Weak Local Supervenience as Physicalism

William Seager, 'Supervenience and Emergence', pg. 1-2
Though I am not sure that is in fact the case. Perhaps one could assume that P is total and that physicalism isn't true of W. This does sound strange though. I will not discuss it further here but it is an interesting question and deserves further thought in the future.
Such as mental properties perhaps.
I am borrowing Lewis' term here. My understanding is that it means that objects are not really important as they do not persist through time. Rather objects are mereological sums of time slices. The important part of a physical subvenient base is the spatio-temporal distribution of fundamental physical properties, not the 'hooks' upon which those properties hang.
Lewis, David. 'Humean Supervenience Debugged', Papers in Metaphysics and Epistemology, Cambridge University Press, Cambridge, 1999. pg. 2
By law here I mean a true universal generalization that is counterfactual supporting, it has modal force.
Kim, Jaegwon. 'Supervenience and Mind', Cambridge University Press, Cambridge. 1993. pg. 64.
Kim, Jaegwon. 'Supervenience and Mind', pg. 58.
I will argue in the third section that this is incorrect.
Seager, William. 'Emergence and Supervenience', http://www.utsc.utoronto.ca/~seager/emsup.pdf. pg. 7.
One might object here that states of affairs do not just depend on one particular state of a system but one might object here that states of affairs do not just depend on one particular state of a system but rather on a series of states or a set of discreet states. This point is well taken. However, I offer the following comments. States of affairs as I am construing them refer to the distribution of higher-level properties rather than trans-temporal events. I am aware that this is not a very persuasive argument. Were one a presentist physicalist then one would agree with me. However, for those who trenchantly hang on to persistentism I offer the following modification. If the state of affairs c depends on a series or set of discreet states to make it true the I shall allow the variable k to range over series of states and sets of discreet states as well as the set of singleton sets of discreet states. That is I shall allow it to range over the power set of K. Problem solved, though I am much more inclined to restrict the range k to the set of singleton sets of discreet states rather on a series of states or a set of discreet states.
It is really important to note that the argument does not turn on this assumption. Indeed it should become clear soon how my methods can be used to argue analogously for deterministic worlds.

It is important at this stage to note that this argument does not show that Weak Supervenience collapses into Strong Supervenience. For this plainly untrue. What it does suggest however, is that if the nature of the intra-world invariance between particular domains A and B is counterfactual supporting, then the Weak Supervenience of A on B is equivalent to a form of Strong Supervenience with the appropriately restricted necessity operators. This is a very intriguing idea, but one which I shall not pursue further here.

I suppose I am discounting the possibility that there are worlds that are nomologically congruent with W in which P+S is not total. Maybe there is a possible world which has the exact same P+S-laws but which has some non-P+S-governed ectoplasm floating around. However, even if one thinks such a world is possible, and I am inclined to doubt this, such a world is not of the relevant sort to defeat my argument. The invariance of state correlations across all P+S-possible worlds is what I am attempting to demonstrate.
This may also require altering the number of fundamental entities, but this is no problem.


Billy McCarthy:
Weak Local Supervenience as Physicalism

Introduction:

Physicalism is, simply put, the thesis that everything concrete is physical. It is an intuitive notion that captures the idea that all of the objects and properties in the world surrounding us are physical. This intuitive idea of physicalism is usually formally stated using the philosophical concept of supervenience. Physicalism is true if and only if everything supervenes on the physical.

As with all serious and deep questions philosophers differ as to the exact meaning of the terms involved in this definition. Indeed even after perfunctory glance one will note that the terms everything, supervene, and physical require disambiguating clarification. In this essay I am going to accept that the concept of supervenience provides a satisfactory framework in which to discuss the relation between higher-level entities and basic physical substrates. It will be my contention that a particular type of supervenience, what I shall call Weak Local Supervenience, is sufficient for a definition of physicalism.

In the first section I will give a precise characterisation of the world W in which I shall set the argument of this paper. In the second section of this paper I shall give a precise characterisation of Weak Local Supervenience. In the third section I shall argue that it is the feature that I shall call intra-world invariance that gives Weak Local Supervenience the sufficient strength and I shall attempt to show that Kim's criticisms of Weak Supervenience are misguided. The nature of the intra-world invariance is counterfactual supporting, and this leads to a collapse of Weak Supervenience, in this particular domain, into Strong Supervenience, in particular nomological supervenience.




Section 1:

In this section I shall discuss the possible world W, the setting of this argument, its physical makeup and the nature of its natural laws. William Seager has offered the following definition of a total theory. "A theory, T, is total if and only if it possesses completeness, closure and resolution. These are jointly defined as follows: Completeness is the doctrine that everything in the world is a T-entity or, in principle, has a non-trivial T-description and as such abides by closure and resolution. Closure entails that there are no 'outside forces' – everything that happens, happens in accordance with fundamental T-laws so as to comply with resolution. Resolution requires that every process or object be resolvable into elementary constituents which are, by completeness, T-entities and whose abidance with T-laws governing these constituents leads to closure." 

Let us now consider W. Let P be the ideal physical theory in W. Ought I say that P is total theory in W? To do so seems somewhat question begging. If I were to make that assumption then any further arguments I make, upon whose strength I presume the truth of my conclusions to rest, would be superfluous. It would seem that I would simply be assuming that physicalism is true and then showing that given that assumption it follows that physicalism is true. On the other hand I do not want to entertain the possibility that W is a world in which a mental substance of the Cartesian ilk exists. I want my initial characterisation of W to permit both that P is a total theory in W and that property dualism of Chalmers obtains in W. Though it might seem that one would need to make contradictory assumptions to achieve this, it is not so. I just need to assume that P in conjunction with a set S of supervenience laws is total in W, and leave it unanswered whether S is a subset of P.

If S is a subset of P then P is total and physicalism is true. If on the other hand S is not a subset of P then there are some fundamental laws linking certain P-irreducible properties, qualia perhaps, to substrates that are P-entities. If S is not a subset of P then W is world in which emergence, qua non-reductive physicalism or property dualism obtains. For instance there may be fundamental psychophysical laws that state that certain mental properties supervene on the brain as a physical substrate. Also it is pertinent to note that P+S, even assuming that S is not contained in P, is total in W according to Seager's definition. Kinds that are P-irreducible have non-trivial P+S descriptions, they obey the closure with respect to P+S, and they are resolvable into P+S entities. The same goes, obviously, for P-entities. Thus P+S is a total theory in W. The P+S theory then gives a full characterisation of the natural laws of W. W can then be described as the P+S system.

A system is a set of interacting or interdependent components forming an integrated whole. W is a system comprising the physical microstructure described by P and supervening higher-level properties of an unspecified nature, those governed by the S-laws. At the macro-level I shall refer to W as the P+S-system. However, at the level of micro-description W can just be thought of as the P-system. The reason for this is the following. P is an ideal physical theory and together with a set of supervenience laws it is a total theory. From this it follows that all of the objects in W are physical. All that might not be physical are supervenient properties. Thus at the micro-level W is a physical system.

Let us stipulate two further points about W. Suppose that W is such that nothing is lost if we speak in anti-haecceitist terms. Also, stipulate that the fundamental properties are local qualities, the perfectly natural intrinsic P-properties of points or of point-sized occupants of points. Also that "the fundamental relations are the spatio-temporal relations; distance relations both spacelike and timelike, and perhaps also occupancy relations between point-sized things and spacetime points." Then W is just the physical system comprised of the spatiotemporal distribution of the P-properties together with those properties that supervene upon the P-system according to P+S. Each temporal segment of the P-system is a state or P-state of the system. Each P-state can be given a complete description in terms of the spatial distribution of P-properties. The P+S state then is just the higher-level description of the subvening P-state. Thus were we to freeze W for an instant we have both the P-state, given by the spatial distribution of P-properties, and the P+S state, the higher level description including kinds found in the S-laws.

Consider now any conceivable state of affairs A within W, that is, any P+S conceivable state of affairs. A can be completely described by the P-state and the properties that supervene on the P-state according to P+S. Thus the P-system, that is, the series of P-states, which are just the series of spatial distributions of fundamental P-properties, is the subvenient base for all truth in W. All states of affairs of any level supervene upon the P-system.

I shall make one further point about the physical makeup of W. Let s be a supervenience law in W. This law will be roughly of the form 'property m supervenes on property p'. In this schema p is a physical property, that is, a spatial distribution of fundamental P-properties. If the properties p and s appear in a supervenience law then it is fair to assume that p and s are nomic kinds in W. As such they are metaphysically and epistemically significant. I shall stipulate that subsets of the P+S-system, such that properties that are are nomic kinds occur only in said subsets, are P+S-subsystems of the P+S-system. Intuitively a subsystem is a subset of the system that displays integrated wholeness, that is, they display structure, behaviour and interconnectivity. This is not meant to be an airtight definition but it is supposed to capture the idea that there are epistemically and metaphysically significant subsets of W that display a unity both metaphysically and epistemically as they are the substrates of fundamental S-properties that appear in the S-laws.

I offer the following as P+S-subsystems without argument: sub-atomic systems, biological systems, neuro-biological systems, psychological systems, sociological systems, the solar system, and the galactic system. Each temporal segment of a P+S-subsystem is a substate. This state can be described purely in terms of the distribution of P-properties. Conceived in this way I shall denote the state as a P-substate. It can also be described using higher-level properties. Conceived in this way I shall denote the state as a P+S substate. Each nomic kind of P+S substate supervenes on a corresponding kind of P-subsystem.

Section 2:

It remains now to describe the nature of the supervenience in question. In order to do this I shall discuss, combine, and modify Jaegwon Kim's concept of Weak Supervenience and William Seager's concept of Local Supervenience. In his essay 'Concepts of Supervenience' Jaegwon Kim gives two equivalent definitions of weak supervenience. Let A and B be sets of properties.
Weak Supervenience 1. The set A weakly supervenes on B if and only if necessarily for any x and y if x and y share all properties in B then x and y share all properties in A.
Weak Supervenience 2. A weakly supervenes on B if and only if necessarily for any property F in A, if an object x has F, then there exists a property G in B such that x has G, and if any y has G it has F.
These definitions are illuminating. There are three important things to note about supervenience so defined. Firstly it captures the main insight of supervenience in general; there can be no change in the supervening set without a change in the subvening set. Suppose x and y are any two objects in a possible world w*. If x and y share the same B properties they share the same A properties. It is impossible that two objects within one possible world share the same subvening properties and not share the same supervening properties.

Secondly, this definition entails cross-temporal correlations. I shall call this Intra-World Invariance. By this I mean that if at t1 in w, x has the B-maximal property B^ and the supervening A-maximal property A^, then if at t2 in w, y has B^ then y also has A^. This point will be central to my defense of Weak State Supervenience later.

Thirdly, the salient feature of weak supervenience, what distinguishes it from strong supervenience, is that supposedly it only holds for objects within the same possible world. It has no built in trans-world modal force. If x and y are objects in different possible worlds then it is permissible that they be B-indiscernible and A-discernible. Thus we might have that in the actual world x has the B-maximal property B* and the supervening A-maximal property A*, but in the possible world L, y has B* but does not have A*. This seems to render weak supervenience very weak indeed. It is this point that leads Kim to discount weak supervenience as too weak to support physicalism. More on this argument later. 

These definitions are helpful, however, given my anti-haecceitist Lewisian perspective, the use of objects in the definition is somewhat problematic. I would rather speak in terms of properties and their spatiotemporal pattern of instantiation. Thus I shall modify Kim's definitions to incorporate the use of systems and states of systems. I will however retain the three features of weak supervenience that I noted above.

William Seager has defined local supervenience. Let w and w' be any two possible worlds. Let U be a family of properties and F an element of U. Let V be a family of properties and G an element of V. Let δ and θ be systems in w and w' respectively. Then the following is the definition of local supervenience.

ww')(F U)δθ(G VGδw Gθw' Fδw Fθw')

Just as Kim's above definition of weak supervenience captured several key aspects of my intended form of supervenience, so too does Seager's. He introduces the idea of systems. However Seager's definition has trans-world modal force and thus is not a form of weak supervenience. Let me modify it somewhat. I wish to preserve his use of systems but confine supervenience to one possible world.

I wish to make one final modification. When we speak of the world scientifically we speak of particular properties and their relations within particular domains. We do not as a rule speak of maximal states of affairs and a universe-wide subvening physical state. I want my form of supervenience to be local, not global. This is motivated both by folk and scientific understandings of the world. Thus the units in my Weak Local supervenience are the P+S-subsystems and their states. These are those subsets of the P+S-system that are the physical substrates for all higher-level properties governed by the S-laws. My particular mental state does not depend upon the entire physical state of the universe but rather upon a much more local subset of the physical system, namely my brain. Every P+S substate of W supervenes on a particular P-substate of W. Let K be the set of all possible P-substates. Let C be the set of all possible P+S substates. Let X be the set of all possible P+S-subsystems. The let kx denote that the subsystem x is in the P-substate k, and let cx denote that the subsystem x is in the P+S-substate c.

I shall give the formal definition of Weak Local Supervenience (WLS).

( (c C) ((x,y) X)((cx k K kx) ky cy)

This states that necessarily for all states of affairs, that is, P+S-substates, for all P+S-subsystems, if c obtains then there exists a state k in K such that x is in k and if any other subsystem y is in P-substate k then c obtains. This has all of the features that I desire for my supervenience relation. I shall now argue that this is a sufficient condition for physicalism.

Let us consider what this formulation gives us. First it states that in W every state of affairs supervenes on the spatial distribution of the P-properties. C supervenes on K. Thus we have that everything supervenes on the physical. This is obviously an important feature of physicalism and Weak Local Supervenience (WLS) has it.

Secondly, not only does WLS give us this, it also gives us an exhaustive list of specific correlations. The incorporation of the specific supervenience correlations found in the S-laws ensures this. For every higher-level state of affairs there is a physical subsystem kind upon which it depends.

Thirdly WLS states that there is a specific subsystem upon which each particular state of affairs supervenes. The second and third points highlight the strong anchoring of all states of affairs in local subsystems. This is an important feature of the world and thus it is satisfying that WLS captures it. For instance we have that human psychological properties supervene on human neuro-physiology only, and that a specific psychological property depends on a specific neuro-physiological state. This again is a strong argument that WLS is sufficient for physicalism.

A further important feature of WLS is that it ensures the intra-world invariance between the higher-level states of affairs and subsystem kinds. If a subsystem x, for x X, is in state k at time t, and is also in state c, for c C, which supervenes on k according to an S-law, then if any subsystem y, for y X, is in k at any time t*, then y is in c. This again is an important feature.

So, we have there exists an exhaustive list of temporally invariant correlations between every state of affairs and a spatial distribution of fundamental P-properties, indeed, given the supposition of Humean Supervenience, we have that, in W, every state of affairs just is a pattern in the spatial distribution of fundamental P-properties. What more is there to physicalism? What features of physicalism has Weak Local Supervenience not captured? There are two purported missing features according to Kim and Chalmers respectively. In the following section I shall discuss them.


Section 3:

The first argument does not criticise Weak Supervenience specifically but rather any form of supervenience definition, which does not require logical necessity. Thus even if we granted that Weak Supervenience does generate a sphere covariation and dependence then it still would not be sufficient for physicalism. This is Chalmers' argument. It is his contention that if all states of affairs do not broadly logically covary with the physical then it cannot be inferred that the S-laws are a subset of the P-laws. I think this is a mistake. I will not argue for it here but I think that the best account of the laws of nature is David Lewis' based on his extensive work in counterfactuals. This captures the idea of exceptionless regularities that are counterfactual supporting. Given this understanding it is Lewis' conclusion that one needs only nomological supervenience, not logical supervenience. This is a complex argument and I shall not go into details here, but it suffices to say that I agree with Lewis. All that is needed is nomological supervenience. If one assumes this then one can infer that S is a subset of P if one can demonstrate that the P+S system strongly nomologically supervenes on the P-system.

The second argument is Kim's. As I mentioned above it is his contention that Weak Supervenience does not have trans-world modal force. There is no sphere, centered on the world in question, of possible worlds in which covariation and dependence of everything and the physical holds. That is, there is no necessity. It is this feature, which is the target of the first argument. As I mentioned above Jaegwon Kim gives two equivalent definitions of weak supervenience in his essay 'Concepts of Supervenience'.

Upon a first reading of these definitions it is difficult, at least it was for me, to see the supposed lack of trans-world modal force. Consider the following. Suppose that in the actual world the set A weakly supervenes on the set B. Suppose x and y share all B-properties in the actual world. That is, suppose they have the B-maximal property B*. Then they share all A-properties, say the A-maximal property A*. Weak supervenience states that necessarily for any x and y if x and y share all properties in B then they share all properties in A. The effect of the necessity operator is to render the statement 'for any x and y if x and y share all properties in B then x and y share all properties in A' true in all accessible possible worlds. One could be forgiven for supposing that this, in conjunction with the fact that in the actual world the B* A* correlation holds, that it follows that the B* A* correlation holds in all the possible worlds in the accessible sphere. This is false, however. For 1 references the sharing of properties only not a particular correlation. The definite description 'the subvening B-maximal property of A*' is not a rigid designator. Though in the actual world it refers to B* it does not do so in every possible world. Its referent can vary from world to world. Thus, the following worlds are possible, or at least not forbidden by Weak Supervenience.

Let A be the set of all mental properties and let B be the set of neuro-physiological and neuro-biological properties. In W B* subvenes under A*. There is a possible world L in which the object x has B* but has A^, not A*. A^ does contain any conscious properties, indeed it is the empty set. Thus we can have an object y in L, a world nomologically congruent with W, with the exact same neuro-physiological and neuro-biological properties that x has in W that has no mental properties, or very dissimilar mental properties, or any possible configuration of mental properties, i.e., zombie worlds.

This problem can be perfectly translated into an equivalent problem in my terminology. Let Cm be the set of human mental properties, and let Xm be the set of the kind of subsystems (the neuro-physiological and neuro-biological systems of humans) on which the elements of Cm supervene, by the S-laws. Let k be a state of Km upon which c supervenes. Then in the P+S-possible world L, a subsystem of kind Xm can be in state k and not be in state c. This is indeed a problem. Despite the positive aspects of aspects of Weak Supervenience, which I have explored, namely the intra-world invariance of higher-level states of affairs and states of subsystems, this objection seems to render such invariance too weak to support dependence. And dependence is a requirement for physicalism. Of this I am in no doubt. Pure arbitrary correlations are not sufficient. The invariance generated by Weak Supervenience is not arbitrary however. It is a counterfactual supporting invariance and I shall now demonstrate this.

I shall first provide an argument that shows that the intra-world invariance of states in W holds in all historically accessible worlds. I shall assume for the moment that some of the fundamental P-Laws are probabilistic. I am inclined to think that this is true as the laws of Quantum Mechanics are fundamentally probabilistic. Then according to the P-Laws the P+S-system can evolve in more than one way. Given a certain P-state s, there exist more than one P-states, s*,..., s*n, such that according to the P-Laws each of s* to s*n can follow s. This is an a priori truth about W. Consider the first state SW1 of the P+S-system. Let H denote the set of possible worlds that can follow from SW1 in according to the P+S-Laws. When W was in SW1 it was possible for it to become any world in H, and it was, in principle, unknowable, that is, it was radically undetermined, which world W would become.

Now, that Weak Supervenience obtains in W is an a priori truth, thus it permanently true in W. Let us consider W in the present. Suppose both, that the psychological properties of humans, Cm, supervene on their neuro-biological systems Xm, and that the psychological properties of specific individuals supervene on that specific individual's neuro-biological system. Then we have that for each element c in Cm there exists a state k, an element of Km, such that if any system x in Xm is in state k then x is in c. Call this statement PC(M). Let us now rewind to the first state SW1 of the P+S-system. Within one world, the correlation of supervening and subvening sets is invariant. It is a cross-temporal correlation. Thus PC(M) was true at SW1. Of course this follows simply from the fact that Weak Supervenience is a priori true in W. From this in conjunction with the fact that SW1 could evolve into any element of H, it follows that PC(M) is true for all h an element of H.

Analogous arguments can be made for all kinds of higher-level states of affairs. Let PS be the conjunction of all specific intra-W state correlations. We can conclude that PS is true in every element of H. This also follows from another line of argument. At SW1 the only element of H is W. As the system evolves each world has the property of being as it was at SW1. Thus each world in H was identical at SW1. Weak Supervenience, and all its specific state correlations, was true a priori at SW1. Such a truth is permanent. Every element of H is just a temporal evolution of the P+S-system from SW1 in conjunction with the P+S-Laws. Thus Weak Supervenience and its specific state correlations are true in every element of H. H is the sphere of historically accessible worlds from W. This is certainly a sphere of necessity. I have thus established that Weak Supervenience does generate trans-world modal force, if one assumes that some of the P-laws are probabilistic.

However, the worlds in question do not exhaust the nomologically possible worlds with respect to W. This still leaves open the possibility that a there exists a P+S-world with different state correlations than those that obtain in W. Indeed if it is the case that W is deterministic then the sphere of historically accessible worlds contains only W. It is clear then that I have not yet shown that Weak Supervenience generates the needed trans-world modal force. The above discussion, however, indicates a method to achieve this. The assumption of indeterminacy provided a natural way to generate divergences between W and other possible worlds. We can take this insight and use it to extend the sphere around W in which the state correlations are invariant to include all nomologically possible worlds, that is, all P+S-worlds.

Consider N, the set of nomologically possible worlds from W, that is, the set of P+S-possible worlds. In every P+S-possible world P+S is a total theory. It is complete, closed and resolute. Every world in this set is just a P+S-possible series of states of the P+S-system. We need then to show how W can diverge into these worlds. Take any possible world n an element of N\H (The set of P+S-worlds less the historically accessible worlds from W). These are the worlds that are not P+S-possible evolutions from the state SW1. The spatial distribution of P-properties in SW1, the first state of the P+S-system in W, cannot evolve into n according to the P+S-laws. Let Sn1 be the first state of the P+S-system in n. We have that in W there are the S-laws, that is, an exhaustive list of state correlations. Let u be an S-law. It is true that u in W, thus it is true that u at SW1.

Now suppose that we break the P-laws by altering SW1. Suppose that we change the spatial distribution of fundamental P-properties so that SW1 is now the exact same as Sn1. So now Sn1 is a state of the P+S-system in W. Given that n is just a temporal series of P+S-states, it follows that W will evolve along the same path (if deterministic) as n, or one of worlds that diverges from W will evolve along the same path as n (if indeterministic). I have a very strong intuition that in this case u will hold in all worlds that evolve from Sn1 as it is an S-law and no S-laws have been supposed to break. The point is that by our law breaking act of altering the spatial distribution of P-properties we both change W into n and preserve the truth of u.

Generalising from this we get that all S-laws are true in all elements of N. Thus every intra-world invariant correlation between the equivalence higher-level states of affairs and the subsystem kinds in W is true in every P+S-possible world. The counterfactual supporting nature of the intra-world invariance of everything on the physical in W leads to the collapse of Weak Supervenience into Strong Supervenience with regards to these domains. I have thus established that Weak Supervenience does create a sphere of nomological necessity.


Conclusion:

In this essay I have given a clear account of Weak Local Supervenience. I have argued that the Weak Local Supervenience of all higher-level states of affairs on the P-substates of the P+S-system is sufficient for a robust definition of physicalism. I have sided with Lewis against Chalmers in assuming that what is needed is the nomological supervenience of higher-level states of affairs upon the microphysical structure, not broadly logical supervenience. I have then argued that Weak Local Supervenience of all P+S substates upon P-states entails the strong nomological supervenience of the P+S states upon the P-states. At this point then all that remains is to question whether the strong nomological supervenience of the P+S system upon the P-system is sufficient to infer that S is a subset of P, that is, whether there is a legitimate sense in which S-entities are not physical. It is my strong feeling that it would be extremely skeptical to continue to suppose that the S-properties are non-physical. Having said that this is what Chalmers does. As I have already noted though I am sidestepping this issue in this paper. It was my intention to argue that Weak Supervenience is sufficient for defining physicalism. If one agrees with Lewis and accepts that nomological supervenience is all that is required, and I do, then I have achieved what I set out to do. Weak Local Supervenience is a strong enough relation to define physicalism if one accepts that Strong Nomological Supervenience is a strong enough relation.




Bibliography:

Chalmers, David. 1996. The Conscious Mind. Oxford University Press, Oxford.

Kim, Jaegwon. 1993. Supervenience and Mind. Cambridge University Press, Cambridge.

Lewis, David. 1999. Papers in Metaphysics and Epistemology. Cambridge University Press, Cambridge.

Seager, William. Emergence and Supervenience. http://www.utsc.utoronto.ca/~seager/emsup.pdf.