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…at Scientific American, with contributions by philosophers Eddy Keming Chen (UCSD), Emily Adlam (Chapman), Alastair Wilson (Leeds), and David Wallace (Pittsburgh). More discussion welcome.
Layman here:
Determinism is intuitively the thesis that if you know the laws governing the universe and have a complete description of the universe at a point in time, you know everything about the past and the future as well (assuming that the laws do not change over the course of time). According to this article, superdeterminism just adds the claim that the initial state of the universe, the first point at which the laws start to "act on something", had to be a certain way. To me that seems to be a claim less about physical rather than metaphysical modality and I cannot see how this follows from a presumably physical theory by Hartle and Hawking.
Furthermore, if this is all what superdeterminism amounts to, why are some people so opposed to it, claiming that it undermines the very notion of science?
Thankful, if someone could help me here.
It's a physical claim because (roughly) the Hartle-Hawking theory specifies the initial state of the universe as well as the dynamics.
More generally, the basic structure of a physical theory is normally that there's a space of possible states, and the dynamics say how any state evolves in time; the usual understanding is that the initial state could be anything, and indeed is different things in different applications of the theory. That distinction potentially breaks down a bit in cosmology, where we can't prepare the system multiple times and where a bunch of different theories consist as much of specifications of the initial state as of specifications of the laws (and, in some cases, break down the law/initial state dichotomy entirely).
It's an interesting and very compact overview article of many facets of the determinism/free will debate merged with scientific views. But by no means is it comprehensive with respect to how else we may view these issues. In a book I and colleagues Joe Campbell and Kristin Mickelson put out last year, in our Intro we set out a careful nomenclature about issues surrounding what constitutes incompatibilism that may be of use in understanding what the multiverse might mean for free will in terms of "impossibilism"–any view that Free will cannot exist. But we also point out that such impossibilism might be entailed by completely distinct matters other than physics/metaphysics, such as the concept of luck. I can cite Neil Levy's excellent book Hard Luck here, which argues that matters that we have no control over, such as our past and what constitutes our origins, both biological and situational, thus matters of luck by any intelligible definition, completely overshadow any other issues about what might constitute our responsibility for our actions, rendering questions of free will moot. Impossibilism by a completely different route.
Thanks.
Sorry, I mixed up strong determinism and superdeterminism.
Hi Peter,
Thanks for your thoughtful comments and questions. In this context, determinism means that the laws of physics plus the state of the universe at some time completely determine the Universe's backward history and forward evolution. This has implications for predictions. For example, if you know the laws of physics and the state of the universe at some time (say the present moment), you can in principle know everything about the past and the future.
There is a stronger notion of determinism, according to which the laws of physics, by themselves, completely determine the complete backwards history and future evolution of the Universe. That is the idea of strong determinism. Insofar as there is an initial state of the universe, then it also has to be completely determined by the laws of physics. This article in Scientific American and my own works discussed here refer to this notion of strong determinism.
By the way, you used the word "superdeterminism" and presumably you are thinking about theories that attempt to violate "statistical independence" to avoid quantum non-locality, as proposed by Sabine Hossenfelder, Timothy Palmer, Gerard 't Hooft, and others. Superdeterminism is different from strong determinism, and neither entails the other. (It's unfortunate the names of these two views are so similar!)
For more on strong determinism, see this article (by myself, forthcoming in Philosophers' Imprint):
https://arxiv.org/abs/2203.02886
Definitions of determinism and strong determinism are discussed in Section 2. The differences between strong determinism and superdeterminism are discussed on p. 5.
For another paper on related topics, see this article (by Emily Adlam, in European Journal for Philosophy of Science):
https://arxiv.org/abs/2110.07656
By the way, I argue against superdeterminism in this paper.
https://arxiv.org/abs/2006.08609
My objection to superdeterminism is that I don't think we can find a simple theory (with simple physical laws and reasonable physical ontology). However, for strong determinism, it can be done, at least in the many-worlds framework, as shown by (1) the Hartle-Hawking no-boundary proposal, and (2) the Everettian Wentaculus.
Thanks for this interesting article. I have not studied the Hawking-Hartle proposal, and am skeptical of the assumption of unitarity built into the Everett Interpretation (as I understand it). But I have a more basic worry: what is the non-verbal issue? There are lots of ways of using the term, “possible”, even “counterfactually possible”. Chen says that Strong Determinism means that “the laws of physics… completely determine the…backwards history and future evolution of the Universe.” But in what sense couldn’t the laws have been otherwise? And in what sense of “determine” do they determine the past and future? Consider the latter question first. Do they physically determine the future? “Metaphysically” determine it? Conceptually determine it? (First-order) logically determine it? Whatever the answer, why is that the important sense? Similarly, if the laws could not have been otherwise, the question arises: in what sense of “could not have”? Certainly, they could have as a matter of conceptual or (first-order) logical possibility. Chen suggests that there might be something nonverbal at stake insofar as counterfactuals are vacuous if Strong Determinism is true. But counterfactuals are relative to a modality. It’s metaphysically and physically impossible (as those terms are ordinarily understood) that any set fails to occur at some level of the cumulative hierarchy. But had, as a matter of wider-than-ordinary possibility, this been the case, then not every set would have contained a ϵ-minimal element. In general, my worry is that kinds of counterfactual possibility are cheap, and one gets different answers to the question of whether the world could have been otherwise depending on the kind one invokes. Can one do more than respond by insisting that the sense in question is “real”, “genuine”, “ontic”, etc. possibility? Or do we just get different answers to questions of free will and determinism depending on the modality that we invoke, with nothing metaphysically special (whatever that could mean) about one kind over another?
I am really puzzled by the way philosophers talk about determinism. Heisenberg's universally accepted Uncertainty Principle means that the state of the universe, or even any subset of it, at any given time, is IN PRINCIPLE unknowable. This can never be overcome by any means such as e.g. more sophisticated apparatus. Also as a side note, the evolution of the universe through quantum transitions is also, as far as we know, in principle unpredictable. So the 'deterministic thesis' is asking for the 'implications' of a counterfactual. It's something like asking 'if in mathematics 1 were equal to 2, what consequences would follow?' (Answer: any proposition at all, true or false.)
If anyone has reformulated the usual questions regarding free will, epiphenomena, moral responsibility etc, in a way that takes account of this in principle unpredictability of physical laws and phenomena, I haven't see it. If they had, I don't understand why so many philosophers are still thinking of determinism based on some kind of 19th century scientific model in which everything is in principle predictable.
It's helpful to appreciate a distinction between the concepts of determinism and predictability:
"The history of philosophy is littered with examples where ontology and epistemology have been stirred together into a confused and confusing brew. The Jamesian vision [of determinism] we are seeking to capture is an ontological vision; whether it is fulfilled or not depends only on the structure of the world, independently of what we do or could know of it. Of course ontological determinism does have epistemological implication and these will be discussed in the appropriate places. But let us not confuse the implications of the doctrine for the doctrine itself. And let us resist the temptation to manufacture "senses" of determinism. Producing an "epistemological sense" of determinism is an abuse of language since we already have a perfectly adequate and more accurate term — prediction — and it also invites potentially misleading argumentation — e.g. in such-and-such a case prediction is not possible and, therefore, determinism fails." John Earman, Primer on Determinism (1986, pp. 7-8)
Hi Justin,
Your questions are excellent, but I may not be able to completely answer them here due to space constraints.
In what sense couldn't the physical laws have been otherwise? Suppose we take physical possibilities to be delineated by the physical laws, then physical laws couldn't have been otherwise, as a matter of physical necessity. Of course, if we are talking about metaphysical possibilities, they could have been different, as there could have been different laws.
Under strong determinism, physical laws are compatible with exactly one physical possibility, so they determine not only conditional facts about what must follow from what, but also how the physical Universe, in its complete microscopic detail, must be. The sense of determination here is mathematical / logical compatibility with the physical laws. (As an example, think of Newton's law of gravitation and law of motion as physical laws of a classical universe determining a set of physically possible worlds, represented by solution curves of the relevant differential equations in Newtonian gravitation theory.)
But one who shares your worry can press further: why is that the importance sense of determination? Why not focus on facts compatible with purely mathematical or logical laws? This is not something you have in mind, but one can go further: why not focus on facts compatible with some other fact, such as "Eddy has two cats?" But that fact is accidental, and not entailed by a physical law. Again, why care about physical necessity, instead of other kinds of necessities?
Now, let me make a purely sociological observation about the free will debate: many people have traditionally been thinking about the relevant sense of necessity as physical necessity. After all, there is no prima facie conflict between logical necessity and human freedom (in the sense of alternative possibility); but there is an apparent conflict between physical necessity and human freedom, if physical laws are deterministic.
What justifies this focus on physical necessity and physical laws? That's a really deep question. At this point one can make a choice. The first option is to follow people such as Marc Lange (1999, 2005, 2009) and try to explain why physical necessity is distinguished, perhaps by appealing to conditions such as counterfactual stability and non-maximality. Interestingly, Lange's proposal of understanding physical laws in terms of counterfactuals is incompatible with strong determinism, because strong determinism violates non-maximality, an important component of his construction of a non-circular definition of physical necessity.
Another option, which I favor, is to be a primitivist about physical laws and accept them as metaphysically fundamental facts that govern the Universe. One can try to draw conceptual connections from laws to other notions in philosophy of science, such as ontology, explanation, induction, and time, and understand why physical laws (and physical necessities) are conceptually distinguished.
I say more about these issues in a little book, Laws of Physics, which has just been published by Cambridge University Press. If you are interested, please take a look. It’s freely available online for two weeks. It also contains some discussions about determinism and strong determinism.
https://doi.org/10.1017/9781009026390
My guess is that you might favor a more pluralistic conception of necessities. That would be an interesting option to explore too. I try to do some of it in my longer paper (forthcoming in Philosophers' Imprint) on strong determinism, section 3.1 "Explanation, Causation, and Counterfactuals":
https://arxiv.org/abs/2203.02886
I'd be happy to chat more. In fact, I'm teaching a graduate seminar on free will this fall with my esteemed colleague Manuel Vargas. And the issues you raise are highly relevant. I plan to think about them this summer.
Hi, Eddy!
Thanks for the thoughtful reply. A few follow-ups:
>Suppose we take physical possibilities to be delineated by the physical laws, then physical laws couldn't have been otherwise, as a matter of physical necessity.
Are you defining physical necessity or taking it as primitive as well? I worry that “a primitivist about physical laws” who tries “to draw conceptual connections from laws to other notions in philosophy of science, such as ontology, explanation, induction, and time” works with two free parameters (“physical necessity” and “physical laws”) whose interpretation is greatly underdetermined. But even if I am wrong about that, what matters is not what we happen to mean by “physical laws” and “physical necessity”. What is important is whether we pick out properties that are worth picking out. Someone who is doubtful of this will doubt the importance of the entire network of ideas – “ontology, explanation, induction, and time” – in favor of close cousins, call them (to use a recent convention) ontology*, explanation*, induction*, and time*.
>Under strong determinism, physical laws are compatible with exactly one physical possibility…The sense of determination here is mathematical / logical compatibility with the physical laws.
I fear that this is too vague. Mathematical and logical compatibility are different. Consider the intersection of a family of sets of points in spacetime, ∩x. Could it have failed to exist if it exists in fact? By the axioms of Comprehension, Union, Powerset and Infinity, this is not mathematically compatible with any physical theory. But it is logically compatible, if Kripke-Platek set theory is consistent. Bracketing mathematical compatibility, “logical compatibility” is ambiguous. Consider a quantum spin system, S, with eigenstates |↑> and |↓>. Is it logically compatible that S is in the indeterminate state of being neither |↑> nor |↓> nor a|↑> + b|↓>, for all complex numbers, a and b? What about the contradictory state |↑> and |↓>? If the logic is classical, then the answer to both of these questions is “no”. But if the logic is paracomplete, allowing for indeterminacies, then the state, neither |↑> nor |↓> nor a|↑> + b|↓>, will be in S’s state space. If it is paraconsistent, then the state |↑> and |↓> will be in that space. If First-Degree Entailment (FDE) governs the possible states of the system, then neither |↑> nor |↓> nor a|↑> + b|↓> as well as |↑> and |↓> will all be possible states of the system, S. The situation is even less straightforward in the context of mathematical and logical pluralism.
>(As an example, think of Newton's law of gravitation and law of motion as physical laws of a classical universe determining a set of physically possible worlds, represented by solution curves of the relevant differential equations in Newtonian gravitation theory.)
I actually don’t feel clear on the definition of determinism even in the Newtonian context (and not because of proposed counterexamples to determinism, like “space invaders”). You write, “if you know the laws of physics and the state of the universe at some time (say the present moment), you can in principle know everything about the past and the future.” But, to return to JB’s point, what kind of “in principle” do you have in mind? If Newtonian Mechanics includes the truths of arithmetic, then it is not even recursively enumerable, much less recursive.
>there is no prima facie conflict between logical necessity and human freedom (in the sense of alternative possibility); but there is an apparent conflict between physical necessity and human freedom, if physical laws are deterministic.
I don’t follow this. If I can’t accelerate past the speed of light, then I certainly can’t type this response and not type it (at the same time, to the same degree, and so forth). Of course, if the view that I am pressing is correct, then I can’t as a matter of classical logical possibility, can as a matter of, say, LP-possibility, and that is all there is to it. Any other question is just about which the candidate meanings for “can’t” we happen to pick out, and this designation may be suboptimal.
>What justifies this focus on physical necessity and physical laws? That's a really deep question….The first option is to follow people such as Marc Lange (1999, 2005, 2009) and try to explain why physical necessity is distinguished…
I appreciate Lange’s attempt to tell us what “physical law”, “physical necessity” and so forth mean out of our mouths, but also to supply us non-circular arguments for their importance. However, I don’t see how his counterfactual criterion applies to logical laws themselves insofar as it appeals to the notion of logical consistency (“laws form a set of truths that would still have held under every antecedent with which the set is logically consistent”). Second, if memory serves, Lange advocates a relativized version of Nolan’s Strangeness of Impossibility Condition, which seems to me to admit of counterexamples like the following: had the laws of physics been dramatically different, the laws of mathematics (or, indeed, logic) would have been the same.
>Interestingly, Lange's proposal of understanding physical laws in terms of counterfactuals is incompatible with strong determinism, because strong determinism violates non-maximality, an important component of his construction of a non-circular definition of physical necessity.
Is this because Lange requires that some counterfactuals are non-vacuous? Again, I don’t see why your view implies otherwise. Why can’t we have two counterfactual operators, one evaluated with respect to the “physically possible worlds” (assuming that we know what those are), and another evaluated with respect to (say) the (classical first-order) logically possible ones.
Eddy (if I may)–Manuel (agreed–an excellent scholar and just terrific person) contributed to our aforementioned book and well knows the luck arguments against possibilist stances on free will. And they do seem to be orthogonal in a sense to determinism considerations about implications for the topic, and may well supersede any such, at least on a metalevel of what matters for moral responsibility. I wonder what he might say about that? His revisionism probably does not take any particular hard stance on what determinism of any variety might imply for free will. But I would certainly love to sit in on your collaborative course!
In much of the history of philosophical debate about free will, and among the lay public today, determinism is understood quite differently than it is in strong determinism. Either laws of nature exist independently of the mosaic of history's events, and laws plus the past together pushed the present into being. Or else laws characterize the dispositions inherent in the materials of the world, such as the freezing and boiling points of water. (I deliberately skip over Humean accounts of laws due to their poor fit with intuitions.) Either way, the laws of nature are quite separate from us. They would be compatible with our never having existed.
But if strong determinism is true, Bill Watterson was prescient:
Calvin: Everyone and everything serves history’s single purpose.
Hobbes: And what is that purpose?
Calvin: To produce me, of course. I’m the end result of history.
Calvin is close to the truth here, only it's not just Calvin who is part and parcel of the most fundamental forces in existence, but all of us and all of the multiverse. This radically changed view of laws should radically change how we think about them. Thus I suggest Emily Adlam is wrong to contrast Everettian strong determinism with traditional determinism on the grounds that in the latter "in some meaningful sense, future events — even though they were predetermined — were mediated through processes that you identify with yourself." The strong laws, unlike laws in the ordinary conception, cannot be divorced from oneself.
Hi Justin,
Thanks for the excellent follow-ups. Here are some responses.
"Are you defining physical necessity or taking it as primitive as well?"
I take fundamental physical laws as metaphysical primitives, and try to define physical possibility and necessity in terms of such laws. This is part of view that Sheldon Goldstein and I call *minimal primitivism about laws (MinP).*
"what matters is not what we happen to mean by “physical laws” and “physical necessity”. What is important is whether we pick out properties that are worth picking out. Someone who is doubtful of this will doubt the importance of the entire network of ideas – “ontology, explanation, induction, and time” – in favor of close cousins, call them (to use a recent convention) ontology*, explanation*, induction*, and time*."
That is a nice way to express the worry. It reminds me a bit of Shamik Dasgupta's argument in "Realism and the Absence of Value" (Philosophical Review, 2018). That's a really deep issue, one that I haven't fully addressed but plan to think more about.
Let me take a step back and say something about the background methodology I employ here. My view is that, if we are scientific realists, we may start with scientific practice and take certain things as given. For example, induction backed by physical laws is epistemically rational, counterfactuals supported by physical laws are practically useful, and physical chances derived from probabilistic laws are good guide for getting around in the world. If the physical chance of my death near the surface of the sun is 100%, I should avoid getting too close to the sun, and it's rational for me to avoid that, etc. Now, one can define a chance* according to some mathematical measure on some space of logical possibilities such that the chance* of that event is close to 0, and proceed to ignore the high physical chance. While that person may be rational*, they are irrational. Insofar as we care about epistemic rationality, practical usefulness, and good guide for getting around, we should care about physical laws. Of course, one can doubt those notions, but such a person may not be inclined to accept scientific realism in the first place.
"I fear that this is too vague. Mathematical and logical compatibility are different."
Good point. I have in mind classical logic and ZFC set theory, as I take it they are the implicit mathematical and logical framework for the majority of contemporary mathematical physics.
"I actually don’t feel clear on the definition of determinism even in the Newtonian context (and not because of proposed counterexamples to determinism, like “space invaders”). You write, “if you know the laws of physics and the state of the universe at some time (say the present moment), you can in principle know everything about the past and the future.” But, to return to JB’s point, what kind of “in principle” do you have in mind? If Newtonian Mechanics includes the truths of arithmetic, then it is not even recursively enumerable, much less recursive."
A differential equation has a space of solutions. That is the sense of "in principle" I have in mind. It's also standard in QM (e.g. solutions to Schroedinger equation) and GR (solutions to Einstein field equations). It's true that we may not be able to compute and obtain all such solutions, as we are computationally limited and can work with at most highly approximate and simplified models. But the space of solutions is still well defined, given classical logic and ZFC set theory.
I think it's an interesting question whether computational constraint (e.g. Turing-strength computation) leads to a tighter sense of "in principle" and a stronger sense of "physical laws." Jeffrey Barrett and I have a new paper showing that reflections about computational constraint and algorithmic randomness lead to a new idea about probabilistic laws and new senses of underdetermination by evidence:
https://arxiv.org/abs/2303.01411
"Is this because Lange requires that some counterfactuals are non-vacuous?"
Basically yes. To define laws in a non-circular way, Lange stipulates that the (first-order) laws of nature together with their (classical) logical consequences forms a set Lambda such that it is the "largest non-maximal sub-nomically stable set" (Lange 2009, p.42). Roughly speaking, Lambda is the largest set that is (1) non-maximal in the sense that it does not contain all (sub-nomic) truths about the universe, and (2) counterfactually stable under any (sub-nomic) proposition consistent with Lambda. The first condition, non-maximality, rules out strong determinism, because strong deterministic laws would entail all (sub-nomic) truths about the universe and the Lambda set would have to be maximal.
By the way, Lange's account entails that strong determinism is metaphysically impossible and not just physically impossible. I regard this as a cost of Lange's account, because strong determinism is logically consistent, conceptually coherent, and scientifically motivated. For more discussions on this incompatibility and the cost, see section 4.4 "Langean Reductionism" in my book, Laws of Physics:
https://doi.org/10.1017/9781009026390
"Again, I don’t see why your view implies otherwise."
My view of laws (MinP) is compatible with the situation where all counterfactuals are vacuous and Lambda includes all (sub-nomic) truths about the universe. In fact, strong determinism is not just compatible with minimal primitivism (MinP) but also a paradigm case of it. If strong determinism is true, laws constrain the universe so much that every non-actual universe is ruled as physically impossible.
"Why can’t we have two counterfactual operators, one evaluated with respect to the “physically possible worlds” (assuming that we know what those are), and another evaluated with respect to (say) the (classical first-order) logically possible ones."
One can freely define counterfactual* with respect to logically possible worlds, just as one can freely define chance* with respect to a measure on logically possible worlds. It's NOT the case that if I had been very close to the surface of the sun, I would* (or would* with high chance*) evaporate immediately. But the operators for scientific deliberation, rational choice, and epistemic induction should be counterfactual and chance, not counterfactual* and chance*.
Thanks again for these helpful comments!
Hi Professor White,
Many thanks for your helpful comments. Perhaps "impossibilism," as you describe, is overdetermined and already established by considerations of luck. In general, I'd like to understand each argument separately before comparing them and seeing if any is redundant. Sometimes we can learn new insights and conceptual connections. Don't you think we ought to consider the free will issue from both the physics/metaphysics direction and the moral responsibility direction? After all, the physics/metaphysics connection to free will is still vastly under-explored, as shown by the case of strong determinism. I will read the volume you mentioned with interest and consider the proposed terminology in your Intro chapter.
I was just talking with Manuel Vargas about this topic, and we've been thinking about whether and how to include some of it in the seminar this fall. One of my goals is to learn more about his views and understand whether such views can remain neutral about the physics/metaphysics issues. I'm very much looking forward to it.
I can send you an update this winter! 🙂
Eddy–you can literally call me Al–thank you so much for your reply. I totally agree with your perspective on examining all facets of the free will issue, as demonstrated in our volume. The last chapter–Free Will Zombies–best captures my present pragmatic stance (this was developed from a paper I presented at Vargas' conference in San Francisco in 2013 BTW). But my third chapter is about my version of determinism–R-determinism, a pragmatically justified form of it based on event ontology and (R)elativized to physical systems so described. For other readers I mention that the book is a Wiley companion series volume–A Companion to Free Will. I'd love to hear an update on your course!
Thanks, Eddy! You write,
> Now, one can define a chance* according to some mathematical measure on some space of logical possibilities such that the chance* of [my death near the surface of the sun] is close to 0, and proceed to ignore the high physical chance. While that person may be rational*, they are irrational. Insofar as we care about epistemic rationality, practical usefulness, and good guide for getting around, we should care about physical laws. Of course, one can doubt those notions, but such a person may not be inclined to accept scientific realism in the first place.
As a general matter, I don’t understand why you think that alternatives to our inherited concepts must stand to the originals as grue stands to blue. Take your definition of Strong Determinism according to which “physical laws are compatible with exactly one physical possibility…The sense of determination here is mathematical / logical compatibility with the physical laws.” I noted that this is really a schema: one gets different versions of Strong Determinism by varying the mathematics and logic. You prefer to plug in ZFC with (first-order) classical logic. But it hardly seems grue-some to define Strong Determinism in terms of the axioms of ZF + AD, Zermelo set theory, or Kripke-Platek set theory instead, to say nothing of different logics. So, I don’t agree with what I take to be your suggestion that considering close cousins to the concepts that we happen to have inherited in science or elsewhere is tantamount to radical skepticism.
>I take fundamental physical laws as metaphysical primitives, and try to define physical possibility and necessity in terms of such laws.
Is the result a deductively defined theory (in the technical sense)? What modal logic do you invoke? (The modal logic of physical possibility seems to me to be another adjustable parameter with no compelling reason to prefer one over all others.)
>Good point. I have in mind classical logic and ZFC set theory, as I take it they are the implicit mathematical and logical framework for the majority of contemporary mathematical physics.
Th(ZFC) is, by definition, axiomatizable, while arithmetic is not. So, like any other theory interpreting Robinson Arithmetic, it misses out on infinitely-many arithmetic statements. Are you defining Laws of Nature in such a way that they are ignorant of infinitely-many truths of first-order arithmetic – e.g., truths of the form “Polynomial, P, has no solutions in the integers”? If not, in what sense are what you are calling “laws” laws? And what do they have to do with Laplace’s Demon, “An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed…for such an intellect nothing would be uncertain and the future just like the past could be present before its eyes”?
>One can freely define counterfactual* with respect to logically possible worlds, just as one can freely define chance* with respect to a measure on logically possible worlds. It's NOT the case that if I had been very close to the surface of the sun, I would* (or would* with high chance*) evaporate immediately. But the operators for scientific deliberation, rational choice, and epistemic induction should be counterfactual and chance, not counterfactual* and chance*.
Returning to my first point, can you explain how it follows that if we expand the domain of worlds with respect to which a counterfactual gets evaluated to logically possible ones, the following must come out false? “If I had been very close to the surface of the sun, I would not evaporate immediately.”
("False" should be "non-vacuously true" in the last sentence.)
I'm thinking Free Will is not the appropriate term for consideration of this topic. Free Will skepticism typically comes from physicists or those that agree with physicists so it might be better to use a term more appropriate to that domain. Causality seems a more appropriate word to use. Consider, if you are willing, this experiment I worked out in my mind this morning. Tomorrow morning around 10 I am going to check these comments. If Dr. Leiter or some other commenter choose to post any reply I am going to role a dice. If it's an even number I will post a new comment containing just the number 1. If it's odd I will post a 0. If there is no reply I will post the score of one of the French Open matches scheduled for this afternoon.
What determines what we will see on this comment board tomorrow? Or, more specifically, what will be the quantum states of the subatomic particles at the position on the hard drive of whatever server is being used to store the data represented by the comments?
I changed my mind. Instead of posting a French Open match score here are the This Day in History entries from Wikipedia. As I type this but before I click Post what am I to think of the subatomic particles on the hard drive where these words will be recorded? Will they be forever entangled with the particles in my brain? Rather, are they are entangled with all the other people whose thoughts and behaviors impacted what is happening in this place and time? Dr. Leiter hosting the board. Those that run and play in the French Open. The Wiki people. This network is far too large and complex to understand. I believe Free Will is an emergent property mediating relationships between humans. Much like the 4 fundamental forces between particles. Without the particles you can't have a relationship between them. Without any humans, you can't have Free Will. Obviously, Free Will, at least our version of it, will disappear when we do.
May 30: Statehood Day in Croatia (1990)
1431 – Hundred Years' War: After being convicted of heresy, Joan of Arc was burned at the stake in Rouen, France.
1723 – Johann Sebastian Bach (pictured) assumed the office of Thomaskantor in Leipzig, presenting the cantata Die Elenden sollen essen in St. Nicholas Church.
1922 – The Lincoln Memorial in Washington, D.C., featuring a sculpture of the sixteenth U.S. president Abraham Lincoln by Daniel Chester French, opened.
1963 – Buddhist crisis: A protest against pro-Catholic discrimination was held outside the National Assembly of South Vietnam in Saigon, the first open demonstration against President Ngô Đình Diệm.
2008 – The Convention on Cluster Munitions, prohibiting the use, transfer, and stockpiling of cluster bombs, was adopted.
BL COMMENT: This amusing (but of dubious relevant) little experiment, is now over.
Hi Justin,
Many thanks for your insightful comments! Please see below for some responses.
"I don’t agree with what I take to be your suggestion that considering close cousins to the concepts that we happen to have inherited in science or elsewhere is tantamount to radical skepticism."
Sorry, the concept of *close cousins* can be ambiguous, and earlier I should have asked to clarify what you meant by that. Now I understand that you are thinking about alternatives that differ only in, say, axioms of set theory (Axiom of Determinacy vs. Axiom of Choice) and/or logics. I thought you had in mind a wider class of alternatives, say, with quite different probability measures and probability spaces.
For the close cousins you have in mind, one has to look at them case by case and see what follows. My gut feeling is that if they are close enough to the inherited ones and are compatible with scientific practices in mathematical physics, they won't lead to significant differences from the standard ones. But maybe you have in mind some concrete examples that show otherwise.
"Is the result a deductively defined theory (in the technical sense)?"
If that means deductively closed, then yes, the defined theory of physical possibility and necessity should be deductively closed.
"What modal logic do you invoke? (The modal logic of physical possibility seems to me to be another adjustable parameter with no compelling reason to prefer one over all others.)"
Is there a reason one has to invoke modal logic here? If one defines a space of physical possibilities as solutions to some nomic equations (e.g. F=ma, Schroedinger equation), represented as curves in a suitable physical state space (e.g. phase space, configuration space, Hilbert space), with the relevant structures (e.g. measures and norms), then one has the minimal structure to make sense of physical possibilities and their relations. One can invoke modal logic S5 so that one can prove interesting theorems about such physical possibilities, but is modal logic necessary for defining physical possibility from laws?
In any case, I tend to think S5 is a good fit for physical possibility in the standard case of physical laws. After all, in the state space relevant to physics, every point (or curve) can "access" every other point (or curve) in the same space. In the case of strong determinism, a natural modal logic is Triv, which is very strong, since p implies it's physically necessary that p.
I've been talking with and learning much from my colleagues Gila Sher and Sam Elgin who are experts in philosophy of logic. But this is something I am still trying to understand better.
"Are you defining Laws of Nature in such a way that they are ignorant of infinitely-many truths of first-order arithmetic – e.g., truths of the form “Polynomial, P, has no solutions in the integers”?"
There can be laws of mathematics, laws of logic, and laws of arithmetic, in addition to laws of physics. I take it that standard practices of mathematical physics rely on ZFC, classical logic, and Peano arithmetic. If that's the case, they should be part of the background theory. (You know that I like Field's approach to nominalistic physics, so in the end I need to tell a nominalistic story about the background theory.) But the physical laws themselves are distinct from the laws of mathematics, logic, and arithmetic.
"And what do they have to do with Laplace’s Demon, “An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed…for such an intellect nothing would be uncertain and the future just like the past could be present before its eyes”?"
First, a small remark: if Laplace has in mind a Newtonian world obeying Newton's law of motion and law of universal gravitation, then he should have included instantaneous velocities among the things that the Demon must know at that moment.
Second, one can consider different versions of Laplace's Demon subject to different constraints. For a totally unconstrained version, the Demon (or Oracle) can know all the logical consequences of the instantaneous state and the Newtonian laws. But for a Demon subject to computational or other resource limitations, the Demon may not know things that are undecidable / unaxiomatizable.
"Returning to my first point, can you explain how it follows that if we expand the domain of worlds with respect to which a counterfactual gets evaluated to logically possible ones, the following must come out false? “If I had been very close to the surface of the sun, I would not evaporate immediately.”"
I did not mean to suggest it follows logically. You are right that if we are considering nomic concepts* that are very close (say by adding a few additional logical possibilities), the counterfactual* may not be false. I was thinking about more dramatic changes to our concepts.
By the way, in the longer paper on strong determinism (p.11 Options 2-3), I consider some nearby concepts of counterfactuals when standard counterfactuals become trivial:
https://arxiv.org/pdf/2203.02886
Here are the relevant paragraphs:
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Option 2: We can understand the relevant counterfactuals for causal modeling and explanation as involving not the universe as a whole but the subsystems of the universe. (As (Pearl 2009, pp.419-20) acknowledges, when you describe the whole universe using interventionist models, causality disappears. See also (Woodward 2016, sect. 10). However, there are many identical (or similar) subsystems of the world that in which causality still exists even if it disappears at the universal level.) Even though the universe could not have been different, we could have been located in other subsystems of the actual universe. Hence, we may construct non-trivial state spaces for the subsystems of the universe, by using ensembles of actual subsystems to represent counterfactual possibilities. This is not very different from a related strategy that has been explored in Everettian theories, according to which we can model counterfactual possibilities as variations in different branches of the actual multiverse. (See Wilson (2020) for a proposal.)
Option 3: We may consider using counterlegals for causal modeling and allow causal variables to range over metaphysically possible but nomologically impossible states. This deviates from the usual practice of disallowing counterlegals, as we assume that the causal structure is fixed by the laws of nature. The relevant counterlegal possibilities can be mapped to points on phase space, configuration space, Hilbert space, and the like, which possess well-understood structure to ensure that not everything goes. (See Tan (2017) for a related idea.)
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Maybe they flesh out two alternative definitions of counterfactual* that are close cousins to the inherited ones.
Thanks, Eddy! Comments follow.
>Now I understand that you are thinking about alternatives that differ only in, say, axioms of set theory (Axiom of Determinacy vs. Axiom of Choice) and/or logics. I thought you had in mind a wider class of alternatives…My gut feeling is that if they are close enough to the inherited ones and are compatible with scientific practices..they won't lead to significant differences from the standard [theories].
I regard the different combinations of logic, math, and modality as serious alternatives. I didn’t mean my comment in a “convince the skeptic” spirit (as interesting as a think that Shamik’s paper and similarly spirited discussions are). But I disagree that the rival proposals “won’t lead to significant differences” from standard theories, by ordinary standards, at least. I illustrated how different logics lead to different state spaces for a physical system. Perhaps you will say that some of those logics aren’t “compatible with scientific practices in mathematical physics”. But if this means that they are empirically contrevened, then I can’t see how. Closing a physical theory under, say, FDE results in a strictly weaker theory of the actual world. What it allows are more possibilities for how states of the system could, as a matter of logical possibility, have been. The probability of seeing these states is a free parameter. The key divergence is merely over how the world could have been – which again raises the question of what is at stake here.
Logic aside, I suspect that substantial variation in choice of mathematics is “compatible with scientific practices in mathematical physics”, if only because not many mathematical physicists have anything like a stable view as to what axioms of set theory we should be allowed to assume. The case of Kripke-Platek set theory is dramatic, avoiding as it does the axioms of Infinity and Powerset, and limiting the Comprehension and Replacement schemes to bounded formulas. However, even the case of ZF + AD is heretical. ZF + AD has much stronger consistency strength than ZFC (it is equiconsistent with ZFC + there are infinitely-many Woodin cardinals), so proves Con(ZFC). Moreover, ZF + AD implies the original formulation of Cantor’s Continuum Hypothesis and the measurability of all sets of reals. Without the AC, not only are pathological constructions of interest mainly to metaphysicians impossible, but arguments from mathematical physics like the following due to Heller fail. “[T]he spacetime manifold M is partially ordered by the chronology relation, and any timelike curve g on M is simply ordered by the same relation. Therefore, on the strength of the maximum principle [which is equivalent to AC] there is a subset h of M, which is simply ordered by the chronology relation, contains g and is maximal with respect to these properties of M….[T]he set h is a timelike curve (1986, 64).”
>"Is the result a deductively defined theory (in the technical sense)?"
If that means deductively closed, then yes, the defined theory of physical possibility and necessity should be deductively closed.
No, I mean: is the theory defined as the set of (first-order) consequences of a recursive set of axioms?
>Is there a reason one has to invoke modal logic here?
Only if you think it makes sense to speak of iterated modalities, or to quantify across the box (and make de re modal claims). If you only want to say things like “it is physically necessary that P”, where P is a non-modal sentence (as Quine did), then modal logic does not enter.
>"Are you defining Laws of Nature in such a way that they are ignorant of infinitely-many truths of first-order arithmetic – e.g., truths of the form “Polynomial, P, has no solutions in the integers”?"
There can be laws of mathematics, laws of logic, and laws of arithmetic, in addition to laws of physics. I take it that standard practices of mathematical physics rely on ZFC, classical logic, and Peano arithmetic….But the physical laws themselves are distinct from the laws of mathematics, logic, and arithmetic.
I don’t understand this. How can you separate the three? Do you envisage a non-mathematical surrogate for the Hartle-Hawking proposal? Wouldn’t it have to have the structure of the original? What would be the point of calling the analog of the Hawking-Hartle state vector “non-mathematical”? Whatever your treatment of mathematics, all laws, whether physical or mathematical, are closed under a logic. Their content is given by their implications. That is how we hope to test them. A first-order regimentation of the Schrodinger Equation closed under classical logic is a different theory from the same regimentation closed under intuitionistic logic.
>You know that I like Field's approach to nominalistic physics, so in the end I need to tell a nominalistic story about the background theory.
I do not think that the platonism-nominalism problem is relevant to my question. Whatever theory you propose, I assume that it will be consistent and represent all recursive functions. So, if it is axiomatizable, then it must be ignorant of infinitely-many statements about integers, what computers will output if programmed in such and such a way, and anything codable as such.
>one can consider different versions of Laplace's Demon subject to different constraints. For a totally unconstrained version, the Demon (or Oracle) can know all the logical consequences of the instantaneous state and the Newtonian laws. But for a Demon subject to computational or other resource limitations, the Demon may not know things that are undecidable / unaxiomatizable.
I don’t mean to introduce any limitations of space, time or energy (although I think, with Aaronson, that computational complexity considerations are relevant to metaphysical questions about physics). Of course, you could imagine a being just knowing the unsystematized mass of truths about the world (including arithmetic), which would not be computably enumerable. But that does not amount to a procedure for determining earlier and later facts from a fixed state, i.e., a procedure such that “if you know the laws of physics and the state of the universe at some time (say the present moment), you can in principle know everything about the past and the future.”
>You are right that if we are considering nomic concepts* that are very close (say by adding a few additional logical possibilities), the counterfactual* may not be false. I was thinking about more dramatic changes to our concepts.
I intended dramatic changes insofar as the class of worlds is greatly expanded. Infinitely-many counterfactuals which had been vacuous come out false. (If the relativized version of Nolan’s Strangeness of Impossibility condition is satisfied, then nothing that was non-vacuously true will become false.) It sounds like you agree that there is nothing unintelligible about counterfactuals involving different laws. You just don’t want to call their antecedents “nomically” possible. But again: what is the non-verbal force of this policy, given that you agree to a translation of everything that one who does regard those antecedents as nomically possible would want to say?
I could imagine there being a non-verbal issue. Think of Peres’ remark that “unperformed experiments do not have outcomes” in connection with Bell’s Theorem. Will Cavendish, Simon Kochen and I worked on an argument, based on the Free Will Theorem, that that any deterministic theory satisfying a consequence of Lorentz Invariance that is consistent with established facts must deny that there is a fact about what would happen in some of 1320 experimental scenarios involving spin measurements. By “must deny”, I mean that it is incoherent not to. One can bypass this argument by giving up on the idea that we can counterfactually conditionalize on the experimental scenarios. One can''t infer from the fact that a particle detected at region B is measured spin up along axis 2 and a particle detected at spacelike separated region A is measured spin down along axis 1, and the particles are in an entangled state such that their spins are perfectly correlated along the same axis, that the particle at A is spin up along axis 2 as well. That would require arguing that, if we had measured the spin of A along axis 2 instead, nothing would have changed at B — a counterfactual. Whether there are other ways to respond, you don’t seem to be making an argument from incoherence.
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