A brood comb

….philosophical and other notes….

Physical Laws, Ontological Underdetermination, God and Fine Tuning

Posted by Tanas Gjorgoski on December 29, 2008

There are probably lot of ways to look at the physical laws, here I will point to two and in relation to those discuss possibility of God.

a)Laws governing the Universe

In the first way the laws are seen as governing the universe. Given the state of the universe at the time t1, the physical laws determine how the universe will be at the t1+dt.

This view is incompatible with the idea of God, as according to this there can’t be any talk about God taking part in determining the events in the Universe. It is then said that God might have made the universe, created those physical laws, set everything in motion, but that from that moment everything happens according to those laws which were set. At this point, a person that believes in God can bring up the fine tuning argument also – that is… that physical laws and constants are set in just the right way for appearance of life (and thus intelligent life). If you change those constants and laws just a little bit, it becomes impossible for this to happen.

Of course it is also possible to take this position with further note that God can and does do things which go against the laws of physics – some kind of miracles. Also there is the possibility that God made the laws in such way that they leave him open hands for intervening without breaking those laws. In such way for example, given the quantum mechanical indeterminacy (we don’t know of a law that fully determines the collapse of a QM system), God has freedom of doing anything, without in fact breaking the laws of physics. We may say, that the laws are intentionally left not fully determining what will happen (I will call this ontological underdetermination, not sure if it is good term, but can’t think of a better one), so that either God is constantly guiding (to some amount) the events in the Universe, or alternatively he is throwing dices when he doesn’t really prefer how certain collapses would happen.  Now, that is I guess consistent position, it does provide a way to make sense of God (and further it makes fine tuning argument possible), but in my opinion it is quite inelegant all over. The explanation is full with choices which are made just to defend the possibility of God, and which explain nothing more but that possibility.

b)Laws as necesary relations between measurables

And that brings us to the second way to view the physical laws. In this view the laws are necessary relations which hold among different measurables (what kind of necessity this is – is it metaphysical necessity, or is it just a necessity in the actual world is separate issue which I will touch on later). In this kind of view the laws are not seen now as governing the universe. So, they are not things which are moving the state of the universe at time t to the state at time t+dt. In fact, the time is now seen as just another measurable, and what the laws tells us is the necessary relations in which the measurables will stand – measurables which are aspects of the Universe (where it is seen as becoming, so that it includes temporal facts). I think firstly that this kind of view of laws is much better than the previous one – it seems really much closer to the actual way the physical laws are specified in physics (through equations, and not through ‘if system is X at t, it will be Y at t+dt’ kind of formulations), and secondly by seeing time as another measurable it is much more inline with the modern theories of physics (relativity and quantum mechanics).

Other interesting stuff is though that ontological underdetermination can now be presented not as an incidental feature of the laws which we add to our explanations post hoc, but as something which can be made sense of metaphysically. Let me try to explain this…

When we speak about measurables, we imagine that those have independent existence in the world, and that they are self-subsistent. So that there is definite fact about how long something is, or that there is a definite fact about how much mass something has, and so on. Now, we should be clear that measuring does incude more than just the reality of the property being measured, as it includes comparing, and thus inevitabely all kinds of complications which are related to that. So, we might measure something in inches or meters, we can’t measure it in nothing. Further, as we know from relativity, when we do the measuring, it will come up differently depending how we (as “measurer”) move. But putting all this aside, I think we usually do allow for the reality and selfsubsistence of the property being measured. It has certain length by itself, certain mass by itself, and so on. But, I don’t think this is cearly true also. It would be true if things would exist as some kind of “bag of independent properties” – in that case we would have to allow reality to each of them, and we would have to allow that it has certain mass, certain volume which is independent from that mass, certain speed which is independent from the volume and the mass, and so on. It might also be, however, that what is ontologically primary is the thing itself, and that those measurables can be thought of only as aspects of it, which don’t have reality of their own, so that there is no *certain mass*, *certain volume* and so on to speak of. Given this, the necessary relations are among the ideal forms of those measurables, where we are just treating them as having self-subsistent reality – we are ignoring that they have no such nature. What we have then described as “governed” by those necessary and fully deterministic laws are the systems in their ideality. But those systems are actual, and there are more facts about them than this ideal description. And thus we should expect that sooner or later, we will see how we can’t figure out the behavior of the system deterministically treating it as mere bag of mutually-determining properties.

The picture we basically have now is this – if, and only as long a concrete system falls under the abstract description (in this case physical description), the relations between the aspects of that physical description will be necessary. But as long we move from that ideal cases to the real world, what is happening in the Universe is underdetermined in relation to those necessary relations. So, QM indeterminacy in this kind of view is not incidental, it is a metaphysical consequence of the physical description failing to fully determine the world. Now, we have, which I think is, more elegant way to make sense of non-physical reasons affecting the world – what is denied is that the world is merely physical in first place. In that way we not only make metaphysical sense of quantum indeterminacy, but also we make sense of the possibility for non-physical reasons being behind the changes of the physical measurables.

Metaphysical necessity, or just neccesity in actual world?

At the end, let me return to the issue of the kind of necessity of the physical laws. It might be that those are necessary just in the actual world, or it might be that they are metaphysically necessary. What I especially see as metaphysically elegant possibility is this second option. It seems to me that it makes lot of sense for them to be metaphysically necessary relations. So, not just that those happen to be such in the actual world, but that those relations have to  be such in any possible world. Or if we use logical in the wide sense of the world, that it is logical for those relations to be the way they are. Now this kind of result (if we ever get to it), is good because it answers why laws are same everywhere in the universe, it can give explanation of the relativity, symmetries, and so on… And basically it would be a way to make sense of there being such necessary relations in first place.

Let me try then to give an analogy with a metaphysical relations that we know hold, and for which we understand why they hold – the arithmetical relations. We can say this – as far a group of individuals don’t disappear or multiply, said simply – as far they fall under the certain mathematical abstraction – say e.g. – ‘being 5 things’, there will be metaphysically (in this case mathematically) necessary relations. Such that for any particular thing in this group, there will be four more things. Or that, those can’t be divided to 3 groups, such that in each group will be identical number of things. So – we have certain necessary relations, which hold just as far the thing at hand falls under the abstract description. But it is clear that real things aren’t reducible to those descriptions – sooner or later, for no reason apparent within the abstract description, the thing will no more fall under that description. We may have 3 rabbits, and they might become 4 rabbits. But that won’t be something which is result merely of the mathematical description. The necessary relations among physical measurables should be then be taken analogously to think case.

It might not be common for a person who beliefs in God to take physical laws as metaphysically necessary relations, which even God can’t change (for simple reason that there is no sense in even thinking of the concept of changing of metaphysically necessary relations), however to me it seems as the most elegant metaphysical view, which even in its metaphysical necessity doesn’t restrict the possibility for non-physical reasons for the changes in the physical aspect.

What should be pointed to is though, that if a person buys this, the Fine Turning no more points to existence of some kind of plan – if the laws have to be the way they are, then there is no sense in asking how come that they are such as they are. I do believe in this metaphysical picture of things, so I can’t count fine tuning as a reason why I should believe in God. However buying this picture does present a reason why one should believe that there is something further than what can be put in the physical descriptions, and is one of the reasons why I believe in God.

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23 Responses to “Physical Laws, Ontological Underdetermination, God and Fine Tuning”

  1. anonymous said

    I just wanted to leave my feedback about your blog. I’d like your blog better if it had shorter, meatier posts instead of long drawn-out paragraphs.

  2. I thought this was good and I agree with much of your thinking. The exception is that I think the true metaphysically necessary relations are contained to a more limited set of logical/mathematical relations, and that the physical laws of relativity and quantum field theory as we know them today are contingent and can differ significantly in different worlds. Best regards,
    – Steve Esser

  3. Hi Anon, thanks for the helpful criticism! I think I would like my blog better like that also :)

    The problem is that I rarely take the time to go through the text before posting so to simplify and cut out unnecessary parts. So, it is mostly the text as it comes out. I will try to fix this, but I wont make any commitments :) Anyway, hope that there is at least something that you can take out of the blog.

  4. Hi Steve,

    Thanks! As for the physical laws, it does seem that the view that they are contingent is not just widely accepted, but that it is so much taken for granted that the other possibility doesn’t even normally appear as an option. So far, I haven’t had luck to meet anyone who is inclined to see them as metaphysically necessary (except few papers which try to get a priori to Special Relativity) . But there is always hope :)

  5. Clark said

    I like the more longer posts myself.

  6. Clark said

    BTW – I think most physicists think there is some “ultimate” set of laws that might be a priori with the rest simply being descriptions of symmetries and broken symmetries that are allowed as possible evolutions of the original laws.

    You see this is cosmology where a lot that we talk about as “laws” are really just descriptions of the way the universe froze out of early energy configurations. So, for example, the charge of the electron is accidental in some sense.

    This is why physics by the 60′s had really turned into a discussion of symmetries with the associated complexities of higher and higher orders of mathematics focused on this. (Say the injection of group theory which really was all about that sort of thing)

  7. Clark said

    Just to add, the blogs I like best (among which is yours) are those blogs where the writers are struggling with ideas and trying to think through them. That doesn’t lend itself typically to short meatier posts. Those sorts of posts (which I sometimes also like) tend to be more the posts of profs writing about what they’ve already figured out.

  8. Thank you Clark!

    About the symmetries, it is symmetries which seem to me as the possible part of the physical laws which is a priori. For example the basic invariances vs. translations through time and space, rotations in space, and so on… seem to me might follow from the very idea of measurement of space, time, etc…

    Re. electrical charge of electrons… this is little disconnected from what you said, but what I mentioned in the post is that I wonder if there IS a specific electrical charge in electrons. Metaphysically to me it makes more sense to speak about the electron as a whole, and then speak about “properties” merely related to its behavior in possible measurements, or its behavior in possible events (including e.g. interactions with other particles). Of course we can speak about electrical charge still if that is the case (in the sense – if we interact with it in such and such way, this thing will (most likely) happen), but we remove the idea of some specific electrical charge existing independently in the electron. (on another side the measurement itself will a priori involve symmetries, and thus, there will be laws of conservations).

    Though, even if the laws are fully a priori, the question still is there… why electrons, why protons, etc… are they natural kinds (formed as you point, in a kind of incidental way), or are they configurations more or less stable because of a priori reasons. I’m more inclined (again metaphysically) towards this second.

  9. mrhamilton said

    God can’t influence the physical world yet some cling to the impossibility. This belief does not warrant a metaphysical exposition on your behalf but may perhaps warrant a psychological evaluation on theirs.

  10. Mrhamilton,

    I’m sure you know that isn’t much of an argument.

  11. phillip Wong said

    Ok. i am a bit slow, but i don`t understand why the laws are metaphysically necessary. Can you give an example?

  12. phillip Wong said

    Ok, i have to admit that i do know some papers where people say the laws are metaphysically necessary, but their reason is different from the way you put it. Their reasoning i think comes from the fact that “natural kinds” have essential disposition, and that the laws are just the description of these dispositions. For example:

    1. Mass m1 and m2 is described by F=Gm1m2/r^2 in world 1.

    1 is metaphysically necessary because in all worlds such that m1* , and m2* are not equal to m1 and m2, then F= Gm1*m2*/r^2 does not hold.

    • Hi Philip, thanks for your comment…

      Yes, that is not the sense in which I mean it… I wonder if this older post might help explain different motivations for the belief that they are metaphysically necessary. And maybe this one here.

      As for an example… there are attempts to ground Special Relativity (SR) simply on the principle on invariance. Given that some of those attempts are successful , the idea that one can a priori come to this principle too, and hence that the whole SR can be figured out a priori isn’t very outlandish.

  13. Phillip said

    thanks for the reply…

    ok..I can imagine a possible world in which f=ma is false, and there would not be any contradiction. Can you explain to me why i can` t imagine such a world?

    In general, a law have the form:

    1. (x)(Gx->Fx) is true.

    To show that 1 is metaphysically necessary, i think you have to show that G=F. I know philosophers that say 1 is metaphysically necessary because G=F, but their reasoning seems to be different from what you are saying here.

    As for your example….

    There are 2 problems:

    problem 1:

    The notion of the a priori is an epistemic notion, while necessity is a metaphysical notion. As such, even if the postuates of SR is a priori, it does not follow that it is necessary.

    problem 2:

    The postuates of GR is not at all a priori. Both postuates reference “laws of nature”, and the “speed of light” , and they both references must be know a posteriori. Therefore, the SR postuates are know a posteriori.

  14. Hi Philip, sorry for being late with the answer, for some reason I didn’t get notified in my email for your response :-/

    1.
    As I said in one of those posts, I find “a priori” term little problematic, and prefer talking about understanding. So, in those terms, the idea is that we can understand necessary relations among things. Like , how we understand the proofs of the math theorems, or, which I think is possible in the case of special relativity, that we might understand how necessary some relation will hold. So, in those posts, I was pointing that some people think that they realized/understood how the relation depicted by the special relativity is necessary. Maybe they are wrong, maybe they didn’t. However, I think it is not obvious that they didn’t.
    So, putting all the convoluted “a priori” talk behind, the thing is this – if one realizes/understoods how some relation is necessary that relation is necessary. (Of course one might doubt that such understanding is possible, but again, given the fact of math, it doesn’t seem obvious that such understanding is impossible)

    This has to do with your question about – why you can imagine a world in which certain physical law doesn’t hold. Imagining doesn’t mean understanding that something is possible. One may imagine very easily something which is impossible. So, I don’t see anything problematic in that possibility to imagine.

    2.
    The idea behind some of those papers is that one can do with “constant speed of light” postulate in case of special relativity. As for GR, I don’t know of any attempt to came to it on a priori considerations only. However, again, what I was pointing to in case of those papers is that it isn’t obvious that one can’t understand the necessary relation between notions in case of SR. If one can do away with constant speed of light as a postulate, what is left is just the invariance of laws, which doesn’t seem as obviously contingent thing.

  15. phillip said

    “Like , how we understand the proofs of the math theorems, or, which I think is possible in the case of special relativity, that we might understand how necessary some relation will hold. So, in those posts, I was pointing that some people think that they realized/understood how the relation depicted by the special relativity is necessary. Maybe they are wrong, maybe they didn’t. However, I think it is not obvious that they didn’t.”

    I am not sure how certain relationships are “obvious” in fundemental laws. The reason i say this is because most fundemental laws reference/describes relationships between observables. These observables could only be know a posteriori. That is why fundemental laws in physics are a posteriori. Examples are space-time, matter. I do not know how anyone could know the nature of space-time by thinking alone.

    “This has to do with your question about – why you can imagine a world in which certain physical law doesn’t hold. Imagining doesn’t mean understanding that something is possible. One may imagine very easily something which is impossible. So, I don’t see anything problematic in that possibility to imagine.”

    What are we talking about here? metaphysical possibilities, or logical possibilities? It is metaphysically that mass M obey the inverse square law in all possible worlds. It does not follow that there cannot be mass M* not of this world, but obeying a inverse cube law.

    “However, again, what I was pointing to in case of those papers is that it isn’t obvious that one can’t understand the necessary relation between notions in case of SR. If one can do away with constant speed of light as a postulate, what is left is just the invariance of laws, which doesn’t seem as obviously contingent thing.”

    The “invariance of physical laws” would be true if and only if “Physical laws are invariant” is true. You can only know if these statements are true in the case that you know what the physical laws are. In such case, you do need to know these physical laws a posteriori. Therefore, Fundemental laws are know a posteriori.

  16. Hi Phillip,

    You say:

    >>I am not sure how certain relationships are “obvious” in fundemental laws.

    I didn’t say that they are obvious. In one of the posts I mentioned in previous comment, I linked to couple of works which analyze the issue of necessity of relations depicted in special relativity on ground on the principle of invariance only. I said that it *isn’t obvious* that something like this couldn’t be true (that is, that we could do away with principle of constant speed of light). If we understand that given invariance there is necessary relation of certain measurables (that is, special relativity), and IF we understand how certain invariance necessarily holds, we will understand how certain relation of certain measurables necessarily holds.

    >>The reason i say this is because most fundamental laws reference/describe relationships between observables.

    And in this I fully agree. Observables are however a specific thing – they are measurables – things which are measured, they depend on there being *measuring*. However measuring is not a natural kind. What is right measurement, and what is wrong measurement (of some specific measurable) is not matter of the universe – it is something that we define. (As an example of this kind of analysis of nature of observables through analyzing the nature of measurement is the Einstein’s analysis of time and space)

    >>What are we talking about here? metaphysical possibilities, or logical possibilities? It is metaphysically that mass M obey the inverse square law in all possible worlds. It does not follow that there cannot be mass M* not of this world, but obeying a inverse cube law.

    Again, I’m not talking about that kind of metaphysical necessity. And, with all respect to those philosophers that you mentioned, I don’t think that that kind of metaphysical necessity tells us anything interesting and very important, it is more semantics than metaphysics :). The necessity of the relations between the observables that I’m buying is better compared with the necessity of relations between mathematical notions, as specified in different theorems.

    You say:
    >>The “invariance of physical laws” would be true if and only if “Physical laws are invariant” is true. You can only know if these statements are true in the case that you know what the physical laws are. In such case, you do need to know these physical laws a posteriori. Therefore, Fundemental laws are know a posteriori.

    We are talking here about specific physical laws, that is – specific relation between observables. I think talking about “physical laws” in general in this case just clouds the matter. The question is simply if some relation between certain measurable holds necessarily, and if we can understand that it holds necessarily. That we may happen to come to figure out certain relation that holds in the universe a posteriori is not very important. From there it doesn’t follow that they are not necessary, nor that we can’t understand that they are necessary.

    Think about how we understand that certain relations in math hold necessarily, e.g. some theorem. We might believe that some conjecture holds (e.g. a posteriori on base of seeing that it works for certain number of cases), but that doesn’t mean that it doesn’t hold necessarily, nor that we can’t understand how it holds necessarily.

  17. phillip said

    “I didn’t say that they are obvious. In one of the posts I mentioned in previous comment, I linked to couple of works which analyze the issue of necessity of relations depicted in special relativity on ground on the principle of invariance only. I said that it *isn’t obvious* that something like this couldn’t be true (that is, that we could do away with principle of constant speed of light). If we understand that given invariance there is necessary relation of certain measurables (that is, special relativity), and IF we understand how certain invariance necessarily holds, we will understand how certain relation of certain measurables necessarily holds.”

    I understand what you are saying. I gauss i ought to be more clear. When i talk about a “Law”, i am talking about the “most” fundemental laws. In the sense that all propositions of SR( special relativity) is reductive to the postuates of SR. These postuates would qualify what i mean by “laws”. I am claiming that we know A posteriori why these “laws” are true. i guess my main point is the following: “The nomic necessity of ALL the propostion of SR” is reductive to the “nomic necessity of the postuate of SR”, and the nomic necessity of SR is know a posteriori.

    “And in this I fully agree. Observables are however a specific thing – they are measurables – things which are measured, they depend on there being *measuring*. However measuring is not a natural kind.”

    Just to be clear. You are using “natural kind” in the sense of W.V Quine?

    “Again, I’m not talking about that kind of metaphysical necessity. And, with all respect to those philosophers that you mentioned, I don’t think that that kind of metaphysical necessity tells us anything interesting and very important, it is more semantics than metaphysics :). The necessity of the relations between the observables that I’m buying is better compared with the necessity of relations between mathematical notions, as specified in different theorems.”

    Mathematical theorms are not really about the “world”. Mathematics could be defined in a purely formal way where each theorm in the formal system is a result of some iterative process of rules of inference and axioms. What gives power to the formal system is in it` s capacity to model the world. In order to model the world, there need to be a correspondence between the symbols in mathematics, and measurable observables in the world. The result are fundemental equations that depict BASIC functional/mathematical relationships between observables. The main point is that there is two use of mathematics. 1. Mathematics as it is used as a basic consequence of rules, and 2. mathematics as a tool that depict/describe basic relations between primitive observables. Any mathematical theorms of type 1, does not really really give us any physical “insight”. It should also be clear that when physicists talk about mathematics, they often use mathematics in the sense expressed in type 2.

    “We are talking here about specific physical laws, that is – specific relation between observables. I think talking about “physical laws” in general in this case just clouds the matter.”

    Ok, let` s me once and for all be clear what i mean by a “law”:

    Definition: Law( G, F)
    1. Law is a non-reductive relations between G s and F s.
    2. Law is a non-logical relation between G s and F s.
    3. G s and F s are either observables, or non-observables.

    Observables and non-observables in 3 has a technical meaning in the philosophy of science, and you can learn more about it by doing a google search.

    Most people that holds the view that laws are metaphysically necessary reject 2, and adopt some type of property essentialism/disposition. etc.

    “The question is simply if some relation between certain measurable holds necessarily, and if we can understand that it holds necessarily.”

    This is the part that i disagree, and frankly, a bit vague. What do you mean by “understand”. How do you come to know a law between F s and G s? What type of relation is it? Most philosophers would say there is a non-logical, nomic relation between F s and G s, but that is pretty much it. There is actually two questions. 1 How you come to know the law, and 2. What is the precise connection between F s and G s that makes the law true. By using the word “understand” is really being vague, and a recipes for bad philosophy. You have avoid/hide from the epistemic, and metaphysical question at hand.

    “Think about how we understand that certain relations in math hold necessarily, e.g. some theorem. We might believe that some conjecture holds (e.g. a posteriori on base of seeing that it works for certain number of cases), but that doesn’t mean that it doesn’t hold necessarily, nor that we can’t understand how it holds necessarily.”

    I have already addressed this issue on some other parts of this post.

  18. phillip said

    After such a long reply( see above). I think it is only fair to illustrate with an example.

    Philosophers use possible worlds in analying notions like necessity, and contingency.
    According to this view, the actual world is a possible world described by TOE( theory of everything). The TOE is a mathematical relations/descriptions between physical primitives( E.g: spacetime, matter, charge). One can think of the physical primitives as undefined terms, and the axioms/rules of inference as being the TOE. One can explain the physical system of the moon moving around the earth by appeal to the rule( TOE), and the physical primitives( space-time, matter). The TOE would satisfy the criterion to be a law.

    This TOE is non-logical in the sense that there need not exist a world
    1: with rules equals the TOE
    2: with a TOE that describes/govern physical primitives( space-time, matter).

    One can imagine infinite many possible worlds govern by different physical primitives, and rules. That is, let S be the set of all possible worlds.
    where each element w in S is defined by rule( R) and physical primitives( PP).

    R is the set of all rules that contain elements TOEk ( k is some integers ). where there exist with probability 1 that there is K* such that TOEK*= TOE.

    Similarly, for PP.

    In such a way, Each element in S can be descibed by for some unigue R*, and PP*. We know with certainty that our world is in S.

    The view of modal realism, ultimate ensemble, principle of fecundity, and princuple of plentitude is the claim that each elements of S exist, and that the ultimate non-reductive truth about reality is that all descriptions, and all physical primitives defined an actually existing world.

    The contingency of our world would just be that we live in one possible world, and not some other possible world.

  19. Phillip,
    Thanks for the long answer, but it seems we are making the issue much more complicated then it is.

    You are explaining a view , which I think is taken for granted today. I understand it, but I happen to believe otherwise, and I tried to explain the reasons in bunch of posts on this blog. Of course, those things (the reasons) never go alone, so they are connected to how one views things like math, language, subject/world relation, etc…

    I say this, because this discussion is getting into this kind of issues (nature of math, its relation to world, the relation between the subject and the world when we raise the question of understanding, etc…), and I feel that it might end up in one big mess. I mean, in response to your last comment, I would now have to go into my holistic metaphysical views, and THAT , I know, will end up in even bigger mess :)

    So, if you found something reasonable in what I said, I’m happy for it. If not, let’s leave it on this.

  20. phillip said

    Ok, i will leave it on this.

  21. Veterator said

    Disregarding from the question whether physical laws are necessary, I must say I do believe an argument for God’s existence can be drawn from the necessity of the world (not just its natural laws).

    If the world is necesary, an ideal knower would find all of his why-questions answered, since he would see that things can’t be otherwise than they are. A world where everything has an ultimate ground or reason to offer to the inquiry of an ideal knower is a rational world, a world ruled by reason. But how could reason rule the world if not embodied in some concrete intelligent being able to govern the world? Reason is in itself an abstract object and abstract objects are causally inert.

  22. Tanasije Gjorgoski said

    Hi Veterator,

    That is an interesting argument, but isn’t it mixing up two senses of “Reason”? The sense where reasons are supplied as answers to “why?” questions, with the sense where “reason” as a faculty of an intelligent being?

    Say that all that there is are the physical laws. When one asks then, why at time t2 the state of the system is such as it is, one can provider the reason for it by referring to e.g. an earlier state of the system (e.g. at t1), and the physical laws.

    Through this answer of “why” a person would hence provide reasons, without at all implying that there is an intelligent being behind those reasons.

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