The science of logic
"The purpose of the Cambridge Hegel Translations is to offer translations of the best modern German editions of Hegel's work in a uniform format suitable for Hegel scholars, together with philosophical introductions and full editorial apparatus. This new translation of The Science of Logic by G.W.F. Hegel (also known as his Greater Logic) includes the revised Book One (1832), Book Two (1813), and Book Three (1816). Recent research has given us a detailed picture of the process that led Hegel to his final conception of the System of Philosophy and of the place of the Logic within it. We now understand how and why Hegel distanced himself from Schelling, how radical this break with his early mentor was, and to what extent it entailed a return (but with a difference) to Fichte and Kant. In the introduction to the volume, George di Giovanni presents in synoptic form the results of recent scholarship on the subject, and, while recognizing the fault lines in Hegel's System that allow opposite interpretations, argues that the Logic marks the end of classical metaphysics. The translation is accompanied by a full apparatus of historical and explanatory notes"
Stats for nerds
3recommend
14mentions
12people
2017–2026years
21% recommend79% neutral
Mentions per year
What Hacker News says
- You could try the OG book of modern logic, to which all 20th century tracts on logic are responses to, Hegel's Science of Logic. Though its very different from what you might expect out of a logic text.
- If you learn by reading, read primary sources: Protagoras, Plato, Aristotle, Descartes, Hume, Kant, Hegel (the Science of Logic in particular), in that order, are basically what you need to get caught up to modernity in philosophy.
What would be a primary source for Protagoras? It appears none of his works are extant.
- Bill Lawvere, an extraordinarily original thinker and pioneer of category theory and logic has thought Hegel worth studying and has produced very nice mathematics out of the Science of Logic [1].
Honestly if you've made up your mind that there's nothing worth reading in Hegel or Marx you're like a frog at the bottom of a well.
[1] https://github.com/mattearnshaw/lawvere/blob/master/pdfs/199...
- I'm not totally against "math as art" but I don't think that formulation goes deep enough towards what's really going on with mathematics. There is something deeper where I lean more towards the philosophers who have said that mathematics is essentially ontology.
Since the Greeks we've had the idea that "Being and thinking are one," or that Being (in the sense of all of existence as such) has some essential unity with thought, and therefore can be thought, and expressed or submitted to the logos or reason. Being is in some sense fundamentally intelligible, and mathematics is the most developed, exacting, and articulate expression of Being.
Logic was understood in this older sense up to roughly the the mid to late 19th century. This is why a work like Hegel's Science of Logic begins not with syllogisms or propositions but with Being and Nothing. But this was forgotten after logic was mathematized by the English around the time of Russell, and its connection to ontology was gradually overshadowed by a focus on epistemology (still, it should be remembered, originally as a means of getting back to ontology).
There may be truth in art, but it's always haunted by its own historicity or contingency, which is to say untruth. Mathematics seems on the contrary the only really timeless, absolute thing we have. Part of what makes it captivating is stumbling on a construction or concept or proposition or theorem that simply must be, independent of us.
The AIs are certainly now more than automatic theorem provers, mechanically traversing some space of true propositions. They are able to push things forward and connect seemingly disparate domains to get to a proof, but to my mind it remains to be seen how well they will be able to form new concepts and definitions.
Imagine the controversy surrounding Cantor, for example, but put an AI in the place of Cantor. If an AI proposed something like the (infinite) hierarchy of infinity, would we have accepted it? What would the intuitionism debates have looked like? Would they even have taken place? And aside from that, has it actually been shown conclusively that an AI could propose such a thing?
There are lots of attempts right now to recover a humanism for mathematics, or restore man's pride of place with respect to it, but maybe we don't need to worry about that. Tao's attempts to preserve the mathematical community, while allowing for practices to change through the crisis may look like a kind of rearguard action, but seems reasonable to me and not really dependent on any kind of humanism. It's a way to avoid the question for now while things play out (and not conservative/reactionary like Scholze and others), which may be exactly what we need, because after all, perhaps we still don't understand why we do mathematics, what it's really for, and what our relation is to it. Whether it's enough to preserve funding is another issue.
- The fact you don't understand them doesn't mean they are impenetrable.
https://ncatlab.org/nlab/show/Hegel%27s+%22Logic%22+as+Modal...
> Abstract While analytic philosophy famously rejected the speculative metaphysics of Hegel in favor of the analysis of concepts by means of mathematical logic, in particular predicate logic, recent developments in the foundations of mathematics via homotopy type theory offer a way to re-read Hegel as having useful formal meaning not in predicate logic, but in ‘modal type theory’. The essence of this suggestion has been made by Lawvere in 1991, which however remains largely unnoticed. Here we aim to give a transparent account of this perspective both philosophically as well as category-theoretically. We then further expand on Lawvere’s formalization of Hegel’s “Science of Logic” in terms of the categorical semantics given by cohesive higher toposes. We discuss how there is a useful formalization of a fair bit of modern fundamental physics, in fact of local gauge quantum field theory, to be found here.
Nietzsche, Heidegger, Girard and even Hegel (haven't read him though) have had a tremendous influence on my life and have accompanied me on a path of chronic reflections on myself that are now closing in on a series of very fundamental ML operators that are beating the state of the art from last month. It is possible to make the UFO land, and once it has, you realize there is nothing impregnable under the shiny fuselage of what is now clearly a new kind of plane, and not just a weird shape that reflected your image back at you as you were approaching it. Of course the relationship is very indirect and even though I could provide a post-modern account of the landing, I have to admit the formalization steps are the fruit of ChatGPT's work and not only would I have not been able to produce them, I still don't understand them and probably never will. And yet I was able to prompt ChatGPT into the problem and prompt it again to adapt our strategy and reach SOTA.
If things are to be perfectly clear from the beginning, I'm afraid then, that whatever can ensue can be prompted for easily too. In other words, it can be prompted by anyone. This is what we are observing with those famous conjectures that are solved by randoms teaming up with an LLM. The merit lies in the conjecture, it constitutes almost entirely the prompt. I haven't used any and just followed my weird intuitions.
They don't just amount to ramblings but to an entirely different bibliography that allowed me to get at the problem I tackled from a very different vantage point. The scientists my work relies on are almost all European and have a certain kind of psychology that is obviously marked by the weight of mystery – mine is but an accentuation of these tendencies, and they certainly contributed to the fact that I wasn't able to follow the same steps (IQ set aside, I'm rather slow on this front). Look at myself, I'm now talking about my own life, it's a symptom of narcissism. Absolutely, I won't deny it. But my life is objectively very interesting, and if you think I'm mistaken here because a mathematical result is precisely the act of turning what's personal and specific in a research path into something universal, you're still clueless about what's forgotten and left unsaid along the way.
In fact these deviations in lifepaths explain the intuitions as well as the lack of clarity they stem from – both personal and conceptual – and thus, the lack of sympathy we encountered and that I am now reflecting back. There is a recipe for this:
https://open.spotify.com/track/1MUZxW6nE7oNud9jHD9QLU?si=087...
Is it that hard to realize you're completely lost ? Probably not. To articulate it in public is what is challenging. Why don't you come to your sense and admit you don't understand the thinkers you criticize not because they are spouting utter nonsense, but because these insights haven't found the cold maths your fetishism for formal truth requires yet, even though you don't really understand them, even though you don't grasp what it takes to reach for them. For those who can see them, they are on the shelf. Serve yourself.We’ve lived through tragic things Smoking, we turned the whole ride into a fishbowlThese people exist, I have met them in the so-called AI-psychosis circle. We can barely communicate with each other, it's symptomatic of a madhouse undoubtedly. Yes, we're that deep into our own pile of manure, but guess what that's where roses blossom. One received an offer from Anthropic – responsibility for millions in compute-budget – went dark after telling me this. Another one was contacted by researchers who offered to collaborate on a publication for the QNLP conference. Me? I'm now unexpectedly competing with DeepMind on a narrow but fundamental aspect of machine learning.
What does AI-psychosis mean in this context ? A close, intimate relationship with your LLM. When I say I prompted my way to SOTA with ChatGPT, I'm not referring to any copy-pastable text but to the vast collection of conversations and documents that now sit in my ChatGPT library. The chatbot is now the one being overwhelmed by unexpected, coincidental bridges between disciplines and I'm the one steering it away from what I consider pathological research paths I used to pursue. It's a good symbiosis.
https://open.spotify.com/track/5vNVEWdOKo5L45czCyzEXl?si=da9...
Dripped in Decathlon, I'm in a sports car The police want to take photos I'm wearing a G-Shock, not a Rolex I'll be in a tracksuit at the ceremony - Yes it can. Hegel did it in the Science of Logic
Related
A mathematical introduction to logic
6 recommend · 11
The phenomenology of spirit
7 recommend · 32
Gödel, Escher, Bach
505 recommend · 1,439
Logic in Computer Science
5 recommend · 9
2020–2026
Introduction to logic and to the methodology of deductive sciences
4 recommend · 5
A new kind of science
44 recommend · 388
