies's view, the determination runs the other way. The laws are independent entities that determine the particular facts about the world. Stuff in the world is arranged the way it is because the laws compelled that arrangement.
One last point about Lewis's account. Lewis acknowledges that there is an important language dependence in his view of laws. If we ignore this, we get absurd results. For instance, consider a system whose only axiom is "For all x, x is F" where "F" is defined to be a predicate that applies to all and only events that occur in this world. This axiom is maximally informative, since it rules out all other possible worlds, and it seems exceedingly simple. Yet we wouldn't want to declare it a law of nature. The problem, obviously, is that all the complexity of the axiom is hidden by our choice of language, with this weird specially rigged predicate. To rule out this possibility, Lewis specifies that all candidate deductive systems must employ the vocabulary of fundamental physics.
But we could also regard lawhood as a 2-place function which maps a proposition and vocabulary pair to "True" if the proposition is an axiom of the best system in that vocabulary and "False" otherwise. Lewis has chosen to curry this function by fixing the vocabulary variable. Leaving the function uncurried, however, highlights that we could have different laws for different vocabularies and, consequently, for different levels of description. If I were an economist, I wouldn't be interested (at least not qua economist) in deductive systems that talked about quarks and leptons. I would be interested in deductive systems that talked about prices and demand. The best system for this coarser-grained vocabulary will give us the laws of economics, distinct from the laws of physics.
There is another significant difference between the descriptive and prescriptive accounts that I have not yet discussed. On the Davies-style conception of laws as rules, lawhood is an element of reality. A law is a distinctive beast, an abstract entity perched in a transcendent aerie. On the descriptive account, by comparison, lawhood is part of our map, not the territory. Note that I am not saying that the laws themselves are a feature of the map and not the territory. Laws are just particularly salient redundancies, ones that permit us to construct useful compressed descriptions of reality. These redundancies are, of course, out there in the territory. However, the fact that certain regularities are especially useful for the organization of knowledge is at least partially dependent on facts about us, since we are the ones doing the organizing in pursuit of our particular practical projects. Nature does not flag these regularities as laws, we do.
This realization has consequences for how we evaluate certain forms of reductionism. I should begin by noting that there is a type of reductionism I tentatively endorse and that I think is untouched by these speculations. I call this mereological reductionism [2]; it is the claim that all the stuff in the universe is entirely built out of the kinds of things described by fundamental physics. The vague statement is intentional, since fundamental physicists aren't yet sure what kinds of things they are describing, but the motivating idea behind the view is to rule out the existence of immaterial souls and the like. However, reductionists typically embrace a stronger form of reductionism that one might label nomic reductionism [3]. The view is that the fundamental laws of physics are the only really existant laws, and that laws in the non-fundamental disciplines are merely convenient short-cuts that we must employ due to our computational limitations.
One appealing argument for this form of reductionism is the apparent superfluity of non-fundamental laws. Macroscopic systems are entirely built out of parts whose behavior is determined by the laws of physics. It follows that the behavior of these systems is also fixed by those fundamental laws. Additional non-fundamental laws are otiose; there is nothing left for them to do. Barry Loewer puts it like this: "Why would God make [non-fundamental laws] the day after he made physics when the world would go on exactly as if they were there without them?" If these laws play no explanatory role, Ockham's razor demands that we strike them from our ontological catalog, leaving only the fundamental laws.
I trust it is apparent that this argument relies on the prescriptive conception of laws. It assumes that real laws of nature do stuff; they push and pull matter and energy around. It is this implicit assumption that raises the overdetermination concern. On this assumption, if the fundamental laws of physics are already lording it over all matter, then there is no room for another locus of authority. However, the argument (and much of the appeal of the associated reductionist viewpoint) fizzles, if we regard laws as descriptive. Employing a Lewisian account, all we have are different best systems, geared towards vocabularies at different resolutions, that highlight different regularities as the basis for a compressed description of a system. There is nothing problematic with having different ways to compress information about a system. Specifically, we are not compelled by worries about overdetermination to declare one of these methods of compression to be more real than another. In response to Loewer's theological question, the proponent of the descriptive conception could say that God does not get to separately specify the non-fundamental and fundamental laws. By creating the pattern of events in space-time she implicitly fixes them all.
Nomic reductionism would have us believe that the lawhood of the laws of physics is part of the territory, while the lawhood of the laws of psychology is just part of our map. Once we embrace the descriptive conception of laws, however, there is no longer this sharp ontological divide between the fundamental and non-fundamental laws. One reason for privileging the laws of physics is revealed to be the product of a confused metaphysical picture. However, one might think there are still other good reasons for privileging these laws that entail a reductionism more robust than the mereological variety. For instance, even if we accept that laws of physics don't possess a different ontological status, we can still believe that they have a prized position in the explanatory hierarchy. This leads to explanatory reductionism, the view that explanations couched in the vocabulary of fundamental physics are always better because fundamental physics provides us with more accurate models than the non-fundamental sciences. Also, even if one denies that the laws of physics themselves are pushing matter around, one can still believe that all the actual pushing and pulling there is, all the causal action, is described by the laws of physics, and that the non-fundamental laws do not describe genuine causal relations. We could call this kind of view causal reductionism.
Unfortunately for the reductionist, explanatory and causal reductionism don't fare much better than nomic reductionism. Stay tuned for the reasons why!
[1] Lewis actually adds a third desideratum, fit, that allows for the evaluation of systems with probabilistic axioms, but I leave this out for simplicity of exposition. I have tweaked Lewis's presentation in a couple of other ways as well. For his own initial presentation of the view, see Counterfactuals, pp. 72-77. For a more up-to-date presentation, dealing especially with issues involving probabilistic laws, see this paper (PDF).
[2] From the Greek meros, meaning "part".
[3] From the Greek nomos, meaning "law".
