On Philosophy

November 29, 2007

The Theoretical Nature Of Identity

Filed under: Epistemology,Metaphysics — Peter @ 12:00 am

Ordinary discourse doesn’t include many appeals to the notion of identity, and certainly not any precise ones, even though truths about identity often surface in the form of claims that two apparently distinct things are actually the same. Thus we might turn to logic for a precise definition of identity. There it is treated as just one two place relation among many, one that holds between every object and itself and which never holds between two different objects. Such a description removes all the mystery surrounding identity, but it is also relatively uninformative. For example, it would be nonsensical to ask why two objects are identical, because that would be equivalent to asking why one object is identical to itself. And clearly there is no reason why an object is identical to itself, that is just a brute fact. Problems also arise with the logical definition of identity when considering possibility and necessity, and in other contexts, which suggest that there is more to identity than the logical relation captures, such that logical identity only reflects the nature of identity in certain limited circumstances.

Given that the logical definition of identity has failed up perhaps we are forced to turn to our ordinary use of identity. But when it comes to our ordinary use of terms such as “the same”, which seem to be those from which the idea of identity is extracted, it doesn’t seem much like a relation at all. Whenever we say that two things are the same there is an implicit understanding that they are the same something. For example, we might say that two people drive the same kind of car, uniting the two distinct objects under the umbrella of a single kind. Now it might be objected that this is simply too broad a conception of identity, that all we really seek to understand is the way in which a brick viewed at one moment is the same as it viewed in another moment. But, even here, we must stipulate that they are the same brick where being the same brick brings with it the idea of a temporally extended object. Otherwise we could object that what we saw in those two moments were really distinct objects, distinct brick-moments. And the same applies when we try to talk about the same brick seen by two different people at a single moment. It could be claimed that there are two non-identical brick-presentations under consideration, and thus to say that they are the same we need to say that they are the same brick, where this time brick brings with it the idea of an observer independent object that can be presented in a number of different ways. Under this conception identity seems to be a concept that is essentially tied to a way of dividing the world into a number of equivalence classes, such that saying two things are the same is really just to say that they belong to the same equivalence class under some division. And thus which things are identical and which aren’t seems completely a product of the way we divide the world, which is itself arbitrary, and thus it is hard to see how claims about identity could be significant, which is the real problem.

That seems odd, because there certainly appear to be important facts about identity, but we can’t easily get back to such facts and something like the logical conception from this starting point. We can’t for example, simply try to redefine identity without any such equivalence classes. Well, we could, but identity defined without such equivalence classes to bring together things that we might otherwise distinguish between leaves us with virtually no cases where identity holds at all. Under identity, so defined, the only time we might legitimately say that two things are identical is when we are referring to the same particular experience of something and saying that it is identical to itself. This would make identity simultaneously trivial and useless. Nor can we recapture the logical notion by simply picking one way of dividing the world into equivalence classes as “right”. Admittedly such a division would fix things to some extent, but the decision about which division is “right” seems itself completely arbitrary. Some might even make the case that the universe is best conceived of as a single object, and that what we think of as different objects, such as different particles at different moments of time, are really just properties of this universe-object, the property of it containing a particular particle in a particular place at a particular time. Certainly we can’t say that this way of logically describing the universe disagrees with our experience, it just makes talking about it a little difficult, and it completely does away with the possibility of any identity relation, since there is only one object that it might apply to, and is thus rendered meaningless simply because it doesn’t distinguish between objects.

A third way to bridge this gap, which we haven’t considered previously, is to consider equality as tied up with language, something that hasn’t come into play yet. The interesting claims involving identity, we might note, are those where we say that two things designated by different names are identical. For example, we might assert that the richest man in Europe is the tallest man in Europe, which could be to claim that those individuals are identical. And thus it might be supposed that identity is really a claim about what two terms refer to, namely the same thing, which couldn’t be properly captured by the suggestions above simply because they had no way to talk about referring. There does seem to be a kernel of truth in this suggestion, but it too has its failings. First of all it is still based on a kind of ordinary understanding about identity, and so still seems vulnerable to what it means for two things to be “the same thing”, which plays a key role in the definition. Again it seems that a division of the world into equivalences classes is necessarily involved. And in this case the division seems even more complicated. Certainly, for example, the richest man in Europe hasn’t been the richest for exactly as long as he has been the tallest, thus we run into problems in saying what exactly “the tallest person in Europe”. Does it mean the time extended person who is the tallest now, does it refer to the person-moment that is tallest now, or does it refer to all person-moments in all times that are tallest, regardless of whether they belong to the same time extended person? To make it true and meaningful we must pick some division, but, again, how to divide the world seems arbitrary. Secondly, it seems to fail to capture some of the ineffable essence of claims about identity. When we claim that the morning star is identical to the evening star we mean to say something to the effect that, roughly, the two objects under consideration are really one object. But so far none of the possibilities entertained have let us make this kind of assertion, because they don’t allow us to talk about two objects in one breath and a single object in the next.

To solve some of these problems I think we need to turn to why we talk about objects in the first place. The idea of objects, I claim, is a device that exists simply to make conceptualizing and theorizing about the world simpler. We divide the world up into objects and assign them properties, and then on the basis of this division and its laws we make predictions and check how well our model matches up to observations. Thus objects are from the beginning our invention, they don’t exist outside of us to find, even though talk about objects can be considered in the domain of objective fact. Thus we can make a distinction between talk about the model and talk about relationships between the model and the world as observed. To say that an object is red or at a particular location is to make a claim about the world, expressed through a relationship between statements about our model and the world. On the other hand, to say that a certain law holds of objects is strictly talk about the model. Of course we can make observations that contradict the proposed law, but we can never observe the law itself. And thus it is more accurate to say that our observations have revealed that the proposed model, including the law, doesn’t accurately reflect the world, rather than saying that they show the law doesn’t exist or is false. We can put this distinction to a number of purposes. For example we might point out that world-model correspondences can be given explanations in terms of the model, we can say why an object has a particular color or location by appealing to the structure of the model and its laws; but we can’t explain brute facts about the model itself, such as its laws, in the same way. But obviously this is tangential to the matter at hand.

So, to return to identity, allow me to simply assert that identity is a claim about the model, not about the world. It is saying that our model contains only one object that will be used to explain what might be thought of as two distinct phenomena, or what were explained using two objects in another model. Because identity fixes the model this explains why we have talking about identity from within the model; once you have decided what your objects are it is fairly useless to go over those facts again. Of course even under this understanding of identity there is still some arbitrariness about what your objects are. For example, we could double the number of objects by modeling the world with two objects wherever previously we had one, with one object accounting for all observations made from galactic north and another for the observations from galactic south. However I would point out that there is nothing “wrong” with such models, they are just a more complicated way of expressing essentially the same facts. But, for the sake of convenience, we tend to go for the fewest number of objects, and thus the maximum amount of identity, arguing that we should use a single object whenever possible, so long as contradictory properties (A and ~A) aren’t assigned to that object. Most importantly, of course, is simply that, regardless of whether there is arbitrariness here, claims about identity are significant, not as facts about the world, but as facts about the model, which makes arbitrariness somewhat irrelevant. I would elaborate further, but I fear I have gone on too long for one day already, so I will leave the rest to the reader (unless some especially interesting complications occur to me later).

August 2, 2007

The Functional Properties Of Simulated Worlds

Filed under: Metaphysics — Peter @ 12:00 am

Under normal circumstances there is no reason to object to the idea that simulated objects can have the same properties as real objects, and thus that simulated worlds can embody all the same functional properties as the real world. For example, let us suppose that a real calculator has the functional property of using algorithm A for addition. It has this functional property as the result of its parts having the right causal connections to each other. A simulated version of this calculator would also implement algorithm A for addition. Although its “parts” would really be data in the software doing the simulation they would still have the same pattern of causal relationships to each other, and hence would have all the same functional properties.

Thus the real world and a copy of it running in software have the same functional properties. Let us suppose that the simulation software running such a world works internally by transforming a block of data that represents the contents of the world from one configuration into another over and over again, thus making the simulation “run”. Consider then another piece of software. This one also transforms a similar block of data over and over again, but it does so randomly (truly randomly, not pseudo-randomly). Now, by an extremely unlikely coincidence, let us suppose that the states of these blocks of data, the one that represents the simulated world and the one being transformed randomly, are identical (for the entire time that the simulation is run). The question then arises, does the data brought about randomly have the same functional properties as the data representing the simulated world? Or, more to the point, is there anything it is to be like to exist as part of that data?

The intuitive response is to say that no, it doesn’t have the same functional properties, because the right causal connections aren’t present. In the simulated world the software that is transforming the data follows certain rules, and those rules create the necessary causal relations. In the case of the software altering the data randomly the software does not create those relations, there is no sense in which the state of the data at one time contributed to the state of the data at future times, and so they were completely unrelated.

This answer, regardless of whether it is right or wrong, is not acceptable. It makes causation between different data states dependant on some external force, namely whether the software really is pushing the data around following the appropriate rules or not. But we can’t make that the standard for whether causal relationships hold because then we would have no way to know whether causal relationships hold in this universe. It doesn’t make sense to talk about something “outside” of our universe making events turn out one way instead of another. No, when it comes to our universe we accept that causation is a description of the patterns we find in events, not some additional force that pushes events one way or another. This is the only reasonable position we can take towards causation without running into certain epistemological dilemmas. Thus, by extension, it would seem that whether or not the right causal relationships obtain between various states of the data is dependant only on the existence of patterns in the state of the data over time. And since the data went through the same sequence of states in both cases then we can describe both of them using the same causal description, and hence the same functional properties must hold in both.

Which is not to say that the original assessment was completely off base. What we have here is perhaps two different perspectives on the data. Obviously the software has certain causal dispositions, and the simulation software and the random software differ in their causal dispositions, despite the fact that on rare occasions they may behave identically. This is because the parts that determine their operation participate in more general patterns, and from those we infer that the software does not necessarily behave in the same way. So our intuition that the data associated with the simulation program had the right causal connections and that the one associated with the random program didn’t was really an intuition about the software, one piece of software does have the right causal relationships while the other doesn’t. However, we can also look at the data by itself. The data by itself also has certain regular patterns, which might be described as causal relationships. And these relationships of course depend only on what the data is, not how it was generated.

Now from our external point of view we have a very different attitude about the progression of these two programs. In the case of the simulation we are quite sure that the regularities expressed so far in the data will continue to hold. Our surety is based on our surety that the causal relationships embodied in the program creating those regularities will hold. In contrast, while observing the progress of the random program we will be quite surprised that patterns exist, and we will expect those patterns to be broken eventually. But from “inside” such a simulation things are the same. There is no information about the process manipulating the data, and so an inhabitant of such a simulation will be in exactly the same situation we are, specifically we have no evidence that the causal regularities we have so far observed will in fact continue. Which is one more reason to believe that whether the program generating the data is likely or unlikely to continue creating the same patterns that have so far been observed makes no difference to the functional properties of the data (not the software), since we are in the same position as an observer inside the data, of not being able to know how likely the same patterns are to continue, and since we can’t know obviously it doesn’t make a difference to the current functional properties of the universe (since if it did make a difference then we could know, via that difference, how likely it is the patterns we have observed so far will continue to hold).

July 21, 2007

Scientific Realism

Filed under: Metaphysics — Peter @ 12:00 am

Realism in general is the position that whether a statement is true or false is something that depends directly on an independently existing reality. For example, to be a mathematical realist is to believe that mathematical entities have their own existence. Since this seems relatively absurd most people are not mathematical realists, but are instead mathematical irrealists, believing that the truth of mathematical statements is decided by some other criterion, such as the ability to construct a valid proof, which doesn’t imply that the mathematical entities themselves have an independent existence.

Here I will defend scientific realism from some of its critics. Scientific realism is the position that the only independently existing entities are those that are involved in the ultimate scientific explanations*, and that nothing else besides them has an independent existence. Scientific realism has some obvious attractions. Since it can explain everything (everything that happens), in principle, it is hard to see what role any other independently existing entities could play. Certainly they couldn’t be required for an explanation, and thus we couldn’t be required to admit that they exist. (Note that we can still talk about other things besides the fundamental scientific objects, we just have to avoid making them something above and beyond those objects; instead identifying particular occurrences of them with particular arrangements of the fundamental scientific objects.) And it certainly seems like a better idea to allow ontology to rest on the objectively sound foundation of science instead of some more questionable category scheme.

But some have misgivings about the way scientific realism does away with the existence of ordinary objects. After all “there is a chair in the corner” is a statement that is not true, strictly speaking, under scientific realism. And realism in general was supposed to be a position that saves our common way of speaking about things from philosophical positions like idealism. But I think this complaint is too hasty. Yes, scientific realism does force us to reconsider our everyday use of language, but unlike idealism it doesn’t force us to view it as completely mistaken. Instead our common use of language can be seen as roughly correct, as simply being too imprecise, but not out-right wrong.

Instead of understanding an utterance such as “there is a chair in the corner” to mean that there is literally some single object, a chair, in the corner, we can instead understand it to indicate that there is some collection of “real” (described by fundamental physics) objects that have the property of appearing like a chair to us. This captures both the ordinary claim that the chair exists, because our new understanding still tells us that something, some collection of particles, exists and the claim that it is a chair by describing this thing as seeming like a chair. So, unlike idealism, this understanding of the “real meaning” of the sentence is not a radical reinterpretation (idealism would tell us that “there is a chair in the corner” means only that we perceive a chair in the corner), rather it is more of a clarification of our original intent, capturing basically the same meaning in terms of the entities accepted by scientific realism.

Of course even this kind of reinterpretation of sentences may leave some feeling uncomfortable with scientific realism, feeling that it has somehow pulled the rug out from under ordinary discourse. But of course this isn’t the case. Even though we aren’t mathematical realists we don’t have problems talking about numbers as if they existed, for convenience. And so there is no problem with talking about chairs, and solidity, and all the familiar components of our world even if we accept scientific realism. We just have to remember that these things exist only as chairs, as solid objects, in the context of our discourse, and that in certain contexts we can’t appeal to things like the property of being a chair, or the property of being solid, except as an abbreviation for a certain scientific description. But this distinction isn’t too hard to make.

* If the physics we have today was the ultimate scientific explanation then these entities would be various fundamental particles. However we don’t know where science will come to a rest, and so we can’t say what exactly the fundamental entities are, but even so there is good reason to believe that at some point there will be theories that explain everything.

July 12, 2007

The Identification of Properties

Filed under: Metaphysics — Peter @ 12:00 am

Ultimately every property is some kind of causal disposition. It is not my purpose to establish that claim here, but claiming otherwise, claiming that there could be two different properties associated with the same causal disposition (or a property associated with no causal dispositions), is absurd. If that were the case how could we know that there were in fact two different properties associated with this single causal disposition? But given that properties are associated with particular causal dispositions we want to know how to identify two properties. This is not, of course, an attempt to determine when two properties always (necessarily) coincide. To do that is easy, we simply look at the causal disposition that defines the two properties, and if it is exactly the same disposition then they are identical. That is not a particularly interesting question, nor is it particularly informative. What is interesting is the cases in which we have two properties, defined as different causal dispositions, which are in some situations identical (or so I would claim).

Here I will lean on color to explain my ideas, since color is a well-understood phenomenon (physically if not psychologically). For the sake of simplicity let us understand being a particular color just as the property of reflecting a particular wavelength of light. And let us also consider the property of being coated in a particular type of paint. The question to ask then is whether an object’s property of being coated in a particular type of paint is identical to its property of being a particular color, despite the fact that being coated in a particular type of paint and being a particular color do not always coincide. At work here is the idea that even though we speak of a property as a general kind of thing most properties do not exist independently. Instead they exist in virtue of a number of microscopic properties of the object, leading us to say that in particular cases that macroscopic property (or at least particular instances of it) is identical to that set of microscopic properties. And different arrangements of microscopic properties may result in the same macroscopic property. Thus we can think of our interaction with macroscopic properties as interactions with particular instances of them, particular arrangements of microscopic properties that give rise to them. (Of course microscopic properties themselves hold in virtue of simpler and simpler properties, until we come to the most fundamental properties, such as “being an electron at a particular location”, which we don’t have enough information to say more about.) Thus while two macroscopic properties may, in general, be different, it is perfectly possible for them to exist in virtue of the same microscopic properties, and hence be identical, in the sense that the particular instances of those macroscopic properties present are identical.

In our example the property of being a particular color holds in virtue of a number of microscopic properties about the shape and density of electrons on the surface of the object. Similarly the property of being coated in a particular paint holds in virtue of microscopic properties involving the placement of various atoms, which involves microscopic properties about the shape and density of electrons on the surface of the object. Thus in our example the property of being a particular color is identical to the property of being coated with a certain type of paint, at least in the case of specific objects (although we may identify them in specific cases in general we would still define them differently).

Now let’s consider an objection to this position, specifically an objection that a “property dualist” about color might make. The property dualist about color is convinced that the property of being a particular color and the property of being coated in a particular type of paint just can’t be identical. Since they aren’t associated with the same causal disposition in general the property dualist about color insists that we can know a priori that they are different properties (they can imagine the object being red without being coated in that particular shade of paint they might say). Of course the property dualist about color is of course confused about the claims we are making, we are claiming that the properties are identical in specific instances because they hold because of the same microscopic facts, which means that whether they could possibly come apart in other situations is irrelevant. That is not the objection the property dualist about color might make; I am just trying to outline a kind of competing position. Now, given this position, they might claim that we have left unexplained the connection between being a particular color and being coated with a particular kind of paint, because certainly we haven’t posited any laws connecting them, nor a causal relationship between the two. But by raising this objection the property dualist about color is assuming what they must prove, namely that they always are different properties. If they were different properties then of course we would need to explain why they occur in conjunction with each other. But the assertion that they are identical in these cases is a complete explanation by itself, assuming that we know what makes a particular set of microscopic properties count as the property of being coated with a particular type of paint, and what makes such a set count as having a particular color (knowing those facts also gives us the epistemic justification to posit an identity in specific cases). Given that making the assertion that a single set of microscopic facts fulfills both roles explains the connection without the need to introduce anything more explaining the connection, which we would have to do if they failed to be identical.

June 24, 2007

A Story About Reduction And Anti-Reductionism

Filed under: Metaphysics — Peter @ 12:00 am

Suppose that there was a class of particles called P-particles that are identified by the fact that they decay into a burst of gamma radiation after 10 seconds. And let us further suppose that this classification was developed at the beginning of research into atomic physics, when it was even harder than it is now to look at what is really going on at the subatomic level. Because of their distinctive properties P-particles are likely to figure into a number of different theories and explanations of particular events.

However let us suppose that later investigations reveal that P-particles aren’t really one kind of particle at all. Instead there are really two kinds of particles that exhibit the decay characteristic of P-particles. Let us call them A and B particles. What is it proper to say in this case? Have we reduced P-particles to A and B particles? Have we eliminated them? Are they a real but non-reducible class of particles?

The anti-reductionist might say that P-particles cannot be properly reduced to talk about A and B particles. We may not simply be able to get rid of the need to talk about P-particles; we may not have the resources to determine whether A particles, B particles, or some combination of the two is responsible for the phenomena that we previously attributed to P-particles. And, moreover, we may not want to do away with talk about P-particles; perhaps it is simply too convenient linguistically to get rid of. Finally, they might argue that the concept of P-particles is simply not properly captured by any talk of A particles or B particles.

But the reductionist may respond to this and point out that P-particles, strictly speaking, no longer exist. What exists is A particles and B particles, since these are the only entities that we need to construct our explanations. P-particles can of course still exist, in a sense, but only as a label for some kind of phenomena that evolves entities that are involved in our best explanations. And, according to the reductionist (rightly in my opinion), such labels can only be part of satisfactory explanations if there is a reductive relation between them and the phenomena they describe. Thus, says the reductionist, either P-particles reduce to A and B particles in some way, or P-particles don’t exist.

I think that the reductionist has the better of the anti-reductionist here, quite possibly because the anti-reductionist has a too narrow understanding of what counts as reduction. The reductionist sees X being reducible as meaning only that X can be said to convey some information about what is going on with what it is being reduced to in particular cases, and that this information explains how X can have its characteristic effects. Anti-reductionists on the other hand see reduction as establishing a one-to-one correspondence between what is being reduced and what it is being reduced to. (Peter Smith has a great paper entitled “Modest Reductions and the Unity of Science” explaining why reduction should be understood as looser than this.) So perhaps the real problem is that the two are talking past each other.

I think the real lesson here is not that reductionists have the upper hand on anti-reductionists, if you grant them a broader definition of reduction than the anti-reductionist uses, but that the reductionist/anti-reductionist dispute in general is orthogonal to the real issues. The real issue is constructing a theory that explains all the phenomena in question. Whether you can reduce other terms to terms in the final theory is irrelevant to the final theory itself. (The final theory being one that perfectly explains all the phenomena.) And the final theory, by its very nature, explains everything that needs explaining. This makes the existence of entities that don’t play some role in the final theory (such as P-particles) irrelevant. Of course this seems extremely unintuitive. How can the existence of these things not matter? But given a final theory that doesn’t contain them the existence of such things is a best a linguistic matter (is there something that exists (is part of the final theory) that we wish to describe using the term?). And whether we wish to continue discussing things using such terms, and whether we wish to continue to frame our explanations using them, is simply a matter of practicality. And so worries about whether they reduce, whether they exist, are not relevant to understanding the world. And if understanding the world is what we are after then we can leave such questions to linguists.

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