Whatever the appeal or merits of his Jungian theorizing, Peterson became famous because he dared to say that the government should not regulate his use of pronouns. Insofar as he seems to have been the only Canadian academic willing to say this morally obvious thing he must be counted as courageous. Moral courage is not uncharacteristic of Canadians in general but is manifestly rare amongst Canadian academics and perhaps amongst academics generally.

Actually, I am making a stronger claim. Not just that there objective facts about complexity relative to any given UTM but that complexity is an objective feature of the world... as objective as velocity. What is relative to UTM is only its *measure* (again, cf. velocity).

Paul, I think you have the gist of it but I encourage you to read others on the topic of algorithmic information theory. The field is very new and full of interesting philosophical upshots. Dropping the "O" does not imply that the relativity goes away, it's just a matter of taking it as given to make the equations a bit tidier. Your remarks don't make it clear if you buy my arguments for "the objectivity of complexity" above, but that is how I "live with the relativity". Best T

Thank you, Paul! I do think that last section is too telegraphic. I was trying to short-circuit an objection to the effect that since algorithmic complexity is language/computer relative that "it's all relative, so we can say what we like." The very narrow issue I had in mind was this: the Humean says that the Humean facts about a world determine a unique set of laws for it. The anti-Humean says contrary sets of laws might have equal claims to governing the same (under a Humean description) world . The point about relativity, by analogy, goes like this: imagine two objects in motion with respect to one another. The question, "which is moving faster" can only be answered relative to a frame of reference and by picking different frames you can get different answers; but there is no frame of reference with respect to which they are not in motion with respect to one another. Likewise, relative to different measures you might get different orderings of complexity, but systems aren't going to be tied in some orderings but not others. Certainly, the whole topic of relativity and its upshots deserves a more extended discussion. I hope to return to it in future posts. As to what "this is supposed to be". I'm not sure exactly what "ontological reduction" might mean in this context. I would simply say that, like The Best System theory, The Computational Theory of laws offers an explanation of what makes some true propositions laws of nature. Best tomkow

Eddy, Thanks for the kind words! What Lewis and we would say about your worlds is that a world governed by the "law of gravity" you describe is not fully Deterministic. A world can be deterministic going temporally forward but not going backward or vice versa. The W1 world pictured in our post is deterministic going backwards in time, but not forwards. The law you give to your world W1 is deterministic going forward but not back. It allows for what Lewis calls "convergence". After the objects contact there is no distinguishing the futures of W1 and W2 and no way of telling how things got to be the way they are. Such laws and worlds are certainly possible, but not fully deterministic. Philosophers often ignore temporally backward determinism but physicists rarely do. Physicists call the assumption that we may infer the past state of the universe from its present state, "The Principle of Conservation of Information". Leonard Susskind calls it a principle more fundamental than the Second Law of Thermodynamics. It's what the "Black Hole Wars" were about. Note that all of this is separable from your question about whether or not W1 and W2 "have the same laws". I agree that W1 and W2 are described by the same laws. It is less clear to me that they are governed by them. To see why I say this you would have to read Computation, Laws and Supervenience but, in any case, this issue doesn't affect the point about determinism.

Jonathan, I think different issues are being conflated here. Note first of all that nothing that we say in this post-- or, indeed, that Vihvelin has said anywhere-- about counterfactuals, laws or determinism, turns on the Computational Theory of Laws. We think our claims here hold for any theory of laws, certainly on the Best System Theory. Nor do I think your worries really have to do with two particle worlds. I think what's bothering you has to do with the fact that, as Hoefer says, "Determinism requires a world that (a) has a well-defined state or description, at any given time". This is so on anyone's definition of 'determinism' but, one might wonder, what gets included in a state description of the world at a moment? One might argue that, because ascribing velocity to a particle seems to entail facts about the future (that unless it collides with something it will be certain distance d in a certain direction from where it is now in t seconds) that velocities don't belong in the state description of a world at a time. But, of course, if that is so it would mean that even Newtonian worlds aren't deterministic (again, on anyone's definition). All of which seems to show that we need a definition of 'state of the world at a time' which allows us to include velocity despite the fact that it seems to supervene on non-instantaneous facts. What that definition should be is an interesting question. David Albert's book Time and Chance has a useful discussion of this issue. You might also want to look at Kripke's stuff on rotating spheres; where he tries to use an argument that velocity is not rooted in a single moment to leverage large scale metaphysical conclusions about essences. If something like this is what you had in mind I think you are right to think there is a problem to be solved here. But so far as I can see it is a problem for any account of determinism or counterfactuals and I don't think that the two particle cases or CTL shed light on it.

That the two-non-colliding-particle system can be described by a subset of Newton's laws proves the point. Such worlds are simpler than Newtonian worlds. Algorithmic Information Theory shows us how we can understand this simplicity as an objective, measurable feature of a world. I think the algorithmic view of laws does raise interesting questions about properties and ontology but I'm afraid I don't understand the ones you ask. Obviously, how we describe the world will affect what we take to be the simplest description of it. Obviously we can't take the properties of the world as "given". Obviously the only way we have of discovering how to carve nature at its joints is to do science. Obviously, you know all this. So what am I missing? I don't think the relativity of algorithmic complexity is relevant to your concerns but if you want to better understand it you'll have to look at The Computational Theory of the Laws of Nature. Thanks for your comments!

I reject the terms of the thought experiment. I do not think there can be "two particle worlds, in which particles never collide but which obey Newton's laws" cf. http://tomkow.typepad.com/tomkowcom/2014/02/computation-laws-and-supervenience.html

I submit that something that takes the form: "Suppose that God came along and reliably told you that [insert vague, ill-worded, contentious and/or incoherent claim here] was true..." Is not a "thought experiment" in any useful sense.

After a public lecture, the philosopher Michael Scriven was challenged by an audience member: "You're problem, Professor Scriven, is that you don't believe in love!" "Of course I believe in it.", he replied, "I've seen it done!"

Daniel, Thanks for your thoughtful comment! I would be very happy if proponents of BSA welcomed CTL. I am absolutely content with saying that CTL is only a refinement of the guiding ideas behind the Best System Theory. As I say in the post, you are welcome to think of the CTL as only an updated version of the Best System analysis; one which replaces Euclid's conception of "System" with Turing's. And I entirely agree that a BSA theorist can-- and some already have-- endorse the conclusions about the logic of laws that I argue for here. I hope though that we also agree that CTL gives us useful new ways to think about laws and to argue for these conclusions. . I like to think Lewis would have welcomed CTL. Had he had it to hand, I think he might not (as he did increasingly in his later work) have taken the course of saying that Humeanism might only be a contingent truth about "worlds like ours". He was, you will recall, driven to this odd position by cases like Armstrong's spinning sphere. That thought experiment was supposed to show there could be worlds which were indistinguishable in Humean terms but in which had different counterfactual/dispositional properties. Lewis thought he had to concede the possibility, but he didn't: I think it clear that Armstrong's story fails in the same way as Carroll's. And, with all due respect, I do think that CTL does a bit more than just "precisify" the issues confronting BSA. A central problem for BSA is to say not just what, precisely, simplicity is but also to say why it matters. CTL gives an answer to that question not obviously available to BSA. I am very pleased to that you are not shocked by the prospect of Nomological Relativity (I can report that some philosophers of my acquaintance find it very shocking indeed). But here I again I think that CTL does a bit more than just restate the old problems more precisely. The problem of "grue" and "green" presents itself as a problem of underdetermination: why inductively project one predicate not the other given the available evidence. It is, in turn, only stepchild to the larger problem of Quinean underdetermination: how to choose between contradictory theories equally compatible with all possible evidence. As I shall argue in a future post, I think CTL gives us a way of solving these problems by understanding that what is at work here is not underdetermination but relativity. Relative to some reference machine, a Gruesome description of the world might be simpler than the one we find natural. What properties we find natural may be an evolutionary accident. As Steve Petersen puts it, it is a matter of what Turing Machine evolution has put between our ears. But, as I argue in the post, we need not take this relativity in our judgments as undermining their objectivity. Except relative to some reference machine or other, there is no theorizing about the order of the world. There is no computational, or cognitive, "view from nowhere". And while different points of cognitive/computational view point of can lead to apparently contradictory claims about laws, counterfactuals and dispositions, the appearance of contradiction goes away when we understand that the claims are consistent and commensurable when understood as relative to our cognitive/computational perspective.

Well, Some of us think that "retaliatory emotions" are not to be so easily dismissed and that they in fact are the foundation of justice. cf. http://tomkow.typepad.com/tomkowcom/2012/07/a-few-short-steps-to-the-gallows.html

This: http://tomkow.typepad.com/tomkowcom/2012/07/a-few-short-steps-to-the-gallows.html might be relevant.

The idea of a "on-line journal" seems to me retrograde and pointless. There *is* a need for for a well produced philosophy content aggregator which is quite a different different thing. I would suggest you direct your efforts in that direction.

Tristan, Thanks very much for your kind remarks. And congratulations on your own splendid blog. It is good to see someone doing philosophy (as opposed to philosophical shmooze) on line. I'm not sure I understand your first point. I agree that there are some counterfactual statements that require that all the A-worlds be C worlds. That is my analysis of "would have to be" (A>>C) counterfactuals. Perhaps you believe there is a class of counterfactuals which deserve this A>>C analysis but which cannot be heard as synonymous with any "would have to" claim? Do you have examples? On your second point. I think your counterexample only shows how the vagueness of the counterpart relation can give rise to vagueness in our judgments of similarity. In your story Einstein writes "paper N" in which he says that light will bend. Assuming the light's bending is nomologically necessary, are the closest worlds at which the light does not bend worlds where Einstein was wrong or worlds at which he wrote something different in "paper N". Here our answer will depend on whether or not we take "saying light bends" as an essential property of paper N. That is, it depends upon whether we are willing to count some other worldly paper as a counterpart of paper N if it advances a contrary thesis. (Compare, "If Woody Allen had written Mien Kampf it wouldn't have been so anti-semitic and would have had more jokes.") And, it seems to me, our willingness on this score will depend greatly on context. If Einstein's acuity is topic of discussion we might suppose that he wouldn't have written "light bends" in a world in which it doesn't. On the other hand if our topic is the accuracy of what Einstein actually wrote we will not treat the contents of paper N as fungible. But I expect you anticipated this move and framed your example to get round it. Your example is: (H) If Einstein had been wrong in paper N, this light would not have bent. I think your thought here was that the Simple Analysis requires the reading under which this is false (because it requires the closest A-worlds to be legal) and yet we are likely to hear (H) as true. But I don't think this works. The reading under which this sentence is true- and the reading we would normally give it-- is one in which the antecedent entails that Einstein said the light would bend. So it reads as: (H'') If Einstein had been wrong to say the light would bend, the light would not have bent. Which seems logically true and so true on any theory of counterfactuals. The reading of (H) under which it is false is, I guess,: (H*) If Einstein had said something wrong in Paper N (but not about light bending), the light would not have bent. But this reading seems to me be precluded for Gricean reasons. I have very hard time imagining any context in which (H) should be read as (H*) because I can't imagine what the speaker might be attempting to communicate. In any case the Simple Theory does not entail anything about how we should disambiguate a sentence 'A>C' when 'A' is genuinely ambiguous between an interpretation which is nomologically possible and another that is not. The Simple Theory, as it stands, doesn't account for the truth conditions of counterfactuals with contra-legal antecedents, but it doesn't require that we pretend they don't exist. I agree that we do need an account of counterfactuals with contra-legal antecedants. I explicitly left them off the table in this post because I think we need first to get clearer about laws. I'll be offering a new theory of laws in my next post.