CONTENTS

1   INTRODUCTION - THE PROBLEM

2   ONTOLOGICAL DEPENDENCE

3  EMERGENT PROPERTIES AND EMERGENT OBJECTS

4   TRANSCENDENCE

5   CONCLUSIONS

2   ONTOLOGICAL DEPENDENCE

The object of our investigation is the ontological dependence relation. Let us introduce the notation:

We can use this to define the property of being ontologically dependent

                         OD(x)      =_df  $y OD(x ,y)

and its negation, the property of being ontologically independent

                         OI(x)       =_df  Ø$y OD(x ,y)

Colloquially we can talk of the OD relation, and of OD and OI objects. The relation so defined is “proper ontological dependence”, that is, an object is deemed not to be ontologically dependent on itself – otherwise we would have to define OD as dependent on something other than itself. We can always construct from this the corresponding “improper” relation

                         OD_I(x, h)  =_df    OD(x, h) Ú (x  =  h)

The OD relation has the properties of a partial ordering:

            antisymmetry:     "x"y[OD(x, y)  Þ  ØOD(y, x)]

            transitivity:             "x"y"z[(OD(x, y) Ù OD(y,z))  Þ  OD(x, z)]

Our informal definition of ontological dependence states that:

 a is OD on b Û (the vanishing of b in itself constitutes the vanishing of a) Ù Ø(a=b)

Another way of looking at the matter is to say is that the OI objects have to be put into an ontology “by hand” as it were, but once they are put there one gets all the OD objects “for free”. The relation is a little like that between axioms and theorems. You put in the axioms by hand and then all the theorems follow automatically (you may have to work hard to find them and prove them, but their truth is assured as soon as the axioms and transformation rules are in place). This analogy is however far from perfect. It is often possible to replace an axiom by one of the theorems and then derive the old axiom as a new theorem. OI and OD objects in an ontology are not interchangeable in this way. Whereas the conditional can be and often is one side of a biconditional, the ontological dependence relations is strictly asymmetric.

It is important to distinguish between ontological dependence and (efficient) causation. We can say, for example, that the heat source within the earth is the cause of volcanoes. If the heat source were to cease, then there would be no more active volcanoes. This relationship is however not ontological dependence, which is closer to logical implication than to efficient causation. The existence of the fundamental objects does not cause the existence of the OD objects; the second objects follow directly from the first without the intervention of some causal link. Intuitively we want to say that although the OD objects are distinct from the fundamental ones on which they are ontologically grounded, they share the same existence. However work is needed before sense is made of this notion of “sameness of existence”.

It is useful at this point to record two further pieces of what might be called the phenomenology of ontological dependence, and in the process qualify the informal definition of the relation in terms of vanishing. In the first place we have to allow for the possibility of transfer of ontological dependence. Although at any one time, the dependent object might be dependent on a particular piece of substrate, it can survive the destruction of the substrate provided it has managed to transfer its dependence to another suitable substrate. To change the argument from the temporal to the modal, although in any one possible world it may be dependent on one particular piece of substrate, this particular connection is not necessary, because in another world it might depend on another piece. All that is necessary is the dependence on some substrate. (The problem with the human person is that as yet we have no way of making this transfer.)

Another ramification of the notion of ontological dependence is the possibility of multiple dependence. This occurs when there are multiple copies of the same dependent object. The novel “Pride and Prejudice” exists only by virtue of its instantiations in printed paper, or in the memory of a person who has memorised it, or, more recently, in electronically stored text. The survival of any one of these versions is sufficient for the survival of the OD object. It is in the context of multiple instantiation that the type-token distinction comes to be made.

2.1       The Problems with Ontological Dependence

Having displayed some of the intuitive features of the notion of ontological dependence, we now want to explore the questions of why there should be such a relation in the world, and under what circumstances objects are OD on other objects. To begin the investigation, it is best to articulate more accurately why the notion of ontological dependence might be seen as problematic. Two separate problems can be identified.

Let us now elaborate these two problems in turn.

A    Existence as a Predicate

Since Kant’s celebrated argument that existence is not a predicate, and even more so since Frege located non-trivial existence claims in the existential quantifier, saying of a concept that it is true of at least one object, statements like “the bricks provide the house with the grounding of its existence” rightly ring alarm bells. It sounds too much like: “the object is yellow by virtue of the way molecules within it absorb light”, or “the object is conical because of the relative position of its constituents”.

We can coherently within a Fregean framework, introduce existence as a first level predicate, a logical constant “e(x)”, as long as it is a trivial predicate, false of nothing. That is to say, all sentences of the form “e(a)” are true as long as the name “a” has a referent. If it lacks a referent, then by the normal Fregean rules of reference, all sentences containing it, including “e(a)” will lack a referent, namely a truth-value. So all sentences of the form “e(a)”, if they have a truth-value, will possess the value “true”.

This existence concept has a similar status to the identity relation. They are both trivial at the level of reference. The puzzle of how identity could be non-trivial was the starting point for Frege’s theory of sense and reference. He accepted that identity was trivial at the level of reference, but brilliantly showed that there was another level of semantics, namely that of sense, at which identity is non-trivial and informative. We can do the same with existence. At the level of reference it is trivial in the way indicated above. At the level of sense it indicates the non-trivial matter of which name senses manage to refer. To say of an object that it exists is the same as saying of the sense we have used to refer to the object that it refers.

Suppose then we make a name sense explicit by definite description, say:

üx[p(x)Ùq(x)Ùr(x)]

 Now we do what was castigated by Kant, and add the existence predicate to the conjunction of properties in the description.

üx[p(x)Ùq(x)Ùr(x) Ùe(x)]

What has gone wrong here? Because the existence predicate is trivially true of everything, it adds nothing to a conjunction, and can be eliminated from any conjunction without loss of truth-value.

This shows what has gone wrong in terms of reference. At the level of sense what has gone wrong is that existence is about reference. The rules of the sense-game are that one first builds up a sense and then sets about determining reference. To insert a requirement of existence within the sense is to usurp the second function within the first, thereby scrambling the functionality of sense.

B     Ontological Extravagance

The starting point for a discussion of what might or might not count as ontological extravagance is Occam’s razor, the principle that one “should not multiply objects without necessity”. For this principle to be useful however, it has to be a supplemented by a description of what might count as “necessity”. The realist answer is that it is necessary to posit an object if and only if it exists, but this begs the real question, namely how are we to tell when one of these objects exists. From this realist perspective, Occam’s razor might be seen as a defence of realism, saying that the multiplication of objects is not at our disposal, but should be undertaken only when the world actually possesses these objects. It does not tell us that worlds with a vast multiplicity of objects are impossible, or are less likely than those with fewer objects; rather it requires us to back up the postulation of new objects with good reasons for doing so.

The general concept of object belongs to the Fregean meta-ontology. Therefore the question of when one should postulate objects belongs to the methodology of Fregean analysis. However Fregean meta-ontology says nothing more about what type of objects there might be, and therefore nothing about under what conditions objects should be posited as being ontologically dependent on others. We must look elsewhere for the source of the concepts “fundamental” and “ontologically dependent”.

Suppose we start with the sense of a name, and we wish to establish that not only that it refers to some object, but that this referent is ontologically dependent on some other objects. To do this we must satisfy three conditions:

·        existence      -  the name-sense in question must refer to an object;

·        distinctness  -  the new object must not simply be identical to one of the old ones;

·        dependence  -  the new object must retain the OD link to some of the old ones.

The investigation of how ontological dependence comes about will proceed by looking at examples. The example which motivated the investigation was the relation between person and body (or, if you like, mind and body). Rather than plunge in at the deep end, and look at this, probably the most complex example, we start with much less problematic examples, and see how these illuminate the OD relation. The initial two examples come entirely from within the realm of the physical:

·        a house made of bricks is OD on the bricks out of which it is made;

·        a wave propagating through a continuum is OD on that continuum.

The first example introduces the notion that material causation, the “made of” relation, is one of the forms of ontological dependence. The house relies for its existence on the existence of its bricks. If they were all to suddenly disappear, then so would the house. The second example is more subtle, and shows that there are forms of ontological dependence which are not material causation. The wave, if it is an object at all, is a different sort of object from the continuum on which it depends. It is not made of the continuum in the same way the house is made of bricks, and yet it makes no sense to think of the wave propagating without their being some underlying dynamical system of whose motion the motion of the wave is an emergent property. (The fact that it makes no sense has not stopped many physicists thinking in these terms, but this merely shows the poverty of philosophical analysis which has been prevalent in physics during the twentieth century.)

2.2            Material Causation and Ontological Dependence

The initial example of ontological dependence is that of a particular house made of bricks. It might be the house in which I am writing these words. To avoid unnecessary complication let us assume that the house is entirely made of bricks. In Aristotelian language, the bricks are the material cause of the house. We then have three different name-senses which potentially refer to the house, differing in what we choose as identity criteria.

It is important to stress that although we have three name senses here, it does not automatically follow that there a three distinct objects. The question of identity or distinctness remains to be settled.

To explore the OD relationships present in this example, and how they come about,  let us drastically simplify it. We start with a world where material causation is the only relation. Suppose we then have two fundamental objects, A and B. (Remember that the word “fundamental” simply means that we start with them – they are put into the ontology by hand rather than being generated.) The presence of material causation in the world means that there is automatically a third object, namely the collection made up of A and B and nothing else that is not a component of A and B. Let us call this collection [A,B]. (This notation using square brackets is chosen deliberately to be similar to the set theoretic notation using curly brackets. However the collection [A,B] is definitely not the same object as the set {A,B}. ) [A,B] is the object materially caused by A and B together, and as such is OD on A and on B.

The guarantee of the existence of [A,B] once A and B exists is part of the definition of the type of material causation we are considering here. If a third object, C were also present, then we would automatically have in our ontology the additional collections [A,C], [B,C] and [A,B,C]. One can imagine alternative conceptions of material causation in which some additional condition is required for the collection to exist. For example if there is some sort of spatial structure also in the ontology, they condition could be that objects have to come into some proximity relation before the collection is said to exist. A possible ontology of objects would then be, for example, A, B, C, [A,B], but no other collections. The contingent collection [A,B] in this case is still OD on its constituents, and we still have in a wider sense a constituency relationship, whether or not we want to call it material causation. (The contingent relationship can even be seen as the first glimmerings of emergence; only in the special case when two objects move into proximity does the new object, the collection, emerge.) In the present example however we shall stay with the version of material causation where the following assertion is true:

Now we can go back to the three conditions for ontological dependence and examine how they come to hold in this simple example. The existence has been put in, “by hand”, by the MC postulate. Distinctness is clearly not a problem. [A,B] is clearly distinct from A and from B. We then confront the central question: what counts as the dependence relation in this example?

That there is such a relation can be seen when we contrast saying and depicting in the example. When we list the names of objects there are three: “A”, “B” and “[A,B]”. If instead we depict them, all we need to do, and indeed all we can do, is draw A and B. This done we have already drawn [A,B]; to depict it separately would be to miss the point. (Here we make the assumption that the MC postulate holds in the world in which we are producing the pictures.) Depiction works directly with reference, where as language arrives at reference via the mechanism of sense. We have three name senses, and they refer to three distinct objects, but those three are already there when we have depicted the two fundamental ones.

2.3            Ontological Dependence and Sense

This argument from depiction shows that the dependence link is present, but does not answer the question of why there is such a link. A possible answer starts from the observation that the name “[A,B]” contains within it as constituents the names “A” and “B”. This expresses the fact that we have to use the senses of “A” and “B” to define the sense of “[A,B]”. If either one of these constituent senses fails to refer, then the composite sense will also fail to refer, which is just the provisional definition we introduced for ontological dependence. Let us make this explicit as a conjecture:

As we explore more complex examples of ontological dependence, we shall test whether this conjecture still holds true.

It is interesting that by talking of the constituents of sense we are invoking something like material causation at the level of sense. This could be why material causation is naturally the simplest example of ontological dependence. It reproduces at the level of reference precisely that relationship which, at the level of sense, gives rise to ontological dependence.

These considerations show us a natural way out of the first of the problems identified above. The existence predicate is informative at the level of sense. This is extended by the conjecture to be true of ontological dependence; we say that it is an informative relation primarily between senses – like its cousin, identity.

On the other hand, ontological dependence feels like an substantive fact about the world of reference. This appears to come about because of the distinctness of the objects; the relationship is inherited by the world of reference as something which stands in a non-trivial way between different objects. On the other hand we do not want it to be a contingent, physical relation, like efficient causation. The element of necessity is provided precisely by the fact that ontological dependence is primarily a relation which occurs at the level of sense.

The contingent aspect of ontological dependence comes about when the object is first presented to us epistemically by some feature other than its ontological dependence. This can scarcely happen with the very simple examples studied above, because there are scarcely any additional features which can be used as those which are known first. (In fact they scarcely have sufficient features for there to be any epistemology.) When we get to emergent objects, they, by definition, have new features, and these can be what we make contact with first. The associated phenomenological name-sense contains no reference to other objects. Only when we make the non-trivial discovery of identity, with some sense which does refer to other objects do we see that our original object is ontologically dependent. This identity might even be contingent, in that there could be objects with the same phenomenological properties which are ontologically independent. (This possibility will turn up below as part of the definition of what counts as emergent.) The OD relation inherits this contingency from the identity link on which it depends.

We might even say that ontological dependence is to the reference of names (existence) what logical implication is to the reference of sentences (truth values). Just as we say that the truth-value is the residual fact that can not be put into the structure of sentences – that is, cannot be expressed in the thought – so existence is the residual property which can not be expressed by putting in another predicate. Just as I have argued that logical implication is a property of the senses of sentences, so I am now conjecturing that ontological dependence is a property on name senses. This account must however also explain the disanalogy between logical connection and ontological dependence, namely the asymmetry of the OD relation. The disanalogy may have the following explanation. Logical relations depend upon the formal causes of thoughts – that is why we have a subject called “formal logic”. Frege’s great achievement in logic was to expose that part of the form of thoughts upon which logical connections depend. Ontological dependence by contrast depends instead on what could be called the material causation of name-senses; it occurs when the names of the substrate objects appear in the specification of the sense of the OD object. This contrast corresponds to the intuition that names are the object-like “lumps” within a sentence, while the incomplete expressions capture aspects of the forms of sentences.

2.4            Ordered Pairs and Ontological Dependence

The collection is the simplest kind of OD object. Now we want to go beyond collections and look at composite objects which are defined in terms of their structure as well as their composition (like the second sense of “brick house” defined above), and at those which are defined entirely in terms of their structure (like the third sense). We can use the ordered pair as the conceptual laboratory in which issues of structure can be examined. The one piece of structure we put into the ontology is the relation “before”. Let us call it “bef(x,h)”. It is an antisymmetric relation:

            "x"y [ bef(x,y) Þ Ø bef(y,x)]

Our existence postulate for ordered pairs is:

Like the collection, the ordered pair (A,B) has constituents, and is OD on those constituents for the same reason [A,B] is OD on them.

What then is the relation between (A,B) and [A,B]? Assuming for the moment that they are not identical, is (A,B) OD on [A,B]? It would seem so, because if [A,B] vanished then so would at least one of A or B and hence (A,B). On the other hand we can not say [A,B] is OD upon (A,B), because the ordered pair can vanish by virtue of the condition “bef(A,B)” ceasing to be true, even though A and B, and hence [A,B], remain in existence. The antisymmetry of the OD relation is not violated. There are two chains of ontological dependence:

            (A,B)  OD on  [A,B]  OD on A    ,            (A,B)  OD on  [A,B]  OD on B   .

It might be argued that the result: (A,B) OD on [A,B], violates the OD conjecture, because the sense of “(A,B)” does not contain the sense of “[A,B]”. However because the relation between the sense of  “(A,B)” and the senses of “A” and of “B” is a form of the constituency relationship extended to sense, it is not unreasonable to stipulate that the presence of the senses of the constituency names in itself constitutes the presence of the sense of the collection name. Therefore the sense of “(A,B)” implicitly contains the sense of “[A,B]”. This implicit presence in the sense does not extend to other objects OD on the objects whose name-senses are already there. Containing the senses of “A” and of “B” does not for example entail containing the sense of “(A,B)”, because there is nothing in the constituency relation between name-senses which is analogous to the “before” relation. With this in place we can avoid having to say that the sense of “(A,B)” is contained in the sense of “[A,B]”, which, taken with the OD conjecture would violate the antisymmetry of the OD relation.

This establishes that if (A,B) is not identical to [A,B], then it is OD on [A,B]. We still have to show that the two are not identical if we are to establish this as an example of proper ontological dependency. A simple argument that they are not identical is as follows:

(1)        (A,B)  ¹  (B,A)                 (from the definition of ordered pair)

(2)               suppose  (A,B)  =  [A,B]

(3)        then we have to say also that [A,B]  =  (B,A)

(4)                         therefore, by transitivity of identity,   (A,B)  =  (B,A)

The conclusion (4) contradicts (1), and so the supposition (2), and well as the analogous supposition (3) must be false.

A counter to this argument notes that the antisymmetry of the “before” relation precludes the simultaneous existence of (A,B) and (B,A). The truth of supposition (2) then implies that “(B,A)” lacks a referent, and therefore (3) lacks a truth value, and so the argument falls to pieces. The trouble with this is that it does too much. It implies that (1) can never have a truth value, as at least one of the constituent names must lack a referent. But we want to be able to assert (1) as following from the definition of an ordered pair. (1) has to be a statement about identity across possible worlds (or across times). The object (A,B) in worlds in which it exists is not the same object as (B,A) in the worlds in which it exists. Since we want to say that [A,B] is the same collection in all of the worlds in which both A and B exist, we can not, for reasons of transitivity, identify it with either of the ordered pairs.

To make the argument truly work we would have to develop a coherent theory of identity across possible worlds (or across times). This is outside the scope of the present discussion, so let us assume here the distinctness argument has been made. The relation remaining between (A,B) and [A,B] is not identity by ontological dependence. We then see that it is a special form of ontological dependence, not to be found in the simpler example where all we had were collections. Let us define the relation of total ontological dependence as:

TOD(x ,h)  =_df  OD(x ,h)  Ù  "y[ OD(x, y)  Þ (OD(h, y) Ú (y = h)) ]

In other words, if X is totally OD on Y, then Y is OD on everything X is OD on, except itself, (since OD is the proper relation). X inherits all its other ontological dependences through its dependence on Y. Ontological dependence which does not have this property can be called partial ontological dependence. Given that (A,B) is distinct from [A,B], then it is totally OD on it, inheriting its partial ontological dependences on A and B through the dependences of [A,B]. It is when ontological dependence is total in this way that proving distinctness becomes a problem. There is no TOD in collection theory because all that a collection could be TOD on is itself, and then the relation is identity not ontological dependence.

Now we try to construct a purely formal object based upon the ordered pair, analogous to the house defined entirely in terms of its shape. This is the object with two constituents, one standing before the other. Formally this is:

                                    üx[$y$z [x = (y,z)]]

The immediate problem with this definite description is that in general it fails the uniqueness test. If there exist ordered pairs (A,B) and (C,D), then there are two distinct objects which fit the description. So we must say that the formal ordered pair exists only in worlds in which there is only one ordered pair. But it still does not matter which one exists. If we compare worlds, one of which has (A,B) as its only ordered pair and the other of which has (C,D) as its only ordered pair, then we can say, as a matter of identity across the possible worlds that we are dealing with the same formal object.

Our example is so simple that there is only one possible form, namely being an ordered pair, and hence only one formal object. Nevertheless the example is the first in which transfer of dependence is possible. Looking at how dependence arises, we see that the OD conjecture has to be generalised to take account of this case. There is no explicit naming of the ontological basis in the definition of the formal ordered pair. The dependence is implicit, through the stipulation that one such ordered pair must exist if the formal pair is to exist. This implicit link, rather than the explicit naming of specific objects, is necessary if transfer of ontological dependence is to be possible.

2.5       The Wave-Continuum Relation

For our next example of ontological dependence, let us consider the relationship between a continuous dynamical system and the waves that propagate through it. For simplicity let us consider a one-dimensional continuum capable of transverse vibrations, such as a violin string, and the transverse waves which can propagate along it.

In this case the distinctness and dependence conditions are not difficult to establish. If the waves are objects, then they would clearly be different from the underlying continuum, and equally clearly they would be ontologically dependent on the continuum. The difficult issue is existence. There is no doubt that wavelike behaviour of the continuum takes place; the question is whether we are entitled to speak of this behaviour in terms of the existence of waves as objects (recall that we are using the word “object” in its general, Fregean sense, and so it is not restricted to lumps of matter occupying regions of space). Is wavelike behaviour simply a feature of the continuum, with talk of objects called “waves” as just a convenient manner of speaking, a useful metaphor, not to be taken seriously as referring to objects which should be included in our ontology?

Because we are looking for a realist ontology, it can not be a matter of choice whether we speak referentially about waves or not. We need to find an objective criterion which allows us to determine when a feature of the underlying system, such as wavelike behaviour, gives rise to the existence of new, ontologically dependent, objects. The classic example of such a putative object is the Cheshire Cat’s grin. When Alice expresses surprise that the grin remains after the cat has vanished, she is articulating the belief that grins, if they are objects at all, are ontologically dependent on the cats doing the grinning. The existence question is whether we need objects called grins at all, in addition to the feature denoted by the predicate “x is grinning”.

The reason we talk about waves as objects in physics is that they show a type of behaviour which is different from that of the continuum. In the case of the transversely vibrating string, they propagate along the length of the string. (Even if the vibrations were longitudinal, the motion of the elements of the continuum would be restricted to small deviations from some fixed position, whereas the waves can travel unrestrictedly along the continuum.) This unrestricted longitudinal motion is in a general sense a feature of the behaviour of the string, and yet it is not the string that moves. We are forced to speak of a wave as that which moves along the string, forced to admit the new objects into our ontology as the bearers of the property of propagation. The same is not true of grins. It is perfectly possible to attribute grinning to the cats, and so no new objects are forced into being.

Once we admit waves as objects, we see that their ontological dependence is of the transferable type. Suppose we have a wave packet occupying at any one time as small region of the string. At any time we could say that the packet is dependent only on the part of the string where it resides. As it propagates onwards, this dependence is transferred to other parts of the string. If the string is coupled to another continuum, say, to the air in which it is embedded, then the wave can leave the string altogether and propagate through the air, and yet we can say that it is the same wave (for example, by virtue of spatio-temporal continuity, and sameness of frequency).

2.6            Interim Conclusions on Ontological Dependence

Our understanding of ontological dependence will deepen further as we explore the special case of emergent objects and the even more special case of transcendence. However it is useful here to pause and summarise what has been learned about the OD relation from the simpler examples.

To establish ontological dependence we need to show that three conditions are satisfied: the existence of the new objects, their distinctness from the old objects, and their residual ontological dependence on those old objects. Which of these is the most difficult to satisfy varies from case to case. In the simpler examples, based on material causation, the existence was postulated as part of the definition of the case, and the hard work lay in establishing what constituted their dependence on the original objects or in arguing that they were not simply to be identified with earlier objects. In the example of waves, drawn from physics, the principal difficulty lay in establishing that it was right to admit the new objects into our ontology.

Just as existence as a predicate, trivial at the level of reference, becomes important at the level of sense, so ontological dependence can be characterised in terms of a property of name-senses. Ontological dependence can occur explicitly by virtue of the presence of other name-senses as constituents of the name-sense in question. Alternatively, it can appear implicitly by means of existential quantification within the name-sense, establishing dependence without specifying exactly which objects count as the ontological grounding. This characterisation in terms of sense does not however prevent ontological dependence being an objective, empirical property of objects. Objects can be presented to us in a way which does not make their dependence immediately manifest; it is then an empirical task to establish the identity relation between the name-sense cast in terms of their immediate properties and that in which ontological dependence is manifest.

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