Theory & Object (Session 3)

Hello and welcome to the third session of Theory and Objects with Rissa Negristani. We're just having a conversation about explication. So yeah, if anybody wants to hop in and just continue on, I think that's fine. the Greek letter mu space and before going forward with regard to normalization techniques or approximation techniques there is something that is always a danger we will get this when

we are talking about, you know, theories of time and time asymmetry via Grunbaum and other people. The thing about approximation is that, you see, when you are moving from one scale of description to another level, for example, microscopic to macroscopic, and of course the microscopic should explain the macroscopic behaviors. And so you have an ensemble at the level of microscopic and a configuration at the level of microscopic. You want to show that whatever the initial condition of the system is at the level of the microscopic, under such boundary conditions, which are basically constraints of the system,

The result yielded at the level of microscopic corroborates the phenomenon that you have observed at the level of macroscopic. However, bridging these two gaps via normalization always has this danger of you might, if you are not careful, bring, namely a light distinction between two levels, bring a macroscopic assumption to the level of microscopic description. A smuggling some assumption from a higher level to a lower level.

At a lower level, we absolutely don't have the assumption of the upper level. the level of the microscopic gas should not have the assumptions of the level of the macroscopic observable gas. But if you are not careful, you might in fact bring some of those assumptions implicitly into your assumptions about the microscopic configuration. And that's when basically things go all right. In terms of scales and levels, are these defined internal to physics in the sense of like the Planck constant or something, or is this simply a question of observability? You see, there are many criteria for distinguishing different levels.

One is a scale. Of course, Planck scale is part of the scale. You can think about crystals, molecules, atoms, quantum fields, particles, so on and so forth. So these are scaling. But the question of distinguishing level is essentially an epistemological and methodological choice in the sense that you might in fact distinguish different levels of physical phenomenon in terms of the regularities, namely nomological invariances, predictabilities, and many other factors. The essay that I mentioned to you, I really would be extremely helpful for you

guys to read Carl Craver essay Levels, which sheds a good light on this whole idea of levels, the metaphor of levels or scales, and why is it important, but also why is it that it can lead to some really sticky problems down the line? I'm just having trouble understanding what the terminology is here because I'm not sure what we mean when we say an explanation is accurate or...

We never say an explanation is accurate. Or adequate. Adequate. Well, explanation inside a theoretical framework. Inside. Always, you see, all statements or claims of science are always context sensitive and require a frame of reference. In the sense that, for example, when I'm saying a frame of reference, we say that Earth rotates around the Sun. That statement is scientifically meaningless,

it's just absurd. You should say that within the Copernican frame of reference, or within the Copernican system, that's your frame of reference, Earth rotates around the Sun. So within a theory we say that such and such parameters once they have such and such configuration they explain the observable phenomena that we have garnered either via naked eye or technical instruments within this theoretical system, within this framework. So explanation is always theory sensitive.

Adequacy of it, meaning that it should be adequate to, with a measure function, namely with a... So measure functions are usually defined in terms of probability logic. So for example, they should be for example greater than 0.7. So your measure functions usually between 0 to 1. So your measure function degree of confirmation is that above 0.7. With this degree of accuracy, they predict the phenomenon, but also in terms of such

and such a range of counterfactual robustness, they explain the phenomenon at the level of observation, within, again, within this theory. This is what we call adequacy. Adequacy doesn't mean that it is, it's not going to change. Of course it's going to change. That's the whole point of science, is that adequacy is always depends on the frame of reference of your theory and the context of your counterfactuals. Is adequacy dependent on utility then? Sorry? Is adequate? No, not utility, not utility. No, no, no. Well, it depends again, probability, logic, statistical, regularities, many things can

be the criteria. And again, these things are fundamentally different based on what kind of, in fact, branch of science we are talking about. Are we talking about physics or are we talking about biology? Are we talking about chemistry or are we talking about Newtonian mechanics? Okay, so any question, any comments? We are a little bit behind. I would like to start very rudimentary account of Kuhn's philosophy and then open it up by way of

Stegmuller which you know Stegmuller is considered to be someone who basically Basically he was a disciple of Carnap and Vienna Circle and he also had read Joseph Smead and Frank Grams' work. So he tries to formalize basically what you might call to be the structuration of scientific theories. But the context of his work was Cohenian structure and dynamic of scientific revolutions.

So he basically started to formalize, logically formalize, what Cohen had tried to say in plain ordinary language. in order to make some of Cohen's insight more accurate and also criticize and challenge some of other claims. He sent his essay to Cohen with the expectation that Cohen will reject it and say bad things about it, but Cohen actually said that I have waited 10 years for someone to actually do this job and I'm so grateful for this. And they started this long correspondence that ultimately led to what you might call

to be a new paradigm of philosophy of science, a structuralism. By structuralism, I do not mean what you have in mind in structuralism in like Lévi-Strauss or philosophical structuralism, but structuralism in philosophy of science. logical capturing of the concept of the structure of theories and also correspondingly their dynamic, their change and their application. So this would be today's topic but first let's see if any of you have comments, something

to say, something to question. Nothing? I have something to ask in relation to Kuhn, and something, I don't know, maybe it's worse for you, but I'm not so much familiar with the story. And the story, so Kun tried to defend in one of his presentations, I could read it, he tried to produce a defense against what he calls strong program. Sorry, what problem?

Strong program. Okay, okay. So basically I have a question about what you call relativism. And I think you already spoke a little bit about it during last sections. Yes. But I keep a question which is, yeah, I just want to make sure I understand completely what's going on there. Well, you see Cohen's relativism and also Segnler's relativism is not the kind of relativism we know, you know, like it's not relativism about knowledge, it's relativism about the scientific method. So these things need to be fundamentally distinguished. Kohn and Seymour are relativists about scientific method.

Within a given disciplinary matrix, which is a paradigm, scientists or a community of scientists have their own tried and proven, not yet disproven methods. and hence they work with it. Inside another disciplinary matrix, they do the same thing. These methods might be fundamentally different. And precisely because of that, the course of the normal science can be said to be actually relativistic from a methodological perspective, but not from a scientific or knowledge perspective. So Kuhn is fundamentally a methodological relativist,

but not epistemological relativist. When we usually talk about relativism in the context of philosophy, we talk about relativism of knowledge, hence postmodernism and all sorts of stuff. But no, they are fundamentally committed to the nature of the scientific claims. It's just that the nature of the methodology the paradigms or disciplinary matrix from the perspective of Cohen and Seymour and also Feyerabend I must say they're relativistic at the end of the day.

So does it mean that yes there's relativism and relativism? Yes, relativism one, relativism two. Relativism one is what you might call to be in the strong sense of the epistemological claims of science or knowledge claims, whereas relativism two is a weak relativism in the sense of methodology or basically the constitution of the disciplinary matrix or the paradigm, scientific paradigm. It just seems like sometimes these two numbers are mixed and this produces confusion. Yes, yes, they do, they do, they do. And so I, this is one of, in fact, one of the points of

critiques of Stegmuller against Kuhn, that they do indeed sometimes, even Kuhn tries really, really hard to keep these separate and make sure that he's just talking about relativity relativism too a similar shows that actually uh both fire up end and con sometime allied the distinction between the two yes we will get to this hopefully next session uh and by the way from this session for I would say the next four sessions, things get a little bit, I must say, nightmarish in terms of formalism and stuff. But bear with me. Like if you don't, I don't go into any kind of details

that requires, you know, a lot of concentration, precisely because the whole course is supposed to introductory but nevertheless sometimes I make this excursion to formal elaboration of what they are talking about and I think I assume I don't assume actually I suppose that you have at least a kind of very rudimentary or basic set theory knowledge. Those of you who are not familiar with formalism or basic notions of set theory, I will put a very, very introductory,

layman-friendly introduction to set theory and logic online on our Google classroom. So you just go through the you know the notions and so it's just basic stuff nothing serious is required at this point so exactly are we going over today like the beginning of the stigma or sorry what exactly we're going over today like the beginning of the stegmuller or yes coen and a second there's uh i will first i will give a very brief view of where a segment actually is

coming from he's trying to synthesize carna with cone okay he tries to do use do this by way of uh SNEEDS formalization. And then, so I will first make this light introduction to Stegmuller, I will go toward, you know, some of its basic concepts that are required for further understanding of what exactly the structure of a theory is, or scientific structure is, talking about axiomatization of systems, the fundamental concepts of a theory structure, namely core, expanded core, and frame. And then next session, we go on full Stegmuller,

and it's not going to be pleasant. Sorry. I've read about half of it. It's not too bad. Well, that book, the reason that I actually suggested that book is precisely because it is a very accessible book. But he has written a number of other books that are extremely, extremely difficult, really difficult. Okay, well good thing that we're focusing on the easy stuff. Yeah, yeah, yeah, no, I mean, yeah, this is supposed to be introductory, my man. Okay, so let us start.

So, you know, in the structure of scientific revolution, which is the most read and the most discussed work of Kuhn, Kuhn provides a, what you might call to be a portrait for the development of science. Of course, the reason that this book is fundamentally revolutionary

is precisely because you should understand that this book was written when Popperianism was in vogue and philosophy of science even though had you know there was philosophy of science, but you can say that philosophy of science didn't want to understand what actually science is, whether it progresses or not. How does it evolve? What are scientific theories? So Popper had, you know, last session and the first session, we talked about it.

Popper really talked about some of these and stuff, but Cohen tries to paint the course of the development of science in a completely different way. In fact, before Kohn, many philosophers of science believe that what you might call to be the progress or development or evolution, depending, of course we will elaborate on these concepts, is what you might call to be a symptom or a byproduct of the philosophy

of science. And the way that they were looking at this idea of scientific progress, what you might call to be almost like a Hegelian idea of progress, and by that I do not mean the real Hegel. I mean, you know, a rather rudimentary or simplistic accounts of idea of progress in in the sense that marched through the history. And of course according to such views it was held that science progresses by increasing

or converging upon truth. In the sense that each scientific phase or each scientific theory, and how one scientific theory is dislodged by another one, is what you might call to be in each of these phase we add a new index of truth to our stock of truth. So essentially what you might call to be the scientific progress was thought to be, this heroic idea of scientific progress before porn, was thought to be as an approximation

of truth. And in the course of such convergence or approximation, past errors are being repaired. And of course, well, the old philosophy of science, philosophers of scientists, needed to also talk about, well, you might say that this is a normal course of scientific progress, But then how can you, for example, explain things like Kepler versus Ptolemyk system, or Newton versus Kepler, or Einstein versus Newton, basically the revolutionary phases? Well the way that they approached such revolutions in science, they thought that these are exactly

like the old paradigm, namely you are approximating truth. You are, each phase is considered to be, add something new to your stock of past truths. And the only difference between the revolutionary and the normal or the extraordinary and the normal is that at the hand of some genius scientist or a community of scientists, just the rate of such progression might be accelerated. Now, in mid-century, in mid-20th century, Kuhn started to heavily read the history of science.

started to from you know his studies in philosophy started to what you might call to be started to formulate a course for the history of science just like for example when Hegel tries to formulate a course for the history of philosophy Kohn started to formulate a framework for the course of the scientific progress, history of science. According to this, what you might call, formulation that Kohn developed, science was no longer

considered to be as a homogenous or uniform endeavor or enterprise, historical enterprise. It was in fact heterogeneous and non-uniform. It entailed an alternation between what he calls normal and extraordinary or alternatively revolutionary phases. So what is really revolutionary phases? By revolutionary phases of science, unlike the old philosophy of science, Kuhn didn't mean accelerated phases of normal

science, namely convergence upon or approximation of truth. Also, Cohn claimed that the structure of scientific revolution qualitatively, not quantitatively, and hence it's not simple acceleration of normal science, qualitatively is different from the course of normal science. So what is normal science in this regard as what you might call to be the matrix, the ordinary matrix of doing science and the history of science?

Kohn made an example for us to understand the course of normal science. He likened the course of normal science to puzzle solving like a jigsaw puzzle. Puzzle solving. Science you can say is similar to the accumulation, a cumulative picture of scientific progress,

at least on the facade. The reason that he likens it to puzzle solving is because you can say that the course of the normal science is not by any means exciting in a historical sense, you know. It's not dramatic by any means. It has one and only one objective. Like a person who tries to solve a crossword puzzle or put together a jigsaw puzzle.

The puzzle solver always anticipates to have at least a reasonable chance of solving the puzzle. That the way that he puts these jigsaws together will depend mainly on his own capabilities as a scientist. And of course the puzzle itself and the method of solution, the method of putting these puzzles with jigsaws together, will have a high degree of familiarity. You should always think about this, that a puzzle solver, like a jigsaw puzzle solver

or a chess player or I don't know, a crossword puzzle solver, essentially you can say that it's not a person who walks in an uncharted territory. That person is familiar with the rule of the games. So he just looks at it as kind of a sort of combinatorial exploration of the possibility of moves that people... It's not even exploration, because exploration really means that you are walking on a chartered territory. Yeah, okay, yeah, that makes sense, you know, so it's just less exploration.

It's a cumulative picture of science, basically. Yeah. It's what you call it. Recombinatorial. Recombinatorial, yes. you know because it's like this is kind of a tangent but um it's worthwhile it's like you know chess you know they've been playing chess for a long time but alpha go found new moves in chess like new entire ways to play the game you know and so there's the difference between you know all the moves which has been done in like the history of chess but then introduction of entirely new strategies. Yes, yes, yes. Of course, the thing is that

those, you see, the thing is that this example might be a little bit confusing. AlphaGo versus Go or Deep Blue versus chess player. You see, it's not that the normal scientists or the course of normal science is not capable of making new moves. But the way of arriving at these new moves is within the matrix of familiarity with the rules and methods. You might think of the revolutionary science as someone who actually makes a new chess, a new game board, fundamentally different from the chess board.

Do you guys still have me? Yeah, you're loud and clear. Okay. So, because puzzles and you know their solutions are familiar and relatively straightforward in the sense that they correspond to established rules and methods, normal science and normal scientists can anticipate to accumulate what you might call to be a growing armamentarium of puzzle solutions or chess moves in this case,

right? On the other hand, revolutionary science is not cumulative, it's not accumulative, precisely because it requires a revision to existing scientific belief or practice existing not existing scientific belief or practice sometimes both sometimes both in fact if you look at major scientific revolution they require both both scientific belief and scientific practice And of course, when a scientific revolution happens, you can say that not every single

one of those achievements yielded through the course of normal science are going to be preserved. are going to be revised and some going to be discarded so and of course precisely because of that, you might actually lose some of your explanatory power. That's a very interesting fact that through the course of scientific revolution, as in contrast to the period of

normal science, you usually lose some of your explanatory power. Imagine, like if you were thinking of the ptolemaic system or i don't know some some ancient thing where for example god explained everything right like let's think of extreme cases here like god explains everything the whole cosmo cosmo genesis so god is ultimate explanatory power and it's of course simple you know people usually say that well basic cosmology the difference between scientific uh for example Copernican or Keplerian system and Keplerian cosmology or Newtonian cosmology and theistic

cosmology is about simplicity. The scientific thing is simpler. That's just completely absurd. It's pure rubbish. It's just some stupid philosopher of science have put it there. Ockham's razor doesn't cut the distinction at this point because from an explanatory level it's much more simpler to explain everything by way of an entity god god is the okam razor you see okam razor is an epistemological tool and it's fundamentally context sensitive you can't just throw it around if you are wielding who comes razor without the context epistemological context

It's like you are trying to wield a rusty club pretending it's Ocum's razor. Of course, you can use this club, beat the shit out of everything and make them simpler. Like the theistic cosmology, everything can be explained by God. So resorting to Ocum's razor doesn't explain it. But God explains everything in theistic cosmology. Whereas in the scientific revolution, post Galileo and post Kepler, you see that we lose swaths of our explanatory powers. We don't know what these phenomenons are.

nor do we nor nor do we know what actually explain or is responsible for the emergence of such phenomena which we are observing so the course of scientific revolution always if not always most of the times is tantamount to the loss of explanatory power precisely because the old theories that are less adequate in a Popperian sense have less restrictions less prohibitions newer theories have more constraints more prohibitions

Questions? Just a quick clarification perhaps. When you talk about loss of explanatory power, you mean it happens because now you've suddenly got a new range of phenomena or that the theories that were before are not capable accounting for. Is it what you mean? Yes, but then you see the new range of phenomenon, you might say these are the anomalies. These are the anomalies. But then precisely in order for you to explain such anomalies,

then you have to have a more adequate explanatory framework, theoretical framework. Of course, this theoretical framework will be more limited to explaining only and only such a range of phenomena and nothing more. And hence, it cannot explain other kinds of phenomena that previously in the older theory were bunched together with the newer phenomena. Reza, and I also have a question. When you talk about normal and revolutionary science, and you talk about, you say, something like combinatorial or recombinatorial exploration, and saying it's not an exploration, I wonder how much is Reza, how much is Kuhn here?

like for example when you say that explanation is exploration is not normal science is not an exploration is it you saying or is it like this is cool cool cool cool says that cool exactly says that normal science does not walk in uncharted territories if you take exploration as if it meant walking in uncharted territories then this is not exploration according you cool sorry I really need to have a get a cigarette one second maybe we should all take a great people want the lovely idea I don't have my earbuds and

I don't want to be like blaring Reza to my Balinese neighbors this sounds like a bad idea all right i'll just tell them uh that we're taking a five minute break so people can just arrest him if they need all right

Thank you. Thank you.

My apologies. Oh, we are going to have a rest. Okay, okay. I see. Well, I can rest here. I had sort of a... It just seems to me that part of Kuhn's split between normal science and revolutionary science, at what point do these coexist? I haven't read that much of him. Well, you see, normal science, for example, you see, normal science and revolutions can

coexist in a sense that, of course, revolutions happen in conjunction with normal science. But for example, for a specific range of theories or a specific theory, a normal science for that theory cannot coexist with its revolutionary paradigm. It's like basically you say that, for example, Newtonian mechanics versus Ptolemaic system. But sometimes they do exist in fact. But you see the only reason that they do exist is precisely because of the scale problem.

That at some scale it is actually better for us to use for example something of a Newton rather than of Einstein. then newtonian mechanics if you are going to for example to some sort of subatomic particle then newtonian mechanics no longer coexist with the einsteinian paradigm You can only resort to the Einsteinian pattern, namely the revolutionary pattern.

So if we talk about the Ptolemian system and scale, it seems like it doesn't work here very well or I have to we have to imagine what kind of scale we're talking about we're talking about entirely every single scale everything all bunched up together because Newtonian system still holds for specific scales yes but not for all the scales though no so I wonder could some theories not coexist like Some don't, yes, some don't. But the best way I think to put it this way is really I think

there's something that is missing in Kuhn precisely because you see this whole idea of the scale and levels is something that is fundamentally new in philosophy of science and it was not around during the time of Kuhn or Popper. It's something that basically is a byproduct of complexity sciences. And from the perspective of complexity of sciences, people started to look at the course of physics or physical systems and how they evolved. But if you really think about the scale, you see that, for example, then the course of the normal science and the course of the revolutionary science can be in fact formulated by way of their explanatory power at the scales.

You see that basically the revolutionary signs are the ones that not only invent scales, basically put forward new explanatory levels, but also accommodate not only the explanation yielded on a previous level, at a lower level, but also add something to it, hence restricting the scope of the levels of the previous explanation, like Ptolemaic versus Newton. You see, Ptolemaic is basically, it's an explanatory regime in which basically there is no scale and everything is basically explained by way of this Aristotelian framework.

And then Newton, restricted to certain kinds of space and hence limits the explanatory power, but also the scale regime of the Ptolemaic system. And then you see what Einstein does to Newton. Again, inventing new scales, restricting the explanatory power, explaining why is that Newton, some of these explanatory powers that were yielded and maintained inside the Newtonian mechanics, were right and hence it accommodates them but also is that why is that the anomalies that could not explain can be explained by the invention of this new explanatory level. Isn't there something sort

of strange about this notion of scale in science because it seems like and my representation of history of science might be wrong but if you were to say to a pre 20th century scientist that there are scales of applicability of science that it they would say that that is in science right why why is that science I think because the amount of constraint that a scale can put on science is far greater than say uh thinking of it in terms of like a what science is able to

accomplish well that's that's why we you see i i hope to write something about this in the future I think this is precisely where we are headed. Yes, that's the whole point. A scale constrains and limits explanatory powers, makes them more adequate, but restricts the explanatory power. You can't explain, for example, the behavior of such and such system by the stuff that you were explaining before at that specific level. Now you have a more fine grained scale and hence you are constrained by its limitations.

And that's why invention of new scales or explanatory powers and hence accumulation of such constraints is coincides, coincides with the emergence of model pluralism. A run-in-the-thumb has this fantastic thing that, you know, the whole idea of a unified theory of everything, the model of the universe, is completely abolished. We should accept this. This is not science. Science requires essentially model to rule in itself. If you have many kinds of constraints, hence you should have different kinds of models,

models of explanatory powers at different scales. And that's what I would say that refinement of the explanatory powers of science is tantamount with pluralisms of methods and models of science. And hence, we are going further and further away from that so-called unified model of the universe or the unified theory of everything. Right. I mean, well then I think there's still like a looming or at least like maybe a slippery slope then, because at what point does methodological relativism or methodological pluralism not slip into epistemological relativism?

yes that that yep of course that that's absolutely a always a danger but I don't think that and you sure if you even if you're careful you might make a light such distinctions but in principle this should not occur this should not take place but however it does precisely because we are just limited beings Science of us is the science of limited beings. I think Wimzat is absolutely top-notch in this whole understanding of philosophy of science. The philosophy of science is simply the science of limited beings, and it should be approached as a science of limited beings. And once we approach it as a science of limited beings, precisely because we are not gods, we don't have intellectual intuition,

intuition, then the idea of model pluralism is a necessity. It can induce error, but also it can induce refinements. They always come together. You see, knowledge and ignorance is not something that is absolute, as Plato had it. Knowledge is nothing but mitigation of ignorance, never accumulation of truth. So does this commit one to like a pluralist ontology as well, or do we think of it purely epist- Not necessarily, not necessarily. No, no, no, no, not necessarily. So you sort of avoid the slippage into sort of bad relativism because-

Yes. ...a relativism with constraints. Yes. When we come to Grunbaum's, I will make a discussion about this old conversation that Grunbaum with Yahuwah Bar-Hilel had. He was an Israeli philosopher of science, and he's, by the way, those of you who know anything about pumping lemma of regular languages and Chomsky hierarchy is basically also was a very fantastic logician and computer scientist and so basically they talk about this about the model pluralism and how we can make sure

that you know such pluralism and relativism at the level of epistemological method does not bottom out in a what you might call to be this wishy-washy relativism. Grunbaum is that one of Grunbaum's solution is that precisely because pluralism is not like we shouldn't think of pluralism of method as this kind of everything exists side by side. People usually in common sense think that pluralism means that you are right, I'm right, that's right you know all of us right no no that doesn't mean but this model is right this model it means that we have to shoot at reality different slings and arrows that is right

it's the idea of epistemological pluralism however there are some arrows that are more effective than other animals there are some models that are more prior than other models physical models are more prior than chemical models so on so forth so is there an inner unity of science then or is it simply always a changing system of translation no no no it is well you might say that translation is always necessary and translate you see one of the things that translation is really the sticky part because in translation you usually allied stuff and

you smuggle some assumptions from one field to where they don't actually belong so you can make all sorts of nasty errors when you are translating just like translating to text Walter Benjamin's task of translator is a good thing. But translation, you can also think about it as a world building. When I am translating this book to an English version, I am not simply copying this into another language. I'm making, reinventing the world of that previous book into a new framework. So yes, is a translation but translatability always need to think thought about in

terms of order of priority epistemological priority in science well this is though I mean I don't think that all philosophers of science thinks such that but I do believe I take side with physicists that if you think biology cannot be explained by physics, then you are not good biologists. So many biologists actually refuse such an idea. It's heresy for them. It's a heresy for them. Of course, this doesn't mean that you should basically reduce biology to physics and get rid of all of its details, but this doesn't mean that you cannot explain it by physical

models like models that physics proper give you um so um uh you briefly mentioned like uh that the israeli philosopher that talks about scale yeah yeah what is it again my question BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHILIN BARHIL

What are the sort of consequences of multi-level phenomena in the computational context, especially when you're using computation to deal with systems at multiple levels? Yes. How does that exactly fit together? Well, I mean, one of the greatest people who have worked on this is James Crushfield. The idea of James Crushfield is that he basically tries to understand, first of all, what an optimal model is and how can it be computationally implemented or captured.

Well, we know that models require a certain amount of noise and a certain amount of orderliness. Arbitriness, randomness, and order. The thing is that, of course, this is a very information theoretic constraint over the kind of model that you should work with. precisely because if the size of your model is too big or too small, the amount of order or the amount of randomness increases out of proportion. And hence, model can be said to be non-optimal. Now, James Crutchfield tries to create a new matrix of correspondence between what you might

call to be the structure of theories and the kind of models that give you at each level, and hierarchy of computational complexity. He actually captures what you might call to be an algorithm, not in a kind of an executed sense but in a more loose sense, an algorithm for a computation of complexity that allow you to show that, to predict the future state of the system by way of its past and present

states. Now this looks easy but it's not easy actually. It's called E-machine or Epsilon machine reconstruction the principle under which this algorithm works is OCOM razor but the computational accountable comes with the formal account of induction and that allows you to basically understand a structure essentially a structure computationally in the sense that what you might call to be a structure is the accumulation of computational constraints. And of course, from moving a lower level to an upper level of this structure,

you require not only to abide by constraints of the, basically past the state of the system, but somehow computationally show or exhibit or display that how given such past the state of the system, you can have some other additional properties at a new period or a structural level of the system. If you really want to look at this, look at James Croshfield Calculi of Emergence. Okay, thank you very much.

Yes, James Crutchfield is considered to be one of the greatest computer scientists today. I mean, he is basically responsible for the entire Santa Fe scene. You know, Santa Fe complexity and computation, you know, when they studied automata. And he is fundamentally, I mean, he draws his, of course, conclusions from Solomono, from Charles Bennett, and many others, but he rectifies some of the main issues with old paradigms of, you know, how to understand models or structures by way of, for example,

theories of induction is really good another person that I can recommend to you is Paul Whitney on this front let me type his name here I think this is the right spelling I'm not sure really So you can check it. Okay, so.

So I was talking about normal science and revolutionary science. I said that not every single achievement of the preceding period of normal science is going to be preserved in the phase, in the revolutionary phase of science. And indeed, a later period of science may find itself without an explanation for a phenomenon that in an earlier period was helped to be successfully explained. It's a quote from Cohen. I talked about that usually most most often theory dislodgements which is the course of the revolutionary science

it coincides with limitation and loss of explanatory power this is usually the term for this loss is called Kun loss, Kun loss, Kun dash loss. So in the standard picture of science we can say that scientific revolutions are kind of like normal science but better then what we call

revolutionary science at some times can be regarded as something more positive to be sought or promoted revolutions are to be sought and promoted on Popper's view also but not because as Popper had had it that they add to positive knowledge of truth of theories but because they add to the negative knowledge that the relevant theories are false Kuhn on the other hand rejected this

Popperian view. Normal science can indeed succeed in making progress only if there is a strong commitment by the relevant scientific community to their shared theoretical beliefs. values, instruments, so on and so forth, and even metaphysical assumptions. This constellation of what Cohen calls shared commitments to the methods, techniques, instruments,

on metaphysical assumptions so on and so forth is what cohen calls a disciplinary matrix also known as paradigm scientific paradigm in so far as commitment to disciplinary matrix or paradigm is required for successful normal science and inculcation of that commitment is a key element in scientific training and information of the mindsets of a successful scientist. This incommensurability and thus tension between the desire for innovation and the necessary

conservativeness of most scientists is what Cohen calls the essential tension. The conservative resistance to tried or attempted rejections or refutations of key past theories means that revolutions are not sought unless under extreme circumstances. We know from previous session that according to the Popperian philosophy of science, his

The vision of philosophy of science requires that a single reproducible anomalous phenomenon be enough to result in the rejection of a theory. That was what we call the atomistic view of basically of science or scientific theories. On the other hand, Kohn's view is that during normal science, scientists neither test nor

in fact seek to confirm the, what you might call to be the paradigmatic theories or the leading theories, the guiding theories of their disciplinary matrix or paradigm. Nor do they regard anomalous results as falsifying those theories contra proper. It is rather the case that anomalies are ignored or explained away if at all possible. So just because an anomaly arises, that does not mean that it is enough in the course of

normal science first to distinguish science from non-science nor lead from the movement from one scientific theory to another more constrained scientific here something that pover believed it is only when according to proper to coin sorry, to Cohen, is only when the accumulation of particularly troublesome anomalies arise and when they pose serious problems for the existing disciplinary matrix that such a change occurs. So what is really a particularly troublesome anomaly?

Well, it is, to put it in simple terms, it is one that undermines the practice of normal science. For example, an anomaly might reveal inadequacies in some commonly used pieces of equipment, perhaps by casting doubt on the underlying theory. Or it might actually be an anomaly that shows that the scope of the previous theory that tried to attempt, that tried to explain the phenomenon, the target phenomenon, is not adequate. there are phenomenon that it cannot explain coherently anymore within with

reference to the theoretical framework so when this accumulation of anomalies occur take place Cohen has a name for it he calls them a crisis so I'm just trying to underline these words because from now on when we are talking about the word crisis or normal science and such and such, we are specifically talking about the specific definitions for them. One thinks that a response to the crisis when it is actually interesting or extraordinary

is going to take the shape of a search or exploration for a revised disciplinary matrix or paradigm, a revision that allows for repairing or discarding of at least most pressing anomalies and optimally the solution of many outstanding unsolved puzzles. The name that Kuhn has for such an exploration is called a scientific revolution.

Any questions so far? These are I think just basic materials. We are just trying to lay out the foundations so we get to the formalisms. Some of you have been extremely silent today, including Chagis. I'm just listening. I'm just really enjoying this. Sure. I have a question if you have one. Absolutely, absolutely. You can always interrupt me. Kun say much about the... Like, how does the transition actually occur?

Does that make sense? I mean... Transition from normal science to revolutionary science? Yeah. Or from one theory to another? From one theory to another. I guess, like, like, I guess my question is... If your thought is constituted through existing in one theory, how does it get reconfigured into the other theory? Well, you see, I think Kuhn, when you read the structure of scientific revolution, he had a little bit of a solution for it, but he never goes anywhere.

It is only when a signaler writes his famous essay and presents it to Kohn and Kohn reads it and replies that he begins to actually formulate this coherently. I'm flash forwarding now. Flash forwarding to what I'm going to talk about at the end of this session and the next session. The thing is that you see every theory at least has a core, an expanded core and a frame. So what is the core of a theory? A core of theory is what you might call to be a fundamental theoretical law. Imagine the second law of Newton. What is the second law of Newton? Can someone please tell me?

That is correct but not really. The second law of Neothan is that for an object, the acceleration of object is always proportional the net of force and inversely proportional to the mass so the real formula is that a equals to Sigma F net force over M this is the expanded core

of the Newtonian mechanics all the law other laws of Newtonian mechanics are actually derived from the second law from this formula proportionality of acceleration to net force and inverse proportionality to mass so the core is the second law the expanded core or other laws sorry someone wanted to say something my apologies I couldn't hear very well what she said about the second war you meant Sigma F what do you mean by Sigma? Sigma net force net force sigma not net force so it also it would also have its own special the with the special

laws those special laws would have their own constraints as well yes yes but nevertheless So every theory, as we will move forward, has, in addition to the framework of that theory, the frame, also has a core and expanded core. These are technical concepts, the jargons of philosophy of science, core and expanded. You can think of a core as a second law in terms of Newtonian mechanics. Every other law in Newtonian mechanics is actually derived from the core. These are called expanded core. theory of Newtonian mechanics. It's been about two weeks since I've read this because I read it for the first class, I guess for the first class I just have been kind of busy, but now I'm looking at it so it's not merely just like the

supplementation with a particular special theory, it's the sum of all of the theories which constitutes the laws in the expanded core, right? Yes, yes, yes. okay okay so you see in reply to your question the transition from one theory to other theory happens so in the course of normal science the core is left intact you can derive so many other laws from the core namely you can evermore expand the core reach the expanded new expanded course new laws new theoretical laws from the core while your theory your core of theory namely for example in

the case of the Newtonian mechanics where the second law of Newton will be left intact the transition from theory one to theory two namely revolutionary fear theorization or theory dislodge occurs when the core of your theory namely the second law is replaced by a new core i sort of want to add to peter's question too because it seems like where would the new information come from if not from empirical phenomena? Because it seems like what the core of the theory is, it's explaining the empirical phenomena.

You see, the whole point is that, Theo, I mentioned this, but when we go to Carnap, this should be more clear. and I hope by the end of the class, not this session, but I mean the whole class, should be clear in the sense that you see empirical observations are just parochial. No scientists actually work with such things. These are not really cores. You see, you have always a mathematical structure, you have a logical structure, or you might have a computational structure, what you might call to be your model. Your empirical statements are caught

up within such theory. So there is no such a thing as empirical observation. These things come hand in hand. These are co-constituted. In the sense that just because I have seen and observation that's what you might call to be refute my previous theory that doesn't lead to a theory transition or the change of the basic core. No, it's when, as Cohen says, and I will formalize it, when accumulation of anomalies, empirical anomalies happen and for which you come up with a new mathematical logical

computational model that try to accommodate such observational statements and only in that sense that we can say that we move from one theory to another empirical observation by no means under any circumstance are sufficient to give rise to a theory transition right but that's I mean that's what I'm trying to say is that then why would the theoretical transformation need to take place were it not for the need to explain empirical phenomena differently yes explaining explaining empirical phenomenon is very very different from

from simply accommodating that empirical phenomenon. You see, explanation is a theoretical factor, not an empirical factor. What kind of a structure can I devise using mathematical physics, using computation, using logic, in order to not only accommodate such an observation, but also explain this observation better than the previous theory. So much so that the core of the previous theory will be replaced by a new law, by a nomological factor.

So just to, sorry to keep on rebutting, but I, When you say explain the empirical phenomena better, you're leaning into the theory to say it's better according to this theory, right? Absolutely. Everything is theory-related. It's theory-dependent. Absolutely. Science is, I mean, when I hear people when talk about empiricism and data and such and such, yes, sure, empiricism is important. But if you are really going to deny the empiricism route in the sense that someone says that, well, you know, that these data that need to be explained, these data are really new and revolutionary, data doesn't mean anything.

First of all, the extraction of data is itself theoretical. If you don't have a model, if you don't have an instrument that is based, that is basically conceived according to a theoretical framework, then how can you actually extract such a data? But not even that. How can you put different data, observational data together? Data fitting requires, in fact, models. All of such an empirical factors, when I'm saying, you see, when I'm talking here about empiricism, I do not mean human empiricism, as if we have some sense data, like raw data.

Raw data is absolutely out of question at this point. We don't have ever going to have raw data. Raw data is just a myth. Like I see some people like talk about raw data, like big data for example, as if it was raw data. This is just a myth of the given. No, all data always going to be framed, extrapolated, fitted, manipulated, extracted, so on and so forth only by way of models. A structure always comes first, that or the second. I think this is getting to what my question is, but then I feel like there's a potential in this conversation now to say,

you know, I think that there is no object to which theory corresponds. and at that point I feel like... Can you repeat it one more time? There is no object to which theory corresponds or theory makes all objects for itself and then... Theory! You see what is a really an object if you are talking about Gegenstand in a Kantian sense, namely a specific sensible object Well, the very word specificity has a logical interpretation, meaning that it requires an existential quantification. It exists.

Existence is an existential quantification. There is no such a thing as something exists without existential quantification. That's just talking. You can talk about angels exist. God exists, all of this stuff. But the reason that when we say that electron exists and by that we do not mean real, we are not talking about metaphysical stuff here. We are talking about logical quantification, existential quantification. An electron exists precisely because between such and such observational statement, rudimentary observational statement, such and such predicates over or sorry over such and such rudimentary observational

statements such and such theoretical predicates exist and between such and such theoretical predicates thus and so a structural relations exist invariance And that's when we can existentially quantify a new entity, a new object. We say electron exists within such and such framework as an index of the structural relations within our predicates over our observational statements, atomic facts.

I don't think this makes Theo wrong though. You know, because he's saying that reason makes its objects for itself. What I would think here… No, you see, reason makes objects for itself, but we are talking here about what kind of object? Are we talking about a logical object or a sensible object, an empirical object? Which is exactly why I think if Thiel ends up making the belief that I don't think such objects exist. They do exist. You see, but that's in metaphysical sense.

The whole idea of science, science does not really interest in things existing metaphysically. only interests in the logical equivalent of the empirical observations and these logical equivalents is not one-to-one it's many to one it's many to one many predicates of theory integrates the relation for the structures of your empirical rudimentary observations so you say that an An electron exists in this logical sense of quantification, existential quantification, within the framework of that theory. But what I feel like is like, I mean, I don't think I disagree with you at least too much here.

But I think, you know, like with, you know, a way to respond to Theo would be something like, you know, like his belief that such objects don't exist, you know, has, you know, implicit logical content. Like insofar as like, you know, he is arriving at the lack of observation. And then maybe that implicit content is not able to be carried forward and is able to be subject to scrutiny. Yes, but I think also Theo, I can see and I hope that next few sessions, particularly when we reach to Afbau, Carnap's Afbau, I think some of this stuff should be answered.

I think the real problem that Theo tries to posit at this point is that knowing him that he's basically a bastard mutant of Kant and Hume, he tries to make a very, you know, actually accurate transcendental skepticism here. in the sense that, okay, so we have some empirical observations about some stuff. And then we have also some logical stuff here. Now, first of all, how are these going to get bridged together? Second of all, what really guarantees that our logical configuration of these observational statements

actually correspond to the real empirical evidence. Or, yeah, I mean, it seems sort of strange to say that... My counter-argument with that there is no real empirical, in a human sense, evidence. Well, that I think, yeah, that makes it stranger because then, I mean, this is coming back, back I feel like coming back to Peter's question is why did why would theories need to undergo scientific revolutions at all well why because precisely because observational statements are just what you might call to be sense that since that don't do not yield any form of knowledge if you say that they

do in fact yield knowledge then you are already in the pit hole of the myth of the given so if that's the case the only say that we are talking coherently about empirical facts or empirical evidence is that they are constituted by the logical or mathematical the constituted theories and the reason that one theory get transited or dislodged by another theory is precisely because we see that some of such observations when we add new observations to our repertoire of

raw evidence come theory or mathematics we see that they don't add up Hence, we need to expand sometimes the core of our theories, but sometimes that is not even sufficient. We need to in fact come up with new theoretical laws to support such evidences and accommodate them. So would you say that it's possible to have observables, but observables such that, you know, we are unable, you know, to say anything further until, you know, we go through the investigation to revise our theory?

like can that can some sort of shadow of something that exceeds our faculties in not exceed our faculties I mean the whole point of what you might call besides I doesn't think about cognitive abilities science always work with idealized observers in the sense that the whole point is that you don't want in fact something such thing as... I'm not just talking about idealized observables though you know I'm saying that... No I'm talking about ideal observer ideal observer not observable ideal observer oh okay okay in the sense that

observables are always perceptual ingredients But even when we are talking about observables, we should understand that these are not pure or raw. They are already yielded within a theoretical or modeled theoretic framework. This whole idea of raw data is just a myth. It just doesn't have any base whatsoever. Any person who has worked in a lab, in engineering, in science, in a statistical analysis knows this, that data as such doesn't exist.

raw data always comes via an established model theory or extracted by an instrument that has been in fact made inside a paradigmatic scientific theory. of induction and of course induction when we I mean science proper I think really was quite clear about this and I'm fundamentally agreeing with him that induction in science does I mean inductive is a nothing doctor inductive ism absolutely does not exist in science science is not

inductivism. It's not as if we are basically drawing data pure and then simply we are making some regularities out of them and then we make out of these regularities, you know, logical relations and predictive relations, so on and so forth. No, no, such things don't exist. oh so one maybe one brief question would be uh just just to wrap this up um like uh and i know that this sort of thing could maybe be caught up in some sort of like hermeneutics of suspicion critique or whatever but like what if you know like is it is it is it conceivable that one can have a strong inclination that, say,

the observables, the proper explanation of observables exceeds our current canon of being able to arrive at judgments of explanation? Yes, yes. That's what you might call to be a realistic thesis. in the sense that you see realism is always a postulate I do not agree well I actually need to talk to Ray about this I don't think that realism is something that you can say that there is really a goddamn reality exists outside

of my mind and basically I have to be constrained by no reality is a postulate of theory or mind in the sense that we always posthume it conjecturally that there are additional constraints observational but also non- observational constraint that show that the current framework of my theory ought to be corrected or sometimes discarded in the case of course of revolutionary science. It's a postulate. Realism is adequately understood as a postulate of thought,

as a postulate of theory. I would say that any person who posits a reality outside of mind as if it really did exist in a metaphysical sense and not theoretical sense, is committing naive realism, the sin of naive realism. So you're saying that to be able to postulate that we could arrive at a theory that gives us more explanatory power or something to that effect is a postulate that we can indeed, you know, go further in being able to explain reality

and thus it being a postulate about such a reality existing. Yes, the whole idea of non-observables is extremely important in the course of scientific revolution. It's something that Cohen never talks about. In fact, the first person who talked about non-observables, namely hypothetical entities, that even though they have not been observed, might be responsible for what we actually do observe, was Boltzmann. Many people call these fictional entities, both in a negative sense and a positive sense, as if they are really, you know, we should get rid of such fictional entities like Quine,

But no, in fact, the course of the history of science throughout the 19th century, 20th century, and 21st century has shown that non-observables are absolutely necessary postulates for the course of scientific progress. You can in fact do course of science without postulates of non-observables, hypothetical entities. Can I ask a question real quick? Sure, absolutely. Okay, so from what I'm understanding you to say correctly with regards to realism is that, and I think this is why you bring Ray Brassier in, which is that it's the thesis that non-conceptual reality is in fact artifacts of our concepts.

And so in some sense, so Ray takes this directly from Larell. And why I'm interested in this is... Early on, early on. I think early on. So he had second phase of non-philosy, yeah. But then where... Because he later became fundamentally Szilardian at this point. Ray? Yes. Ray, yes. So, but then, and then you mentioned something that's really interesting to me, which is that the only way in which you can determine these concepts are through their logical structures, or the way in which there's no raw data,

it's simply logical structures and stuff like that. And so I'm concerned because I could make the argument that, and this goes to Theo's argument, which is that there's a point in which you could say that there's a divide between your concepts and non-conceptual reality, even though it's an artifact of it, but there could be a zero-sum game of conceptual re-description where concepts don't reach non-conceptual reality. Well, that's what you might call to be a zero-sum game, is the course of the normal science. what you see what Cohen tries to explain is that you see during the normal course of science okay

for example think about this that for example we are talking about you know equations of motions in the Newtonian mechanics one so forth and of course we can we telescope see this stuff and everything is being corroborated. Everything is in harmony. But then we see some, within the framework of this theory, we anticipate, we either anticipate that there might be in fact other kinds of orbital trajectories or we actually do observe them like the

orbit of Jupiter or any of no or Neptune and then once such observations accumulate or such anticipations within the theoretical framework accumulate then we say that well that is true that all the previous orbits that we were trying to describe were conforming to our theoretical framework and in fact constituted by their structure but then why is that we both for example anticipate other kinds of trajectories precisely because of the mathematical

the theoretical structure of our theory or because we have in fact observed orbits or orbital trajectories that do not conform with our theory. So this is the moment that we say that okay this means that we need to come up with a new theory in which new cores can be positive and hence we can drive more laws from them, hence expanding the core. so much that they can not only accommodate the accumulation of these anomalous observations,

but also anticipate new kinds of behaviors in universe. Really, what is really important here is the co-constitution thesis. the co-constitution of empirical observations and this structure of theories par excellence so so do we still say that so something is given but it but the structure of what's given is not given so so we always have to construct the structure of the object but the object is still given so so yes the object is not given you see the object if we are I think

philosophy of science is Kantian still to this day particularly cool and I think is Kantian so as a signal there however they are not trying to understand the difference between object and theory by way of for example between the difference between a priori and Cantina priori and since that and they are trying to think about it in terms of how basic matter of factish observational atomic observational statements are being constituted but also

elaborated, their relations being elaborated, their structure being elaborated within a theoretical framework which is entirely a logical edifice or a mathematical or computational edifice. Even object is not given, nothing really in the course of science is given. Right, but so the object is not given as a unity so as a unity of sense as a unity yes as a unity is not given right but but there is a given like so what laro would call like given without givenness there there is that might be my call to be atomic facts and atomic facts by themselves are never are never adequate to overthrow a single theory it's the relation between such given without

givenness such observational statements the relation and this relation can only be obtained inside a theoretical framework. And this relation that might pose a danger to the theory core and hence somehow overthrow it. So that's an event. But is it really an event, Adam, in the sense that if you think that event is something of an eruption, eruption, this is not an eruption however, you see articulation of relations between atomic observational statement is more of an accumulation of criteria of coherency,

consistency, the structuration, so on and so forth. It's what you might call to be a logical inevitability. So it's not an event because it's inevitable in some sense. Logically, logically. Within the framework of a theoretical structure, it's inevitable that it leads to more anomalies and more anomalies to the point that you can no longer obtain a structural relations between them within that theoretical framework. And hence they no longer corroborate your theoretical core theoretical law. And hence that's a time that scientists would say that,

okay, I can do two things. Either supplement an additional law that can accommodate them, or, and if it doesn't, you are on the course of normal science. But sometimes it's impossible, no matter how much supplement you added, as long as the previous law, the core law is in place, you see that anomalies are stacking upon one another. And hence, that's the time that you say that maybe I should change the theoretical core. Moving from Newtonian mechanics to Einstein's system. So how would this work with pure mathematics? I really don't know. I need to think about it. I really need to genuinely think about

it. I suggest to you read this chapter of Stegmuller in that book that I recommended to you where he actually starts it from a mathematical perspective. It's a chapter called One second, sorry. It starts around page 25.

It's called theory nets instead of expanded cores. And Stegmuller tries to actually make an analogy with the way that a mathematician works precisely because there is a correspondence, but I genuinely am not too much familiar with how I can pitch this way, scientific, empirical science way of changing a theory and the way that mathematicians come up and reinvent a new mathematical object. Can I possibly ask a question about that or will it be better to post on the classroom

since we're... No, no, no, you can. Don't worry, we are... Of course, Theo always has more questions. Just talking about mathematics, and this may be running kind of in front of the train, but in regards to Stugmuller, so he seems to have this sort of a Hilbert program running in his head, saying that basically scientific theories ought to be axiomized. they should be somehow represented and in his work he presents it up as sort of a set theoretical model but i wanted to ask is um i know i asked a similar question during the first session but i think here it's uh much more kind of evidence-based uh what i wanted to ask is basically oh i apologize

uh do you by any chance think that for example something like change in foundations of mathematics For example, formulating axiomatic systems not through set theory, but something, you know, of a higher dimension like homotopy type theory or category theory. Do you think that in any way bears laden only different solutions to problems? something like you know uh just saying that if we apply category theory or we apply homotopy type theory it's easier to solve i don't know fermat's last theorem through the uh geometrization of arithmetic or do new foundations in your opinion make for something for a more radical change

maybe like solving something unexpressible yes even well that's a really a difficult question that's a really difficult question you say uh i mean i i want to express the view of your countryman andre rodent uh precisely because he believes um that yes changing the axiomatic systems might coincide with a change in the kind of structures that we do discover and we can talk about. So yes, it would be a fundamental. But then Stegmuller, however, thinks that axiomatization

of theories is an auxiliary part of the theories. It is, yeah, sure. It is part of, actual fundamental part of the theories, but what you might call to be axiomatization is what you might call to be simply a way of elaborating the concept of a structure, namely relation between sentences inside that theory. and nothing more. But I, of course, this is just, I'm just simply saying this tentatively, I take side with Rodin.

Rodin, I think, is right that if we say that object is constituted, existentially constituted by the concept of a structure, which is always theoretical, then change in the axiomatic configuration of the set theory might in fact reveal fundamentally new structural relationships and hence constitute objects very very differently. Do you think that it may have something to do with scientific revolutions? Because the way, of course, Stuckmuller, yes, as you have mentioned, makes the case that

it's auxiliary so it's not sorry essential but it seems to me something akin to the guttel system if you can move it to an axiomatic level if you can formalize it well then you have the guttel sentence and that is kind of unescapable it's of course may not be essential but if you have that possibility then you're faced with some sort of ramifications for explanations of your theory and And that kind of, I feel, coincides with the question of, quote unquote, like irrational data that Kuhn poses as being this climax of the end of the normal science. And I was simply wondering whether you think that basically introducing new foundations

may simply truly provide a solution to those? So maybe foundations is, if we can potentially move scientific sentences, scientific meanings, theory meanings into an axiomatic level, would then a revolution consist of changing the syntactical core basically? Well, this is, you see, we'll look at this problem. It's basically what you are trying to formulate is what you might call to be the transition from Karnav phase one to Karnav phase two. Karnav phase one is the logical structure of the wall, afbaw, in which systems are

axiomatized and basically all non-observable statements are written in terms of Ramsey sentences and does anyone know what Ramsey sentences are here so very very short Ramsey sentences what you might call to be due to Frank Ramsey British philosopher is that when precisely because when you say that an electron exists and I got a sorry an electron is real so is it is it is basically or does is an electron real. Carnap thinks such questions are pseudo questions or pseudo problems.

No scientist thinks of such things. So when he tries to represent the course of theory of structuration, he resorts to something called a Ramsey sentence. And Ramsey sentence This is what you might call to be a sentence in which, by way of some correspondence rules, you translate your non-observable statements, like an electron is real, to observable statements, hence, fundamentally getting rid of those old metaphysical bloatware.

So this is the question of Paul that he tries to basically translate all of such endeavors in science into logical formalism and hence the question of a structure, mathematical and logical structure. But then he sees that such a project fails and then he goes and writes a new book which you might call to be a sequel and a, what you might call to be a repairing complementary sequel to about his logical syntax of language, where he tries to talk about this idea that

if we take, if we completely divest the formalism of language, and by that I mean general language, natural language and turn it into a calculus so we can talk about the kind of structures are being obtained between such symbol designs or symbols within the calculus of language then that will enrich our notion of our objectivity i think i think that that that in principle should be true that in principle should be true revolutionizing

revolution basically revolution in the realm in the formal dimension of theory can in principle lead to revolution in objectivity precisely because you can elaborate and diversify object by way of different formal or structural relations. So is relation then ontologically prior? I mean, so is relation... Not ontologically, not ontologically.

Okay, epistemologically. Theoretically, epistemologically, yes. And that would be prior to, I don't know, sets or properties or other kind of formal... Well, you see, when we are talking about sets, even within a set, you can even think about membership in terms of relationships within properties. of a given phenomenon that has been indexed by a set. But also you can think about relationships of relationships, namely sets that bridge one set to another. So you don't buy Bajiu's claim that you can sort of bottom out in the empty set as the sort of fundamental content of thought?

Well, I mean, these are I think really sticky questions precisely because when we are talking about thought, what do we exactly mean? Are we thinking about objective thought or are we talking about something like formal thinking, like Platonic idea of thought? You see, if it's objective, absolutely not. If it is logical, maybe. The whole notion of thinking needs always to be traded very, very carefully because our thoughts are not homogeneous.

Are we talking about objective thinking? Are we talking about logical thinking? Are we talking about, for example, perceptual thinking? These are all fundamentally different. None of them are, I mean, Kant had already shown this. perceptions are thoughts but perceptions are uncritical judgments uncritical thoughts cognitions are critical thoughts but there are also categorical thoughts laws of understanding which are purely formal But so, sorry to ask so many questions, but like, so if logic then in some sense is still

the foundation of science, like reason in the Kantian sense, does that not mean that whatever would be a basis of logic and insofar as logic through science is applicability to the world, then whatever we ground logic in would kind of be our fundamental ontology in that sense? Yes, yes, yes. Ontology is a predication, is a logical predication. Ontology, I mean, this is usually Salar's Quine actually, Quine, starting from Quine, the whole idea of ontological reals or realia is essentially a predication, existential quantification over a logical domain.

Otherwise we can't talk about such things. And of course the implication of such a thing, Karnal actually was a proponent of such a view, that if we expand the concept of formal structure by way of, for example, reinventing new formal languages, symbol design, elaboration of formal structure, so on and so forth, then principle in theory it is possible to expand the structure at the level of objectivity at the level of being renegotiate our boundaries with objectivity or with the intelligible

And this is one of, in fact, one of the most, I think, revolutionary, obscure, extremely undervalued pieces in 20th century that comes from Vienna Circle and particularly from logical positivism that only recently has been recognized. But you see traces of it in Carnap, in Sellars, in Quine, in Max Schellig, so on and so forth. It's quite actually a very, what you might call to be, almost unsettling thought that

The more we expand the resources of formalism and logic in principle, see in principle is very important, in principle we can expand the domain of the intelligible reality precisely because the structure of reality is nothing but the kind of relationships between observance observational or matter of factual atomic statements which are being indexed by logical relationships namely logical structures.

Okay, let me get, finish this corn thingy and tomorrow, I mean next session we will fresh, we will start fresh Seigmuller. I really would like you to look at Seigmuller's book, read the introduction and skim through it. particularly search the word core, expanded core, and frame, these three words, and also… I hope this is included in the document that you said, which is… You can find the LibGen. Yeah, well, I'm looking at structures and dynamics of theories, reflections…

no that's not what i recommended this is the one that i recommended um oh okay uh i i recommended this one it's called uh the structuralist view of theories we'll bring this segment a possible analog of the bourbaki program in physical science but the i assume then this need include still worth reading so i will i would like you before i move forward because uh look for these things core expanded core frame possible models and uh potential partial models precisely because

uh the majority of the formalism that uh next session we are going to work and it's going to be a little bit too dense, I would like you to have at least some familiarity with such concepts before we move forward because this is, things can get fundamentally dense and incomprehensible if you do not know have a basic familiarity with such concepts. So anyway, back to Kun, I was saying that so basically I talked about crisis the notion of paradigm disciplinary matrix so on and so forth the thing is that Cohen believes that science does progress in contrast to

to sociologists who interpreted Kohn's paradigm of scientific revolution as in fact, as if Kohn says that, for example, the progress of science is always under the limitations and constraints of sociological, basically current. But that's not what Kohn says. believes that the idea of scientific progress is a progress and it's a social progress in the sense of community of science scientists but not everything that is social means that is substantively social and hence essentially the social factors of scientific progress are intrinsically

scientific rather than generically sociological. So in that sense Cohen believes that science does indeed progress in the scientific sense even through revolutions, even when we say that a theory has dislodged another theory we are talking about progress. However, the idea of scientific revolution and the loss of explanatory power or Cohen loss, according to Cohen, rules out the traditional accumulative

portrait of normal scientific progress. The revolutionary search for replacement paradigm, or what you might call to be a replacement core in the sense that I talked about, for example in terms of Newtonian mechanics, is driven by the failure of the existing paradigm to solve certain important anomalies. replacement or dislodgement paradigm, dislodging paradigm had better solved the majority of those puzzles or it will not be worth adopting in place of existing paradigm. Also, even if there is some current laws, a worthy replacement must also

retain much of the problem-solving power of its predecessor. So you can see that Szilardzian in fact picture of the scientific progress or the refinement of the scientific image in a sense what you might call to be Kohnian in the sense that the new theory not only retains some parts of the old theory explains the core problems of the previous theory but also explains the phenomenon whose accumulation for the previous theory were deemed as anomalies or a crisis.

So however, during such a transition from T1, theory 1 to T2, when we are talking about replacement or dislodgement of the theory core, there might be some loss of qualitative explanatory power. Hence we can say that revolutions do bring with them an overall increase in puzzle-solving power. The number and significance of the puzzle is an anomaly solved by the revised paradigms, exceeding the number and significance of the puzzle solutions that are no longer available as a result of Kuhn's loss.

However, Kuhn is quick to point out that any inference from such increases to improve nearness to truth is not a good inference. So it's not that Kuhn does not believe that basically increasing power of puzzle solving can be understood as a premise for an inference whose consequence means that essentially the

succeeding theory has converged further toward truth. As I mentioned earlier on, Kuhn fundamentally disagrees with such picture of scientific progress as approximation convergence upon truth. He actually believes in an evolutionary picture of science. However, when I am saying evolution, we should know that by evolution I mean more something like Darwinian rather than like Aristotelian framework of evolution In the sense that this kind of scientific progress, whether in the course of normal

science or the revolutionary science, usually lead to diversification, expansion or complexification of puzzle solving powers. However, which is more like a Darwinian evolution, however it does not mean that as if science, the evolution of science is evolving around an ideal form or an ideal true theory, as if like for example the evolution of an organism could be thought into Aristotelian teleological as it basically, the human is basically, as it evolves, is converging more and more toward a perfect divine form.

That's not what Kuhn is talking about when he talks about the evolutionary picture, the scientific progress. Another thing that is extremely important with, as I mentioned, with Kun's philosophy of science is the notion of the disciplinary matrix or paradigm. When Kun talks about scientific paradigms, he usually uses the word exemplar, which are

usually you might call to be exemplars or exemplifications of what he calls mature science, namely a science that allow for coordination of a scientific community around a set of methods, techniques and instruments rather than this kind of inhomogeneous competition of scientific forces. So, this was a really, really light introduction to Cohen. Now, I would like to, before ending

this session, reading you some of the notes on Stegmuller's idea of Cohen and how he tries to expand these rudimentary concepts into a full-fledged, formal, logical portrait of scientific theories. So now you can think about scientific theory as not some kind of extraordinary supernatural thing but in terms of models, concrete models. Okay? For that I need to go a little bit flash forward again and talk a little bit of some of the

motivations behind what you might call to be development of a Sigmuller's and formalizations of Cohen's view of scientific revolutions and scientific progress. Some of these, majority of such presuppositions for a Sigmuller, as I mentioned, are Carnapian, precisely because he was a disciple of Carnap. And as we shall see in future sessions, that Carnap is the first person in philosophy of science who provided the opportunity for reinventing

what science does at a logical, formal level. Main thesis. Carnap's program of logical reconstruction of concepts from the Aufbau, Aufbau is basically just a regular term for the logical structure of the world, is one of his most famous works. Carnap's program of logical reconstruction of concepts from the above is analogous with the structuralist program of logical reconstruction of scientific theories.

Kuhn's ideas are precisely reformulated by Stigmuller in a formal framework with the Estigmuller structuralist approach. So what is the core tenet of Baal? It's a program for logically reconstructing our knowledge of the world in a structuralist terms, in the sense of philosophy of science. This means that the description of knowledge are, at the bottom, structural descriptions. What would be the connection then between Aufbau and a structuralist philosophy of science?

In his book in 1991, Moulin says, says, to be more precise, the use of Carnap's of Baal, I propose here, consists in reinterpreting Carnap's constitution of theories as a formal explication of the notion of an ideal observer, i.e. an epistemic subject provided with the essential constituents of an ideal observational language to check any empirical statement made in theoretical science. When we are talking about an ideal observer,

we are not talking about, you know, a human being, a perceptual subject, so on and so forth. We are really, if you want to think about an ideal observer, think about a recording tape, a computer. Its interactions with the world are being recorded as traces on this tape, but then such statements are being parsed by way of a formal syntax. In a structuralist philosophy of science, the primary aim is to provide a program for analyzing

science. This concerns issues of logical reconstruction of theories, but also intentions of describing the social phenomenon of the scientific enterprise. Hence, according to Stegmuller, there is no ideal observer in Carnapian sense when we are talking about scientific progress. Yet it might be in the context of a specific scientific theory, but not when we are talking about scientific progress. There is no ideal observer in the sense of Carnap, but there is also the motivation of applying logical tools of such an ideal observer

in order to reconstruct our knowledge of the world. In Afbaho section 16, Carnap introduces his structural descriptions of knowledge. He says, every scientific statement can in principle be so transformed that it is only a structural statement. But this transformation is not only possible but required. for science wants to speak about the objective. However, everything that does not belong to the structure but to the material, everything that is ostended concretely, is in the end subjective. From the point of view of constitutional theory, this state of affairs is to be expressed in the

following way. The series of experiences is different for each subject. If we aim in spite of this at agreement in the names given for objects constituted on the basis of the experiences, then this cannot occur through reference to completely diverging material, namely subjective, only through the formal indicators of the object structures. Again, in section 66, it says, how should science come to objectively valid statements, if all

its objects are constituted by an individual subject? Well, the solution to this problem lies in that of course the material of the individual streams of experience is completely diverging. But certain structural features agree of all streams of experience. Science has to restrict itself to such structural properties, since it aims to be objective. and it can restrict to structural properties as we have seen earlier, for all the objects of knowledge are not content but form and they can be represented as formal structural entities.

So Afbao, you might say, is an outline of the epistemological program of early logical empiricism. This is a view which is different from the structuralist view of philosophy as advanced by Sneed, Kohn and Seymour. Nevertheless, in our Paul as in a structuralism, there is, in both of them, there is this emphasis on a structural descriptions of our knowledge of the world. In Structuralism, this description is made of our empirical theories, whereas in Carnap's program, structural descriptions are provided directly of our knowledge.

However, both share the view that our knowledge should be best described in form of structures. When Carnap starts with structurally describing our knowledge of the world, Structuralism describes this knowledge indirectly through the structural description of our empirical theories. So Cohen's conception of theory changed after these preliminary remarks about Carnap's and structuralism. You can say, according to Cohen, a scientific community is a group of people that shares and uses the same paradigms.

Normal science and extraordinary science differ. Normal science is a scientific activity as puzzle solving, to use Cohen's words. Scientific research is guided by a paradigm. Anomalies can occur. This can lead to a crisis in a certain field. Such a crisis once accumulated can, but must not lead to extraordinary science. Extraordinary science. One paradigm is substituted by a new one. A scientific revolution occurs. The scientists which were applying the old paradigm cannot successfully communicate with the scientists obeying the new paradigm. Now, there are at least four components for a Konian disciplinary matrix for a paradigm.

One, symbolic generalizations. In order to comprise knowledge, certain symbols are introduced and generalized. A concrete example are equations as symbolic generalizations. So essentially, all paradigms are laid in formal languages and generalization of symbol design, which we talk next session in terms of axiomatic systems, but in future sessions about the logical syntax of scientific languages. Two, models. There are heuristic models and ontological models.

Heuristic models are more like fictions. Ontological models do correspond partially with the world. For example, we imagine that planets and stars are actually round only for practical reasons. Three, values. The methodological values shall guide the scientific research and raise questions of technological applicability. Also, questions of the coherence of the research. For example, certain research areas might not be addressed for ethical reasons or practical reasons. We accept the methodological value of theory simplicity. Four exemplars. These are the paradigmatic applications, the concrete instantiations of a paradigm.

Such concrete cases show how a paradigm actually works. These are especially well-working intended applications of a paradigm. Now, Kuhn recognizes explicitly the enriching contribution to his program provided by SNEED and in a more systematic way by Stegmuller. After I mentioned that Stegmuller sent his essay to Kuhn. He says, to a far greater extent and also far more naturally than any previous mode of formalization, Esnit's formalization lends itself to reconstruction of theory dynamics, the process by which theories change and grow. Esnit also suggests, and Stegmuller elaborates the possibility that at least some cases of change,

of course, corresponds to what I have called scientific revolutions. through the SNEED formalism does, though SNEED formalism permits the existence of revolutions, it currently does virtually nothing to clarify the nature of revolutionary change. I see, however, no reason why it cannot be made to do so. And I mean here to be making contribution toward that end. So who is really this SNEED? I mentioned his magnum opus last session. He's what you might call a person who gives us the formal means to actually understand

and accurately picture the course of scientific evolution. Both the structure and dynamics, namely the range of application, scientific theories. The logic of scientific progress. Esnit's 1971, The Logical Structure of Mathematical Physics, is the pioneer work of a structuralist philosophy of science. The methodological tools of this view are developed there and applied to mathematical physics. Through Esnit's original proposal, though Esnit's original proposal is mainly motivated in providing the logical framework in an statement view for the description of the logical structure

of physical theory in chapter seven which is one of the most difficult ones he mentions the field of theory dynamics this is exactly what stegmuller starts to accommodate and appropriate and identifies what Coen's calls philosophy of science or dynamic of science and scientific structures. So a second layer in his works starts to adopt this Asnidian view, Asnidian and formalism and develops a full-fledged,

a structuralist view of scientific progress. Almost what you might call to be a model theoretical view of what actually science is and how does it evolve and how it evolves. Sigmular offers a detailed analysis of Kohn's concept of paradigm particularly. Before moving forward, perhaps I should talk a little bit just about what we mean as structuralism here in philosophy of science. Structuralism, you can say, owes its name to the fundamental thought, the most adequate

way of interpreting and understanding what a scientific theory is does not consist in conceiving it as a set of statements or claims, but rather in conceiving it as a form or collection of different types of complex structures which themselves are built up of simpler ones. So in a structuralist view, sorry, in a structuralist philosophy of science, an empirical theory

consists of its models, which are sequences of the following form. me just very quickly share my screen and we are I just give you these two pages so we have a little bit of stuff to work with until next session do you do you see this the screen yeah okay in a structuralist philosophy of science and empirical theory consists of its models which are sequences of the following form is essentially an order set D1 to DM, R1 to RN. The DI are so-called basic sets and RJ are relations constructed on these sets.

The elements of DI comprise the ontology of the theory. That is to say they contain the objects of which the theory is about. rj are usually functions. We'll talk about these in much more details. They usually are functions mapping empirical objects into real numbers or some other mathematical entities. An example, the potential model MP, actually I have written it incorrectly, it should be a possible model MP, which means that basically a model that has some theoretical statements

and some non-theoretical statements of classical collision mechanics. MP or possible model equals to a quintuple PTRVN. P is a finite 9 empty set. T contains exactly two elements and R of course is real number. V, the product of Pt, maps onto R3, and m, v is velocity by the way, m is momentum, p to r plus. p is a set of discrete bodies that can be called particles, t is a set of instants,

v is the velocity of function assigning to each particle p, and point of time is velocity as an element of r3. Velocity is a time-dependent vectorial function whose range are triples of real numbers. It assigns a three-component vector, one component for each direction of space, to each particle at each time. m is the mass function assigning to each particle its mass. Now, of course, I should have added a small p as well. in the sense that you also need an additional element which is called position and position

inside classical collision mechanics is in fact a non-theoretical component and hence so you have some theoretical components, theoretical functions here, things like velocity and momentum, which are absolutely theoretically laden, and something like position of the particle, which is not really theoretical, and hence that's why it's called a possible model. So basically in the next session I will argue how we can in fact really give this a structural view of all scientific theories in the sense of this logical formalism. In the sense that if we think about for every theory

we have a dynamic namely a range of application and a structure and a structure usually has a core, an expanded core and a frame and a core itself has theoretical and non-theoretical functions it has possible models and partial potential models and so on so forth i will all describe these entities and then we will create what you might call to be a stegmuller a structuralist view of the scientific method and then we will hopefully two sessions from now or three sessions from now, we will try to take a step back

what I have introduced as a structuralist view of scientific progress or science or the course of science in terms of Carnap's logical empiricism and then his later works on the logical syntax and then trying to elaborate about all of this new views emerged in philosophy of science in reference to the preenial questions of philosophy rationalism and criticism theory structure objectivity so on and so forth as I mentioned it

would really really would would be helpful if you can just skim through a a Stegmuller's book, the one that I suggested. So you can get a little bit of a familiarity with these things because from at least for the next three or four sessions things will be a little bit too dense and unfortunately I try to, I really will try to make sure that all of these stuff going to be, you know, elaborate at an introductory level but certain things unfortunately require some you know prior familiarity so just to confirm the stegmuller text is the structural structuralist view of theory and that's going to that's going to touch on the

possible models potential and partial uh formal models partial partial potential models of potential partial models and mp possible models mpp potential partial models okay which basically means that they don't have theoretical stuff theoretical statements in them and also you have m which is basically law the core the the basically they're just the the fundamental laws like for example the second law of newton So laws are models, and this is working in the sense of model theory? Model theoretic, yes. Usually all of the structuralist views in philosophy science require a certain kind of commitment to model theoretic view.

So it's a question of these formal statements being satisfied when mapped out? coherency, reducibility, we'll talk about and then we will try to show that once we picture the structure of scientific theories in thus and so matters by way of such formal research, then we can think about more coherently about theory comparison, comparing a successive theory to a preceding theory, or reducing one theory to another, or inferring one theory to another theory. So basically we will think about all possible scenarios of theory dynamics between multiple

theories, hence capturing the fundamental idea of Cohenian distinction between normal science and extraordinary or revolutionary science. So before you mentioned that we should probably read some set theory, but now you're making model theory, so maybe we should... Set theory, I think set theory, when I'm saying that model theory, I didn't mean it in the what you might call to be model theoretic in the sense of mathematics basically model theory in the sense of philosophy of science but set theory would be enough even I think that even some familiarity with naive set theory

would do it you don't need to go to any kind of you know fancy set theory just nice that theory would be enough and can you either send me that set theory introduction or yes yes yes i actually sent it to uh jeff i think jeff is not here today he's here oh he's here yeah i'm here oh okay okay so i will just plagiarize from what i sent to jeff and sent to everyone plagiarize away i plagiarize away so this isn't model theoretic like mathematically no No, no, no, it's model theoretic when I, yes, I mean, model theoretic in mathematics and in language are fundamentally different things, and model theory in mathematics and in language are different, model theory in philosophy and science is different. It's just basically the idea that theories can be understood as models.

as a model. So is there a question about whether a model satisfies an axiom system? Yes, they do. But within, not within pure axiomatic system. This we will talk about in the next session. There is a difference between an axiomatic system and an axiomatized theoretical system. In the course of science we deal with application of axiomatic systems to scientific theory. Hence our theories are being axiomatized. This doesn't mean that they fully conform to the constraints of an axiomatic system.

It's rather that the statements of such theory, the laws and constraints, are being axiomatized in reference to a certain axiomatic system, Carnapian, informal Hilbertian, formal Hilbertian, and so on and so forth. All right, I'm going to end the broadcast now, and if anyone has any last-minute questions about reading or assignments for next week, we can talk about it. I suppose I had promised to go out in 2.30 right on the spot. But it's OK. You can pose the last question. Then I have to go.

Only logistical questions about assignments will. Thank you, everyone, for all the great input. And you should realize one thing You want to turn it off? Sure. All right.