Keith’s Conundrums: The Metaphysics of Counting

Keith Douglas

Last time, I asked about 13 weird items from my childhood. Let’s discuss two responses. Alex provided a confusing song title from a few years before my time. Conditions, metaphysically, are properties, so a condition of a condition is a higher order property. Acceleration can itself change over time; this is called “jerk.” So this might be a higher order property. It has also been suggested that laws of nature are higher order properties as they, so to say, tie two properties together. This would make for the “laws of laws” that some talk about to be third order. So a little metaphysics makes the song he recalled a little less confusing.

David suggested “if that is a thing” as a current example. Continuing the metaphysics theme, I find that phrase awkward because things and events are disjoint in metaphysics, and many of the examples are events, not things. For example, going to the dentist “is a thing” by this contemporary usage, whereas that’s an event type by my metaphysical views.

I now analyze the 13 items from last time, as promised. Please refer back to last month’s column for the numbering.

1. This is likely one of the jokes, but it was even more amusing because the “real life” Sgt. Slaughter was a pseudonym used by a professional wrestler, itself a form of drama or theatre. (Or dance. I have heard it claimed that professional wrestling is closest, artistically, to something like ballet. I do not take a stance on the metaphysics of art here.) Incidentally, an adult puzzle that occurred later was the reference to Sgt. Slaughter on Babylon 5. Apparently this was the name of one of John Sheridan’s early commanding officers. So maybe the joke continues. (Sheridan, creator of Babylon 5, also worked on the 1980s G.I. Joe cartoon, so a “crossover” wouldn’t be unreasonable, except that it would require Slaughter to be a 300 years old.)
2. I offer, as a half joke, the idea that in Transformers “matrix” was used in its archaic sense of “uterus,” not in the linear algebra sense or the “it sounds cool so why not?” sense. Why? The Matrix of Leadership is stored within the torso of the possessor and allows for creation of new life.
3. I cheated on this one. While I remember Fraggle Rock from childhood, I only remember this line from watching as an adult, just before I was at a conference about the philosophy of time, so a philosophy of space cue was not surprising. That aside, it is almost exactly right: Aristotle at one point tries to figure out where the heavens are. He concludes that the outermost heaven is not anywhere because it has no minimal containing external surface. So where is Wembley; what is his place? The air (or water because Fraggles swam from time to time) surrounding his body. Here is where he is in, indeed!
4. In my view it isn’t consistent. I do remember as a child wondering who we were supposed to give the magic penny to or who not to.
5. I have no idea! If I did, I would be teaching this great revolution in ethics! I do think that the show is correct. There are times to be selfish, and times to be selfless. Turn turn turn. (The original poem, in Ecclesiastes, is almost right as far as I remember. It makes one error in my view. Hint: Aristotle, amongst many other topics, worked in biology. More in another column; the readers can try to guess what I have in mind.)
6. I never told my parents about the debate, but I suspect that they would have been in favour of sometimes making an ally out of an enemy. I found the Cold War inexplicable as a child and still find races to kill each other incredibly distasteful. Compete over chess or hockey or even Tiddlywinks, not over who can point the most missles at the other guy, please! And that’s consistent with sometimes teaming up.
7. This novel was one of my sister’s favourites. I did not read it until I was an adult, so I am borrowing what might have been her perplexity. I have no idea whether she thought of the problem I raised. Needless to say that the Transformers use is much later than the one in the book. In the book, given the religious themes that are tacit throughout, and that the character is “Meg,” I suspect the reference is to the metatron, the name of the visible manifestation of god in some Jewish traditions. Is this also referenced in the 1982 Disney movie? (I suspect that’s where, approximately, Megatron and hence Galvatron, etc., got their names.)
8. I like The Infinite History the most of all the combinations that do, literally, work. I don’t think this one is supported by the text, though. 
9. In retrospect, I think my guess from my childhood is likely correct. If you had to get a replacement part for a Canada-USSR game in Montreal, I’d guess that an American figure will be in less demand than a Canadian one! I will never know, of course.
10. The remark about the period-appropriate cell phone is important, because Mac makes it clear he (like me) hates them. Assuming that he stuck with his opinion, I imagine then the answer to my question is zero! Of course you can picture Pete or Jack wanting him to carry one, maybe even Nikki, Penny (is she the magic penny?) or one of the Deborahs. (Yes, watch again: There are several Deb(o)ra(h)s.)
11. The multiple coincidence is that, I dare say. But as for Tweety and Big Bird: I don’t know! This is especially strange since I am pretty sure Big Bird at least would be addressed in a way that the audience could tell.
12. Maybe the singer of the song should have gotten one of those magic pennies (see above) and had enough love to give his girlfriend more than eight percent! This also plays into #8 and the interpretation of infinity implied by the Magic Penny song. If the magic penny gives the possessor aleph nought love units, and the singer thus gives any finite amount, he is now actually giving LESS of his (total) love to his girlfriend than before! And I don’t know how fractions work in nonstandard analysis, so if it is an unbounded (rather than actually infinite) amount of love units produced, we might have the problem of summing some weird series. Maybe he should give his girlfriend the harmonic series of love units? (Sorry that I had to just miss Valentine’s Day on that one!)
13. I dare say this is possibly the most obscure “for the adults” joke I have ever heard. Did Phoenician traders bring the Arabic numerals to Europe from India? I’d have to check the history of numerical notation I have around somewhere, but that sounds right. Of course, the timeline is wrong. This would have been after the Roman period; but then again, we don’t know the dramatic date of the video, and Roman numerals are (or were when I was small) still taught, hence the show talking about them. (I remember also wondering what the difference between a number and a numeral was, which the show also jokes about.)

The Metaphysics of Counting

We’ve touched on infinites, counting, etc. I would like to address some of the metaphysics of counting today (hence all the metaphysics we also alluded to earlier) and apply it to one specific case.

A man in his 60s lives nearby and takes the bus from the same stop as I do from time to time. A gregarious fellow, he seems to be well liked in the neighbourhood and talks at length to those around him. Recently he commented to the effect that he “used to remember everything.” Ignoring for the moment that this cannot be literally true, what does a charitable version of this claim involve?

A metaphysical principle, popularized by the philosopher D. Davidson and originating from his Doktorvater, W. V. O. Quine, can be captured in the slogan “No entity without identity.” The idea is that one should have some idea how to count, or “distinguish,” somethings of a given type before admitting that type into one’s ontology (i.e., the views concerning what exists). This is at first blush psychologically plausible; it is not without reason that Sesame Street teaches “same and different” as well as counting, which seems to depend on it. The Nobel Laureate in chemistry, R. Hoffman, has also suggested that distinguishing “the same and not the same” is extremely important. The logician and philosopher H. Wang has suggested the same thing, remarking that the philosophers of mathematics who regard the “primal arithmetic intuition” as being “1, 2, …” are perhaps wrong in this light.

I would like to suggest that “memories” are a good challenge for the Quine-Davidson view. Consider the phrase: “I forgot that, I’m sorry.” This seems to, grammatically at least, suggest a single item. Does anyone ever say: “I forgot those” where “those” are the memories rather than the items the memories seem to refer to? Maybe, during, say, an oral examination. But what is this counting? If I give you three apples, they are three because each has a distinct place or something like that, and hence you can individuate them and apply the number words to them. What makes one memory rather than another? If I think for three seconds about the Aristotle-Wembley Fraggle view of space again, is that three memories, each following the next, of one second each? You can see there is a sort of Zeno’s paradox here. Yet continua, at least at first glance, are all over the place. Can Count von Count from Sesame Street make good use of the phrase “Continuum many field chunks, ah ah ah!”? (Especially transfinite extensions of children’s songs and stories — think 99 Bottles of Beer on the Wall — have long been the subject of jokes.)

The use of “uncountable” to mean the larger infinities than those of the natural numbers would rule out this as “impossible” usage, at least if the character were to try to “get there,” by his usual 1, 2, 3, etc. Yet my experience informally teaching rudiments of set theory is that people find it weird to regard the first infinity (or rather the zeroth) as countable, an example of where a stipulative definition is confusing. So it isn’t continua, necessarily, that are the problem.

There are also common phrases — “Thanks for the memories!” — where the plural is used. So we have more than one, I guess, and a good time is where at least two are created. I thought at first that one could count memories (in principle) by counting how many neurons had their LTP state changed by one input, but then had to immediately backtrack. Why? Because “one input” suffers the same problem. We should know by now (thanks to D. Dennett) that inputs to the brain do not easily break up like that. Moreover, the changes in the proteins on the surface of the neurons occurs in such a way that what we might recall later because of this is massively distributed. The entire nervous system is the organ of memory, rather than one part or another like one might think.

This distributed nature of memory has a practical consequence for me, at least sort of, at work. As readers may know I work in cyber security where I design regimes of security controls for modern AI systems. These are like us in one way at least: Their memories too are distributed. Why is this a practical concern? Data deletion. With a traditional database, one can write a command in the relevant language to delete a record given some aspect of its content (usually an identifier, to ensure uniqueness). If by contrast, in an ANN, one is asked to delete information about a respondent who does not want their data used, how does one do this? One way is to remove the record from the training set and retrain the network, rereleasing it, etc. This is often slow and hence the confidentiality protection just mentioned. Risks availability is another value I am charged with helping to protect. What to do?

I encourage any comments, concerns, discussions, etc., about any of the topics we discussed today. See you in April!