A simpler argument about essentially ordered series

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In the previous post I explained what an essentially ordered series is and gave an argument to the effect that every such series must have a first member. While I still think the argument works, discussions about the post with others have led me to realize that we can give a considerably simpler argument for the same conclusion.

Start with a case of one thing causally influencing another, say Alice picking up her mug from the table. The thing doing the causing (Alice) is the agent and the thing being influenced (the mug) is the patient. Both the agent and the patient contribute something that enables the causation to occur, namely the actuality in the agent and the potential in the patient,[1] and the causation itself consists in these contributions coming together in such a way that the potential can be actualized by the actuality.

A causal series is a series of successive causations. When this occurs, the members of the series fall into one of three categories: the first member (if there is one) is an agent without being a patient; the last member is a patient without being an agent; and each intermediate member is in some sense both an agent and a patient. For any intermediate member, its agency and its patiency will coincide either accidentally or essentially. They coincide accidentally when the actuality whereby the member is an agent is to some extent distinct from the potential whereby it is a patient. For instance, when Bob lifts Charlie so that he can grab an item off the top shelf, Charlie has the potential to be lifted and the actuality of grabbing, where the latter is distinct from the former.[2] An intermediate member’s agency and patiency coincide essentially when the actuality whereby it is an agent just is the actualization of the potential whereby it is a patient. For instance, when Alice moves a stone in a shape on the ground using a stick, the actuality in the stick whereby it moves the stone just is the actualization of its potential to be moved in that way.

This essential coincidence of agency and patiency captures a unique middle ground between the “pure” agent and patient that we started with, and for this reason we introduce a third term to describe this sort of member: instrument. Similar to an agent, an instrument has an actuality in virtue of which it actualizes the potential of something else. Unlike an agent, this actuality is something the instrument receives from another as part of the functioning of the causal series rather than something that it contributes itself. Similar to a patient, then, the only thing the instrument contributes to the series is the potential. But unlike a patient, the potential contributed by the instrument is the potential for actualizing a potential in the next member of the series.

By contrast, the accidental coincidence of agency and patiency does not require us to introduce another sort of member, since in this case the intermediate member is separately a patient of the member preceding it and an agent of the member succeeding it.

We are now in a position to introduce the distinction between two types of causal series. An accidentally ordered series is a causal series in which the agency and patiency of every intermediate member coincide accidentally, whereas an essentially ordered series is one in which they coincide essentially. In other words, none of the intermediate members in an accidentally ordered series are instruments, while in an essentially ordered series all of them are instruments.[3]

Given this distinction, we can see quite easily that every essentially ordered series must have a first member. After all, if any such series didn’t have a first member, then the only members in the series would be the instruments and the patient. But instruments and patients only contribute potentials to the series, and therefore this series would not have any actuality in it. But without any actuality, no potentials can be actualized to bring about any effect. And therefore, this series wouldn’t in fact cause anything at all.

[1] More technically, a contribution of a member M to a causal series S is some intrinsic feature of M which makes it possible for S to obtain and which it does not receive as part of S obtaining.

[2] There can still be some overlap or dependency and still be considered distinct, so long as the actualization of the potential is not identical to the actuality.

[3] We are restricting ourselves to causal series where there is at least one intermediate member so that we can give succinct versions of these definitions.

7 responses

  1. ummderrr Avatar
    ummderrr

    I just found your blog which is great. Can you email me (I had to provide my email to post this so hopefully you can see it). I would like to ask you a question about philosophy. Thanks.

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  2. 800 ressources sur l’existence de Dieu – Par la foi

    […] A Simpler Argument about Essentially Ordered Series – Rolland Elliott (article de blog) […]

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  3. Avatar
    Anonymous

    Hello Roland, I’m the anonymous person you sent me the link to here. I saw your POST above and I’m going to give my answer.

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  4. Avatar
    Anonymous

    l personally liked the response. I think a defender of the view that every essentially ordered series (ES) is infinite would reason as follows: (i) all causes in an ES are instrumental, (ii) no instrumental member in an ES has the relevant causal power on its own, (iii) each intermediate member does possess the relevant causal power.Putting on the hat of an infinitist, I would say that your use of the idea that every instrumental cause in an ES contributes “only potentially” to the series is ambiguous. Since an instrumental cause transmits some power to the patient in the chain, it must possess some power itself, even if only qua inherited (to reference Jonathan Schaffer’s notion of inheritance of reality). In my view, this implies that every instrumental cause contributes actually to the series, because nothing can give what it does not have; if the instrumental cause does not inherit any power, then it cannot play any causal role—whether principal or intermediate. The notion of inherited reality and power is fundamental for speaking of regress in fundamentality or grounding.So, granted: in an ES, every cause is instrumental—but this does not imply, at least for an infinitist, that the power of instrumental causes is lost without a foundation. They would instead claim that every instrumental cause has a power that is infinitely inherited (infinitely downward, so to speak).The most viable strategy for a Thomist, then, would be to embrace contemporary foundationalist projects—such as Schaffer’s own—in terms of regress in grounding and ontological chains structured by inheritance of reality. But unfortunately, Schaffer’s argument for inheritance of reality is questionable (see Cameron [2022]).Let me know if you’d like a more formal or more casual version

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  5. Roland Avatar
    Roland

    We should not conflate essential orderedness with inheritance as used by contemporary grounding theorists. I acknowledge that there is some overlap in how the two ideas are used, but they are nevertheless different—Trogdon calls this out in his paper, “Inheritance Arguments for Fundamentality”. Two differences are salient: inheritance seems to apply to accidentally ordered relations as well, and inheritance is not about series.

    The second point is perhaps key at understanding where your hypothetical infinitist goes wrong: a casual series is one slice through a broader causal network, and this network will often include both essentially ordered and accidentally ordered relations. This is true even in the simple case of the hand moving the stick moving the stone. Between the hand and the stick there is both an accidentally ordered relation (wherein one physical thing pushes against another) and an essentially ordered relation (wherein the hand causes the stick to have a particular accelerated motion). We have to be specific about which of these we’re considering for a particular series. Regarding the former relation, the stick contributes actuality to the causation, since one thing pushing another presupposes the actuality of the other. Regarding the latter, the stick contributes only potentiality, because it does not have the power move itself in any way other than constant rectilinear motion.

    Thus, in the essentially ordered series of motion from hand to stick to stone, the stick contributes only potentiality. Of course, there are other related series in the broader causal network to which the stick contributes actuality, but that is besides the point.

    Now, it is true that in the essentially ordered series in question the stick has actuality, since it is by this actuality that it is able to move the stone. But this actuality is not contributed by the stick to that series—it is a result of the series rather than something presupposed by it.

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    1. Avatar
      Anonymous

      But the problem the infinitist raises against the defenders of foundationalism is that they assume an analogy which presupposes that the nature of the series must not regress infinitely.

      I’ll include a passage that explains this more clearly.Book :Ross P. Cameron Chains of Being Infinite Regress, Circularity, and Metaphysic chapter 25 “So while the numbers regress and the events regress are structurally analogous, we might find the principles that yield the regress objectionable in one case but not the other, because while each regress entails that there are infinitely many things of kind K, whether that is a vice may depend on what kind K is, and whether we have independent reason to think that the domain of Ks is a finite one. Yielding infinitely many things of kind K might be a vice when the kind in question is events separated in time, but not when the kind in question is natural numbers structured by the successor relation .”

      This is surgical for me, because many of the cases used to argue that every essentially ordered chain must be finite rely on analogies that borrow their viciousness from empirical examples: the carriage pushed indefinitely by horses, the infinite bank loan of a fixed sum of money, and so on.But the reason these cases are vicious is not because they involve an infinite regress — that would be to adopt a particular stance in the theory of regress, namely regress monism, which is entirely questionable.

      These empirical cases are vicious simply because we have empirical assumptions that falsify them: there aren’t infinitely many horses; there aren’t infinitely many bank accounts, and so on. Or more precisely: horses are not the kind of thing that can exist infinitely; bank accounts are not the kind of thing that can exist infinitely; infinite loans do not exist.

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      1. Roland Avatar
        Roland

        The examples used by accounts of essentially ordered series are not meant to be understood as arguments by analogy, but as illustrations of the analyses they propose of such series. It is from the principles in these analyses that we deduce that such series cannot be infinite. In my case, the salient principle is that intermediate members in an essentially ordered series contribute only potentiality to that series, so that if there is no first member then there is no actuality for the series, and therefore no series.

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