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Chapter 10: A Tutorial on Causal Significance

  1. May 7, 2005 #1


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    Having laid down the foundations for a theory of causal significance in chapter 9, we can begin to investigate applications of its principles in order to get a firmer grasp on the concepts and derive some theoretical results. Rosenberg demonstrates applications of the theory of causal significance by using a simple toy physics, where there is only one type of level-zero effective property, charge, which can take on values of either + or -. ('Charge' in this context is just a simple level-zero effective property introduced for the sake of this demonstration, and is not to be confused with the word as it is used in physics.)

    Diagrams are presented in the text to illustrate instances of charge embedded in various kinds of causal circumstances. In these diagrams, charge is given a spatiotemporal context by being plotted against an axis of space and an axis of time. Also explicitly depicted in the diagrams is the underlying receptive structure connecting instances of charge in time and space, producing a directed graph where receptive connections are the edges and instances of charge are the nodes.

    The following is a (crude) representation of what these diagrams look like in the text:

    Code (Text):
       t3 |  +
          |  ^
    t     |  |
    i     |  o
    m  t2 |  - o---> +
    e     |    
       t1 |  + o---o -
    The +s and -s are instances of charge located in space and time. The extended lines between them denote receptive connections binding them into causal nexii. These receptive connections create three distinct level-one natural individuals in this diagram. (In the text, boxes are drawn around the individuals to explicitly denote their presence.)

    The first individual, at time t1 (call this I1), is an individual with spatial breadth. The two 'o's on either end of the receptive connection represent the 'slots' in the receptivity into which the + and - 'fit.' The instances of charge in I1 are symmetrically connected, meaning that each receives causal constraint from the other. Notice that this is a causal relation existing across space rather than across time. Causal relationships are thought of as strictly temporal according to our common sense notions of causation, but this need not be the case in the more general theory of causal significance.

    The next individual, I2, is located at time slice t2, extending across space similarly to I1. A noteable difference is that the rightmost 'o' in the receptive connection has been replaced with an arrowhead. This signifies that there is an asymmetric causal link between the - and +. The + is receiving causal constraint from the -, but the - is not receiving causal constraint from the +.

    Finally, there is an individual I3 that stretches across time, from t2 to t3. I3 corresponds to the traditional notion of a temporally extended causal process. Notice that the - at t2 is a member of both I2 and I3; individuals can be bound to more than one instance of receptivity.

    Rather than reproduce diagrams like the one above for each illustrative example, instead I will use the more concise notation for natural individuals introduced in chapter 9. The general form of this notation for a symmetrically connected natural individual Im is [In-1.i.In-1.j...In-1.k]n.m. The brackets and dots represent Im's receptivity, which symetrically binds Im's component individuals, denoted as the 'In-1.i' terms. n is the level of nature at which Im exists, and the i, j, k, and m subscripts are labels used to refer to each distinct individual at each level of nature. For instance, I1 from the diagram above is written as [+0.1.-0.2]1.1 using this notation. A generic individual name can be replaced with its value in the notation in order to make its value explicit; for instance, if a charge I0.1 is positive, it can be written +0.1 to signifiy this fact. If its value is indeterminate, I will sometimes write it as ?0.1 in the following to emphasize its indeterminacy.

    In the case where component individuals are bound asymmetrically, we use an arrow (=>) in place of the dots, pointing from the constraining individual to the constrained individual. So, I2 from the diagram above would be written as [-0.3 => +0.4]1.2, and similarly I3 is written as [-0.3 => +0.5]1.3. Note that this notation does not differentiate between temporally and spatially extended individuals, and for this reason the examples that will be introduced below will be ambiguous about whether the causal processes involved are spatial or temporal, even though they are explicitly presented as one or the other in the text. However, this ambiguity will not matter for most of the examples' illustrative and theoretical purposes. For those examples where a spatiotemporal context can be helpful for one reason or another, I will explicitly provide one.

    The Character of Causal Processes: Tiers of Constraint

    First tier: causal laws. There is still some work to be done in constructing our toy world: We must specify a causal law that describes the compatibility relationships that obtain among instances of charge that are bound by a common receptivity. This will be a universal law that operates on each set of instances of charge that share a common level-one receptivity. The causal law determines which joint states for the effective properties in a nexus are permissible and which are impermissible. A simple causal law for this toy world is as follows: Each value of charge, + or -, must have an odd number of occurences in any natural individual where that value of charge occurs at all. (Note that the diagram above conforms to this causal law.)

    Causal laws, receptive structures, and effective properties combine to realize operations of causal significance. The causal law describes the general relations of compatibility for effective properties; receptivity creates an infrastructure that defines the scope of an effective property's causal significance for other sets of effective properties; and the independently possible values of effective properties occupying that receptive infrastructure constrain eachother directly, as described by the causal law. As Rosenberg sums it up:

    The process of causal constraint. Let us analyze how these principles apply to specific causal circumstances. Let's start with three instances of charge which are, as of yet, indeterminate. Call these C0.1, C0.2, and C0.3. Given no receptive context, there are eight potential joint states for these charges: {+,+,+}, {+,+,-}, {+,-,+}, {+,-,-}, {-,+,+}, {-,-,+}, {-,+,-}, and {-,-,-}. These are the charges' independently possible joint states. Now suppose that these instances of charge are bound up into the following receptive structures:

    I1.1: [?0.1.?0.2]1.1
    I1.2: [?0.2.?0.3]1.2

    Given a receptive context, causal laws can now operate. The manner in which causal laws operate is by placing constraints on effective properties' (EPs') independently possible joint states. The EPs themselves can only instantiate those values which are consistent with the joint states that are not filtered out by the causal law. In some cases, exclusion of certain joint states entails the exclusion of certain possible values for an EP, in which case the EP becomes more determinate.

    Recall that the causal law for this world is that the number of instantiations of a particular value of charge, + or -, within a level-one causal nexus must be either zero or odd. Thus, both I1.1 and I1.2 can only take on one of two states, either [+.-] or [-.+]; [+.+] and [-.-] are excluded from possibility by the causal law. Furthermore, note that the charge C0.2 is shared by both I1.1 and I1.2. As a consequence, it figures into the constraint relations of both individuals. In particular, whatever value it has in the one must be consistent with the value it has in the other, so (for instance) if I1.1 took on the determinate state [+0.1.-0.2], the only possible state left for I1.2 would be [-0.2.+0.3].

    Taking all this into consideration, the only possible joint states for the charges once they have been bound up in the particular way described by I1.1 and I1.2 are {+,-,+} and {-,+,-}. Six of their eight independently possible joint states have been filtered out by the causal law, in conjunction with the particular receptive structure they entered into. As it turns out, in this example that constraint on the joint states is still not sufficient to determine any particular value for any of the charges. According to the first joint state allowed by the causal law, ?0.1 can take on a + value, and according to the second it can take on a - value, and likewise for the other charges. Suppose for an instant that the causal law had been different, such that the only allowable joint states were {-,+,-} and {+,+,+}. In this case, the filtering of joint states would have forced C0.2 into the determinate value +, although C0.1 and C0.3 would have remained indeterminate.

    Tier 2: receptive structure. Notice that the structure of the receptive connection plays an important role in causal processes beyond just determining which effective properties come to have direct causal significance for eachother. The structure of receptivity can also make a difference to the manner in which effective properties are constrained. For instance, suppose the three charges were receptively bound within just one individual:

    I1.3: [C0.1.C0.2.C0.3]

    In this case, the possible joint states allowed by the causal law are different than those detailed above, as a direct consequence of the new receptive structure. The possible joint states of the charges for I1.3 are {+,+,+} and {-,-,-}, rather than {+,-,+} and {-,+,-} as above.

    Tier 3: independently determinate effective properties. Let's now consider the original causal situation described above, but this time with asymmetric receptive connections. That is, suppose the receptive structure existing among the three charges is as follows:

    I1.1': [+0.1 => -0.2]
    I1.2': [-0.2 => +0.3]

    Recall that if two individuals A and B have a symmetric receptive connection, then both receive causal constraint from eachother; on the other hand, if A and B have an asymmetric receptive connection, e.g. [A => B], then B receives causal constraint from A but not vice versa. In Rosenberg's formulation, all it means for two individuals to be asymmetrically connected is that the constraining individual is already determinate when considered independently of the nexus of which it is a member. (So, for instance, in an individual X of the form [A => B], we could say that A is determinate when considered independently of X.) The reasoning is that if an individual is already determinate, it cannot receive further causal constraint by definition, because it is already maximally constrained. On the other hand, an indeterminate individual is always receptive to further constraint, and so is always on the receiving end of receptive connections.

    Thus, the formulation for the two revised individuals above can be read as follows. The charge +0.1 is determinate when considered independently of I1.1' (perhaps it has been forced to take on the + value because of constraints placed on it by other charges in other causal nexii). In essence, it is a 'given' in this multiple constraint satisfaction problem. The causal law and receptive structure active here, in conjunction with the fixed value of +0.1, thus forces C0.2 to take on a - value. -0.2, then, is likewise determinate when considered independently of I1.2', and likewise forces C0.3 to take on a + value. The specific possibility space of values for effective properties given to a causal nexus, then, adds another tier of constraint to the space of possible values that can pass through the filter of causal laws in a given receptive structure. The more determinate the effective properties are when considered independently of a causal nexus, the fewer possible joint states there are, which in turn further constricts the possible values the effective properties can instantiate.

    Higher-level causation. The process of causal constraint described here for level 0 effective properties bound into level 1 individuals generalizes for higher-level individuals. Suppose we have the following level 1 individuals:

    I1.1: [C0.1.C0.2.C0.3]
    I1.2: [C0.4.C0.5]
    I1.3: [C0.4.C0.6]

    (Note that C0.4 is a member of both I1.2 and I1.3.) These can be receptively bound into a level 2 individual as follows:

    I2.1: [I1.1.I1.2.I1.3]

    The causal law on I2.1 can then act to exclude some of the independently possible joint states of the level 1 individuals, thus moving them and their constituents towards determinacy. Suppose that the causal law on level 2 individuals is a straightforward extension of that for level 1 individuals: i.e., the sum total of +s instantiated within the level 1 individuals bound within a level 2 individual must be either zero or odd, and likewise for the number of - values. The independently possible joint states for the level 1 individuals (also called the prior possibility space presented to I2.1) are:

    1) { [+.+.+]1.1, [-.+]1.2, [-.+]1.3 }
    2) { [-.-.-]1.1, [+.-]1.2, [+.-]1.3 }
    3) { [+.+.+]1.1, [+.-]1.2, [+.-]1.3 }
    4) { [-.-.-]1.1, [-.+]1.2, [-.+]1.3 }

    The causal law at work here eliminates 3) and 4) as potential joint states, thus constraining the space of the leve 1 individuals' possible effective states. An effective state for a level n individual I is defined as an ordered set of the level n-1 effective properties which are bound within I. The notation we have been using to describe level 1 individuals, then, is basically just a manner of writing their effective states; thus [+.-], [-.+], [+.+.+], and [+.-.-.+.-.....+] are some examples of what the effective state of a level 1 individual might look like. Notice that [+.-] and [-.+] are distinct effective states, because the ordering is different.

    The ordering matters because each ordered item represents a unique 'slot' in an instance of receptivity, and the outcome of causal constraint in a nexus is sensitive to specifications of which individuals are bound to which instances of receptivity. For instance, suppose we have a receptive structure of two overlapping level one receptivities, e.g. [C0.1.C0.2] and [C0.2.C0.3.C0.4]. C0.2 is a member of both individuals, and thus the value it takes on will affect the values of the other two charges. The two possible outcomes are [+.-0.2] and [-0.2.-.-], or [-.+0.2] and [+0.2.+.+]. Without specifying an ordering here, we could not determine whether the second individual should be [+.+.+] or [-.-.-], even given that the other two-place individual is already determinate.
    Last edited: May 12, 2005
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  3. May 11, 2005 #2


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    summary, part 2


    Metaphysical and epistemic determinism. Given this model of causation, we can differentiate between two kinds of determinism: metaphysical and epistemic. A metaphysically deterministic process is one whose individuals' constraint structures permit them to have only one possible effective state; i.e., the effective states of the individuals involved in the process are determinate. [+=>-] is an example of a metaphysically deterministic process. Metaphysically deterministic processes are such that, given sufficient knowledge of part of the process, other parts of the process can be known by inference. An epistemically deterministic individual is one that is not metaphysically deterministic, but whose character can be inferred given certain assumptions or background knowledge. For instance, [C0.1.C0.2] is not metaphysically deterministic, but it is epistemically deterministic; given knowledge of the causal law and receptive structure, we can deduce that a statement like "If C0.1 were positive, then C0.2 would have to be negative" must be true. Metaphysical determinism implies epistemic determinism, but not vice versa.

    Natural and causal laws. Suppose there is a long sequence of overlapping, two place receptivities binding instances of charge, where each charge is understood to occur at a particular point or duration in time. Such a process is depicted follows:

    [+0.1.-0.2], [-0.2.+0.3], [+0.3.-0.4], ...

    where each C0.i is understood to occur at some time ti. The effective character of this process, then, is essentially that the value of charge oscillates as a function of time. A natural law, like a law of physics, could be written to describe its oscillation as a function of time. Such a natural law, however, is not to be confused with the causal law that governs this process. The natural law describes the lawful regularity of instantiations of charge values over time, whereas the causal law describes the relationships of compatibility within the causal nexii in which the instances of charge are bound. The causal law explicitly describes the causal significance of the process, whereas the natural law only describes a regularity of property instantiation and is compatible with a deflationary Humean attitude about its causal character.

    Notice also that just being in possession of the natural law would be enough to allow us to infer the values of charge at various times in the past or future, given information about its value at a particular point or duration of time. Thus, the natural law is sufficient to subserve epistemic determinism.

    Immediate and mediate causal interactions. Suppose we have the following individuals:

    I1.1: [+0.1 => -0.2]
    I1.2: [+0.1 => -0.3]
    I1.3: [-0.2 => +0.4]

    A crude diagram of this set of individuals will be helpful for our purposes here. Let the vertical axis represent space and the horizontal axis, time:

    -0.2 => +0.4
    +0.1 => -0.3

    The thing to notice here is that -0.3 and +0.4 are forced to take on opposite values, even though there is no receptive connection between them. Indeed, if we extend the temporal processes in the diagram above with further overlapping two place receptivities, e.g.

    ... => +0.4 => -0.6 => +0.8 => ...

    ... => -0.3 => +0.5 => -0.7 => ...

    then we'd find that there is a natural law describing the regular oscillation of the two spatially separated charges in time, such that they must always have opposite values. We might say that the charges are responsive to eachother's values, but from the diagram it is clear that this responsiveness is not due to direct receptive connections between the two at any given instant. Rather, they are responsive to eachother because of a chain reaction of sorts that began with I1.1. The two values of charge in I1.1 were constrained to be different because of the various tiers of constraint in action in this world, and this difference between the charges was then propogated across time along two distinct and non-overlapping receptive paths.

    We can give an account of immediate and mediate causal interactions in terms of receptiveness and responsiveness. An immediate causal interaction between individuals is one in which those individuals directly place causal constraint on eachother by means of a shared receptivity. In the above example, I1.1 is the only immediate causal interaction occurring across space. A mediate causal interaction between individuals is one in which those individuals are responsive to eachother (in the sense of 'responsive' used above), but are not receptive to eachother. In the above example, the regular opposition of the charges' values at each point in time is not the result of an immediate causal interaction, but rather is mediate. In particular, it is mediated by, or through, I1.1.

    (technical note: For those reading the book, note there is a small error in diagram (e). Only one of the receptive connections here is presented as being asymmetric, when in actuality, they should all be asymmetric.)

    Emergent effective properties and causal laws. Recall that an individual In's effective state is defined as an ordered set of the effective properties belonging to its In-1 constituents. An interesting result from this theory is that individuals with distinct effective states can have the same effective properties, where an individual In's effective property is defined as the contribution it makes to the constraint structure on other level n individuals within a level n+1 nexus. For instance, [+.-] and [-.+] are two level one individuals with distinct effective states. Recall that the causal law for level 2 individuals defined above defines the sum of + and - instantiations in level 1 individuals as the relevant feature over which the constraint structure operates. Because [+.-] and [-.+] have the same number of +s and -s, they contribute the same constraint to other level 1 individuals within a level 2 nexus, and thus they instantiate the same effective property.

    In general, an emergent effective property for a level n individual is defined as a multiply realizable contribution to the constraint structure on a level n+1 nexus. Two distinct effective states s1 and s2 form a realization base for an emergent effective property within an individual In+1 if and only if it is always possible to replace an instance of s1 with s2 within In+1, while holding all other conditions constant, without changing the set of possible states for the other individuals bound within In+1. In other words, if the difference between s1 and s2 does not make a difference to the total constraint structure of a nexus, then those effective states instantiate the same effective property within that nexus. s1 and s2 realize the same effective property tout court if they place the same effective constraint within all possible In+1 individuals. In the toy world we have been analyzing, [+.-] and [-.+] realize the same effective property tout court.

    Thus construed, effective properties are defined in informational terms-- a difference that makes a difference in a certain causal context-- rather than in terms of lower-level constitution. The sort of emergent effective properties described here would be at least partially resistant to a reductionist analysis, since an emergent property is consistent with the existence of more than one type of lower-level constitution.

    This theory also permits the existence of strongly emergent causal laws. In the above examples, we defined the causal law on level 2 individuals to be a straightforward continuation of the causal law on level 1 individuals, but it need not have been that way. For instance, we could have defined a causal law on level 2 individuals such that the number of + and - charges, respectively, found in the level 1 constituents must be either zero or even (rather than zero or odd). This would be a strongly emergent causal law, in the sense that it is consistent with the level 1 causal law, but is not entailed by it.

    Such strongly emergent causal laws could also ground the existence of strongly emergent effective properties. Because the causal law on a nexus establishes a constraint structure by delineating what features of bound individuals' effective states are subject to relations of compatibility, in essence it is the causal law that defines what effective properties exist at a level of nature and how they interact. Such a law could quantify over sets of lower level properties, treating them as a fundamentally new kind of singular, higher level effective property. For instance, a strongly emergent level 2 causal law in our toy world might define compatibility relationships for pairs of level 0 effective properties bound within level 1 individuals, and describe compatibility relationships for those pairs. In the text, such a law is provided. It individuates the sequence pair [...+.-...] as having one kind of compatibility constraint, and maps the other three sequence pairs to another kind of compatibility constraint. Thus, the causal law subserves the existence of two strongly emergent effective properties-- one is realized by the [...+.-...] sequence, and the other has the remaining possible sequence pairs as its realization base.

    Epiphenomenal individuals. Rosenberg characterizes epiphenomenal individuals in the context of this theory as ones whose existence does not constrain the prior possibility space of the lower-level individuals they bind together. For instance, the level 2 individual [ [+.-] . [+.-] . [+.-] ] is epiphenomenal, because the set of possible joint states of the three level one individuals it binds is not constrained at all by its presence. Essentially, it does no effective causal work.
  4. May 11, 2005 #3


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    summary, part 3

    Wider Metaphysical Issues

    Possibility and actuality. The theory of causation we have been discussing identifies causal significance with an operation on a space of possibilities. But what is the metaphysical status of this space of possibilities? In order for any real causal work to be done, it seems the space of possibilities upon which causation operates must also, in some sense, be real. More formally, we can say that the following two statements are logically inconsistent:

    1. Possibilities are just fictional constructs. (actualism)
    2. Real powers of causal production/constraint exist in the world. (realism about causation)

    If we take (1) to be true, then we must likewise take any account of causation that appeals to possibilities and probabilities to be merely a convenient explanitory construct, rather than a description of some objectively existing natural relation. So (1) and (2) cannot both be true at once; if we accept one, we must reject the other. (This conclusion does not follow for a purely deterministic account of causation, but Rosenberg holds that an adequate theory of causation must cover the nondeterministic cases.)

    Combining this argument with previous arguments for realism about causation, we arrive at a composite argument against actualism. Recall the arguments from chapter 8: If we are not realists about causation, then we must lapse into a severe solipsism of the present moment, and we also cannot account for the unity of the world. Therefore, we should be realists about causation. Since realism about causation is inconsistent with actualism, we should reject actualism and be realists about possibility, lest we fall prey to the profound metaphysical and epistemological problems presented in chapter 8.

    In particular, the kind of realism about possibility we need in order to be realists about causation is an abstract modal realism, where possibility and actuality are different modes of existence and there is some metaphysical process of becoming that connects the two. Abstract modal realism is to be contrasted with concrete modal realism, a view which holds that all possibilities enjoy the same kind of (concrete) existence, and the actual is only contrasted with the possible via indexical facts. Note that on an abstract modal realist view, the actual is not identified with all that is real, and likewise that the words 'possible' and 'abstract' denote a kind of existence, rather than non-existence. The broad metaphysical picture is one in which the actual, natural world stands at one pole of existence, contrasted against a background of possibility that sits at the other pole. If this is what the world is like, then we cannot fully understand the natural world without understanding its metaphysical backdrop of possibility and the relationship between the two.

    Rosenberg proposes a model for understanding this broad metaphysical picture of possibility and actuality-- and later, facts about space, time, and the unity of the world-- but cautions that his proposals are speculative and tentative, only taking the first steps towards exploring a wider space of possible ways of understanding these issues. His primary intent is not to give a definitive account of these issues, but rather to assert that these are topics worth investigating, to point along a possible direction of inquiry, and ultimately to inspire further investigation in these matters.

    On Rosenberg's proposal, the actual, natural world exists against a metaphysical background of possibility. The actual and possible embody two modes of existence, each of which can be characterized by a set of closely related terms: on one pole is the abstract, potential, indeterminate, and incomplete, and on the other is the concrete, actual, determinate, and complete. ('Complete' and 'incomplete' are used here in the sense introduced in chapter 9: an instance of receptivity is complete iff all its slots are saturated; an effective property is complete iff it is in a fully determinate state; and a compound individual (level 1 or higher) is complete iff all its component individuals are complete.) The actual and its backdrop of possibility are related by a process of becoming, whereby an abstract individual 'moves' through a space of possibility, from pure potentiality (maximal indeterminateness) to actualization (maximal determinateness). Rosenberg thinks the metric on a space of possibility would be degree of determinateness, although he concedes this is an issue that needs further treatment. (NB: It is important to understand that this process of becoming is not temporal; it is not a change relative to time, but rather a connected series of states in a space of possibility.)

    It is useful to characterize the process of becoming in terms of contextualization, where context is provided by receptive connections. To be fully abstract and indeterminate is to be completely free of context and capable of being placed in a range of possible contexts; to be concrete and determinate is to be fully immersed in a definite context. Inbetween these two extemes lies a gradient where abstractness and concreteness are a matter of degree, corresponding to the degree to which an individual is immersed in a context. An individual 'traverses' this gradient from pure potentiality to actuality by receptively binding to other individuals, thus taking on a fuller context in the causal mesh. With each new receptive binding, an individual becomes part of a greater context-- that is, it becomes subject to new sets of causal constraints, thus making it more determinate.

    The following list of definitions provides a working vocabulary for talking about this model and also nicely encapsulates its basics:

    An important consequence of this view is that there is more to the nature of an individual than its actual expression in nature. We should not identify an individual with its hit, but rather with its entire ingression-- the hit is just the tip of the metaphysical iceberg, so to speak. In addition to an individual's definite state in a concrete context, we should also take it to have components of varying indeterminateness and context independence. These indefinite components describe the individual's potentials, and correspond to points along its ingression from pure potentiality to actuality.

    Space, time, and the unity of the world. Explaining the unity of the world emerged as a problem for Humean views in chapter 8, but it is handled readily by the theory of causal significance: Unity within a level of nature is achieved by overlapping receptive connections (i.e., individuals that are bound to more than one instance of receptivity), and unity across levels is achieved by the receptive binding of level n individuals into a novel level n+1 individual. The unity of the world as a whole is constituted by the causal closure of the world's receptive networks within and across all levels of nature.

    In order to explain the direction of time, Rosenberg proposes a bolder move that turns some of our common sense notions of causation, space, and time on their heads. Rather than assuming that the causal mesh exists in a more fundamental backdrop of space and time, Rosenberg suggests that we can reduce spatiotemporal facts themselves to facts about the structure of the causal mesh. The motto for this view is, "there is a causality condition on locality, not a locality condition on causality" (p. 157). A related motto, courtesy of Brian Cantwell Smith, is: "Distance is what these is no action at."

    Once we take up this line of inquiry, the direction of time seems to find a natural explanation by way of asymmetric causal connections. Let us define a cascade as a series of individuals with overlapping, asymmetric causal connections. A simple example of a cascade is the following:

    ... => +0.1 => -0.2 => +0.3 => ...

    Each charge in this example is a member of two nexii: one in which it is on the constraining end of a connection, and another in which it is being constrained (e.g., -0.2 is a member of the following nexii, one in which it is unilaterally constrained and the other in which it is unilaterally constraining: [+0.1 => -0.2] and [-0.2 => +0.3]). This regular pattern of unilateral causal constraint, subserved by this unique type of asymmetric receptive structure, is what is proposed to underlie the direction of time.

    From here we can see how time itself might arise from the causal mesh. Recall that an asymmetric connection in a nexus N is one in which the constraining individual is already determinate when considered independently of N. For any given individual I that is bound within a cascade, then, I's past should consist of those individuals that lie 'downstream' from it in its cascade-- i.e., those individuals which are already determinate when considered independently of it. Likewise, I's future should consist of those individuals that lie 'upstream' from it in its cascade-- i.e., those individuals for which I is fixed. Time slices should correspond to the occurence of each individual bound within a cascade (so, e.g., -0.2 in the cascade above demarcates a distinct instant or duration of time).

    Rosenberg's proposal for the manner in which space is constructed from the causal mesh is a bit more complicated. Given an individual I in a cascade as a reference point, we first need a method whereby we could determine what other individuals occupy I's time slice just by using facts about the structure of the causal mesh. Given that information, we need to find a way to recover facts about spatial distance and direction, again just by using the causal facts.

    I will reproduce the rules Rosenberg proposes for making these constructions, so as not to sacrifice any of their rigor, and then give brief explanations of each. Given an individual I0.r bound within a cascade as a reference point, an individual I0.j occupies I0.r's time slice if and only if

    (1) picks out the set S of individuals to which I0.r is symmetrically bound. (2) picks out the set T of individuals that are symmetrically bound to those individuals in S, and likewise the set U of individuals that are symmetrically bound to those in T, and so forth. (3) essentially states that if it takes I0.r some time t to be able to causally influence an individual I0.d, and if it likewise takes I0.j the same amount of time t to be able to causally influence I0.d, then I0.r and I0.j must occupy the same time slice. Because we have already identified the passage of time with the occurrence of successive individuals bound within a cascade, we can measure t by counting the number of asymmetric links that lie between I0.r and I0.d.

    Having identified the individuals that occupy I0.r's time slice, we need to recover facts about the spatial locations of these individuals relative to I0.r. In particular, we need to be able to determine distances, directions, and neighbor relations. Rosenberg proposes the following rules for finding I0.r's neighbors, assuming that space is a discrete grid:

    (1) allows for point-like entities that can simultaneously have many properties; (2) allows for spatial extension; and (3) ensures that only those individuals that figure into I0.r's immediate causal future are its spatial neighbors. In effect, what we have done here is to construct locality by reference to immediate causal significance through time, thus making good on the statement that there is a causality condition on locality rather than vice versa. It follows that the spatial distance between two individuals is equivalent to their causal distance over time, where causal distance is understood in the same general manner as causal equidistance, as used above. The more asymmetric links in a cascade that separate two individuals' causal significance for some future individual-- i.e., the more time it takes for them to be able to exert causal influence on a common target-- the further apart they are in space.

    Rosenberg considers that spatial direction could be established by reference to signaling paths, where "signal" is defined as "a change to the effective state of an individual hit or hits within a cascade that can be propogated in some way to another cascade" (p. 216). A signaling path, then, would be the specific individuals and receptive connections in the causal mesh-- or, the specific nodes and edges in the directed graph-- through which the change in effective state propogates. Each neighbor of I0.r that could form the basis of a signaling path beginning from I0.r would form the basis of a spatial direction.
    Last edited: May 14, 2005
  5. May 14, 2005 #4


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    One very interesting consequence of the way the theory of causal significance is formulated is that it allows for higher-level individuals to be determinate while their lower level constituents remain indeterminate. The theoretical work behind this is found in part 2 of the ch. 10 summary above, in the section titled "Emergent effective properties and causal laws." In the text, this discussion can be found on pages 199-203 and 208-210. Basically, the reasoning is

    1. an effective property of an individual is a contribution that individual's effective state makes to the constraint structure of the causal nexus within which it is bound;
    2. in certain circumstances, more than one effective state could realize the same contribution to a nexus's constraint structure;
    3. therefore, there can be a many-to-one function from lower-level effective states to higher-level effective states.

    Thus, according to the theory, a level n individual could have a determinate effective state S that is compatible with the existence of (say) two lower-level effective states s1 and s2. If there were no further constraints on s1 and s2, they could remain in the indeterminate state "s1 or s2," or equivalently, "potentially s1 and potentially s2 and not potentially any other state," even as the higher-level individual they help constitute is determinate. The general principle here is that high-level determinateness need not imply determinateness on the lower levels; the lower levels need only be determinate to the degree that they are compatible with the higher-level determinateness.

    There are obvious and striking parallels here with quantum mechanics. The world is determinate on the macro-level, but on the quantum scale we can have a superposition of possible states, apparently very much like the aforementioned "potentially s1 and potentially s2 and not potentially any other state." On some interpretations of QM, we should be abstract modal realists about this superposition (certainly Rosenberg would be, following the arguments in ch. 10). The repeated parallels with the theory of causal significance and the logic of QM is worth noting. On the one hand, it raises our confidence that there really might be something to the theory of causal significance after all. On the other, it emphasizes deficiencies in our ordinary notions of causal responsibility, which seem to be violated by the counterintuitive logic of QM on account of being too restrictive, having too many parameters fixed on what could be a more general account of causation (see ch. 9).

    The preceding even seems to offer an insight which might prove fruitful in approaches to QM. It suggests, as Rosenberg calls it, a middle ground in accounting for how the quantum scale indeterminacy could exist simultaneously with macro scale determinateness. Perhaps it is something like what the theory of causal significance predicts; perhaps it really can be the case that indeterminateness on the small scale can be completely compatible with determinateness on the large scale, without something like collapse of the wavefunction needing to be invoked-- in spite of how counterintuitive that might seem. If nothing else-- even if the theory of causal significance is false-- we have a story that makes rational sense of how this seemingly contradictory state of affairs could be, which in itself is an impressive feat that could spur further insights.
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  6. May 14, 2005 #5


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    I also find Rosenberg's proposal for a reduction of spatiotemporal facts to causal facts to be quite interesting and prima facie plausible; however, I recognize that my lack of a high level education in physics prevents me from making both further insights that might build on the model, and sharp critiques that might detract from it. I'd appreciate if anyone with a strong working knowledge of general relativity and/or background independent approaches to quantum gravity could chime in their thoughts. How compatible is Rosenberg's approach to these physical models of spacetime? Can you see any areas where Rosenberg's model could be enriched by a more extended treatment? Can you identify any ideas that seem to be inconsistent with well established physical theory?
    Last edited: May 14, 2005
  7. May 16, 2005 #6
    Hypnagogue, perhaps you are not strong in quantum physiscs, but you do really know how to expose philosophy (or whatever it is what we are doing here). I find brilliant your explanations of the chapters of the book, and at least for me extremely helpful to better understand Rosenberg's ideas.

    I also find quite striking the sort of convergence of some points of Rosenberg's causal significance with some controversial and deep aspects arising from the interpretation of quantum theory, and of the attemps to unify general relativity (GR) and quantum theory (QT), in particular those dealing with spacetime either as a background for the theory, or as an emergence within the theory itself. And, of course, for Rosenberg, while proposing a very comprehensive theory, the idea of a preestablished spacetime background can't be satisfifying at all. I think that one of the main isues of loop quantum gravity, for instance, deals precisely with the attempt of developing spacetime as a consequence of the theory itself.

    I am really far myself of having a good understanding of quantum physics, but I try to do some reading about, and perhaps within some years (I prefer not to think how many), I may have some grasp of it. At this point, I dare to recommend some readings that I find very insightful, and in some parts resonating with the ideas in Rosenberg's book. Or so it seems to me. They correspond to the interpretation of QT by Ulrich Mohroff, which he has named somewhere "The Pondicherry Interpretation" of QT.
    I find that he has recently open a web page where some of his articles are collected:

    He is a vedantist (one of the branchs of hindu philosophy), but this shouldn't make think his as an unortodox physics point of view. On the contrary, I've seem very few so clear and rigorous explanations of QT. But the fact is that QT is pointing to a failure of our intuitive ideas about space and time, and Mohrhoff reveals this by taking very seriously that they are relational properties depending not just for their value but for their existence itself upon what happens in the rest of the world. Other subjects also adressed by Mohrhoff, for instance, would be the misleading consideration of QT as involving a possible explanation of consciousness; the epistemic cut among mental causation and physical causation; the displaying of "reality" as an "up to bottom" process, rather than a "bottom up" one as the way in which science seems to be engaged in; etc.

    But I don't want to take this post too far from the real content of this thread, that is Rosenberg's book. I just thought that it could be helpful to complement some of the ideas we are encountering
    while reading it, as you suggested, Hypna. Hope it hepls.
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  8. May 16, 2005 #7
    Sorry about that, the right link is:
    http://www.flyservers.com/members5/thisquantumworld.com/whois.htm [Broken]
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  9. May 20, 2005 #8
    Questions to Rosenberg’s proposal about the causal foundation of time and space

    Thank you Hynagogue for your summary and questions, I'm also waiting for a reply of a physicist. Some questions:

    Are there special effective and receptive properties that underlie time and space? In the toy world there are charge cascades, because charge is the single effective property. It seems that the collection of all asymmetric causal laws (i.e. determinate effective properties and asymmetric receptive constraints) underlie time and that all determinable effective properties together with all symmetric receptive constrains underlie space. But do we not need a more specific proposal (at least when specifying the directions in space)?

    Time and space are introduced in one level of nature, level-zero individuals. Are there other spaces and times on other levels?
    Suppose there are some: How do we understand the objective scientific measure of time and space? On which level could the human access time and space occur?
    Suppose space and time exist only in level-zero individuals: How can we have access to them?
  10. May 21, 2005 #9


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    Rosenberg doesn't mention anything about special kinds of receptivities that would underlie space and time. Effective properties only figure in to the extent that they determine when a receptive connection is symmetric or asymmetric-- i.e., what matters is just degree of determinateness. So special effective properties aren't needed either. But I don't see why this is a problem-- why would special kinds of properties be needed to ground facts about spacetime? In what way would they need to be special?

    BTW, Rosenberg doesn't identify time with the set of all asymmetric connections-- he supposes that time supervenes on cascades, long strings of overlapping asymmetric connections. I imagine it could be the case that there exist asymmetric connections that are not found in cascades, and thus do not figure into facts about time.

    This is a good question. As you say, Rosenberg presents it as if level-zero receptivities determine the facts about space and time for all levels, but it seems this model could be consistent with a number of co-existing spacetimes, corresponding to receptive structures at different levels of nature. I don't think this is a necessary consequence, though; another interpretation or formulation might describe one coherent spacetime whose facts are determined by receptive structures at many different levels. The matter of how levels of nature factor into the construction of spacetime is certainly one of the issues left ambiguous by Rosenberg (perhaps on purpose).

    I do think that the construction of a space and time would have to be something that extends across levels, though. For instance, in the discussion on possibility and actuality, Rosenberg mentions that the general principles of his model of causation allow for a world whose lower level individuals never reach determinacy, even though the high level individuals do. In such a world, there could be no asymmetric connections on the indeterminate lower levels, and thus there could be no basis for time on these levels. Temporal ordering could only occur on the levels of nature that have networks of asymmetric connections on a wide scale. Depending on one's interpretation, it seems this could imply that the temporal ordering of the lower level individuals is enforced by higher-level structure, or even that the lower level inherently has no temporal relations. Either way, it's clear that facts about receptive connections across many levels of nature would be needed to tell the whole story about such a world's space and time.
    Last edited: May 21, 2005
  11. May 26, 2005 #10
    determinate but incomplete individuals

    thank you for your good proposals to understand the supervenience of time and space. A conceptual question: The graphic p. 213 illustrates Rosenberg’s thesis that

    (Actual implies) Determinate implies Complete

    But there are higher level individuals that are determinate but not complete. Completeness implies that the sub-individuals of a higher level individual are determinate but determination of the higher level individual requires no determination of the sub-individuals.
    Rosenberg’s concepts also imply that an undetermined quantum state is no part of an actual world (because it is no hit). Are all quantum states in the actual world determined from a higher level of receptivity, perhaps above the human level, so that something in the actual world exists at the quantum level? (I would accept that there is no time as usual in the quantum sphere but is this sphere really not actual?)
  12. May 27, 2005 #11


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    You are correct, this is an error in the text; if a high-level individual's effective state is determinate, this does not strictly imply that the effective states of its constituent individuals are also determinate. You can mentally replace the word "implies" with the weaker "indicates"-- if we discover that a given high-level individual is determinate, that might constitute suggestive evidence that its constituents are also determinate, but this evidence alone would not be conclusive.

    I think this theory should be taken to imply that indeterminate quantum states do not, in fact, exist as part of the actual world. This result is not as counterintuitive as it might seem on first glance, though, and is actually rather tautological. An "actual world" is just defined as a maximal set of interconnected hits, so it follows by definition that indeterminate individuals are not to be considered part of an actual world; they are individuals that have not fully ingressed. Nonetheless, the actual world is still richly interconnected to its metaphysical backdrop of possibility, so indeterminate individuals (such as indeterminate quantum wavicles) could still exert and receive causal influence from the actual world by means of receptive connections.

    A useful metaphor for thinking about this is as follows: Imagine a huge iceberg floating in an ocean. The iceberg itself represents a large causal mesh of receptively bound individuals, and the surrounding space represents the metaphysical possibility space. The vertical axis defines an ascending gradient of determinateness, such that any part of the iceberg below the surface of the ocean is indeterminate, and any part of the iceberg above the surface is determinate.

    On this metaphor, the part of the iceberg jutting above the surface represents an actual world, and the part below, its metaphyiscal backdrop of possibility. So there is a clear demarcation of the actual world from the possible, and this demarcation is not arbitrary, but rather grounded on an objective feature of nature. Nonetheless, this does not imply that the two regions are causally or even existentially sundered. Although from the surface one can only see the tip of the iceberg (the actual world), it is nonetheless richly interconnected to its submerged counterpart (the backdrop of possibility); indeed, the two are parts of the same whole, and they hold direct causal significance for eachother.

    If the iceberg were to float upwards, its movement would represent an ingression whereby the newly emerged portions of the iceberg have become determinate, and thus part of the actual world. Having emerged from the water, the once obscured portions of the iceberg could now be observed directly-- this is analogous to the process of 'measurement' in QM whereby an indeterminate quantum state becomes determinate upon being measured. Short of lifting the iceberg upward, we could just observe the visible tip in order to infer facts about the region sitting below the surface; likewise, we have been able to infer facts about indeterminate quantum states by observing determinate states of affairs in the actual world.
  13. May 28, 2005 #12
    Hi, Hypnagogue, Tychic.
    I have some problems with the characterization of an individual. Considering the most general definition of individual: "any set of natural individuals of level n bound into a completed receptive connection constitutes a natural individual of level n+1", and the subsequent of hit as: "the point of an individual's ingression at which it is complete", the problem that arises to me is that the character of an individual , or its hit, is determined by the whole web of receptive properties. I understand that there can be indeterminateness of the sub-individuals, but as soon as we talk about a particular individual in a particular level, it must be determinate. But this determination, in my view, is only possible from the standpoint of knowing all its receptive properties. And that, I think, is a metaphysical standpoint. From an epistemical point of view, we dont'n have access but to certain natural laws, actualizations or continuations of those receptive properties, hints of them so to say, but not real receptive properties as such.
    Applying Hypnagogue's metaphor of the iceberg, we could also think of the web of receptive properties and causal laws as the iceberg, and the natural laws as the part of the iceberg that we actually see. But, to characterize an individual as such, it seems to me, from the definitions, that we should have to do it from the metaphysical standpoint (seeing the whole iceberg), not just from the epistemical standpoint (the visible iceberg).
    My point is, how at a particular level we can say "this" or "that" constitute an individual. I think this is also related to Tychic's questions about the actuality of quantum states or of two qualitative identical spheres as individuals.
  14. May 29, 2005 #13


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    Not necessarily-- we can talk about indeterminate quantum states, after all.

    You're correct to point out that there are epistemic problems with knowing about receptive properties. They can't be observed directly (only effective properties can be observed in the empirical sense per the arguments in chapter 9), so we could only try to infer things about their existence and character. You're also correct to point out that we would need a detailed account of the receptive aspects of causation in natural phenomena in order to create a full account of natural individuals.

    Rosenberg discusses recepetivity and its relationship to the physical world in more depth in chapter 11, and the issue of discovering the character of receptive connections and natural individuals in the world in chapter 14 (particularly sections 14.3 and 14.4). The basic idea behind discovering what natural individuals exist in nature is to find physical clues that indicate the sort of causal relations featured in a high-level causal nexus. A high-level natural individual would be a system whose component states depend upon global constraint conditions on the system as a whole. Coherent quantum systems and systems featuring rich feedback mechanisms are proposed to be two kinds of systems meeting this requirement, and thus two kinds of systems that might constitute high-level natural individuals in the world. This issue is discussed in more detail in chapter 14.
  15. May 29, 2005 #14
    Yes, you are right Hypnagogue. I didn't express it well, perhaps I should have said individuals from the point of view of an actual world,
    I think it is again the same doubt, the indeterminate quantum state would belong, as an individual to the metaphysical space of possibilities, which I think it is outside of our epistemic acces. My problem is with the identification of individuals in an actual world. But, as you say, receptivity and its connection with the physical world is adressed in next chapters. Sorry, I must admit I haven't read so far.
  16. May 29, 2005 #15


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    If it were completely beyond our epistemic access, how could we have formulated a successful quantum theory? I think there's clear precedent for a successful study of the non-determinate aspects of the world.

    No problem, these are good questions and it's natural to ask them at this point. I'm just deferring heavy discussion until we get to the parts of the book that discuss these issues in more detail.
  17. May 30, 2005 #16
    Universals in possibility space?

    Hi antfm,
    nice that you are joining to our possibility-actuality discussion. I also like Hypnagogue’s iceberg metaphor. (Rosenberg himself is talking about a well that is widening in the space of possibility. See p. 212-3.)

    I think that causal laws and receptivities are not the only things lying in space of possibility. Each grasping of an individual in a theory abstracts from the causal context and grasps only an abstract individual. (Exception: individuals in a determined state when considered independently, but I suppose these are very rare if there are some at all.)
    In this context it is pleasant that Rosenberg avoids the concept of a particular (concrete object) in the book. This makes sense because (i) only the hit, but not the individual is concrete and because (ii) there are individuals without a hit.
    I think Rosenberg’s theory of ingression offers a good ontological place for universals: as determinable effective properties and as certain sortals – the latter corresponding to receptive relations.

    I like this story but the bad association of the metaphors of the iceberg and the well is that an universal (and therefore an abstract individual) can be instantiated and “ingressed” more than once, see the picture in Rosenberg, p. 214.

    A further question: Do you think that quantum measurment could need cross-level receptivity?
  18. May 31, 2005 #17
    Hi Tychic,
    Thanks for welcoming me to the discussion but I'm afraid I can't be of much help. I'm interested in Rosenberg's theory, but as a simple pedestrian. My backgroud is not too good, and reading time and PF lurking too short. I appreciate very much the discussion you are having here. It's being very heplful to improve my understanding of concepts and ideas in Rosenber's book.

    I agree with your view of the space of possibilities, and also find significant that Rosenberg mantains a very open view about concrete objects in an actual world. I think it is much more comprehensive to stick to the concept of the hit, as the tip of an ingression, for our epistemic acces to an individual, rather than to the individual proper.
    I don't know if the idea of universals that you mention fits Rosenberg's scheme. Perhaps you could expand this point a bit more.

    About physical theories and natural laws, Hypnagogue cites two, in particular, as systems that could very well exemplify the characterizations of individuals in the actual world:
    We will consider them in more detail in next chapters, I hope.

    About this point and quantum theory (QT), concretely, that we have already mentioned in the discussion, Rosenberg's proposal seems also very open and uncommited to a particular interpretation of QT, what in my opinion stregthens his position.
    As Hypnagogue says as response to one of my objections:
    What I think is an importantant point. QT is very successful, but it is so in its practical predictive aspect, and it is very controversial and varied in its interpretational aspect. (I recall famous Feynmann's dictums about QT: "nobody understands it", or "shut up, and calculate"), but as Hypnagogue signals, Rosenberg is precisely using that direction towards which QT seems to be pointing: the failure of our intuitive understanding (not of the epistemic acces, as I suggested) of the actual world.
    Rosenberg could be using that interpretive failure as a pointer to a deeper level of understanding of an actual world, without the necessity of commiting to a particular interpretation. Physic theories can be enlarged, honed, improved, but they can't finally give the complete account of an actual world and its causal background. But I still don't see clearly how that epistemic gap can ve handled.

    Another point related that you mention is the question about measurement, or observation in general. This has been adressed from inside QT itself (I don't know how successfully) with the theory of decoherence, for instance. But I think that from Rosenberg's description perhaps we should rather treat it, as counterintuitive as it may seem, as another tie of receptive properties among observer and observed, and as such as a new actualization of an individual's ingression in the actual world.

    There are some more points that you introduce. For example, the one about sortals. You are giving me a hard time (in the good sense) revising those concepts. But I think you are right and they might be relevant to the discussion. Perhaps you could also, if you feel like it, expand those ideas a bit more.
  19. May 31, 2005 #18
    Thank you for the good words, antfm. I also appreciate this discussion with you and Hypnagogue and I will try to clarify my position. Happy belated birthday to you, Hypnagogue, I wish that you can keep hold of your courtesy in all your activities!

    I think our epistemic access to an object is not only through the properties of the hit (=the concrete effective properties). What bares us from supposing that (i) the more abstract effective properties do affect us (because they are also part of the individual) and (ii) also the receptive property that enables us to think of this thing as one thing (instead of a plurality of “smaller” things that fill the space)? It is one thing because it is as a whole in other relations to its context as a similar plurality of “smaller” things.
    But I guess this proposal neglects too much the difference between epistememology and ontology. I’m note sure of this.

    My thoughts about universals and sortals:

    Rosenberg’s approximates the concepts of
    - concrete and determinate
    - abstract and determinable
    (Other authors make other discriminations of concrete and abstract: p.e. the abstract is not in space or the abstract cannot exist in itself. These discriminations correspond to other concepts of abstract and concrete.)
    Rosenberg’s distinction between abstract and concrete (also) does not correspond to the distinction between universal (=something repeatable) and particular. Each concrete entity has its particular part (=the hit) and its universal part (=the rest of the iceberg).
    It is possible to isolate some parts of the iceberg below the surface of the ocean. We do this when we speak of an uncontextualized determinable, an abstract effective property or an unsaturated receptive property. In the former case I would propose to speak of an universal, in the latter of a natural kind (= an ontological sortal). An uncontextualized determinable can be determined/ actualized in many contexts. I think this actualization is a kind of instantiation. Rosenberg’s introduction of potentiality and possible world comprises multiple actualization and thus instantiation. (See the definitions of page 211, cited in your chapter précis)
    --- Attention: The misleading aspect in the characterization of abstract properties as universals is that each abstract property exists only once in the possibility space (of all worlds) and is in this sence no abstract property is repeatable.
  20. Jun 2, 2005 #19
    Hi Tychic. Many thanks for sharing your thoughts.

    I think I see the clasification that you propose. It makes a lot of sense to me. But I do not see it as the route that Rosenberg has taken. What is your aim when proposing this clasification? Do you think it covers some aspect that is not clear in Rosenberg's proposal?.

    Still, I am a bit confussed with the identification abstract effective property/universal. How would you solve the contradicting point that they could be ingressed more than once?

    I'd also appreciate your view about the quantum measurement problem according to Rosenberg's scheme. I think it's relevant at this point.

    Too many questions, I know. But don't feel commited to answer. I find you ideas very interesting. Don't want to misunderstand them.
  21. Jun 2, 2005 #20
    Antfm, thank you for your questions. I’m not sure whether or not there are many mistakes and misunderstanding in my argumentation.
    With my classification I wanted to clarify my introduction of the concepts of sortals and universals, which marks of the limits of the metaphor of the iceberg. Rosenberg asserts that his theory has „consequences for discussions of […] Platonism“ (p. 273) which interested readers could "consider for themselves". I do this but I also follow from the mention of Platonism that not only abstract properties but also universals have their place in his theory and also not only natural individuals but also natural kinds.

    To clarify my proposal: Take A and B as two different individuals on the same level whose hits do not overlap. I would say that one point P below the surface of iceberg A can be part of iceberg B (while P staying on the same level of depth). I think that it is the same abstract effective property P that takes part in the ingression of A and B.
    I do not find this thesis in the book, but I think this could support to interpret Hypnagogue's thesis, that individuation is no ontological problem. (Abstract properties below the surface of determination exist only once and the individuation on the concrete level is wholly managed of the context.)

    Antfm, I do see no contradiction, please tell me if there remains a contradiction in this proposal?

    I guess your contradiction is the following: The unmeasured quantum states would be the same in all similar experimental settings if one takes them as universals.

    I answer: Yes insofar as there are universals. No insofar the undetermined quantum states are bounded in locality (it is not necessary that they are bounded to one place but only a space of possible places). And this may be done by additional abstract properties that forbid the collocation in the possibility space of the undetermined property bundles. The constraint to fill this and only this space region is an abstract property that can be instantiated many times. I hope this is a plausible way around the contradiction.

    I do not know much about decoherence. Does this physical phenomenon contradict to my solution?

    I want to add that I assent to your and Hypnagogues interpretation of Rosenberg’s handling with quantum physics. The openness to many interpretations is natural with his introduction of causal significance. You are right in the following comment

    I’m not sure whether it makes sense in physics to speak of entangled electrons as an individual. They have not to be individuals, but I would like it for the simplicity of the theory that there could be at least candidates for individuals on the quantum level. Do you have some proposals?
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