 So the talk is called The Abstractions Adequate to Chinese Historical Phenology. To start with a quick glance at the philosophy of science in Chinese Historical Phenology. And the way I got to this is basically the question that I'm interested in today and that I think the project is interested in to some extent is to what extent are differences in Chinese reconstructions, methodological differences, which then boiled down to differences in the philosophy of science, and then to what extent are the differences of how to analyze a particular poem or something like that. So it is a contentious business, Chinese Historical Phenology. There are disagreements, and Baxter and Sagar explicitly promote a paparian philosophy of science. And their critics reject this. So Schüffler, but actually basically all of their critics one way or another say either they're misusing this paparian methodology, or the problem is that they're using it. And so let's call them Baconians. So they're empiricists. So we have the Baconians, the empiricists, and then the paparians where the term that would correspond with empiricists is hypotheto-deductivists, which is not a very nice term. So that's why I'm going with the Baconians and paparians. And once I got started on this, you start having to read these people like Popper and Bacon and whatnot. So somewhere I would like to actually think more about philosophy of science as, let's say, how the philosophy of science has been consumed by Chinese historical phenologists and maybe what it says about how they work and maybe make my own recommendations about how we can maybe communicate better, but I'm not going to do that today. It's too big, too complicated. So I'm just going to jump straight to my philosophy of science. I'm a Marxist. So let's look at Marx's philosophy of science. So in capital, he says, in the analysis of economic forms, moreover, neither microscopes nor chemical reagents are of use. The force of abstraction must replace both. So I think it's clear this comment could be about any social science that we use abstraction in our methodology. That's from capital. And then from a contribution to the critique of political economy, he actually discusses the history of economics from this philosophy of science perspective. And this is a long quote, so forgive me for that. But he says, OK, the economists of the 17th century, for example, always started out with the living aggregate population, nation, state, several states. But at the end, they invariably arrived by means of analysis at certain leading abstract general principles, such as division of labor, money, value, et cetera. As soon as these separate elements had been more or less established by abstract reasoning, there arose the systems of political economy, which start from simple conceptions, such as labor, division of labor, demand, exchange value, and conclude with state, international exchange, and world market. The latter, which is from abstract to concrete, is manifestly the scientifically correct method. The concrete is concrete because it is a combination of many objects with different destinations, i.e., a unity of diverse elements. In our thought, it therefore appears as a process of synthesis as a result and not as a starting point, although it is the real starting point and therefore also the starting point of observation and conception. And then to end, by the former method that's going from the concrete to the abstract, the complete conception passes into an abstract definition. By the latter, abstract definitions lead to the reproduction of the concrete subject in the course of reasoning. So he's promoting, and this is the famous phrase, the ascent from the abstract to the concrete. So then the first thing we need to do in our scientific enterprise is identify the correct abstractions. So that's why the talk is called The Abstractions Adequate to Chinese Historical Theology. So in terms of this methodology, I want to look at two case studies before getting to Chinese Historical Theology. And I look first at mathematics. And in this methodology, we're talking about a synthesis of a Baconian moment of identifying the abstraction, and then if you like a Popperian moment of applying the abstraction in the reproduction of the concrete. And to speak in Hegelian terms, I think that Marxist philosophy of science is the synthesis that comes after the thesis of the Baconians and the antithesis of the Popperians. So OK, so I looked at mathematics. We're going to look at the relationship between integers and rings. And then at least in my mind, then we would also look at the relationship between the reels and fields. But I can only force so much algebra on you. So I leave that as homework. So we'll look at the integers. So what are the integers? We all know the integers from childhood. They're the positive and negative numbers, if you like. So what are the integers? They're a collection of things, things like 0 and 2 and 17 and minus 25. And they have two operations, addition and multiplication. OK, so now we're just going to sort of we're pretending to be naive. We're like, OK, there are these things, the integers. There are little poise. We're going to play with them and see how they work in a very inductive, empiricist way. And so what do we find out? We find out that 2 plus 3 plus 4 is the same as 2 plus 3 plus 4. They're both 9. And that is the principle of associativity. And then we also find out that 2 plus 3 is the same as 3 plus 2, which is 5. And this we call commutativity. Then we have the observation that 2 plus 0 is the same as 0 plus 2. That's just commutativity again. But then we get 2 back out. So basically, if you add 0 to something, you get the same thing back. That means 0 is an identity element. And then we also observe that there's something called an inverse element, which is basically for anything, like 2, for instance, I can find a thing negative 2 that will sum to the identity element. So you can always pair things off in order to get the identity element. And then I will more quickly whiz through the properties of multiplication. So we also get associativity. We also get commutativity. We also get the identity element. But we don't get the inverse element, right? Because then we would be looking at the rational numbers and not at the integers. But there's one last principle. So yeah, we do get the identity element. Now, one last principle that I haven't touched on, which is how do we bring multiplication and addition together? And it's this. It's that multiplication is distributive over addition. This sounds technical, but you know it. And you've known it since fifth grade. So 2 times 3 plus 4 is the same as 2 times 3 plus 2 times 4. And they're both equal to 14. OK, so that was all just reminder from grade school math. How do the integers work? But now, having done that, having done our Baconian business, we can move on to do the paparian business, where we turn those observations into sort of biots, sort of abstractions that are methodological assumptions. So what's a ring? A ring is a set of elements with two operations, addition and multiplication. And here, addition and multiplication should be just understood as in quotes. There are two operations that we're calling addition and multiplication, where addition is associative commutative and there is an additive identity and additive inverse, and where multiplication is associative, commutative, and there is a multiplicative identity, but not necessarily, at least, a multiplicative inverse, and where multiplication is distributed over addition. So just in terms of the logic of my argument, these start as observations about how the integers work, and now they become a definition of what a ring is. And then we just observe that there's lots of things that are rings. There's 0 all by itself. I leave that to you. You can think about 0 plus 0 is 0. 0 plus 0 plus 0 is the same as 0 plus 0 So it's just 0 all by itself that fills these properties. And then also, the integers did. That's no surprise, because we define these properties based on integers. But then we also have things like the integers modulo 4, which basically just means just the numbers 0, 1, 2, and 3, where 3 plus 1 is 0. So you can think of it just going in circles. It's like you're doing, if you only had four integers, you could still get all those properties out of it. And then I mentioned the Boolean ring just because maybe some of you have heard about Boolean algebra, which is logic. It's like things with P and Q. And it's also the operations of set theory, which are isomorphic with Boolean logic. So some of you might have heard of that. But then there's lots of fancy stuff, things with polynomials and piatic numbers and whatnot. So it's just to say, now that we've started from our abstractions, we can explore the concrete, not that any of these things are particularly concrete, and see that, oh, the integers are just one sort of beast in the zoo of rings. OK. So that is, I'm saying, going from rings to integers is the ascent from the abstract to the concrete. So I think that's the methodology that I want to use when doing Chinese historical phonology. So the question is, what abstractions should I use? So in order to actually, we can look at historical Chinese phonology for abstractions. But I think for clarity of presentation, I'm turning instead to the decipherment of Egyptian. And I would, with equal fun, like to do the invention of writing in Samaria. So one is sort of, we as modern understanding what the ancients were doing. It's sort of a movement from writing to sound. And then the other one is, if I want to write something down for the first time, how do I do it? A movement from writing, sorry, from sound to writing. It's also sort of forward in history. So I think these two contrast nicely. But I don't have time to do Samarian. So I'm not going to do it. Yeah. But now, a look at the decipherment of Egyptian. So it turns out that the Egyptians put proper names in cartouches. And this fact, which initially was just a conjecture, is what really allowed the decipherment of Egyptian. And although the Rosetta Stone is the most famous object in terms of the decipherment of Egyptian, because it has Egyptian and Greek on it, actually the Philae obelisk is what proved decisive. And actually, something about just a side note on British colonialism. The Philae obelisk is extremely important document for the decipherment of Egyptian. It's just sitting in some guy's yard where it's been sitting since his family bought it from Egypt. OK. So this is the name Ptolemy, as it's written on both the Rosetta Stone and the Philae obelisk. So this is our starting point, which is we have two bilingual inscriptions. They both have Ptolemy and Greek on them. They both have the same thing in a cartouche. So it's probably the name Ptolemy. And then we just force Ptolemy. We say, OK, this must be pronounced Ptolemy. And then we can say, OK, maybe the square is a P, and maybe the little half circle is a P. And now that's our starting point. And this is all, this is actually how Champollion deciphered Egyptian. So it's not a thought experiment. It's actually like how we did it. OK. So then on the Philae obelisk is another name, which from the Greek inscription he could figure was Cleopatra. And then just notice that we've already got here the L, the E, the O, and the P in just in a different order. So if you just looked at this and said, OK, I'll throw in it. I think you've got that game show in the 80s, like give me an L or something. So you were given L, E, O, and P. And then you've got Cleopatra in the Greek. So then you sort of force the rest of it on there. And then this is what you get. So just spell that out. So Ptolemy occurs on both objects spelled the same way. The four signs are common to both names, L, E, O, and P. And then also both instances of A are written the same way in Cleopatra. It says eagle, right? So that like, oh, Cleopatra has two O's and there are two eagles. So probably that's an A, OK. But then notice that the sign T in Ptolemy and the sign T in Cleopatra are written with two different signs. So maybe you say, OK, maybe things aren't going so well. But Champolion said, ah, who cares? So and then I will sort of say this is an act of abstraction, right? He's ignoring the difference because he's like, well, they're both T's, I know from the Greek, yeah. And he assumed they both had the same value T. This is this is wrong. Yeah, like now we would say one is a T and one is a D. But one point I want to make is it's wrong in a very special sense, which was a necessary mistake. Science could not have made progress without this abstraction, right? OK, and then we look at Alexander. So Alexander Ross, I tell you because the S is relevant on the filet obelisk. And if we just look at it using the letters we already know, so far we have A, L, S, E, T and R. And then these three question marks. Yeah. So then Champolion guessed, I just mentioned that. We have these letters already. And then Champolion guessed that these are K, N and S. Where N is the only new letter, yeah. So so so this is an interesting sign of, you know, progress in the settlement. We're getting to the point where we're not getting, you know, the number of new letter of new sound values we're getting is going down. But then he has to introduce more of these transitive relationships among signs so so that we have two ways of writing K that are like the sort of boop thing and the bull thing. And we have two ways of writing S, which are the sort of, you know, bishops, whatever it is, staff thing. And then this thing is actually a bolt over a door. OK, so and then. I mean, I haven't really gone into the Egyptological literature, but it sounds like it seems like in some cases, most cases, we know these are also wrong again, but in the case of the S, it's not so clear. Yeah. So maybe the Egyptians did just have more than one way to write S. Yeah. So yeah. So some of them turn out to be wrong, but wrong in a kind of necessary way, sort of logically and historically necessary abstraction to make. And I think that's the way to think of it. It's not a mistake. It's an abstraction. Yeah. And then as we progress in our science, we go from the more abstract to the more concrete. So now that Egyptian has has gone further, having existed at this more abstract level, it can fill in these details. Yeah. OK. So what are the abstractions that we use methodologically in deciphering Egyptian? I think they are alphabetization, which you can think of as a function f sub a that maps letters in Greek into letters in Egyptian. So, for instance, F of T is this symbol. So and I'm using Roman letters more properly. I should use Greek letters. I should say F of tau or something. But, you know, I thought it would just be more friendly if I use the Rome letter and then F of P is the square and so on. Yeah. So that's one abstraction we have is this process of alphabetization, which is a map from Greek into Egyptian. And then we also have another abstraction, which is transit transitization, which is a function like F sub T, which maps Egyptian back into Egyptian. And this, for instance, brings us from the sort of mound to the hand. Those are both T and it brings us from the, you know, the foot to. This isn't actually a foot, but I'll call it foot to a bowl. That's K and the sort of staff to the doorbell. That's S. Yeah. But so it's so in the one case, we're identifying, you know, characters in different alphabets. And in the other case, we're identifying characters within the same alphabet. And I think just if we if we step back, I showed you, you know, how I'm calling it, if we step back, we said, what was he doing? He was making these two moves. Yeah. And I think these are the two moves that we should allow ourselves in, well, in historical phenology in general, perhaps, but let's say in Chinese historical phenology. So now I've got my my tools, which I think of as like the geometry, his tools are a straight edge and a compass. And then you say geometry is whatever you can do with that straight edge and compass. And here in in the sort of philological study of historical phenology, you know, our two tools are our alpha alphabetizers and our trans advisors. So so in the Chinese context, then alphabetizer is a map from something that's not Chinese. Yeah, some some alphabet of letters, if you like, it's not Chinese into Chinese. And the trans advisor is some map from inside the Chinese writing system to somewhere else inside the Chinese writing system. OK, so now I will just go through yeah, some examples, right? So now I'm going to try and move from the abstract to the concrete. I should gesture the other way, right? Is an ascent from from the abstract to the concrete. OK, so and I'll do these each, which is, say, alphabetizers and trans advisors in sort of historical or I'll do sort of a Joe dynasty, Han dynasty. And then if you like, sort of middle Chinese period. So first loans in and out of Chinese. So the word for chariot in Chinese, at least I think comes from not Sanskrit, but Indo-Aryan, but I give you the Sanskrit form. So that's, you know, if I allow myself to associate those two words, then I've also created a map from from that phonology to that those those characters or that character. Right. And then similarly with Tiger, Tiger is I think what we can say with confidence borrowed from Southeast Asia somehow as a word. So I give one as an example. So one has club. And back to Mr. Carr, we can start up. I think actually I have another paper just about the work of Tiger. I think you can get them even closer looking together. But but I don't want to use my reconstructions, right? I want to use Baxter and cigars reconstructions for for sort of consistency and clarity. So anyhow, those that's that's a sort of Joe dynasty, if you like, alphabetizer. Now, if we look at a Han dynasty, alphabetizer, we have Indic Buddhist Indic words being written in Chinese. So for instance, Varanasi, we write with these characters. So that's a way of alphabetizing, you know, those characters. And then also a canista. Yeah, so and then this time I've given Schuessler's Han dynasty reconstructions just just as a kind of visual aid, right? The principle is directly between whatever the the non-Chinese thing is and the Chinese characters. And then I'm not really going to talk about it today because it's a bit of a complicated matter in its own right. But the alphabetizer par excellence in Chinese historical phonology is, of course, the rhyme. Tables, yeah, so not the rhyme books, but the rhyme tables because they give information about articulatory phonetics for particular characters. They say like, you know, this character had a voiced veeler fricative as its as its onset. Yeah. So quite explicit phonetic information in the rhyme tables. OK, so now moving on to to transit advisors. We have in the Joe dynasty, we have phonetic series, which you should all be familiar with now, because this is what the James is talking about. So we have a character used as a phonetic component of another character. So that creates a map from one character to another character. It's a transit advisor. Right. And in terms of my choice of word, transit advisor, it means if I already associated one of the characters with the pronunciation like mea, then somehow it doesn't mean it's exactly the same pronunciation, but somehow the other characters that participate in that transitive relationship are associated with that pronunciation. Right. And then from the Han dynasty, maybe like something like a pair on a mastic glove. So here we have this is a quote from a commentary quoting an earlier commentary, because this this gloss is due to his works are not preserved. They're only preserved in quotations. But anyhow, so this guy says due to read this character ball as Paul, which and then poor means a ball rush with better leaves. OK, so these these glasses are like, you know, I sometimes say like just an example, right, you say, what does what do you mean in French? Well, what do you is something that you sit in while you are the countryside that goes by. Right. So this attempt of the of the of the Han dynasty philologists to come up with a word that shares both sort of somehow the semantics and the and the the phonology. So anyhow, that's a transit relationship, right. It says associate this character with this character. OK, and then moving on to the sort of middle Chinese, of course, we have things like a bunch of chains. So these are a bunch of upper-speller chains where, you know, so Lou, if we look up, it's a bunch of the initial is long, and then we look at the frontier and the initial is lock and so on. And so you can create a transitive relationship between different characters with function. And so, like, say, just returning to what I was I was sort of presaging a moment ago, the Ryan books are transit advisors. They're not alphabetized. And I think that's an important thing to to recognize that, like, Ryan books are only giving you equivalence relationships among Chinese characters. And the Ryan tables are the things that allow you to fill in those equivalence relationships with phonetic information. OK, so now, you know, you are asking yourself, when is he going to talk about graph theory? OK, so so just at the very end of the talk, just a note about graph theory, which is that alphabetizers just define bipartite graph, right. So imagine that, like, I don't know, that, like, Buddhist Indic words are the red nodes and the Chinese characters that write them are the blue nodes. This is, you know, any alphabetizer relationship can be formalized with a bipartite graph. And then similarly, similarly, any any transitive relationship can be formalized with a there's not even a really word for it, but not by a part of graph, just a simple graph or a unit part type graph. And so I think it's now possible to, you know, at least dream about Chinese this the the both the source material and if you like, the study of of this Chinese historical phonology, Chinese historical phonology as the creation of this beautiful, you know, mathematical object, which is the union through time of these different bipartite and unit part types graphs. And that that gives you a way of sort of imagining, I think, more than visualizing the kind of the totality of Chinese historical phonology as an abstract object. OK, so that was, you know, my effort to find the abstractions adequate to Chinese historical phonology. Yeah, and and thank you very much for your attention. Let's say for me personally, I only came to this through Chinese by virtue of the specific challenges that Chinese characters present. Yeah. And I think it's not a coincidence that the the parallels that I found helpful were Egyptian and Sumerian, which are actually script systems that are structurally quite similar. Right. But once you have them as tools, it's clear that like, let's work. Let's say we're just talking about the historical phonology of Greek, right, where, like, you can just kind of read it. But but if you're interested in, like, how second century Greek different than sixth century Greek, you will use these two operations. You'll say, like, well, how are loan words adapted into Greek, our Greek words written in foreign scripts, you know, what kind of relationships do we get inside of Greek? Like, I don't know if the Hellenistic Greeks even, you know, rhymed or something. But but yeah, so I, you know, so I would say, like, you know, not to make it about me. It sounds arrogant, but I discovered these because of particular features of Chinese, but I think they're good in general for, let's call it his philological historical phonology. And the reason why I say that is because there's a whole new kind of historical phonology, which is reconstruction, right. And in reconstruction, I think I like to think in terms of the geometry and his two tools, right. Or actually, like, I think about like, in a lot of go in Japanese storytelling, you get to have like a fan and a handkerchief, and that's it, right. So, so what are the the tools you allow yourself? So I would say in reconstruction, you allow yourself a regular phonology and analogy. Those are the only two moves allowed in the game. And for sort of philological historical phonology, they are alphabetization and transitivization and then also like a methodological assumption that I haven't talked about here, but I think it's both sort of obvious that needs to be pointed out, is some kind of, you assume some kind of continuity to history. Methodological, right. Like, is Han Chinese the direct linear descendant of Zhou, Chinese probably not, but we assume it is in order to find out when it is not, right. And I think that that's also an assumption that's always made in historical phonology, is that you assume, you know, direct continuity through history, like, like there's a whole another direction I could go in that I'll just sort of gesture at, which is technological progress and how technological progress works. And if I can, again, sort of turn to Marx, he describes it as, I won't get it right. There's a very beautiful passage, I think it would be interesting about, like, materializing knowledge. You take knowledge and you put it in an object, a physical object, right. And so, like, I don't know, like a water mill is somehow, you know, the knowledge of how to change water to flour, changed into a machine, right. And so I think that one of the sort of glorious things about if you like digital humanities is that we need to make our methodology both extremely abstract and extremely explicit in order to teach it to a machine. And so, like, whether or not we'll actually succeed in making, you know, I don't know, Linguo, the magical robot who does historical phonology, you know, I don't care. But I think that as a goal trying to teach something to a machine is a useful process for discovering, or let's say, making explicit what it is you've always been doing, yeah, at a different point. The spiral again. Yeah, exactly, yeah. And actually, there's, I mean, I'm going to, that there's this philosopher, Robert Brandon from Pittsburgh, who I think is extremely good on this, as like, you know, to the extent we can, like it's a dangerous word, progress. But to the extent we can talk about scientific progress or philosophical progress, it's the act of making explicit in words what was already somehow an implicit social practice. Similar to the kind of, oh, we discovered this for Chinese and then realize it works for all historical phonology. I think when we discovered that this is true of progress in philological historical phonology, we discover it's true of all scientific progress, right? And that's why I chose to use the example of mathematics because we think of like, I don't know, mathematics or physics as like, this is where empiricism actually works or this is where abstraction actually works. Whereas I think this, you know, dialectical model of the synthesis of Bacconian and Poparian moments is actually how all scientific progress works. And so it's sort of like, well, you know, if I like, if I can end saying something provocative, if we realize that Marx is just right in his theory of how this works, we'll make faster progress by embracing that as a methodology rather than, and that's where I'm trying to sort of, you see this sort of camp of, you know, the Bacconian, the Bacconian, the Bacconian, the Bacconian, the Bacconian, sort of screaming to each other. I feel like, you know, let's step back and figure out how this actually works. And then maybe we can move past this argument.