The hottest Logic Substack posts right now

And their main takeaways
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Top Philosophy Topics

Natural Ordinal Addition

Infinitely More • 7 implied HN points • 15 Mar 26
🔬 Science Logic
  1. The natural sum and product (Hessenberg operations) make the ordinals into a commutative semiring, contrasting with standard ordinal arithmetic where addition and multiplication are not commutative.
  2. The natural ordinal operations match the operations on surreal numbers, so the ordinals under natural addition and multiplication form a subsemiring of the surreals.
  3. There are five independent, self-contained ways to define the natural sum and product—order-theoretic, computational, proof-theoretic, and others—and all five are equivalent, giving complementary perspectives and routes to generalization.

Unreal numbers

lcamtuf’s thing • 4489 implied HN points • 15 Feb 26
🔬 Science Logic
  1. Natural numbers can be built from a base element (zero) and a successor rule, and addition and multiplication follow from simple recursive definitions.
  2. Integers and rationals are formed by ordered pairs and equivalence classes so subtraction and division have in-system representations, and these extended sets remain countable.
  3. Computable numbers are those a Turing machine can approximate and are still countable, but the real numbers are uncountable (by diagonalization), so most reals cannot be computed.

1,000 CFETs, SK Hynix Next-Gen NAND, Interconnects Beyond Copper, 2D Materials, and More

SemiAnalysis • 9799 implied HN points • 13 Jan 26
🕹 Technology Logic
  1. 3D NAND makers are still squeezing more bits by adding layers and decks; SK Hynix’s 321-layer V9 boosts capacity a lot and its multi-site 5-bits-per-cell idea shows big logical-density potential, but these tricks add serious process complexity and cost.
  2. Metals are changing to beat copper limits: Samsung is using molybdenum to cut wordline resistance in NAND, and ruthenium is emerging for ultra-fine interconnects with textured ALD that can greatly lower line resistance at tiny pitches.
  3. Two-dimensional materials keep promise for sub‑10 nm logic because they reduce source‑to‑drain tunneling, but real-world barriers—wafer‑scale integration, low‑bias contacts (especially p‑type), variability, doping methods, and modeling—still need to be solved before they become manufacturable.

Let the silence have you

Silentium • 499 implied HN points • 21 Oct 24
📖 Philosophy Logic
  1. Silence can be a powerful tool for reflection and personal growth. Taking time away from noise helps us better understand ourselves.
  2. Embracing moments of silence can lead to greater clarity and peace of mind. It allows us to recharge and connect with our inner thoughts.
  3. Creating spaces for silence in our daily lives is important. It can improve our mental well-being and help us focus on what truly matters.

There is no next

Silentium • 939 implied HN points • 15 Oct 24
📖 Philosophy Logic
  1. Embrace the present moment. Focusing on now can bring peace and clarity.
  2. Silence can be powerful. Taking time to be quiet helps you connect with your thoughts and feelings.
  3. There’s no need to always look for the next big thing. Appreciate what you have instead of constantly wanting more.
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The field

Silentium • 619 implied HN points • 11 Oct 24
📖 Philosophy Logic
  1. Silence can be a powerful tool for personal reflection and growth. Taking time away from noise helps us understand ourselves better.
  2. Embracing silence can lead to greater creativity and inspiration. It allows our minds to wander and generate new ideas.
  3. Creating a space for silence can improve mental well-being. It's important to disconnect from the busyness of life sometimes.

The empty hand

Silentium • 799 implied HN points • 07 Oct 24
📖 Philosophy Logic
  1. Silence can be a powerful tool for reflection and understanding. Taking time to be quiet helps us connect with our thoughts and feelings.
  2. The metaphor of the 'empty hand' suggests being open and receptive. It encourages letting go of distractions to find clarity.
  3. Inviting silence into our lives can lead to personal growth. Embracing quiet moments allows us to gain insight into ourselves and the world around us.

The art of discernment

Silentium • 539 implied HN points • 12 Oct 24
📖 Philosophy Logic
  1. Discernment is about making clear choices. It helps you decide what is right for you in different situations.
  2. Silence can be a powerful tool for gaining clarity. Taking a moment to pause can improve your understanding and judgment.
  3. Practicing discernment can enrich your life. It allows you to navigate complex decisions with confidence and purpose.

"But" vs. "Yes, But"

Astral Codex Ten • 22299 implied HN points • 12 Jun 25
📖 Philosophy Logic
  1. It's important to acknowledge when you're wrong in a conversation. Saying 'Oh, you're right, my mistake' helps keep discussions respectful.
  2. Admitting mistakes can show others that you're open-minded and capable of real dialogue. It makes the conversation more engaging for everyone involved.
  3. You can still hold your beliefs while recognizing faults in your arguments. This helps you reflect and grow in your understanding over time.

Counting to Epsilon Naught

Infinitely More • 35 implied HN points • 04 Mar 26
🔬 Science Logic
  1. Counting ordinals continues past the finite numbers to ω, then ω+1, ω+2, and onward through blocks like ω·2, ω·3, … so that each new limit ordinal begins a new ω-long era.
  2. By iterating these constructions and forming longer and longer exponential towers—ω, ω^ω, ω^(ω^ω), …—we reach ever higher ordinals, and the supremum of all finite such towers is the ordinal ε0.
  3. ε0 is the first ordinal fixed point of exponentiation by ω (so ω^ε0 = ε0), and there is a computable notation system for all ordinals below ε0 with important applications like Goodstein’s theorem and the Hydra game.

Gödel's beavers, or the limits of knowledge

lcamtuf’s thing • 7958 implied HN points • 30 Jun 25
🔬 Science Logic
  1. Gödel's incompleteness theorem shows that in any consistent mathematical system, there are truths that cannot be proven within that system. This means no system can fully capture all mathematical truths.
  2. The busy beaver problem illustrates how there are limits to what we can compute; some functions can't be determined, just like how we can't always know if an algorithm will stop running.
  3. Even though we can create programs that seem powerful, like those that could prove big math ideas, there are inherent limitations to knowledge and computation due to the nature of math itself.

Good if make prior after data instead of before

DYNOMIGHT INTERNET NEWSLETTER • 796 implied HN points • 18 Dec 25
📖 Philosophy Logic
  1. When the true hypothesis space is large or continuous, compressing it into a single coarse prior hides important differences and can produce misleading posterior probabilities.
  2. It often helps to look at the data first to see which distinctions matter, then define finer categories and ask how likely you would have judged those categories before seeing the evidence.
  3. In practice the simplest practical fix is to refine your hypothesis categories so the data likelihood is roughly constant within each category, because grouping poorly can under- or overestimate the probability of different outcomes.

Điều tra sự cố là làm gì?

Thái | Hacker | Kỹ sư tin tặc • 2396 implied HN points • 22 Mar 24
🕹 Technology Logic
  1. Investigating incidents involves more than just technical tools and techniques; 80% success comes from logical reasoning and keeping calm.
  2. Investigating an incident requires thinking about the 'why' before deciding on the 'how'; it's about determining the investigative direction.
  3. Confirmation bias, the tendency to seek information that supports preconceptions, can hinder incident investigations; focus on evidence-based conclusions instead.

Oudépote Legomenon

Orbis Tertius • 129 implied HN points • 10 Feb 26
📖 Philosophy Logic
  1. A hapax legomenon is a word recorded only once, but the bigger the corpus you check the fewer true hapaxes there are, and publishing a supposedly unique word instantly removes its uniqueness.
  2. If you count any sequence of words as a hapax, entire texts or novels can be unique, yet copying or embedding those texts undoes that uniqueness, so only lost or never-transcribed works could truly be one-offs.
  3. An oudépote legomenon is something never written, and more generally there are things never conceived, but as soon as you write or conceive them they stop being 'never', so you can never point to a concrete example.

Why I Ran Away from Philosophy Because of Sam Bankman-Fried

The Honest Broker • 26862 implied HN points • 04 Nov 23
📖 Philosophy Logic
  1. The philosophy of Effective Altruism may prioritize long-term consequences over immediate actions, leading to risky ethical decisions.
  2. Analytic philosophy, specifically of the Anglo-American variety, can promote perspectives that prioritize maximizing pleasure, potentially leading to damaging outcomes.
  3. Beware of philosophical systems that justify harmful actions by focusing on a 'larger context' and be cautious of practitioners who calculate consequences before performing acts of kindness or generosity.

Can You Hate Everyone In Rome?

Astral Codex Ten • 7020 implied HN points • 03 Jan 25
📖 Philosophy Logic
  1. It's possible to feel a strong dislike for a whole group of people in a certain place. This often happens when we don't connect with others' beliefs or actions.
  2. People can feel frustrated with societal norms and expectations, leading to a sense of isolation. This happens when individuals feel out of place among the crowd.
  3. Understanding and empathy can help bridge these feelings of alienation. Finding common ground with others can ease negative feelings.

Open Thread 356

Astral Codex Ten • 5712 implied HN points • 18 Nov 24
📖 Philosophy Logic
  1. The open thread allows people to discuss anything and ask questions freely. It's a space for sharing ideas and engaging with others.
  2. Comments from the community can provide new insights into historical topics, like the early Christian views on abortion and marriage. This shows how understanding can evolve with discussion.
  3. Game theory continues to evolve, with strategies like Win-Stay, Lose-Shift gaining attention for their effectiveness in cooperation compared to older strategies like Tit-for-Tat. It's interesting to see how competition shapes these strategies in different contexts.

Skepticism or Imperfection?

Fake Noûs • 117 implied HN points • 10 Jan 26
📖 Philosophy Logic
  1. Fine-tuning is the strongest argument for an intelligent designer, while the problem of evil is the strongest argument against a perfect God; skeptical theism replies that our limited minds can’t see God’s reasons.
  2. Skeptical theism uses a chess-master analogy: when an expert makes a move you don’t understand, assume there’s a good reason you can’t see; but that analogy is weak because in chess you already know the expert exists and is superior, whereas we don’t have that secure background for God.
  3. A simpler explanation for apparent gratuitous evils is that the creator is imperfect—less than all-powerful or all-knowing—since claiming God is less than all-good doesn’t explain why obvious horrors wouldn’t be prevented.

Yes, Arguments Stand Or Fall Based On Their Merits But The Messenger Still Matters And If You Allow Resentful People Into Your Head, You’ll Be Fooled Into Carrying Their Rage As Your Own

Rob Henderson's Newsletter • 1496 implied HN points • 04 Jun 25
📖 Philosophy Logic
  1. Arguments should be evaluated based on their strength, but who presents them also matters. It's important to think about the source of the message.
  2. If you let angry or resentful people influence you, you might start to feel their anger too. It's easy to take on emotions that aren’t yours if you’re not careful.
  3. Being mindful of who you listen to can help you avoid unnecessary negativity. Surrounding yourself with positive influences can lead to a healthier mindset.

Aristotle on Luck

Classical Wisdom • 2181 implied HN points • 23 Jun 23
📖 Philosophy Logic
  1. Aristotle distinguishes between luck and chance, pointing out that luck involves events that occur unexpectedly without necessity or regularity.
  2. Luck requires conscious decisions and human intent, while chance is simply a coincidental occurrence without purpose.
  3. Understanding luck and chance can lead to philosophical questions about the universe and our existence.

Münchhausen's TriLLMa

Contemplations on the Tree of Woe • 904 implied HN points • 11 Jul 25
📖 Philosophy Logic
  1. The Münchhausen Trilemma shows that we struggle to justify knowledge without falling into circular reasoning, infinite regress, or arbitrary assumptions. Understanding these limitations helps us think more clearly about what we know.
  2. Foundherentism combines foundational beliefs that are irrefutable with a coherent belief system. This approach can help us understand how both human and AI knowledge might overlap.
  3. Advanced AI methods reveal that its internal structures may reflect human-like understanding. This means that AI isn't just mimicking human outputs but is following similar processes in understanding the world.

Cowen's First Law is an epistemological superpower

inexactscience • 539 implied HN points • 27 Mar 24
📖 Philosophy Logic
  1. Cowen's First Law suggests that every argument has weaknesses. Understanding these flaws helps you think more critically.
  2. You can test how honest someone is by checking if they mention their arguments' weaknesses. If they don't, that's a sign to be cautious.
  3. It's important to recognize that not every argument is wrong. Some things, like basic logic, can be completely accurate. Balance is key to understanding knowledge.

Aristotle vs the Stoics: part II, ethics

Figs in Winter: New Stoicism and beyond • 943 implied HN points • 12 Jan 24
📖 Philosophy Logic
  1. Stoics focused on practical philosophy of life, while Aristotle was more into theoretical inquiries.
  2. For Aristotle, a flourishing life required virtue and external goods, while for Stoics, virtue alone was sufficient.
  3. The ultimate goal of life for the Stoics was living in agreement with nature, while for Aristotle, it was a contemplative or politically involved life.

Highlights from the Comments on "A Measured Response"

Maximum Effort, Minimum Reward • 958 implied HN points • 02 Jun 25
📖 Philosophy Logic
  1. The measure problem is important for understanding theories about the multiverse. It questions how we can measure probabilities when there are potentially infinite versions of the universe.
  2. Philosophers generally agree that the universe seems fine-tuned for life. They suggest various explanations, like the possibility of a designer, a multiverse, or deeper laws of nature.
  3. It's crucial to define the problem and the space we're working in when discussing probabilities. Ambiguous terms can lead to misunderstandings in arguments about fine-tuning.

Robot Philosophy

Egg Report • 569 implied HN points • 10 Feb 24
📖 Philosophy Logic
  1. In the realm of computation, complex statements can be broken down into simple ones, reflecting a mono-causal, universalist view of reality.
  2. Projects like AI and VR are attempts to recreate intelligence and reality, each carrying metaphysical claims about the simplicity and illusory nature of complexity.
  3. Engaging with computers and writing code trains individuals to think in a certain way, guiding them towards a robotic mindset and reinforcing metaphysical assumptions.

The Fractal Ratchet

Desystemize • 1966 implied HN points • 20 Oct 24
📖 Philosophy Logic
  1. There are two main ways people understand the world: one focuses on strict evidence and science, while the other values common sense and personal experience. Both have their strengths and weaknesses depending on the situation.
  2. The 'fractal ratchet' concept explains how deeper scrutiny often leads to discovering more detail, but it can also make comparisons difficult. When you look at things more closely, you might keep finding more complexity instead of reaching a clear 'true' answer.
  3. When making decisions or forming opinions, it's important to know when to rely on precise measurements and scientific reasoning versus when to trust your intuition and common sense. Balancing both approaches can help you navigate complex issues more effectively.

Hidden Open Thread 367.5

Astral Codex Ten • 1307 implied HN points • 06 Feb 25
📖 Philosophy Logic
  1. This is a community space for paid subscribers to share thoughts and interact.
  2. The post highlights ongoing discussions and provides a platform for engagement.
  3. It focuses on topics relevant to the subscribers, fostering a sense of connection.

Ordinal arithmetic

Infinitely More • 30 implied HN points • 22 Jan 26
🔬 Science Logic
  1. The series develops the basics of ordinal arithmetic—standard addition, multiplication, and exponentiation—and then moves on to topics like indecomposable and irreducible ordinals, Cantor normal form, and binary ordinal representation.
  2. It introduces the natural (Hessenberg) ordinal operations, which are commutative and make the ordinals into a commutative semiring, and it will study the natural ring of ordinals ⟨Ord⟩ inside the surreal numbers, asking about expressions, algebraic properties, and unique factorization.
  3. This essay first lays a rigorous foundation by giving order-theoretic and recursive definitions of the standard ordinal operations, which the later, deeper investigations will rely on.

Formal and Dialectical Logic

Philosophy for the People w/Ben Burgis • 319 implied HN points • 31 Mar 24
🚌 Education Logic
  1. The post discusses the concept of "dialectical logic" and how it relates to the traditional logic taught in academia.
  2. The author shares their experiences of giving lectures and talks on philosophy and politics in different locations.
  3. The content is available for paid subscribers, providing more in-depth insights and discussions.

Anthropomorphizing the Russell paradox

Infinitely More • 41 implied HN points • 05 Jan 26
📖 Philosophy Logic
  1. Cantor’s diagonal argument shows that for any set there are always more subsets than elements. You can see this intuitively by imagining people and their committees or fruits and their salads.
  2. Applying the same diagonal idea produces Russell’s paradox, which shows that allowing every property to define a set leads to a contradiction, so there can be no single universal set and set formation must be restricted.
  3. Modern axiomatic set theory (like ZFC) provides a robust foundation that achieves much of the logicist goal of grounding mathematics in logical principles, though there is still debate about whether every axiom is purely logical.

A Conversation Between A Philosopher and an AI Researcher

Teaching computers how to talk • 115 implied HN points • 19 Nov 25
📖 Philosophy Logic
  1. AI is not just a library of knowledge; it does more than store information. It can analyze, create, and have conversations, making it unique compared to traditional libraries.
  2. Cultural and social technologies, like AI, reflect human beliefs and the ability to pass information across generations. This shapes how society evolves, just like the printing press and the internet did.
  3. While AI can produce novel ideas, it's more about reading patterns from the information it has seen before. If it creates something new, it's similar to a random mix of ideas rather than true creativity.

Please take my weird moral puzzles quiz

DYNOMIGHT INTERNET NEWSLETTER • 468 implied HN points • 17 Jun 25
📖 Philosophy Logic
  1. A survey is created to gauge people's moral beliefs on unusual scenarios that challenge common ethics. It involves questions about difficult decisions we might face.
  2. The scenarios include serious topics like abortion and euthanasia, but also quirky ideas involving advanced AIs and future societies. This mix aims to provoke thought about morality.
  3. Participants are encouraged to respond honestly and intuitively, with the creator assuring no tricks are involved in the survey.

Going Vertical: Gate All Around, 3D DRAM, 3D NAND - Kokusai Electric IPO

SemiAnalysis • 3636 implied HN points • 15 Oct 23
🕹 Technology Logic
  1. Kokusai Electric is a significant player in batch Atomic Layer Deposition (ALD) for thin film deposition processes in the semiconductor industry.
  2. The use of batch ALD in memory fabs is advantageous for processing high aspect ratio structures like NAND and DRAM, leading to better step coverage and film thickness control.
  3. In logic fabrication, ALD is crucial for complex structures like FinFET and 3D NAND architectures, allowing for precise deposition and enabling advancements in semiconductor technology.

Michael Shermer LIVE with Coleman Hughes!

Common Sense with Bari Weiss • 32 implied HN points • 14 Jan 26
📖 Philosophy Logic
  1. Experts will explore how skepticism, evidence, and reason help us tell truth from falsehood amid conspiracy theories, deepfakes, and post-truth politics.
  2. There’s an intimate live conversation and a casual post-show meetup in New York where attendees can ask questions and argue in good faith.
  3. Access is limited and behind a paywall — paid subscribers get exclusive presale ticket access, and there are monthly and annual subscription options.

Ultrafinitism as arithmetic potentialism

Infinitely More • 25 implied HN points • 12 Jan 26
📖 Philosophy Logic
  1. Ultrafinitism can be fruitfully seen as a form of potentialism, which clarifies its philosophical commitments and lets us give a formal treatment of ultrafinitist theories.
  2. Models of finite arithmetic naturally extend step by step to larger models (M+, M++, and so on), presenting arithmetic as a growing structure even without committing to a single completed limit model.
  3. The potentialist view highlights that mathematical truth can depend on how a theory develops, and it provides a natural framework for discussing and adjudicating different ultrafinitist positions about mathematical existence.

What is an ad hominem attack?

News from Those Nerdy Girls • 314 implied HN points • 02 Feb 24
🚌 Education Logic
  1. Ad hominem attacks insult a person's motive or character instead of addressing the content of an idea or argument.
  2. Ad hominem attacks create distrust of the individual and divert attention away from the actual issue.
  3. To combat bias from ad hominem attacks, focus on facts, recognize diversion tactics, and practice self-reflection.

Ultrafinitism

Infinitely More • 48 implied HN points • 12 Dec 25
📖 Philosophy Logic
  1. Ultrafinitism is the view that only relatively small or computationally accessible numbers truly exist, and extremely large numbers conventionally discussed by mathematicians are denied.
  2. This stance is different from general anti-realism because it accepts small numbers as unproblematic while treating very large numbers as ontologically different or nonexistent.
  3. A central challenge is the 'draw the line' objection: it’s hard to specify where feasible numbers stop and huge ones begin, and this makes concrete questions about enormous expressions difficult or undecidable.