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Modal Metaphysics and the Priority of Causes in Hume's Treatise

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  • Ariel Melamedoff (New York University)

Abstract

In his Treatise of Human Nature Hume claims to demonstrate that simultaneous causation is absolutely impossible; all causes must precede their effects in time. I argue that considering Hume’s modal theory can reveal two important and previously unaddressed features of this argument. First, Hume’s modal metaphysics explains how he is able to infer from the claim that it is possible for some object to be simultaneously caused to the claim that it is possible for all objects to be simultaneously caused. This inference, I argue, is justified by Hume’s combinatorial modal theory for relations. Second, his distinction between absolute and natural modality raises a problem that has not yet been identified in the literature. Hume’s conclusion is that simultaneous causation is metaphysically impossible, but one of his premises relies on a mere natural impossibility (that every beginning of existence requires a cause). This is an intractable problem: Hume cannot get the conclusion he wants because it depends on an equivocation between two strengths of modality. 

Keywords: Hume, Metaphysics, Causation, Modality, Time

How to Cite:

Melamedoff, A., (2024) “Modal Metaphysics and the Priority of Causes in Hume's Treatise”, Journal of Modern Philosophy 6. doi: https://doi.org/10.25894/jmp.2393

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03 Sep 2024
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Introduction1

In Book 1, Part 3 of his Treatise,2 David Hume argues that our idea of the causal relation can be fully analyzed into three component relations. These are the relations of spatio-temporal contiguity, temporal priority, and necessary connection. Hume goes on to spend nearly all of T1.3 giving an account of necessary connection.3 Yet he spends little time on his discussion of the relations of contiguity and priority. In particular, his argument that causes must be temporally prior to their effects (T1.3.2.7) is exceedingly brief and quite confusing. To reject alternate theories, Hume appeals to what he calls an ‘establish’d maxim’ of metaphysics in a reductio against the view that a cause might be simultaneous with its effect. He then proceeds to draw inferences that a variety of interpreters have thought are invalid or even self-contradictory: he argues that the very possibility of simultaneous causation would entail that all objects exist contemporaneously, and that time does not pass.4 Immediately after presenting this argument, Hume tells the reader that if they are not convinced, they should not worry since ‘the affairs is of no great importance.’

I argue that considering Hume’s modal metaphysics can reveal two important and previously unaddressed features of this argument. First, his modal metaphysics resolves one of the most pressing extant interpretive issues: how Hume is able to infer from the claim that it is possible for some object to be simultaneously caused to the claim that it is possible for all objects to be simultaneously caused. This inference, I argue, is justified by Hume’s theory of relations. Based on an analysis of the representational capacities of the imagination in the Treatise, I develop a modal theory for relations that supports inferences of this kind. Second, his distinction between absolute and natural modality raises a problem that has not yet been identified in the literature. Hume is trying to conclude that something is metaphysically impossible, but one of his premises relies on a mere natural impossibility—that no object can begin to exist uncaused. This, I argue, is an intractable problem: Hume cannot get the conclusion he wants because it depends on an equivocation between two strengths of modality.

Section 1: The Priority Argument

In this section I present the Priority Argument, as well as some of the scholarly controversy surrounding it, to get a clear starting point for my own interpretation. Hume’s Priority Argument, in its entirety, goes as follows:

Some pretend that ’tis not absolutely necessary a cause shou’d precede its effect; but that any object or action, in the very first moment of its existence, may exert its productive quality, and give rise to another object or action, perfectly co-temporary with itself. But beside that experience in most instances seems to contradict this opinion, we may establish the relation of priority by a kind of inference or reasoning. [i] ’Tis an establish’d maxim both in the natural and moral philosophy, that an object, which exists for any time in its full perfection without producing another, is not its sole cause; but is assisted by some other principle, which pushes it from its state of inactivity, and makes it exert that energy, of which it was secretly possest. Now if any cause may be perfectly co-temporary with its effect, ’tis certain, according to this maxim, that they must all of them be so; since any one of them, which retards its operation for a single moment, exerts not itself at that very individual time, in which it might have operated; and therefore is no proper cause. [ii] The consequence of this wou’d be no less than the destruction of that succession of causes, which we observe in the world; and indeed, the utter annihilation of time. For if one cause were co-temporary with its effect, and this effect with its effect, and so on, ’tis plain there wou’d be no such thing as succession, and all objects must be co-existent.

If this argument appear satisfactory, ’tis well. If not, I beg the reader to allow me the same liberty, which I have us’d in the preceding case [regarding the spatial contiguity of cause and effect], of supposing it such. For he shall find, that the affair is of no great importance.5

There are a few points of general agreement among interpreters of this passage. The first is its conclusion: Hume aims to show that it is absolutely impossible for a cause to begin to exist at the same moment that its effect begins to exist.6 The second is the formal structure of the argument: it is a reductio ad absurdum showing a contradiction arises if we assume the possibility of simultaneous causation (together with some other plausible premises). The third is that it is a two-stage argument, as I indicated in the text above. Hume first aims to show that [i] the possibility of one simultaneous cause entails Causal Simultaneity: that all causes are simultaneous with their effects. He argues for this through what he calls an ‘establish’d maxim.’ Once this intermediate conclusion is reached, Hume then aims to show that [ii] if all causes are simultaneous, then time would not pass, which is absurd. He argues for this by arguing that Causal Simultaneity entails Universal Simultaneity: that all objects exist contemporaneously in the same instant.

Though there is no consensus in the literature as to how to understand the argument,7 Ryan (2003) provides the latest and most promising reconstruction. He does so by extracting from Hume’s established maxim the claim that every cause acts as soon as possible, as well as noting that the Hobbesian background of Hume’s text should indicate that ‘cause’ refers to sufficient causes. From this he is able to conclude that if it is possible for a cause to act simultaneously, then that cause actually acts simultaneously. Otherwise it would be acting at a later time than the soonest possible, violating the established maxim. Here is Ryan’s reconstruction:

  • 1. At least one sufficient cause is possibly simultaneous with its effect (assumption for conditional proof).

  • 2. All sufficient causes act as soon as possible [the “establish’d maxim”].

  • 3. If a sufficient cause is possibly simultaneous with its effect, then it is in fact simultaneous with its effect (from 2).

  • 4. At least one sufficient cause is simultaneous with its effect (from 1 and 3).

This is not yet the intermediate conclusion Hume wants out of the first stage of the argument: it only gives us the conclusion that given some cause which is possibly simultaneous, that cause is in fact simultaneous. We are not yet warranted to generalize to the intermediate conclusion that all causes are simultaneous. Since Hume is arguing for an impossibility claim, defending it requires arguing against the possibility of a single case of simultaneous causation, and so this is where the reductio must begin.8 This is why Ryan adds an enthymematic premise which will make the argument work by allowing us to generalize from the existential possibility claim:

  • 5. If at least one sufficient cause is possibly simultaneous with its effect, then all sufficient causes are possibly simultaneous with their effects [enthymematic premise].

  • 6. All sufficient causes are possibly simultaneous with their effects (from 1 and 5).

  • 7. Causal Simultaneity: All sufficient causes are in fact simultaneous with their effects (from 3 and 6).

We thus get the conclusion that if there are any sufficient causes, they are all simultaneous with their effects. But what justifies attributing this enthymeme to Hume? I think this is the largest extant interpretive question about the Priority Argument. Ryan argues that Hume bases this assumption on the principle that all causes are on equal ontological footing (2003: 37–8). Whatever is true for one cause should be true for them all unless we have reason to think otherwise. Ryan suggests that Hume had some assumption like this in the background, so he was not concerned about his move from the possibility of the existential case to the universal case. The burden is on the opponent to draw a distinction in kinds of causes, not on Hume to defend his assumption that they are the same.

I do not think this can be the complete answer, however. Many philosophers have believed that some causes have certain features that others lack. As a relevant example, many medieval philosophers, inspired by Aristotle’s discussion of causal simultaneity in the Posterior Analytics, held the view that whether a cause acts simultaneously depends on what kind of cause it is. According to Bonaventure, for example, light acts simultaneously, but machines do not.9 If Ryan is right about Hume’s justification for this premise, it would beg the question against some widely respected views that deny his conclusion that simultaneity is impossible. A good justification for this enthymeme should come from a broader principle, and I offer such a justification on the basis of Hume’s modal theory of relations in Section 2.

The second step of the argument also requires some additional argumentative resources that Hume does not make explicit. The absurd conclusion – that time does not pass – requires at least two more premises. The first is Hume’s theory of time, presented in T1.2.3.7–11: that time is nothing over-and-above the ordered succession of objects. Under a more robust conception of time, one could claim that the passage of time itself is a partial cause of some effects.10 The second additional premise is what we can call the Causal Maxim: the view that every beginning of existence requires a cause. One could avoid the inference from Causal Simultaneity to Universal Simultaneity by claiming that some objects come into existence uncaused. On this assumption, there could be a chain of simultaneous causes at each moment, and a chain at the next moment with no causal connection to its temporal predecessor. In Section 3, I investigate this assumption in connection with Hume’s view that it is not absolutely impossible for an object to begin to exist without a cause. I argue that the Priority Argument’s reliance on the Causal Maxim means that it can never show what it purports to show: that simultaneous causation is absolutely impossible.

Section 2: Hume’s Combinatorial Modal Theory

In this section, I address the enthymeme identified in Ryan’s reconstruction of the first half of the Priority Argument: that if one cause is possibly simultaneous with its effect, then all causes are possibly simultaneous with their effects. I believe Hume is entitled to this inference by views on modality and relations which he has defended earlier in the Treatise. The model I develop here has application beyond the Priority Argument: it justifies similar inferences in any cases involving external relations (spatiotemporal, causal, and diachronic identity). Given the scope of this paper, I do not consider other applications; but my reading of the Priority Argument gives us a clear model of the kind of reasoning licensed by Hume’s modal metaphysics.

In Part 1 of Book 1 of the Treatise, Hume endorses what we can call the Conceivability Principle:

CP: if some state of affairs S is conceivable, then S is metaphysically possible.11

The CP is not original to Hume. Other early modern philosophers, notably Descartes, also held this view.12 But Hume’s views on cognitive psychology turn the CP into a powerful premise in some of his most famous arguments. It is crucial to Hume’s system in the Treatise that the mind possesses only one representational faculty: the imagination.13 In Hume’s view of the mind, to conceive some state of affairs simply is for ideas in the imagination to be arranged in such a way as to represent that state. So Hume is also committed to:

One Cognitive Faculty: a state of affairs is imaginable iff it is conceivable.

Any states of affairs that are imaginable are also conceivable, and they are therefore real metaphysical possibilities by the CP. Given the view that there is only one cognitive faculty, the CP justifies some of Hume’s most significant metaphysical and epistemological commitments. For example: if we merely grant that we have the ability to imagine an object beginning to exist without a cause, we are thereby committed to Hume’s conclusion that it is not metaphysically necessary for every beginning of existence to be caused.14

In Sections 2.1.–3, I consider Hume’s views on the powers of the imagination in order to draw conclusions about the range of metaphysical possibility in Hume’s system. I begin with Hume’s claim that the imagination has the capacity to separate, conjoin, and recombine any of its ideas (T1.1.4.1; 1.3.7.7). In Section 2.2, I argue that Hume is committed to the view that if some arrangement of external relations r is imaginable among some objects, then it is imaginable among any objects that can participate in relations of the same type as r. In Section 2.3, I argue that the recombination principle licenses the Priority Argument’s inference from the possibility of one simultaneous cause to the possibility that every cause is simultaneous. This can allow us to reconstruct Hume’s arguments along Ryan (2003)’s lines without needing to appeal to an undefended enthymeme in the process.

2.1 Relations and Recombination

There are many ways of thinking about recombination principles. For example, Efrid and Stoneham (2008) exposit and defend a Lewisian conception of modal recombination based on the claim that anything can coexist with anything else and anything can fail to coexist with anything else.15 It is not hard to make the case, based on his Separability Principle, that Hume has a similarly combinatorial view in the case of objects: any two distinct objects could coexist or fail to coexist.16 Since any two distinct objects can be imagined to exist separately and no distinct objects entail each other’s non-existence (T.1.1.7.3), it follows that objects can be recombined in the imagination. In this paper, I am concerned with Hume’s views on recombination in the case of relations among objects. Simultaneous causation is a relation; if there were a recombination principle for it, then we could infer from the possibility of some objects standing in this relation to the possibility of any objects standing in this relation (the relation could coexist or fail to coexist with any objects). Recombination principles for relations are more complicated than for objects. In fact, it will not turn out to be the case for Hume that a relation could coexist with anything and fail to coexist with anything. Before we can tackle the metaphysical question of recombination, we must begin with our representational capacities, which are our guide to metaphysical possibility in Hume’s system.

Some terminology to start. I will use the notion of an arrangement of relations. To understand what this means, imagine three objects (A, B, and C) lined up next to each other in a straight line, each five metres apart from the nearest object. We can find many relations between them: A is to the left of B, and B to the left of C; A is closer to B than to C; etc. Each of these relations is a particular token of a broad kind of relation, the spatial kind. I will refer to the structure of relations as the arrangement of relations in this state of affairs. If we replaced A, B, and C for three other objects (D, E, F) in our example, but maintained all the relations the same, we would have a new state of affairs consisting of the same arrangement of spatial relations, but distinct objects. The relations in this new state would be isomorphic to those in the previous, and the only difference would be which objects are being related by them. These arrangements will always have a relation-type. In the example, it is an arrangement of spatial relations, but it could also be an arrangement of spatiotemporal relations if I added considerations about temporal priority, or even an arrangement of spatiotemporal-causal relations if it also included details about what causes what.

An unrestricted recombination principle for a relation-type R, as I am defining it, is a principle which says that whenever it is possible for an arrangement r of type R to be imagined holding among some n objects, it is also possible to imagine r holding among any n objects. I will argue that Hume does have a recombination principle for certain relations (which I call external), but it is not unrestricted. With this terminology in hand, let us look at Hume’s views on relations and see in what sense there might be a recombination principle for them.

Hume claims in T1.1.4.1 that ‘all simple ideas may be separated by the imagination, and may be united again in what form it pleases’ (emphasis added). The claim that the imagination may reunite ideas in ‘what form it pleases’ suggests that there are no limitations on how the imagination can re-arrange an idea once it has access to this idea. Later, Hume gives similar formulations that are not restricted to simple ideas only. For example, at T1.3.5.3 he claims the imagination ‘transposes and changes them [i.e., its ideas] as it pleases,’ in contrast with the memory, which presents ideas in the same arrangement as the impressions they are derived from.

So far, these have all been statements about separating, combining, and mixing ideas in the imagination. For the purposes of understanding Hume’s view of metaphysical possibility, however, we need a recombination principle that applies not merely to ideas in the mind, but to the intentional objects which those ideas represent.17 Hume seems to think that he is entitled to appeal to such a recombination principle of objects:

the imagination has command over all its ideas, and can join, mix, and vary them in all the ways possible. It may conceive objects with all the circumstances of place and time. It may set them, in a manner, before our eyes in their true colours, just as they might have existed. (T1.3.7.7, emphasis added).

We should take note of the quick shift from talk of recombining ideas in the imagination to the claim that we can conceive objects with any spatiotemporal relations. I have not made the case that Hume is entitled to this inference, but it is quite clear that Hume himself thought he was justified in assuming that the imagination could recombine objects into spatiotemporal relations as it pleases.18

A recombination principle follows from Hume’s statement at T1.3.7.7: if I can imagine some objects being five metres apart, then I could imagine any objects being five metres apart.19 After all, ‘being five metres apart’ is a ‘[circumstance] of space and time,’ and I can imagine objects with any and all spatiotemporal circumstances. Spatiotemporal relations are only one of seven types of relation Hume identifies at T1.3.1. The statement of the recombination principle I cited at T1.3.7.7 does not state that only the spatiotemporal relations among objects can be recombined; but it does not mention the other kinds. In what follows I aim to show that space and time must only be an example of a broader principle, one which applies to any external relations.

2.2 Restricted Recombination for External Relations

At the start of Part 3 of Book 1 of the Treatise, Hume distinguishes two kinds of relations. The first are relations that ‘depend entirely on the ideas they relate’ (T1.3.1.1). The relation of resemblance is a paradigm case. If I think of two blue dots, I have thereby thought of two things that are related by the same colour relation. I cannot replace the two blue dots with any arbitrary object without thereby destroying the same colour relation that held between them. Hume counts ‘resemblance, contrariety, degrees in quality, and proportions in quantity or number’ as relations that depend entirely on what they relate (T1.3.1.1). I will refer to these as relations that are internal to their relata.20 To think of two objects is to think of the internal relations between them, because these are relations that result from properties that are inseparable from their objects.

There are three other relations – spatiotemporal relations, causal relations, and relations of identity21 – that Hume says ‘may be chang’d without any change in the ideas’ of the objects they relate. Unlike the first class, these relations are entirely independent of their objects. I will refer to these as relations that are external to their relata. To think of two objects is not yet to think of their causal, spatiotemporal, or identity relations, and one can always think of the objects without any particular external relations holding between them.

There can be no non-trivial recombination principle for internal relations. Recombination is simply the ability of the mind to exchange some objects for others while maintaining their circumstances the same. This cannot be done with relations that depend entirely on their relata. If I think of two blue dots and thereby think of the same colour relation holding between them, there is no meaningful sense in which I could replace one of the objects while maintaining the relation unchanged. Internal relations, in virtue of being internal, are not the kind of relation whose objects can be recombined.

The same does not apply for external relations, which we can see from their definition. Hume says external relations can always be changed – that is, some particular relation-token can be imagined to cease to hold and be replaced with a different token of the same type – without any change in their objects. If I can think of two objects as being five metres away from each other, I can also think of those objects not being five metres away from each other, or instead standing in any other token of the same type (spatial). It is clear from Hume’s definition of external relations that some recombination principle must hold for them. Consider the case of causation. If we have a non-combinatorial view of causation, then there could be some objects A, B, and C such that A can be caused by B but never by C. This is impossible given Hume’s statement that external relations can always be changed without requiring a corresponding change in their objects. When we stipulate that A and C cannot be causally related, we are committing to the claim that some changes in the causal relation do necessitate changes in the objects themselves – for example, C could not stay the same while its causal relations change to include a causal relation to A.

We should not be too quick to think this recombination principle will be unrestricted, however. A recombination principle for a relation type R is unrestricted if it says that if some relation of type R is imaginable among some objects, then it is imaginable among any objects. But this is too strong for Hume. For example, he believes certain objects – like passions – are not spatially located and stand in no spatial relations whatsoever (1.4.5.10). If we had an unrestricted recombination principle, we could recombine the objects of the state my chair is five metres away from my desk into the state my anger is five metres away from my desk. This leads to contradiction: my anger is both non-spatial and standing in a spatial relation. Since Hume thinks contradictions are unimaginable and impossible (Lightner 1997), this is an unacceptable result.

We can formulate a principle that does not give rise to contradictions by adding the following clause: the recombined objects in the newly imagined state must each be imaginable in at least one relation of the same type as that of the arrangement. Since passions cannot be imagined in any spatial relations, they cannot be recombined into states of affairs involving spatial relations.22 I argue below that this clause follows from Hume’s views on contradiction. A suitably restricted recombination principle for external relations would look like this:

Imagination Recombination Principle (IRP): if it is imaginable that some arrangement of external relations r of type R holds among some objects, then it is imaginable that r holds among any objects which can be imagined in some arrangement of type R.

What types can take the place of R in the above principle? At the very least, R can stand for arrangements consisting of temporal, spatial, identity-over-time, or causal relations – that is, the types of relation Hume identifies as external in T1.3.1. In addition, given the recombinability of these relations, it follows that R can also stand for an arrangement of relations of two or more of these types. For example, we can have an arrangement of two objects that are five metres apart and occur two minutes apart. Since each relation is recombinable with any other relation-token of the same type, it follows that the whole arrangement is recombinable with any other arrangement of a spatial and a temporal relation holding between two particulars – say, 10 light-years in distance and eight seconds in time. So the variable R can also take compositions of the four external relation-types: not just temporal relations, but also spatiotemporal relations, or temporal-causal relations, etc.23 This feature will be relevant when we come to apply the IRP to Hume’s argument against simultaneous causation, which falls under a relation-type composed of both temporal and causal relations.

Hume’s views on contradiction explain the inclusion of the final clause of the IRP, that the objects in the recombined state must be objects we can imagine in some relation of the same type as our arrangement. According to Hume, it is impossible to imagine a contradictory state of affairs, a state in which something both exists and does not exist (Lightner 1997). There are two ways such a contradiction could arise with respect to the IRP. First, a contradiction could arise if the external relations are incompatible: for example, a state in which an object A is thought to be earlier than B and B thought to be earlier than A. An incompatible arrangement would render both the initial state and any recombination of it unimaginable. We can call this an external incompatibility, since the relations are incompatible with each other regardless of which objects they relate. On the other hand, a contradiction could arise only after the recombination, which means there is no inherent incompatibility in the arrangement of relations. This is an internal incompatibility, which arises because of features that are inseparable from the newly recombined objects.

We can put together this thought about internality and contradiction with the definition of external relations to get our restricted recombination principle. Since an object’s internal properties are inseparable from it,24 this means that if an object cannot be imagined in some external relation r of type R, it cannot be imagined in any relation of type R. There are no objects that could be imagined to be five metres away from each other, but not 10 metres away from each other. This would require a certain token of an external relation to be special with respect to this object; but as Hume says in defining externality, the tokens of external relations can always be substituted for other tokens of the same type, regardless of the objects.

This leaves us with the following disjunction in types of contradictions. If an object A cannot be imagined in an external relation r of type R, then either: (i) r involves incompatible external relations, so no object can be imagined to participate in r; or (ii) A cannot be imagined to participate in any relation of type R, because it is internally incompatible with R-type relations. If we derive a contradiction from recombining objects of external relations, it means that either the relations were incompatible to begin with, or the new objects are not of the right kind to participate in relations of this kind at all (as with passions and spatiality).

Finally, it is important to note that spatiality is a special case for Hume: there are no objects that are non-temporal or non-causal in the way that passions are non-spatial.25 Hume explicitly says that every object can be conceived to participate in some causal relation or another (T1.3.2.5), and a non-temporal object is one that could never be followed or preceded by anything. Such an object would be a necessarily eternal existent, an unchanging being that could never begin to exist or stop existing. There is no place in Hume’s system for an object like this. This means that as long as our initially imagined arrangement of external relations r involves no spatial relations, any contradictions arising from recombining objects in r must be due to an external incompatibility. If a spatial relation is part of the arrangement, then we must also check whether the contradiction arises from the inclusion of a non-spatial object in the recombined state of affairs.

2.3 Metaphysical Recombination and the Priority Argument

We can now straightforwardly derive a metaphysical recombination principle for external relations. Given that Hume accepts the Imagination Recombination Principle, One Cognitive Faculty, and the Conceivability Principle, the following principle must also hold:

Metaphysical Recombination Principle (MRP): if it is imaginable that some arrangement of external relations r of type R holds among some objects, then it is metaphysically possible that r holds among any objects which can be imagined in some arrangement of type R.26

Metaphysical Recombination follows from views that Hume accepts once we have the restricted recombination principle of the imagination, the IRP. And we can find some evidence that Hume noticed this connection by seeing that the MRP justifies premise (5) in Hume’s Priority Argument, the claim that if it is possible for some cause to act simultaneously, then it is possible for any cause to do so as well.

Recall that what was missing from Ryan’s reconstruction of the Priority Argument was a non-question-begging principle that could justify this assumption. Since both causal and temporal relations are external for Hume, we can apply Metaphysical Recombination to derive this premise as follows. Two objects being related by both simultaneity and causation is an arrangement of external relations. By the MRP, if an object could participate in some temporal-causal arrangement – for example, if it could be caused by something that precedes it – then it can participate in any causal-temporal arrangement that does not include incompatible external relations. As I argued at the end of 2.1, all objects can participate in at least one causal-temporal arrangement (nothing is non-temporal or non-causal). And if there could be one case of simultaneous causation, which is the antecedent of the conditional (5), then simultaneous causation is not an incompatible arrangement of relations. According to Hume’s modal metaphysics, it follows from this that any two objects whatsoever could be related by both simultaneity and causation.

Hume’s final aim in the Priority Argument is to show that simultaneous causation is impossible, meaning it could never hold among any objects. Here too my analysis of the Metaphysical Recombination Principle can help us. Since there are no non-temporal or non-causal objects for Hume, if any contradiction is derived from imagining a temporal-causal arrangement r, then the arrangement r must include incompatible relations, meaning that no object could participate in r. This is precisely Hume’s strategy in his reductio: assume conditionally that some objects can be simultaneously caused to show that this leads to a contradiction. Given Hume’s modal metaphysics, he would then be warranted in concluding the arrangement involves incompatible external relations, meaning that no objects can be related both by causation and simultaneity. This means that Hume is perfectly justified, by more foundational commitments in his metaphysics, in inferring from the possibility of one case of simultaneous causation to the possibility of all causes acting simultaneously. The enthymeme Ryan identified in the Priority Argument turns out to be a theorem of Hume’s modal metaphysics.

Section 3: Hume’s Two-Level Modal Theory and the Causal Maxim

3.1 Absolute and Natural Modality

Only a few paragraphs after presenting the Priority Argument, Hume asks whether it is absolutely necessary for every beginning of existence to be caused. He is questioning the Causal Maxim, which was a widely held view in early modern philosophy. His conclusion is that this is not absolutely necessary. His basis for this conclusion is the claim that we can conceive of an object not existing at one time, and existing at a later time, without also thinking of any cause for this. Since what is conceivable is metaphysically possible by the CP, spontaneous generation is possible, and the Causal Maxim cannot hold with absolute necessity.27

Yet later in the Treatise Hume commits himself to determinism: nothing can come about unless it is determined by a prior cause.28 To make this consistent with his claims in 1.3.2, we must note that Hume thinks there are two senses modal terms can have. The first is an absolute sense, according to which all that is conceivable is possible. Let us call this modalityA for ‘absolute.’ In 1.3.2, Hume argues that it is not necessaryA for an object to begin to exist uncaused.

There is another sense of modal language which is captured by his account of ‘necessary connexion’ later in T1.3. On Hume’s account of causation, an effect is necessarily connected to its cause just in case it meets certain criteria laid out in Hume’s two definitions of cause (T1.3.14.30).29 This sense of modal language can be used to make a claim like: ‘The same cause always produces the same effect’ (T1.3.15.4). This claim is false if the modal terms are understood as modalA terms. Instead, I will call this narrower modality natural modality, and indicate its use with the subscript modalN. In the case of the causal maxim, it is necessaryN for every beginning of existence to be caused, but this is not necessaryA.

As Garret points out, these two ‘species’ of modality have a fundamental commonality: they both have to do with ‘the inability to think otherwise’ (Garrett 2014). The absolutely impossible is unthinkable because we cannot think a contradiction.30 This is the strongest kind of unthinkability for Hume, corresponding to the strongest kind of necessity (absolute). Its source is the internal character of the ideas involved, which is why ‘contrariety’ is among the for Hume. Natural necessity, the kind involved in causal reasoning, also has to do with an inability to think otherwise. But the source of this inability is not the internal character of the ideas, since the ideas of causes can always be separated from the ideas of effects. Instead, it is the result of our customary tendency to infer from one idea to the other, a tendency derived from our experience of constant conjunction (T1.3.14).31 While it remains possible to think of a cause and effect separately, it becomes psychologically difficult to do so. And even if we can imagine the two as separate, we cannot come to believe that they are separate, since belief is determined by the vivacity of ideas (T1.3.7.5) and a causal inference results in a lively idea of the effect (T1.3.14/EHU5).

The commonality between the two kinds of modality lies in the inability to believe: we can always believe what is possible, never what is impossible. Their difference lies in the ability to conceive or imagine: if we cannot believe something but we can still imagine it, then it is absolutely possible even if it is naturally impossible. This means that natural modality is strictly narrower than absolute modality, since we must be able to represent something in order to believe it, but we need not believe everything we can represent. Anything that is absolutely impossible is also naturally impossible, and, inversely, many things are necessaryN that are not necessaryA, so we cannot infer from a natural impossibility to an absolute one.

Hume himself says that it is ‘natural for men, in their careless and common way of thinking’ to conflate these two kinds of necessity (T1.4.3.9). We are apt to think that when there is a necessaryN connection between two things, it is impossibleA that they should be separated. Hume is careful not to make the same mistake, for example when he rejects the absolute reading of the Causal Maxim in T1.3.2. I argue in Section 3.2 that the Priority Argument can only work under such a conflation. Given Hume’s sharp distinction between these two levels of modality, the Priority Argument cannot achieve its goal of showing that simultaneous causation is absolutely impossible.

3.2 The Priority Argument’s Modal Equivocation

As we saw earlier, Hume can only infer from Causal Simultaneity (that all causes act simultaneously) to Universal Simultaneity (that all objects are contemporaneous) if he assumes every object has a cause. Otherwise, there is no way to draw the latter conclusion, since objects could always come into being at subsequent moments without any causes. Without the Causal Maxim, Hume cannot infer to the collapse of time, the absurd conclusion of the Priority Argument.

Given his modal theory, even adopting the Causal Maxim will not help Hume draw the conclusion he is aiming at in this passage. This is because he himself admits only a few paragraphs later that the Causal Maxim cannot hold with the strength of absolute necessity (T1.3.3). Even if the Causal Maxim is true, it is merely necessaryN for every beginning of existence to be caused, not necessaryA. This means that any absurd conclusion Hume draws from Causal Simultaneity will only be necessaryN. Even if he could derive a contradiction (which I have not argued he can, since the collapse of time is not in itself contradictory), this would only be an impossibility in the natural sense in which everything is determined by causes, not an absolute impossibility.

One aspect of Hume’s modal theory – the recombination of external relations—can help him get halfway with this argument, from the possibility of simultaneous causation to Causal Simultaneity. But given his two-level modal theory, he can never derive a contradiction from this. The absurd conclusion may be absurd in a colloquial sense, but not in the technical sense of being inconceivable. On Hume’s theory of natural modality – which depends on his definitions of causation—it is indeed the case that simultaneous causation is naturally impossible. But the promise of the Priority Argument was to give a demonstration for this claim, and Hume cannot provide one by the lights of his own modal metaphysics.

3.3 Possible responses

The threat of modal equivocation is a serious one, which I believe is intractable. By his own lights, Hume cannot reject the view that it is possibleA for all causation to be simultaneous without the collapse of the temporal series. How should we interpret the Priority Argument, and its place in Hume’s theory, given the tension it stands in with Hume’s modal metaphysics? I provide three brief suggestions for interpretive directions to address this problem.

One plausible response is that Hume is intending to use his opponents’ assumptions, rather than his own. The Priority Argument is, after all, a reductio. Hume only needs to show that his opponents’ views are in contradiction.32 Hume claims that the Causal Maxim ‘is commonly taken for granted in all reasonings, without any proof given or demanded’ (T1.3.3.1), and no other philosophers had clearly distinguished between two levels of modality as he does in the Treatise. But this reading faces a significant problem: in order for Hume to draw the conclusion that all objects exist simultaneously, he must also assume his own theory of time, which says that time is nothing over-and-above the succession of objects. If one does not have this assumption, it would be possible to claim that the passage of time itself could act as a partial cause, thereby undermining the inference from Causal Simultaneity to Universal Simultaneity. This would also undermine the inference from Universal Simultaneity to the ‘utter annihilation of time’ (T1.3.2.7), since on a non-reductive view, one could maintain that time still passes even if there is no succession of objects. While there had been reductionist theories of time before Hume,33 it is not reasonable to assume that his opponent would concede to Hume’s metaphysics of time. It is difficult to maintain that the Priority Argument proceeds entirely with his opponents’ assumptions, rather than his own.

A second approach, more promising in my view, is that scholars have been wrong to think that the Priority Argument’s conclusion involves absolute impossibility. Perhaps Hume would be happy to show that simultaneous causation is impossible in the natural sense of the term. This would avoid the problem of modal equivocation I have raised. It may also help to explain why Hume does not provide an argument that Universal Simultaneity is a contradiction. The claim that all objects exist simultaneously is hard to reconcile with our experience, but it does not appear inconceivable and Hume never argues that it is. This would be less of a problem if Hume’s aim is only to argue for the natural impossibility of simultaneous causation. This reading is therefore promising, but faces direct textual problems. Hume begins the passage by announcing that his opponents ‘pretend that ’tis not absolutely necessary a cause shou’d precede its effect’ (T1.3.2.7). This suggests that he is setting out to reject the view that simultaneous causation is possible in an absolute sense. The reading on which Hume intended to conclude simultaneous causation is only naturally impossible does not appear to contradict the opponents’ view.

Finally, we may suspect that Hume himself was aware of the failure of this argument, and indicated as much at the end of the passage. Hume ends the Priority Argument by telling unconvinced readers that they ‘shall find, that the affair is of no great importance’ (T1.3.2.8). Only a few paragraphs after the Priority Argument, Hume argues that it is not necessaryA for every object to have a cause – the very premise that I have claimed undermines the Priority Argument. One possible interpretation is that Hume is subtly referring to his two-level modal theory in this final disclaimer at the end of the Priority Argument. There is no strong evidence that this was his intention, but if it were, he would be precisely right that the affair is of no great importance. On Hume’s view, the Priority Argument – and any other argument aiming at a demonstration about the nature of causation – would ultimately depend on a fallacy of equivocation between different senses of modality. In the end, Hume reiterates his claim that causes must be prior to effects as one of his ‘Rules by which to judge of causes and effects’ (T1.3.15.4). There, it follows not from ‘establish’d’ metaphysical principles, but from Hume’s account of the psychological process by which we come to make causal inferences.

Conclusion

Reading the Priority Argument in the context of Hume’s modal metaphysics can improve our understanding of the first phase of this argument. The imagination’s ability to recombine objects it represents in external relations licenses his inference from the possibility of one case of simultaneous causation to the possibility of all objects being simultaneously caused. This interpretation fills in the crucial missing step in Ryan (2003)’s reconstruction, thus providing a complete account of the first half of the argument. The freedom Hume grants to the imagination – together with the Conceivability Principle—underpins a powerful theory of modality. This has already been noted in the case of the recombination of objects, and Hume has rightly served as an inspiration for combinatorial modal theories in recent metaphysics.34 But the implications of his metaphysics of relations have not been properly appreciated. I hope the analysis in Section 2 of this paper can serve as a basis for further exploration of the role of the modality of relations in Hume’s work. The fact that Hume clearly appeals to this feature of his metaphysics in the Priority Argument indicates that he is aware of the theoretical work his theory of relations can do. This opens interpretive questions I have not addressed. For example: how much theoretical weight does the distinction between internal and external relations bear in the Treatise, given the sharp difference in the modality of these relations? Does this modal theory play a role in his account of space and time (T1.2) or diachronic identity (T1.4.2)? And how does the modal theory of the Treatise relate to the later Enquiry, where Hume omits reference to the internal-external relation distinction?35

While Hume’s views on modality support a contentious inference in the Priority Argument, they also undermine the second half of the argument. Hume’s two-level view of modality prevents him from ever deriving a contradiction from the supposition of simultaneous causation. Scholars have mostly focused on the first step of the Priority Argument, but I believe it is this second step, from the simultaneity of cause and effect to the simultaneous existence of all objects, that poses the sharpest interpretive problems.36

Abbreviations of David Hume’s works

T: A Treatise of Human Nature: Volume 1: Texts, ed. David F. Norton and Mary J. Norton. (Oxford: Clarendon Press, 2007).

EHU: An Enquiry concerning Human Understanding, ed. Tom L. Beauchamp. (Oxford: Clarendon Press, 2000).

Competing Interests

The author has no competing interests to declare.

Notes

  1. Thank you to Don Ainslie, who helped me immensely in the early stages of writing this paper, and to Don Garrett, who has commented on countless drafts of this project. David Chalmers and John Richardson helped me sharpen my arguments at a key stage in the writing process. I benefited greatly from discussion with audiences at the 2019 and 2021 Hume Society Conferences, the 2019 Princeton Graduate Conference, and a 2019 Washington Square Circle talk at NYU. I’m especially grateful for the careful comments I received from Stefanie Rocknak, Elizabeth Goodnik, and Aaron Higgins-Brake. My understanding of Hume’s modal theory was largely developed through conversations with Damian Melamedoff-Vosters and Jorge Ferreira. Thank you to Todd Ryan and Michael Burton for helpful discussion of the Priority Argument. [^]
  2. Hereafter cited as ‘T’ followed by Book, section, part, and paragraph numbers as found in (Norton and Norton 2000). [^]
  3. Hume justifies this by claiming that ‘’tis chiefly this quality [i.e., necessary connection], that constitutes the relation [of cause and effect]’ (T1.3.15.5). [^]
  4. A tradition of interpreters has thought Hume appeals to premises that contradict his conclusion; see Russell (1912) and Stroud (1977). [^]
  5. T1.3.2.7. Note that this argument does not reappear in Hume’s account of causation in the Enquiry concerning Human Understanding (EHU), though Hume still maintains that causes are temporally prior to effects (EHU7). [^]
  6. There is some controversy about whether the relevant simultaneity regards beginnings of existence, or whether the point is about objects that overlap in their temporal extension. Brand (1980) and Beauchamp and Rosenberg (1974) read it as the latter; I follow Ryan (2003)’s argument that it is better read as regarding beginnings of existence. [^]
  7. For dissenting accounts, see Beauchamp and Rosenberg (1981); Kline (1982); Kline (1985); Lennon (1985); Wilkie (1950). I think Ryan’s account is superior to each of these (though he only discusses Lennon’s and Beauchamp and Rosenberg’s at length). None of these authors considers the argument in the light of Hume’s modal theory as I do here. [^]
  8. Munsat (1971) and Costa (1986) read the argument as starting from the universal claim that any cause whatsoever may be simultaneous. As Ryan shows, this cannot be Hume’s argument, since that would not constitute a proper defense of his view, which is that no case of causation can be simultaneous. For that, we must generate a reductio against the possibility of the existential claim, not the universal one. [^]
  9. Bonaventure is only one example of a common scholastic view that causes sometimes act simultaneously and sometimes diachronically; see Fox (2006), Ch. 2. [^]
  10. Thanks to Michael Burton for discussion of this step in the argument. [^]
  11. T1.1.7.6; T1.2.2.8. I borrow this terminology from Garrett (1997), Ch. 1. See Van Woudenberg (2006) for a defense of this principle against objections; see Chalmers (2002) for a recent discussion of whether and in what sense conceivability may entail metaphysical possibility. Kail (2003) argues that it is only the capacity for clearly or adequately conceiving ideas that entails metaphysical possibility. [^]
  12. Norton and Norton (2007) identify Descartes’ Objections and Replies, Arnauld and Nicole’s Logic, and Gravesande’s Explanation of Newtonian Philosophy as containing predecessors of Hume’s Conceivability Principle. [^]
  13. See Garrett (1997) Ch.1. The rejection of the intellect as a separate faculty that is involved in conception and representation is a pillar of Hume’s philosophical system in the Treatise. Hume does distinguish between imagination, reason, and memory; but his view of conceivability always involves appeal to imagistic perceptions, which are characteristic of the imagination. [^]
  14. Hume has some arguments at T1.3.3 for why we should think we can imagine this, but the crucial point is that imaginability is all he needs to argue for to get this conclusion. [^]
  15. This is based on Lewis’ (1986). [^]
  16. See Garrett (1997), Ch. 3 for an argument that Hume endorses the Separability Principle in the case of objects. [^]
  17. Note that my discussion of objects in this section is about intentional objects (i.e., what the mind represents as existing in the world); it is not about external objects in the sense of actual extra-mental causes of our representations. [^]
  18. For interpretations of how we come to form ideas of objects, see Ainslie (2015) and Rocknak (2013). [^]
  19. It might seem from Hume’s phrasing of the principle that we don’t need this statement to be in the form of a conditional. We might simply phrase it as the principle ‘a mind can imagine any objects being five metres apart.’ But Hume does need to conditionalize this principle. Someone might simply never have acquired ideas of spatiotemporal relations. Under Hume’s empiricism, we cannot assume that this person is able to imagine objects being five metres apart. But given that one is able to imagine some objects as being five metres apart, which requires spatial ideas, it follows that one could imagine any objects in such a circumstance. This is why the imagination’s powers need to be considered as being combinatorial rather than simply spontaneous: it can recombine relations it is acquainted with among objects it is acquainted with, but it does not follow that it can generate new ones. [^]
  20. This nomenclature has been standard since the early twentieth century; see Heil (2009): 313–16 for an overview. [^]
  21. Hume does not think of identity as a reflexive, symmetric, and transitive relation holding between all objects and themselves, as contemporary philosophers might. He instead uses ‘identity’ to denote something closer to the diachronic identity relation holding between the temporal parts of an object represented as enduring. See T1.4.2.30. [^]
  22. Hume is clear that the imagination cannot represent passions or other perceptions as having a location (T1.4.5.10). [^]
  23. Thanks to Liz Goodnik for pushing me to clarify this point. [^]
  24. I use internal property to refer to whatever feature of an object is responsible for the object entering into an internal relation (for example, its colour). The idea of this feature must be ‘inseparable’ from, and thus essential to, the idea of the object. [^]
  25. For simplicity, I leave out the relation of diachronic identity. This relation is complicated by the fact that Hume’s analysis of it in T1.4.2 involves both temporal relations and relations of resemblance (which is internal). This is compatible with diachronic identity being recombinable, though the resemblance requirement will impose restrictions on which objects can be substituted into an arrangement involving diachronic identity. These details are not necessary for the Priority Argument, which does not involve identity relations. [^]
  26. We should make note of how I’ve translated the representational terminology in the IRP to the metaphysical terms in the MRP. First, we still start from an imaginable state of affairs, since the CP only gives us a one-way entailment from conceivability to possibility. Once we have an imaginable state, we could always imagine a different state with the same arrangement of relations but any arbitrary set of imaginable objects (excepting internal contradictions). Once we have this second state, we can apply the CP to conclude that the latter state is metaphysically possible. [^]
  27. Kail (2003) argues that there is space within Hume’s system for absolutely necessary connections between distinct objects, and that we may (contingently) be incapable of recognizing these connections because our representations of external objects are inadequate. This reading of Hume’s modal views may be able to circumvent my objection to the Priority Argument, if it collapses natural and absolute necessity. [^]
  28. T3.1.3. In fact, he commits himself to the even stronger ‘doctrine of necessity;’ see Garret (1997), Ch. 6. [^]
  29. See Garrett (1997), Ch. 5 for a classic treatment of Hume’s definitions of cause. [^]
  30. See Holden (2014) for an expressivist account of the relation between conceivability and absolute possibility in Hume. [^]
  31. See also EHU7. [^]
  32. This raises the interesting question of the target of the Priority Argument. Norton and Norton (2007) suggest the target is Hobbes, from whom Hume borrows the ‘establish’d maxim.’ I doubt that the whole passage is directed at Hobbes’ view; after all, Hobbes himself accepts that all causation is simultaneous (Ryan 2003: 33), which is the conclusion of the first half of the Priority Argument. But when it comes to the second step in the Priority Argument this is more reasonable, as Hobbes certainly did not accept that all objects exist simultaneously. [^]
  33. See Fox (2006). [^]
  34. For example, the view that there are no necessary connections among distinct existences, a core thesis of combinatorial modal theories, is typically referred to as ‘Hume’s Dictum.’ [^]
  35. See Millican (2017), who contrasts the Treatise theory of relations with Hume’s fork, the distinction between matters of fact and relations of ideas in the first Enquiry. His analysis of the modal aspects of the theory of relations differs slightly from mine. [^]
  36. See Landy (2020) for a defense of simultaneous causation against the collapse of time, in the context of Mary Shepherd’s causal theory. Huemer and Kovitz (2003) defend a simultaneous view of causation as well. [^]

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