Archive for the ‘conceptualism’ Category

Postscript on Diachronic Discrimination Failure

Monday, April 6th, 2009

This postscript to the Transcending Zombies series is primarily a follow-up to the remarks on Raffman-style nonconceptualism. Would my objection to the Raffman-style case against conceptualism be defeated by an experimental design that tried to better control for possible context effects of the presentations of the colors? The sort of redesign I here have in mind might go as follows. The stimuli presented in each distinct presentation in the diachronic discrimination case would be one of figures 1 and 2.

colors1

figure 1.

colors2
figure 2.

The task put to the subject is to make a “same as before, yes or no?” judgment about colors appearing on the right side of each display. Synchronic discrimination tasks could use just one of figures 1 and 2 and ask, say of figure 1, if the left and right regions contain the same color.

Such an experimental design is aimed at avoiding the accusation that the colors presented in the synchronic and diachronic contexts are colors presented in different contexts and it thus may not be assumed that there is a color-appearance that is constant across contexts. In this new experiment, the color context of the right-hand color in figure 1 is arguably the same as the color context of the left-hand color in figure 2 since figures 1 and 2 are just spatial rotations of each other.

Does such an experimental design help to defeat the conceptualist? One point in favor of the conceptualist is that in the experiments using figures 1 and 2, there may no longer be a failure of diachronic discrimination. The subject, in being presented with figure 1, is in a position to conceptualize the color on the right as the lighter of the two. Further, the subject may re-conceptualized the diachronic task as, in seeing fig 2 after fig 1, judging whether the lighter of the two has changed its relative spatial location.

Raffman’s Rainbow Unraveled

Monday, March 30th, 2009



Colors perceived but not remembered.

Conceptualized content plays a central role in both the Transcending Zombies argument and my Allocentric-Egocentric Interface theory of consciousness. One of the main lines of resistance to such views hinges on an alleged fineness of grain of sensory experience that outstrips conceptual resources. In this and the next post, I suggest that such allegations are overblown. I develop this suggestion by examining a line of thought concerning color experience.

There exist color pairs sufficiently similar to be indiscriminable across a memory delay while sufficiently distinct to be discriminable when presented simultaneously (Perez–Carpinell et al., 1998; Raffman, 1995). So, for example, two paint chips presented side by side will be clearly and correctly distinguished as having distinct colors, but if presented one after the other, the viewer will be uncertain whether they have distinct colors. Though, for simplicity, I’ll just be focusing here on color, the point generalizes to aspects of vision other than color and also to other sensory modalities besides vision. There are thus a wide variety of stimulus pairs that are discriminable in simultaneous presentations but indiscriminable in serial presentations.

As Raffman (1995) argues, if we make certain natural assumptions concerning the relations of concepts to memory, then the existence of such stimulus pairs puts pressure on the suggestion that conceptual contents exhaust the contents of experience. If the conceptualized is to be equated with the remembered and the recognized, then the existence of such stimulus pairs suggests that experience outstrips our concepts. Whatever constitutes the awareness of the chip that is not sufficiently remembered, that awareness fails to count as the application of a concept since that awareness fails to satisfy the re-identifiability criterion on concept possession.

I want to attack Raffman’s argument by calling into question what seems to be one of its key assumptions. The conclusion that conscious experience has non-conceptual content seems to depend on assuming that the colors are present in consciousness in the same way regardless of mode (simultaneous vs serial) of presentation. The assumption seems to be that in every case in which the paint chips are different there must be corresponding elements in consciousness that are different and in every case in which the paint chips are the same there must be corresponding elements in consciousness that are the same.

The assumption works in the context of an argument for nonconceptual contents of consciousness as follows. If I am not able to correctly conceptualize, that is, correctly judge that the second of a pair of serially presented chips is a different color, even though I can distinguish the pair members in simultaneous presentations, then how can this serve as a basis for the conclusion that there is a non-conceptual consciousness of the distinct colors? Such a conclusion would follow if it were further assumed that in spite of the colors of the chips not being available to conceptualization they were available to consciousness. Putting this in terms of qualia, the simultaneously presented and distinguishable chips, chip 1 and chip 2, give rise to corresponding qualia, quale 1 and quale 2. When the chips are presented serially, the subject is unable to correctly judge/conceptualize the difference between the chips, but the chips nonetheless make a corresponding difference in consciousness by triggering, serially this time, quale 1 and quale 2.

(Indeed, in a version of the argument due to Kelly (2001, see especially p. 398, fn. 2), it is experiences, not paint chips (or emulating Kelly’s lingo “shades as the subject experiences them” not “shades that the subject experiences”) that are distinct and serially presented.)

However, such an assumption is questionable. We may begin to appreciate what’s questionable about it by noting that differences in presentation often result in differences in color perception. Context effects are well known in the literature on color perception. In normal lighting conditions, one and the same paint chip may seem gray or bright yellow depending on what else is present in the visual field. And these context effects need not involve a difference in what light arrives at the eye from the paint chip in question. Nor are they explained by interactions between retinal cells. The perceptual effects of context depend on higher levels of the visual processing hierarchy than the retina.

We may model an explanation of the failure to serially discriminate simultaneously discriminable chips as due to different perceptions arising from the same chips presented in different contexts. Presenting a chip by itself on one occasion and with another chip on another occasion is to present the chip in two different contexts, contexts that give rise to differences in the perception of the color of one and the same chip.

It is open, then, for the conceptualist to explain the relevant cases as follows. Serially presented paint chips are experienced/conceptualized simply as e.g., blue regardless of whether they differ in reality with respect to shade. Simultaneously presented paint chips are experienced/conceptualized as one being e.g., a darker shade of blue than the other. Of course, it is in no conflict with the account I am defending in this paper to posit sub-personal and/or unconscious intermediaries that are non-conceptual. So perhaps it is the case that presenting the same color on different occasions or in multiple locations results in the color being present to the sub-personal or unconscious mind as the same, regardless of whether the color is presented in the simultaneous or the serial context. However, what I am keen to deny is that what makes it into consciousness will be the same regardless of simultaneous versus serial context.

Previous Posts:
1. Introducing Transcending Zombies
2. Anti-Skeptical Maneuvers
3. I Know I’m Not a Zombie
4. Some Remarks on Phenomenal Knowledge
5. The Egocentricity of Phenomenal Knowledge
6. The Knowing and the Known
7. My Physical Properties Fix My Conceptualized Contents
8. My Physical Properties Fix My Egocentric Contents
9. TZ & AEI

Phact Check, Heck

Tuesday, December 9th, 2008

How determinate can phacts – phenomenal facts – get? Can they be so determinate as to outstrip introspective access?

Does it make sense that there could be determinate aspects of phenomenology inaccessible to introspection? It strikes me as odd: I would have thought that phenomenology just was whatever is accessible to introspection. I’m curious what others think of this.

A take contrary to my own is due to Richard Heck (2007, pp. 129-133). Paraphrasing, Heck’s claim is as follows.

Whereas it is available to introspection that I believe of both my car and computer that they are gray, I cannot introspect the determinate contents of my perceptual phenomenology concerning the upper left and lower right patches of a 10 x 10 grid, even though my phenomenology has such determinate contents.

Heck doesn’t provide a visual aid, but I thought it would be fun to cook one up. Check out these patches!

untitled-1-copy.jpg

Figure 1. Is it accessible to introspection whether the upper left and lower right patches are of the same determinate shade? Is it a part of your phenomenology that they are?

Reference:
Heck Jr, R. G. (2007). Are There Different Kinds of Content? In B. McLaughlin & J. Cohen (Eds.), Contemporary Debates in Philosophy of Mind (pp. 117-138). Oxford: Blackwell.

Presentations Presented Presently

Tuesday, November 13th, 2007

Numbers of people (more than one) have asked for the following, perhaps because they are students in a class soon to be examined on the topics contained within. Others may be interested as well. Below are PowerPoint slides for talks closely associated with Chapter 5 & 6 of The Subjective Brain.

Transcending Zombies [link to download]

Phenomenal Consciousness and the Allocentric-Egocentric Interface [link to download]

Just the Phacts, Ma’am.

Monday, September 24th, 2007



Recycle

Originally uploaded by Pete Mandik

Eric Schwitzgebel and I have been having an interesting (to us, at least) exchange in the comments on his recent post “Three Reasons to Mistrust Reports about Ongoing Conscious Experience“. At issue in our exchange are questions concerning introspective reliability concerning phenomenological facts or “phacts” as I called them. Eric is somewhat famous now for his many interesting arguments against introspective reliability. I tend to side with people who think that there are important senses in which introspective judgments can’t be wrong.

An interesting case, and one that Eric raises, concerns people’s judgments about the nature of their visual field. More specifically, people tend to vary over times and across subjects in their judgments concerning how much of the visual field is clear. The determinate colors and shapes of peripherally presented objects cannot be seen clearly. But people vary in their opinions about whether this is so.

Key question: do people vary in their accuracy of judgments of the phacts of the matter? That is, do some but not all of them get the phacts right?

The answer to the key question depends, of course, on what the phacts are. And one possibility that needs to be dealt with is that the variation in judgments is matched by a corresponding variation in phacts. On an extreme version of this possibility, everyone is right, they’re just right about different phacts.

One way to characterize resistance to this possibility is as interposing a third realm between a first realm constituted by objective facts concerning stimuli and sensory receptors and a second realm constituted by various conceptualized reactions to stimuli. Supplying a third realm gives something for items in the second realm to be mistaken about yet, unlike items in the first realm, look like candidates for genuine phenomenology. A lot of what Eric claims people to be mistaken about look to me to not be mistakes about phenomenology, but instead mistakes about what’s going on in the first realm (or mistakes about relations between the first and second realms).

Worries about a third realm can be put by saying that we really have no idea what sorts of denizens would populate it. In the case of the visual field, third-realm denizens would include peripheral objects that are colored and shaped but have no determinate color and no determinate shape. Do we really understand the suggestion that there can be such objects? And aside from questions about what objects would be, there are the various questions that arise about where they would be. No one’s ever found anything like that in anyone’s brains, and the items that populate our external environments certainly don’t fit the description.

It’s not enough to motivate the postulation of the third realm to say that we already know what it is, that it’s whatever makes it the case that there’s something it’s like to be conscious. Nor is it enough to counter skeptical resistance by characterizing that resistance as requiring reductive definitions. Reductive definitions are beside the point at this stage in the game, we just want something informative to “what are you talking about?” kinds of questions. No one has a reductive definition of a duvet, but could probably say something more informative about duvets beyond “if ya gotta ask, ya ain’t ever gonna know” kinds of responses.

The most pressing challenge for friends of the third realm is to say something informative about it such that it would be something separate from the second realm. This is because the second realm seems to be best suited for handling the sorts of weird indeterminacies that arise for phacts – indeterminacies like being indeterminately colored or having an indeterminate number of speckles.

See also:
[How do you know that you know what you are talking about when you talk about qualia?]
[Transcending Zombies]

On Not Splintering Appearances

Monday, July 23rd, 2007

Eric Schwitzgebel, as usual, illuminatingly plumbs the depths of introspective error at his Mind Splinters blog. Of particular recent interest are reports of some exchanges he’s been having with Dan Dennet over how to reconcile the possibility of introspective error with the sorts of authorial authority granted to the introspector by Dennettian heterophenomenology and first-person operationalism. (Schwitzgebel’s most recent post is here, which is a follow-up to this earlier post here.)

I think Schwitzgebel is on to something when he suggests we try to draw the distinction between what errors can and cannot be made in terms of a distinction between phenomenal judgments and what’s “behind those judgments”. I think, however, he missteps in his description of such a distinction in terms of two senses of “seems”. Dennett is no friend of the phenomenal/epistemic distinction between senses of “seems” that many philosophers follow Chisholm and Jackson in drawing. Also worth keeping in mind is Dennett’s negative reaction to so-called “real seemings” expressed in Consciousness Explained and elsewhere.

So how best to flesh out Schwtzgebel’s insight regarding Dennett interpretation? I think one can do this with a single (epistemic) sense of “seems” and a distinction regarding the way’s things are with regard to our seemings.

To give a very clear illustration of this distinction, consider a substance dualist who judges a piece of wax to be melting in the heat of their fireplace. One way things are with respect to the dualist’s seemings is that it seems like he can tell by sight that the wax has changed shape. And about this they are correct: it does seem he can tell by sight that the wax’s shape has changed. But another way things are with respect to the dualist’s seemings is that they, the seemings, are identical to brain states. And about this the dualist is quite wrong (or, more humbly, clearly might be wrong).

To relate this to an example discussed by both Schwitzgebel and Dennett, consider the case of peripherally presented playing cards which, to the surprise of many subjects, cannot be identified by suit or even color (though their motion may be readily apparent). I urge that we avoid cleaving senses of “seems”. We should not describe the case as it epistemically seeming to subjects that the periphery is clear and phenomenally seeming blurry. Instead we should say the following:

It seems to the untutored observer that he or she has detailed information about the color and suit of peripherally presented cards. However, in reality the subject does not have detailed information about the color and suit of peripherally presented cards, even though it may really seem that way to the subject.

[See also, some of my earlier posts on senses of "seems": Bursting Apart at the Seems; Bursting at the Seems 2: Electric Boogaloo; Transcending Zombies.]

playing-cards.jpg

What else can you Johnson?

Monday, July 16th, 2007

In furious response to the alleged irrefutability of Berkeley’s idealism, Samuel Johnson kicked a rock and declared “I refute it thus�. As long as rocks can be Johnsoned, idealism about them is not forthcoming. What else admits of Johnsoning? In particular, are qualia easily Johnsoned?

One might think that they clearly are, for whatever surety we gain from rocks by kicking them will be matched by a painful quale if the rocks are kicked with improper footwear.

However, one thing to be concerned about here is that the Johnson maneuver is too swift and violent to avoid conflating issues of existence and concept-independence. An idealist unmoved by the kick may grant that rocks exist while continuing to deny their existing independently of our rock conceptualizations. And one may grant realism about rocks while maintaining the concept-dependence of various non-rocks. The question of what non-rocks may admit of Johnsoning is best discussed by keeping distinct existence and independence.

Postponing qualia for a moment, let’s adopt or adapt some examples of Dennett’s: being famous and being a suspect. While having star-power is one thing, fame is another and no one is actually famous without the actual conceptualizations of others. Similarly, while being guilty of a murder is one thing, being a murder suspect is another and no one is actually a suspect without the actual conceptualizations of others. Perhaps in the case of being a suspect, others are not required insofar as an amnesiac may suspect themselves of having committed a murder. Nonetheless, being a suspect, like being famous, exhibits concept-dependence.

A sophisticated contemporary idealist about fame is denying the concept-independence, not but not the existence of, famous people quafamous. And so, what’s a sophisticated contemporary Johnsonian supposed to do? It’s not clear that going around kicking famous people is going to prove much of interest to the current question.

A similar lack of clarity attaches to the postponed question of qualia. Whatever painful qualia set in as a result, either directly or indirectly, from a bout of star kicking, the qualia aren’t obviously independent of one’s conceptualizations. Indeed, insofar as it will be obvious to one that one has painful qualia, one will have concepts adequate to forming the thought that one has painful qualia. (This latter point is further developed in the discussion of the first premise of my Transcending Zombies argument [link].)

samuel_johnson.jpg
Fig. 1. …and Johnson’s all, like, WTF!?!?

I’m Koo-koo for Kelly Cases. Cocoa Puffs, Not So Much

Wednesday, June 20th, 2007



Cocoa Puffs

Originally uploaded by Kindin

Suppose that it’s true that (1) a is F and that (2) b is not F. What would prevent a subject from judging that (3) a and b are distinct? There are several options.

The No-Relevant-Information option: The subject believes neither (1) nor (2)

The Incomplete-Information option: The subject believes either (1) or (2) but not both

The Inferential-Failure option: The subject believes both (1) and (2) but nonetheless fails to infer (3)

Not all of these options are equally appealing.

The Information Deficiency Options

Note that both the No-Relevant-Information option and the Incomplete-Information option are consistent with there having been some prior time in which the subject had the beliefs which, according to the options, the subject currently lacks. So, for example, it would be consistent with the Incomplete-Information option to say of the subject that at time t, the subject perceived and thus believed that (1) a is F; at time t + 1 perceived and thus believed that (2) b is not F; and at time t + 2, when queried about whether (3) a and b are distinct, doesn’t know because the subject has already forgotten either that a is F or that b is not F. It would likewise be consistent with the No-Relevant-Information option that the subject has forgotten at time t + 2 both (1) and (2).

However, insofar as the No-Relevant-Information option and the Incomplete-Information option are cashed out in terms of memory failure, the threat looms that the re-identifiability criterion for concept possession is unsatisfied. Of course, this sort of threat looms only if it is assumed that, for example, time t+1 was the first and only time the subject has a mental representation of b and the representation in question is atomic. If the alleged belief attributed in (2) is a first and fleeting atomic representation of b, then it is a poor candidate for a concept of b. If so-called demonstrative concepts are supposed to be atomic one-shot representations, then the memory-failure versions of the No-Relevant-Information and Incomplete-Information options point out serious problems for the demonstrative-concepts defense of conceptualism.

The threat to conceptualism posed here by memory failure can be headed off, however, if instead of construing the representations of a and b as demonstratives, we construe them instead as descriptions (definite or otherwise). Thus would the representations be non-atomic and even if b is being represented for the first and last time, its representation is composed of parts each of which may have a life history satisfying the demands of re-identifiability.

Another way of cashing out the No-Relevant-Information and Incomplete-Information options would be in terms of a failure of perception instead of memory. So, even though the subject might be presented with stimulatory conditions potentially conducive to perceiving that a is F and b is not F, the subject nonetheless fails to actually perceive that either that a is F or that b is not F. (This may be precisely the sort of thing going on in change-blindness.) Insofar as we can cash out the No-Relevant-Information and Incomplete-Information options in terms of perceptual failures, the kind of worry the non-conceptual content proponents want to raise about the representation of a and b gets blocked. This is because it no longer looks like we have a representation of, e.g., b that fails to be a conceptual representation. Insofar as we are relying on the sort of perceptual failure described above, there’s no need to attribute a representation of, e.g., b at all.

The Inferential-Failure Option

Turning now to the Inferential-Failure option, the question arises of how there can be such a failure of inference without raising doubts about whether the subject actually believes (1) and (2) in the first place. There are various ways this might get cashed out, none of which make the Inferential-Failure option a particularly plausible model for Kelly cases.

Way One: Either (1) or (2) are believed non-occurently. I’m sure that it’s common to have beliefs but not draw the simple logical conclusions of those beliefs precisely because the beliefs are not currently contemplated. Problem: Kelly cases involve occurrent mental states, so standing or abeyant beliefs are poor models.

Way Two: Either (1) or (2) are really complicated, like some proposition from string-theory, and thus their deductive consequences are not immediately apparent. Problem: Kelly cases involve experiences of colored paint chips. That ain’t rocket science. Another problem: Why would complication block inference? If it’s due to a load on memory, then this threatens to collapse this response into memory-failure versions of the No-Relevant-Information and Incomplete-Information options.

Way Three: Either (1) or (2) are believed occurrently but non-consciously. Problem: If the topic is non-conscious mental processing, then I’m not interested in the topic anymore. I’m interested in versions of Kelly cases that involve conscious experience. Insofar as Kelly cases involve conscious states, then un-conscious states are poor models.

I currently can’t think of any other Ways, so I currently can’t get excited about the Inferential-Failure Option

The Bottom Line
The conceptualist has some promising options for providing intellectual models of Kelly cases. Kelly cases can be modeled either in terms of perceptual failure or memory failure. If they are modeled in terms of memory failure, then a demonstrative-concepts defense is no longer available. But a conceptualist response would be available nonetheless.

Intellectual Kelly Cases

Tuesday, June 19th, 2007



Abstract Algebra

Originally uploaded by evaxebra

One way to approach the question of how conceptualists should best handle Kelly cases is by attempting to construct intellectual analogs of Kelly cases. Since one way of viewing conceptualism is as an attempt to model perception on judgment, we can clarify issues by approximating, in judgment, what’s going on in Kelly cases.

There are a few forms that intellectual Kelly cases might take. I’ll call them the singular form, the definite form, and the general form.

In all three forms, we must construct analogs to both the simultaneous and serial presentations essential to Kelly cases. In all three forms, the analog of the simultaneous presentation will involve a judgment of distinction which will be roughly contemporaneous with some other judgments and the analog of the serial presentation will have these judgments comparatively more spread out in time.

In the singular form, the simultaneous half of the Kelly case will involve the simultaneous judgments that
(1) a is F
(2) b is ~F
(3) ~(a = b)
and the serial half will have the judgments (1) and (2) occurring at separate times and the judgment of (3) withheld.

In the definite form, we replace (1), (2), and (3) with
(1) The F is G
(2) The H is ~G
(3) ~ (the F = the H)
respectively.

In the general form, we use instead
(1) All Fs are Gs
(2) All Hs are not Gs
(3) No Hs are Fs and no Fs are Hs.

Regardless of whether we utilize the singular, definite, or general forms, we may express the concern about the satisfaction of a re-identifiability criterion for concept possession along the following lines. If a subject withholds judgment (3), doubts are raised about whether the subject is actually making the judgments attributed in (1) and (2). Related doubts are raised about whether the subject possesses the concepts required to make the judgments in (1) and (2).

Consider, for an example that conforms to the general form, a case in which you are attempting to teach some new concepts to a student. You ask the student, “Are all Fs Gs?” and they answer “yes”. They also answer “yes” to “All Hs are not Gs?” But then when you ask “So, no Hs are Fs and no Fs are Hs?” If, at this point, they answer “no” or “I don’t know” then you start to have doubts about the student’s conceptual prowess. Perhaps the student is incapable of making simple inferences or holding more than a few propositions in their short-term memory. Or perhaps the student has not yet mastered the concepts of Fs and Gs and thus, when they answered “yes” they didn’t really understand what they were answering “yes” to. They weren’t really thinking that all Fs are Gs.

On the other hand, if there ever is an intellectual case that conforms to either the singular, definite, or general forms, that is, if there is ever a case in which a subject can withhold assent to (3) without it being the case that they don’t grasp the concepts required for (1) and (2), then the conceptualist has a model upon which to base a response to the challenge posed by the Kelly cases.

Concepts, Contexts, and Kelly Cases

Friday, June 15th, 2007

In some cases, colors descriminable in simultaneous presentations are indescriminable in serial presentations. I’ll call such cases “Kelly Cases” for they play a central role in Sean Kelly’s arguments against the conceptual constitution of perception (hereafter, “conceptualism”) (Kelly, S. 2001. “Demonstrative Concepts and Experience” The Philosophical Review, 110, 3: 397-420).

Of course, a more accurate description of Kelly’s target is a demonstrative-concepts defense of conceptualism. My intent here is to defend conceptualism without relying on demonstrative concepts.

Kelly cases raise trouble for conceptualism only if accompanied by certain assumptions. One assumption, discussed quite a bit by Kelly, is a re-identifiability requirement on concept possession: in order to have a concept of something, one must be able to identify that something on separate occasions. Another assumption, discussed very little, if at all, by Kelly, is that the perceptual contents in the simultaneous and serial presentations differ only with respect to their time of presentation.

The first assumption doesn’t bother me too much. I question the second assumption.

There are lots and lots of cases in which the context of presentation messes with the discriminability of the colors presented. One of my favorites involves the color contrast cubes depicted below.

color-cubes.jpg
Figure 1. This is awesome.

In this image, the “blue” tiles on the top of the left cube and the “yellow” tiles on the top right are actually neither blue nor yellow but the same shade of gray. See a cool animated demonstration of this over at Dale Purves’s Lab webpage here.

It’s open, then, for conceptualism to be protected by treating simultaneous and serial presentations as different contexts that give rise to differences in perceptual content. Of course, the question arises of how to characterize the differences conceptually. It would be consistent with conceptualism to say something like that in the simultaneous half of the Kelly case, the concepts applied are a concept of, say, green plus the concept of difference-in-shade; and that in the serial half of the Kelly case, there is no application of the concept of difference-in-shade.

Note that the defense of conceptualism sketched here is not the demonstrative-concepts defense of McDowell and Brewer that constitutes Kelly’s main target. I envision that the demonstrative-concepts defense would have to say something like that in the simultaneous half of the Kelly case, the concepts applied are the demonstrative concepts that-shade-1, that-shade-2, and the concept of difference; and that in the serial half of the Kelly case, there is no application of the concept of difference. The question arises, however, of what is going on besides a failure of noticing a difference in the serial half. It must be either that (1) the serial case involves neither that-shade-1 nor that-shade-2, (2) only that-shade-1 is applied, or (3) only that-shade-2 is applied.

An objection to this version of the demonstrative-concepts defense that may be raised at this point is that neither (1), (2), nor (3) would constitute the satisfaction of the re-identifiability condition on conceptual content. So, for example, in (2) the shade identified in the simultaneous half of the Kelly case as that-shade-2 is not being re-identified.

Thankfully, I’m not leaning on demonstrative concepts here, and thus the problem raised is somebody else’s problem.

[UPDATE (6/19/2007): I really don't like the last three paragraphs of this post.]