My paper on indecision is part of a much larger project. The next step in that project is to provide a formal theory of probability in which it is not always possible to say of outcomes either that one is more probable than another or that they are equality likely. That theory needs to be sufficient to explain the behavior of rational economic agents.

I began struggling actively with this problem before the paper on indecision was published. What I've had is an evolving set of axiomata that resembles the nest of a rat. I've thought that the set has been sufficient; but the axiomata have made over-lapping assertions, there have been rather a lot of them, and one of them has been complex to a degree that made me uncomfortable. Were I better at mathematics, then things might have been put in good order long ago. (I am more able at mathematics than is the typical economist, but I wish that I were considerably still better.) On the other hand, while there are certainly people better at mathematics than am I, no one seems to have accomplished what I seek to do. Economics is, after all, more than its mathematics.

What has most bothered me has been that complex axiom. There hasn't seemed much hope of resolving the general over-lap and of reducing the number of axiomata without first reducing that particular axiom. On 2 January, I was able to do just that, dissolving that axiom into two axiomata, each of which is acceptably simple. Granted that the number of axiomata increased by one, but now that the parts are each simple, I can begin to see how to reduce their overlap. Eliminating that overlap should either pare or vindicate the number of axiomata.

I don't know whether, upon getting results completed and a paper written around them, I would be able to get my work published in a respectable journal. I don't know whether, upon my work's getting published, it would find a significant readership. But the work is deeply important.

The law has long treated the images of living persons as something like trademarks, so that the use of such images without the consent of those persons is restricted in various ways. Over the last few decades, there have been efforts — some successful — to turn these images into property of a sort that may legally be bequeathed upon death, as opposed to such images lapsing into the public domain.

The potential monetary rewards increased simply as celebrity became more culturally important. And the evolution of CGI has made it possible to fabricate the appearance of persons in video, not only increasing opportunities to make money from such images but to use those images in ways that many of us would see as grossly abusive (for example, in pornography).

Reflexively, quite a few people want law at a Federal level to protect the images of the dead. But there is some reasonable question as to whether the US Constitution empowers the Federal government to act.

The rub comes by way of Article I §8, which enumerates the powers of Congress. It specifically empowers Congress

To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;

As I've explained, this enumeration did not creäte copyrights; it instead gave Congress limited power to protect them; without that empowerment, the matter would simply have been left in the hands of common law and of the legislation of the constituent states. But neither §8 nor any other part of the unamended Constitution makes explicit mention of intellectual property of any other sort, and it is an unreasonable stretch to suggest that there is implicit reference to similar such property, exactly because there had been a felt need for explicit mention of the rights of authors and of inventors. Any prerogative to protect the images of the dead was left in the hands of the constituent states.

I used the word unamended advisedly, because one might try to make a case that the Fourteenth Amendment empowers the Congress to treat personal images as continuing to be property beyond personal death. But one can legitimately make that claim only if somehow the associated rights are basic rights of persons (or of US citizens as such) or can be shown to derive from basic rights; the Fourteenth Amendment doesn't empower Congress to reconfigure legal rights ad libitum.

There's a wide-spread propensity to confuse great desirability with moral necessity. But the penalties of law are always ultimately acts of violence, and there's a need for more than emotional appeal when the law forbids something. So, while it would be greatly desirable for the images of the celebrated dead to be treated with something like the respect that they would have received when alive, a solid case should be made for regarding them as property, or indeed they should be regarded as not property.

Some efforts to make personal images into property that remains such beyond the death of the persons have focussed on getting constituent states to have it treated as such in law. It's perhaps worth noting that the Fourteenth Amendment might be read to block the constituent states from converting these images to property (though I am sure that no court to-day would accept that reading).

To-day in the bistro, an unfamiliar girl perhaps six years old sat near me on the same bench. She was joined after a few minutes by a woman, probably her mother, who sat on the other side of their table. The little girl was interested in me and in my attention. Years ago, the drill for me would have been to engage her in brief conversation, asking her name and so forth, and probably answering questions about what I were doing. To-day, it was to turn briefly to give a friendly smile to her, and then turn quickly back to my business, all without pause.

Our notions of proper behavior have changed because Americans are generally far more concerned and otherwise anxious about threats to children, especially sexual threats from adult men. I share that concern and anxiety. I don't know whether things have become more or less dangerous than once they were, but honestly I think that question is secondary. Even if our world is less dangerous for children than in the past, I want us to be concerned; if it was once less perilous, none-the-less I wish that we'd even then been more vigilant.

(The Economist used to make a practice of mocking Americans for our fear for children. Perhaps they still do. I don't expect that it has occurred to them, in the wake of the various scandals concerning the sexual exploitation of children in the UK, that perhaps they have once again been mistaken in their presumptions of superiority.)

Yes, I'm saddened that I couldn't have had that short conversation. But I don't live in the world that ought to be, and in this case I cannot make ours a better world by acting as I would if it were. Had I interacted with the child in a more inviting way, I would have helped to foster norms and expectations that are exploited by predators. She didn't much need to talk to me. She does need to be spared some of the awful possible outcomes of the world in which we live.

In Chapter 6 of Through the Looking Glass by Charles Lutwidge Dodgson (writing as Lewis Carroll), a famous and rather popular position on language is taken:

When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to mean — neither more nor less.

If Mr Dumpty's words simply mean whatever he intends them to mean, then the rest of us are not in a position to understand them. If he provides us with verbal definitions, we must know what the defining words mean. He could not even declare in a manner intelligible to us that he meant most words in the same sense as do you or I. We might attempt to tease-out meanings by looking for correlations, but then we would be finding meanings as correlations, which assumes properties (such as stability) that represent more than pure choice on the part of Mr Dumpty. Having been made perfectly private, his vocabulary as such would have no practical value except for internal dialogue. There is a paradox here, which Dodgson surely saw, yet which so very many people don't: If Mr Dumpty's apparent declaration were true, then it could not be understood by us. He might actually just be making some claim about breakfast. We might take (or mistake) his claim for a true proposition (that his vocabulary were purely idiosyncratic), but any co-incidence between his intention and our interpretation would be a result of chance. We could not actually recognize it for whatever proposition it actually expressed.

In order to communicate thoughts with language to other persons, we must have shared presumptions not only about definitions of individual words, but also about grammar. The more that such presumptions are shared, the more that we may communicate; the more fine-grained the presumptions, the more precise the communication possible. In the context of such presumptions, there are right ways of using language in attempt to communicate — though any one of these ways may not be uniquely right or even uniquely best — and there are ways that are wrong.

Those who believe that there are right ways and wrong ways to use language are often called prescriptivist, and generally by those who wish to treat prescriptism as wrong-headed or as simply a position in no way superior to the alternatives. Yet, while one could find or imagine specific cases where the beliefs concerning what is right or wrong in language-use were indeed wrong-headed, forms of prescriptivism follows logically from a belief that it is desirable for people to communicate, and especially from a belief that communication is, typically speaking, something rather a lot of which is desirable. As a practical matter, altogether rejecting prescriptivism is thoughtless.

To the extent that the same presumptions of meaning are shared across persons, the meanings of words are independent of the intentions of any one person. Meanings may be treated as adhering to the words themselves. Should Mr Dumpty take a great fall, from which recovery were not possible, still his words would mean exactly what they meant when he uttered them. A very weak prescriptivism would settle there, with the meaning of expressions simply being whatever were common intention in the relevant population. This prescriptivism is so weak as not often to be recognized as prescriptivism at all; but even it says that there is a right and wrong within the use of language.

Those more widely recognized as prescriptivists want something rather different from rude democracy. In the eyes of their detractors, these prescriptivists are dogmatic traditionalists or seeking to creäte or to maintain artificial elites; such prescriptivists have existed and do exist. But, more typically, prescriptivism is founded on the belief that language should be a powerful tool for communication as such. When a typical prescriptivist encounters and considers a linguistic pattern, his or her response is conditioned by concern for how it may be expected to affect the ability to communicate, and not merely in the moment, but how its acceptance or rejection will affect our ability to understand what has been said in the past and what will be said in the future. (Such effects are not confined to the repetition of specific pattern; other specific patterns may arise from analogy; which is to say that general patterns may be repeated.) Being understood is not considered as licensing patterns that will cause future misunderstandings.

In opposing the replacement of can with the negative can't in can hardly, the typical prescriptivist isn't fighting dogmatically nor to oppress the downtrodden, nor merely concerned to protect our ability to refer to the odd-ball cases to which can't hardly with its original sense applies; rather, the prescriptivist is trying to ward-off a more general chaos in which we can hardly distinguish negation from affirmation. (Likewise for the positive could care less standing where the negative couldn't care less would be proper.) When the prescriptivist objects to using podium to refer to a lectern, it's so that we continue to understand prior use and so that we don't lose a word for the exact meaning that podium has had. We already have a word for lecterns, and we can coin new words if there is a felt need for more.

The usual attempt to rebut prescriptivism of all sorts notes that language evolves. Indeed it does, but prescriptivisms themselves — of all sorts — play rôles in that evolution. When a prescriptivist objects to can't hardly being used where can hardly would be proper, he or she isn't fighting evolution itself but participating in an evolutionary struggle. Sometimes traditional forms are successfully defended; sometimes old forms are resurrected; sometimes deliberate innovations (as opposed to spontaneous innovations) are widely adopted. Sometimes the results have benefitted our ability to communicate; sometimes they have not; but all these cases are part of the dynamic of real-world linguistic evolution.

The Evolution Card is not a good one to play in any event. Linguistic evolution may be inevitable, but it doesn't always represent progress. It will not even tend to progress without an appropriate context. Indeed, sometimes linguistic evolution reverses course. For example: English arose from Germanic languages, in which some words were formed by compounding. But English largely abandoned this characteristic for a time, only to have it reïntroduced by scholarly contact with Classical Greek and Latin. (That's largely why our compounds are so often built of Greek or Latin roots, whereäs those of Modern German are more likely to be constructed with Germanic roots.) It was evolution when compounding was abandoned, and evolution when it was reädopted. If compounding were good, then evolution were wrong to abandon it; if compounding were bad, then evolution were wrong to reëstablish it. And one cannot logically leap from the insight that evolution is both inevitable and neither necessarily good nor necessarily bad to the conclusion that any aspect of linguistic practice is a matter of indifference, that nothing of linguistic practice is good or bad. One should especially not attempt to apply such an inference peculiarly to views on practice that one dislikes.

In his foundational work on probability,[1] Bernard Osgood Koopman would write something of form α /κ for a suggested observation α in the context of a presumption κ. That's not how I proceed, but I don't actively object to his having done so, and he had a reason for it. Though Koopman well understood that real-life rarely offered a basis for completely ordering such things by likelihood, let alone associating them with quantities, he was concerned to explore the cases in which quantification were possible, and he wanted his readers to see something rather like division there. Indeed, he would call the left-hand element α a numerator, and the right-hand element κ the denominator.

He would further use 0 to represent that which were impossible. This notation is usable, but I think that he got a bit lost because of it. In his presentation of axiomata, Osgood verbally imposes a tacit assumption that no denominator were 0. This attempt at assumption disturbs me, not because I think that a denominator could be 0, but because it doesn't bear assuming. And, as Koopman believed that probability theory were essentially a generalization of logic (as do I), I think that he should have seen that the proposition didn't bear assuming. Since Koopman was a logicist, the only thing that he should associate with a denominator of 0 would be a system of assumptions that entailed a self-contradiction; anything else is more plausible than that.

In formal logic, it is normally accepted that anything can follow if one allows a self-contradiction into a system, so that any conclusion as such is uninteresting. If faced by something such as X ∨ (Y ∧ ¬Y) (ie X or both Y and not-Y), one throws away the (Y ∧ ¬Y), leaving just the X; if faced with a conclusion Y ∧ ¬Y then one throws away whatever forced that awful thing upon one.[2] Thus, the formalist approach wouldn't so much forbid a denominator of 0 as declare everything that followed from it to be uninteresting, of no worth. A formal expression that no contradiction is entailed by the presumption κ would have the form ¬(κ ⇒ [(Y ∧ ¬Y)∃Y]) but this just dissolves uselessly ¬(¬κ ∨ [(Y ∧ ¬Y)∃Y])
¬¬κ ∧ ¬[(Y ∧ ¬Y)∃Y]
κ ∧ [¬(Y ∧ ¬Y)∀Y]
κ ∧ [(¬Y ∨ ¬¬Y)∀Y]
κ ∧ [(¬Y ∨ Y)∀Y]
κ (because (X ⇔ [X ∧ (Y ∨ ¬Y)∀Y])∀X).

In classical logic, the principle of non-contradiction is seen as the bedrock principle, not an assumption (tacit or otherwise), because no alternative can actually be assumed instead.[3]. From that perspective, one should call the absence of 0-valued denominators simply a principle.

[1] Koopman, Bernard Osgood; The Axioms and Algebra of Intuitive Probability, The Annals of Mathematics, Series 2 Vol 41 #2, pp 269-292; and The Bases of Probability, Bulletin of the American Mathematical Society, Vol 46 #10, pp 763-774.

[2] Indeed, that principle of rejection is the basis of proof by contradiction, which method baffles so many people!

[3] Aristoteles, The Metaphysics, Bk 4, Ch 3, 1005b15-22.

Science is reasoned analysis of — and theorizing about — empirical data. A scientific conclusion cannot be recognized as such unless one understands the science.

It might be imagined that one can recognize a conclusion as scientific without understanding the science, by recognizing the scientists as such. But the popular formula that science is what scientists do is vacuous when taken literally, and wrong in its usual interpretation. Someone can can have an institutional certification as having been trained to be a scientist, and have a paid position ostensibly as a scientist, and yet not be a scientist; for those who actually understand some scientific area, it is fairly easy to find historical examples or perhaps present cases.[1] To recognize a scientist as such one must recognize what he or she does as science, not the other way around.

Even if it is in some contexts reasonable to accept conclusions from such persons on the basis of their social standing, it is not scientific literacy to accept conclusions on that basis; it is simply trust in the social order.

The full understanding of a scientific expert isn't always necessary to have a scientific understanding of the reasoning behind some of the broad conclusions of a scientific discipline. But in some cases of present controversy with significant policy implications, the dispute over the relevant conclusions turns upon issues of applied mathematics, and perhaps other things such as thermodynamics. No one can be scientifically literate in the areas of controversy without understanding that mathematics and so forth.

In many of the disputations amongst lay-persons over these issues, I observe people in at least one group who assert themselves to be scientifically literate, when they are no such thing, and to accept science, when they are not positioned to know whether what they are accepting is science. These are actually people who simply trust some part of the social order — typically, those state-funded institutions that declare themselves to engage in scientific research.

[1] It is certainly easy to find what lay-persons will acknowledge as examples. However, some of these ostensible examples are actually spurious.

A few years ago, in the title of an entry discussing the implications for the world of the failing health of Hugo Chávez, I alluded to a motto that ends leave a beautiful corpse[1]. That entry considered an observed practice:

When a charismatic leader dies aburptly while still in power, his or her supporters quickly begin building a mythology of what would have been accomplished had he or she lived.

I drew attention to how this mythologizing bears upon social policy:

The mythological episode of such leadership is treated as having the same standing for purposes of comparison as does historical fact. When an opponent tries to construct an argument founded on logic and general fact against policies associated with that leader, supporters treat the mythology as if it is a disproof by counter-example. What’s really happening then is that Faith is being mistaken for empirical data.

While death significantly amplifies the power of the mythologizing of a leader who was not given full opportunity to effect the programmes that he or she chose, death isn't essential for there to be some mythologizing; I noted that there was a developing narrative of what President Obama would have done had his party retained a majority in both chambers of Congress for the whole of his terms.

As it happens, charisma is also inessential, though it very much helps. And an odd substitute for direct charisma has been demonstrated. Barack Obama inflamed so much inverted narcissism on the part of his followers that a great many of them chose to treat his successor, Hillary Rodham Clinton, as if she were magnificent though she is signally lacking in charisma.

At the same time, her health is failing her, and had she been elected to the Presidency, she would not likely have served through a full term. There would have been an odd sort of race between how rapidly she did things that repelled those who had been her supporters, and when she left office. Depending upon the outcome of that race, she might have left a beautiful corpse.

But Ms Clinton has lost the race for Presidential Electors. Although a few of her supporters cling to an implausible hope that the Electoral College will not merely turn its back on the detestable Donald John Trump but will elect Clinton (as opposed to some Republican other than Trump), she will not be President. And the mythologizing is already under-way, even to the level of having Ms Clinton imagined as rather prettier than she is.

One does not have to regard Mr Trump as even tolerable to resist the mythologizing and to see Ms Clinton for what she has been. She has repeatedly been one of the people causing the United States military to engage in the slaughter of innocent people, for stated goals that haven't been obtained because they haven't been obtainable. She has engaged in calculated support of domestic policies such as the War of Drugs and aggressive incarceration policies that have literally led to many thousands of deaths and to the ruin of many thousands of other lives. She and her husband have got rich exactly as brokers of political influence. She has privately spoken against some policies as corrosive while publicly supporting them — or vice versa — depending upon the expected flow of dollars and of votes. She has casually disregarded laws, in the expectation (thus far vindicated) that her connections will insulate her from being charged, let alone convicted.

If Ms Clinton is to be made into a beautiful corpse, it is rather fitting that this transformation be effected while she is undead.

[1] In full, the motto is Live fast; die young; leave a beautiful corpse. It is an elaboration of an earlier motto of live fast and die young. A popular variant is Live fast; die young; leave a good-looking corpse.

The original definition of racism, and the one still found in standard dictionaries, is a theory or an adherence to a theory that merit is in part intrinsically a function of race

However, a few decades ago, some social theorists began insisting upon a new definition of racism, under which one could not be called a racist unless one not only were prejudiced against some racial group, but had social power. Devotees of this new definition variously baldly restate it, as if the restatement makes it so, or cite the theorists, as if such citation makes it so.

Those who make a special study of a subject sometimes take a term in popular use, and give it a peculiar, somewhat new definition. (For examp!e, we see that in physics, with the uses of energy, force, and work; and we see that in economics, with the definition of unemployment.) But what usually characterizes these redefinitions is that somewhat loose notions are replaced with more explicit, more precise, and otherwise more workable definitions. (For example, when an economist uses unemployment, she usually excludes people who have quit one job for another, but have not yet started that next job, because joblessness of this transitory sort is not typically considered to be a social ill.)

Alarms really ought to go-off about the redefinition of racism. The original concept was quite coherent and useful; if it were not coherent, then the redefinition (which essentially adds a condition) would inherit the incoherence. Racism on the part of people with little social power still has significant social consequences; any legitimate use of the new concept is far more sharply limited than that of the original concept.

Let's imagine that someone prejudiced against those outside his own major racial group makes a solo walking tour of Los Angeles. As he travels from one neighborhood to another, he gains or loses social power as the ethnic compositions of those neighborhoods vary. His beliefs about the relation between race and merit needn't change (and should not be expected to do so much if at all). Yet by the mere act of travel through a large city in which ethnic groups are not uniformly distributed, under the redefinition he would repeatedly go from being a racist, to not being a racist, to again being a racist. It would be extraordinary and dangerous to make a solo walking tour of all of Los Angeles, but a great many people regularly move across communities of different ethnic composition. Application of the proposed redefinition of racism would routinely become unworkable, under circumstance in which the standard definition remains quite workable.

There are certainly legitimate applications of the concept of socially empowered racism, but in those applications we can call it socially empowered racism or something similar.

When a concept loses its associated symbol, it becomes harder to discuss or even to think about that concept. Further, the response to symbols is largely emotive. Whether people learn by reason that something is good or that it is bad, or they are simply led to accept some valuation by imitation of those in their society, people come to associate positive or negative feelings with the words used for those things. Old concepts given new words don't provoke the same response; old symbols given new meanings carry with them some or all of the old feelings. Those who have adopted a new redefinition of racism can thus escape the recognition of racism, and the felt need to condemn some instances of racism, by allowing themselves to believe that some people simply cannot be racists, by virtue of their social standing.

We are simply dealing with an attempted hijacking of language, for purposes of subverting clear thought and discussion. That is most plain when the word racism has been introduced into some discourse with its standard definition, and in response it is insisted that something conforming to that original definition is not racism because it does not conform to the proposed redefinition. But any non-standard use that is not flagged as such is still a subversion of rationality. Those who have participated in the attempted hijacking are knaves or fools or both.

Most or all of us have heard or read of the question of how many angels can dance on the head of a pin. This question was introduced to satirize and to dismiss a problem that challenged scholastic philosophers, namely Given that there are things that do not have body but do have location, can two or more of these things occupy the same location at the same time? Now, we might labor the idea of body; but suffice it to say that it were presumed that things with body could not simultaneously occupy the exact same location, but that there were things of another class that could occupy the exact same location as could a thing with body. The question then was whether they could occupy the same location as other things of their own class.

One of the ways in which this puzzle had bearing was on attempts to understand the nature of devils (fallen angels) and how they might interact with ordinary people. The question thus actually had bearing on the witchcraft mania.

But another way in which this question had bearing was in consideration of how we distinguish one thing from another, perceptually and conceptually. In theory, two things might be identical except for location, but the distinct locations perhaps permit us to discern that there are two things, rather than one. And, if the location of an object at any one time is unique to that object, one can combine a description that might fit many other things with that location to identify a singular object, and thus to have an intrinsically singular corresponding concept, as opposed to a concept that might fit more than one thing.

That perhaps seems perfectly sound, but I don't understand space as other than a structure of relationships. For example, when a physicist asserts that objects of mass warp space increasingly with that mass, I take this to be no more or less than a claim that objects of larger or smaller mass have different spatial relationships with things, and cause other things to have different spatial relationships each with others. (The latter implies that a spatial relationship involving the object of mass underlies the spatial relationships amongst the things other than that object.) When we attempt to distinguish objects based upon location, which is a matter of relationships amongst objects, remarkable considerations arise.

First imagine a very small universe, having just one body in it. A universe is not small by virtue of one hitting a wall after travelling some distance; it is small by virtue of having a non-Euclidean geometry, such that after a relatively short amount of travel one finds oneself back where one started. As light travelled from the object, it would eventually find its way back to the object. If one could somehow see, as if within this universe, and looked in various directions, with sufficiently strong vision, one might see the object, seemingly off in the distance, even if the view began as if one were standing right at or on the object. Seemingly beyond the object, one might see the object yet again, and so forth. That's the experience in one sort of universe. Now imagine an infinitely large universe, as if built by tiling duplicate sectors, in which there were infinitely many objects, positioned to given the same experience as in the first universe.

I declared that a universe had just one object; I declared that a universe had infinitely many objects. I don't actually believe that the apparently second universe is intrinsically distinct from the first. I think that we may conceptualize the first universe as the second, and vice versa, and that the count of objects is an artefact of our conceptualization. Of course, if there were no more than indiscernible differences amongst what seemed to be infinitely many objects, then I might claim that there were no practical differences from a universe of one object; but I here make the stronger claim that, if there are no differences beyond perhaps whatever is captured by the two given descriptions of location, then these descriptions are each of the same universe. It would simply beg the question to insist that one universe is different from the other in that one were finite but configured so that it seemed infinitely repeating, while the other truly were infinite and repeating. Granted that viewing as if within the universe seems to locate a means of viewing close to one object. (One might even imagine oneself invisibly located as an additional object in the universe.) But how is the location of that means near one object distinct from its location near all of them? (How is oneself's being located in the universe near one object distinct from the location of a perfect duplicate of oneself being near each of them?)

In a universe more like our own, if we had what seemed to be two otherwise indistinguishable objects at different locations, there would be other discernible objects that seemed to support a distinction. What we might regard as one object would be near to various other objects, and far from still others. Likewise for what we might regard as a different object, with a distinct set of things.

Let's mentally step away from that scenario for a bit, and return to the scholastic problem of things that do not have body but do have location. If two of these things are otherwise indistinguishable, and if they can occupy the same location at the same time, then ex hypothesi there is no way to distinguish one from another when they do occupy the same location. (The space occupied might be different when both moved into it — for example, it might become less translucent — but that doesn't mean that we can distinguish one of two things from another. And if the properties of these things are not in some sense additive or subtractive, but combine according to inclusive disjunction — that is to say that the attribute is either there or not, but has no further possible ordering to it — then we cannot tell how just many of these things are there by discernment of these properties.)

But, when they occupy the same location, I ask whether there are in fact two things. What would be the difference of two such things coming to occupy one location from two otherwise identical things coming to be one thing at one location? Perhaps what seemed one thing might again become two, but that wouldn't prove that they had remained distinct at the one location. Perhaps one thing might have become three, each just like the two from which the one had been formed. My experience (and, as I believe, yours) is that this has never happened. But I know of no logic that prevents it from happening; it merely violates my present best guess of the physical laws (which entail principles of conservation). If what seemd to be two things came together and seemed to be one, and then that one thing seemed to become three, some person might guess that what had earlier seemed to be two things were atually three things, two already in combination. But if all the attributes combined in conformance with inclusive disjunction, then in what sense would that be different from just what had seemed to happen?

If we accept that two otherwise indistinguishable things become one thing when they occupy one location, does that thing continue to exist should it become two things? Is it one of the two things? both of the two things? each of the two things? Is the proper answer different when the two things are indistinguishable except for location from what was one thing?

(If we are transporting some very great criminal by paddy wagon and, upon arrival, find three persons, each indistiguishable from the person whom we tossed into the wagon, and each insisting that he is just that person, do we treat each of them as that person, or charge each with no more than abetting an escape, on the theory that it is most likely of any given one of them that he is not that person? This problem might be primarily epistemological — so that one of the three suspects is our original perpetrator even if we shall never know whom — but that's bad enough; and we can make it still more fundamental if we allow for teleportation and for matter duplication.)

Let's mentally step back to the scenario of two otherwise indistinguishable objects at different locations in a universe rather like our own. Are these actually two objects, or one object that is bi-located, or one object in one location that appears as two locations because of a strangeness of space? Do these three descriptions actually distinguish different realities? If we mark one of these apparently two objects and see an identical mark appear on the other, do we regard it as the same object, or as two objects such that one is some sort of sympathy with the other? If we mark what seems one object and a mark does not appear on the other, do we regard this as proof that there were never one bilocated object nor a weirdness of space, or do we interpret this case as of one object becoming two distinct objects (with an end to the bilocation or with an adjustment of space), perhaps exactly as a a result of our action? (The classic formulation of Ockham's Razor is entia non sunt multiplicanda præter necessitatem. If we posit that there were always two objects, are we conforming to that prescription?)

Because space need not be as Euclid had insightfully assumed and as Platon and Kant had thoughtlessly presumed, we can interpret any case where we have what otherwise must be a single thing simulatenously occupying multiple locations as in fact that single thing in one location. The practical cost, however, is that we are compelled to identify locations by the things occupying them (and not merely by the things about them); but we had set-out to identify things by the locations that they occupied!

Let's say that we have an object in a strange space, so that it is effectively bilocated, and we point to it and say this. Assuming that we don't also say not that, pointing to the other apparent location, is there any problem? It is one thing to incorporate mistaking of one thing for two into an assertion; another simply not to recognize some of the characteristics of that one thing. (There is a problem if Selina Kyle cries I am in love with Bruce Wayne, not with the Batman! but there would have been no such problem had she simply declared I am in love with Bruce Wayne!)

But if the case of two otherwise identical but differently located objects (perhaps each in perfect sympathy with the other) and the case of one apparently bilocated object are really just different descriptions of the same situation, then the applicability of not that — and number more generally — seems in some cases to be an artefact of the descriptive framework. Especially in the context of such implications, some people will insist that one of these descriptions must surely be mistaken, even if as a practical matter we cannot tell which. (Some people will further insist that the description that conforms to simpler spatial relations (that of two objects in perfect sympathy) is the one that is more likely correct; other people will insist that the description that requires fewer objects (that of a bilocated object) is more likely correct.) However, the apparent contradiction isn't internal to either description, and each description may be translated into the other. That one of them is right doesn't make the other wrong.

If I cannot point to something and say this and thereby distinguish it not merely from everything not there but from everything not it, then how can I have an intrinsically singular concept? To baldly incorporate singularity into a concept is just question-begging. (One ought not to say that two spheres are exactly alike except just in-so-far as one is unique, or is uniquely unique.)

Where, then, is singularity to be found? I think that it is to be found in experience, literally. The raw stuff of experience is sensation and sense-perception, not conception. (We may have concepts of sensations, but sensations are not themselves concepts; we may have concepts of sense-perceptions, but sense-perceptions are not themselves concepts.) Percepts and concepts are constructed to explain sensation and sense-perception. Those percepts and concepts may be perfectly accurate, but they are not intrinsically singular except to the extent that we associate them with sensation or with sense-perception. That is to say, for example, that we have a cluster of sensation or of sense-perception, and we have or build a concept of something by which to explain it, which concept is not singular except in-so-far as we implicitly or explicitly add to it the attribute of causing that particular cluster. And, if we do that, then we must in such case commit to a concept that does not allow co-location of otherwise identical things. That is not to say that we forbid co-location in general; but that singular concepts cannot be fitted to such co-located things. (It is probably a very bad idea to construct an explanatory model that employs co-location of otherwise identical things all of whose attributes combine in accordance with inclusive disjunction.)

In any case, the alternatives to exploring such considerations are dogmatism and nihilism. There is nothing intrinsically practical about dogmatism nor about nihilism, which stand in the way of our understanding the universe as deeply as we might and of our helping those who lose (or never find) their ways in their own attempts to understand the world. The scholastics who worried about the relationship of location to identity during what have come to be dismissed as the Dark Ages were concerned with foundational questions of what we ought to practice. It is fine to jest about their efforts only if the joke does not hide the truth.

I'm not a great fan of Star Trek, for reasons that I won't labor here; but at times it provides useful cultural references.

Various people have drawn a comparison between the Clinton campaign and the Borg, prompting me to put together this logo And then to make stickers and magnets with it available at CafePress. Presumably anyone voluntarily displaying one of these magnets or stickers would be doing so ironically.

(For what little it's worth, I endorse no candidate, and still will not be voting for the least of the n evils.)

Up-Date (2016:07/29): Resistance is difficult. Yester-day after-noon, I received notice from CafePress that my graphic was being investigated as a possible violation of intellectual property. This charge is absurd, in that the Clinton logo and slogan are too simple to be copyrighted and no trademark protection has been attempted; likewise for the Borg reference. And, even if the Clinton logo and slogan were intellectual property, none-the-less my use of these elements would constitute fair use. (Though it must be admitted that, since I am not satirizing the Borg, if there were intellectual property there then my use would be more questionable.)

While the image is under investigation, the items on which it was to be placed are unavailable. A decision is supposed to come within 48 hours of the announcement. Of course, someone at CafePress may make a partisan call; such actions have become commonplace. In that case, I will look for a different service through which to get things produced.

Up-Date (2016:07/29): Resistance continues. CafePress simply chose to misrepresent the design as in violation of their stated content policy. So, as I said that I would, I've begun migrating to alternative vendors. I will also be billing CafePress for my labor.