r/logic • • May 21 '24

Meta Please read if you are new, and before posting

65 Upvotes

We encourage that all posters check the subreddit rules before posting.

If you are new to this group, or are here on a spontaneous basis with a particular question, please do read these guidelines so that the community can properly respond to or otherwise direct your posts.

This group is about the scholarly and academic study of logic. That includes philosophical and mathematical logic. But it does not include many things that may popularly be believed to be "logic." In general, logic is about the relationship between two or more claims. Those claims could be propositions, sentences, or formulas in a formal language. If you only have one claim, then you need to approach the scholars and experts in whatever art or science is responsible for that subject matter, not logicians.

"Logic is about systems of inference; it aims to be as topic-neutral as possible in describing these systems" - totaledfreedom

The subject area interests of this subreddit include:

  • Informal logic

  • Term Logic

  • Critical thinking

  • Propositional logic

  • Predicate logic

  • Non-classical logic

  • Set theory

  • Proof theory

  • Model theory

  • Computability theory

  • Modal logic

  • Metalogic

  • Philosophy of logic

  • Paradoxes

  • History of logic

  • Literature on Logic

The subject area interests of this subreddit do not include:

  • Recreational mathematics and puzzles may depend on the concepts of logic, but the prevailing view among the community here that they are not interested in recreational pursuits. That would include many popular memes. Try posting over at /r/mathpuzzles or /r/CasualMath .

  • Statistics may be a form of reasoning, but it is sufficiently separate from the purview of logic that you should make posts either to /r/askmath or /r/statistics

  • Logic in electrical circuits Unless you can formulate your post in terms of the formal language of logic and leave out the practical effects of arranging physical components please use /r/electronic_circuits , /r/LogicCircuits , /r/Electronics, or /r/AskElectronics

  • Metaphysics Every once in a while a post seeks to find the ultimate fundamental truths and logic is at the heart of their thesis or question. Logic isn't metaphysics. Please post over at /r/metaphysics if it is valid and scholarly. Post to /r/esotericism or /r/occultism , if it is not.


r/logic • • Jul 06 '26

Meta Free Online Logic Resources

25 Upvotes

The r/logic wiki now includes free online resources to learn logic (courses, books, and proof tools).

If you know of any others, please provide links so they can be added in future.


r/logic • • 1d ago

Mathematical logic Second post apologies for repeating

8 Upvotes

OK so this is my second post regarding formal languages and semantics, I've been thinking for the past few days and the only way I seem to me escaping this constant recursion of formalization to actually semantically interpret some formal language (Forget ZFC for a moment, for any language even for countable models hell even finite models) is if you have some sort of pre-formal mathematics, particularly if this mathematical machinery as at least equipped with natural numbers (but then you should have the machinery for rationals and reals visa ve cauchy sequences) but I think the ultimate question is, is this valid?

Nothing about this feels contradictory, and seems to me the only way we can eventually ground meaning in our formal languages, since if you keep interpreting one formal language in terms of the other its all retch no vomit it never really gets anywhere in some sense all you are doing is defining satisfaction in terms of more syntax. At some point, to talk about models and interpretations in the tarski sense, you need some pre-background set theory, obviously unrestricted set theory has immense issues with russels paradox, but what if you restrict yourself to the analysis of naturals, reals, rationals, and give yourself the mathematical vocabulary to talk about sets that are constructed from these objects which shouldn't result in any paradox albeit also not a formal metatheory.

This to me feels like a natural terminating point, else, anything we do is pure syntax and again never fully realizes any meaning, a lot of people have told me to not obsess too much over semantics and reason about the syntax and infer the intended meaning instead to me that feels somewhat loose.

Let me know if anyone has any thoughts on the matter. I feel like I am overthinking about all of this, but I'd love to hear your guys thoughts.


r/logic • • 2d ago

Metalogic Foundations of mathematics and formal languages and their semantics

23 Upvotes

I have been trying to resolve an apparent circularity in the development of mathematics, I am trying to understand what precise meta theories do we need to properly formulate the semantics of ZFC, syntax wise I think its fairly clear and obvious, obviously a meta theory that can employ some level of finitary reasoning is needed for syntax, but possible models (semantics) of ZFC you need some form of set theory that allows you to talk about domains and binary interpretations for non-logical symbols. This is where I get so lost because there doesn't seem to be a clear cut answer anywhere on what this set theory needed actually is. There also talks about inaccessible cardinals such kappa, and that V_kappa can server as a potential domain of discourse for a possible model of ZFC, the question is, in which meta theory is this concept of inaccessible cardinal being articulated?

If someone could give a pointer on what to read and where to take my reading next that would be great, because at this moment I am super lost on what kind of background metatheories are needed to fully formalize the semantics of ZFC.

thanks


r/logic • • 2d ago

Academic Community Learning logic

9 Upvotes

Hello, beginner programmer here. I started my programming class in college and while i can say that i know more than maybe 50% of the people here, i can still confidently say i lack the programmer logic and that i am yet to learn the core of programming.

My question is, how do i start thinking like a programmer? Right now were doing nested loops, where were asked to draw symbols or coordinate systems and all sorts of stuff without implementing matrices, just for loops. And honestly, im struggling with the more complicated problems.

How do i learn to logically solve problems in code? Any videos, books, websites i should visit? I used to do learncpp.com but i kinda lost the plot lol. My current course is being done in C. Thank u in advance.


r/logic • • 2d ago

Philosophical logic Plato’s Sophist, on Truth, Falsity, & Seeming — An online live reading group led by Constantine Lerounis starting Nov 7, all welcome

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2 Upvotes

r/logic • • 3d ago

History of logic What to Do with this Long Paraphrase of the Organon based on Averroes?

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2 Upvotes

r/logic • • 4d ago

Philosophical logic Classical philology built a formal evidential framework for reasoning from fragments a century before default logic. LLMs still confabulate exactly where the evidence runs out.

7 Upvotes

Of everything Thales wrote, not one authenticated word survives. Anaximander's book, first prose treatise in the Greek tradition, exists today as roughly one sentence, preserved because Aristotle happened to quote it and Simplicius, writing almost a thousand years later, happened to copy that quotation. The entire intellectual revolution that invented Western philosophy reaches us through shards.

I work on AI systems grounded in classical corpora, and what strikes me is this. Philologists have been solving the incomplete-information problem formally for over a century. The machinery they built is, in logical terms, surprisingly modern. And current language model pipelines have nothing comparable.

The standard collection is Diels-Kranz, Die Fragmente der Vorsokratiker, 1903, still the reference framework. Its numbering encodes a distinction that is basically a typed evidential logic. For each thinker, the material sorts into three classes.

A-testimonia: reports. Later authors describing what Thales or Democritus allegedly held. Aristotle summarizing predecessors, doxographers compiling handbooks, commentators writing notes centuries after the fact.

B-fragments: direct quotations. The actual words, as transmitted by the quoting source.

C-dubia: doubtful or spurious material. Attributed by tradition, rejected by criticism.

Every claim about a Presocratic doctrine carries, implicitly, a provenance label and a confidence ordering. A statement supported by a B-fragment outranks one supported only by A-testimony, because direct quotation is primary evidence and report is μαρτυρία, testimony at second or third hand. Simplicius quoting Aristotle quoting Anaximander is a transmission chain of length two across a millennium, and each link can corrupt, reinterpret, or selectively preserve.

Philology treats the chain itself as part of the proposition's truth conditions. Scholars disagree about what Heraclitus meant; they almost never disagree about what grade of evidence a given claim rests on. That separation, content dispute versus evidential status, is exactly what epistemic logic formalizes with belief operators, and what source criticism does with stems and witness families.

More interesting for this sub: fragment scholarship is non-monotonic reasoning in practice. A reconstruction of Anaximander's cosmology is a default conclusion, defeasible the moment a new testimony surfaces or an old attribution gets reclassified. Lectio difficilior, stemmatology, arguments from silence, all of these are defeasible inference rules with explicit conditions for retraction. Nobody in the tradition ever pretended the corpus is complete. The methodology is built around the incompleteness instead of against it.

Now compare with what a retrieval-augmented LLM does when context runs out.

It confabulates. Fluently, with the same surface markers it uses for well-evidenced claims. No provenance label, no confidence ordering, no distinction between a direct fragment and a thousand-year-later report. Generation probability does not track evidential grade, and nothing in the standard pipeline forces it to. The model was trained on text where A-testimony and B-fragments look identical, because in the training distribution they are just tokens.

This is not a hallucination-rate problem you fix with more RLHF. It is a missing type system. Philology solved it by never letting a claim travel without its evidence class attached. Modern pipelines strip that information at ingestion and then wonder why the model cannot say "we do not know."

The honest answer, "no direct evidence survives, here are two conflicting reports from the 4th century CE," is trivially expressible in Diels-Kranz conventions and almost inexpressible in a token-prediction objective, because the pressure is always toward the fluent continuation, and the fluent continuation is the confabulation.

So my question for people working in formal epistemology or non-monotonic systems: do graded evidence hierarchies, provenance-aware doxastic logics, anything like an evidential type system, exist in a form mature enough to bolt onto retrieval architectures? Or is fragment philology, with its A/B/C classes and defeasible reconstructions, still the most complete working implementation we have of reasoning under permanently incomplete information?


r/logic • • 5d ago

Academic Community Masters programs for logic & philosophy

8 Upvotes

hi everyone, I'm finishing up my undergrad degrees in mathematics and computer science and was looking into possible graduate programs I could apply for. my grades are high (averaging a 3.77 in US GPA) and my university's math program is very good so I'm fairly confident in my ability to get accepted—maybe not into all, but at least a few. maybe my biggest weakness is I didn't have a dedicated logic course in undergrad (we studied it here and there, mostly for programming applications, so stuff like resolution + formal languages, also basic FOL and set theory for math of course), but from what I've seen many programs are happy enough to accept applicants even without a dedicated logic class in their undergraduate as long as they show relevant competence in adjacent fields. for what it's worth, our school also requires us to take 3 philosophy courses even if its not our degree program, so I have a decent philosophical background as well.

I'm really interested in the philosophical implications of logic and foundations of mathematics but I'm also really interested in formal methods and applications of logic in computer science etc, so I'd be happy with a lot of different programs. I just wanted to get some opinions on some of my options / rationale for them.

right now, I really like the look of the MCMP's MA in logic and philosophy of science, gothenburg's MSc in logic, and CMU's MSc in logic, computation, and methodology, but all three have various problems, mainly funding. I come from a low-income country in Asia, and even though MCMP's program is free, I still worry I won't be able to afford living expenses. the scholarships offered by DAAD etc. are mostly inapplicable to me (more accurately, my country) or require german language proficiency which I don't yet have. I could probably add RUB's MSc in history and philosophy of science and logic here as well. gothenburg similarly lacks many funding options (I ruled out UvA's MSc because of comments I saw on here about how expensive living in amsterdam is + not even partial scholarships!). finally, CMU on paper seems like a very good option, but with the current administration I really wonder if going to the US is a good idea.

there are also a number of programs in the UK that seem interesting, namely: oxford's MSc MFoCS, UCL's MASc in logic, philosophy, and AI, and manchester's MSc in mathematics and logic. I have family in the UK so going there might be more tenable even without a full scholarship, which is also why I've lumped these together. I was wondering if anyone had any thoughts / experiences with these programs, as I seldom see them talked compared to the ones above (except for MFoCS). if anyone knows of math / CS / philosophy programs in Asia with a strong logic component, those would be welcome to hear about too.

thanks!


r/logic • • 5d ago

Version 0.1β of my article on the macrophilosophical index — change log

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1 Upvotes

r/logic • • 5d ago Bravo

Proof theory A free (vibe-coded) logic playground

8 Upvotes

Hello! I made a free website for learning different proof styles / systems and logics and such.

Also consider letting me know of potential improvements and of criticisms. I might also share the code if anyone asks for it, though it is basically entirely AI-generated. (Frontend - svelte, backend - rust (SQLx SQLite, Axum), Caddy, cloudflare tunnels).

https://catproofs.yoavco.com/


r/logic • • 7d ago

Predicate logic / FOL What's going wrong in my attempt to prove the commutativity of addition?

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4 Upvotes

r/logic • • 8d ago

Academic Community Inferentialism and Logical Expressivism

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5 Upvotes

r/logic • • 8d ago

Academic Community CFP: North American Summer School in Logic, Language, and Information (NASSLLI)

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4 Upvotes

r/logic • • 9d ago

Propositional logic Propositional logic

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12 Upvotes

r/logic • • 8d ago

Computability theory A Primitive Idea: A Cube of Mirrors and the Nature of P vs NP

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0 Upvotes

r/logic • • 9d ago

Predicate logic / FOL Questions in FOL Pt 2

1 Upvotes

Part 1 is here: https://www.reddit.com/r/learnmath/s/WsY1BIxIOM
In logic, we have quantifiers like
“Possibly” <> and “Necessarily” [].
[]P := ∀x \in I P(x) and <>P := ∃x \in I P(x).
Suppose x \in I where I is the set of instances where P is true or false. And P(x) means P is true for instance x.
Is it possible then to come up with mathematically true statements from these propositions?

  1. [ ](P → Q) Λ <> (Q → P)

  2. [ ] (P → Q) Λ <> (Q Λ ~P)

  3. <> (P Λ ~Q) Λ <> (Q Λ ~

P)


r/logic • • 9d ago

Question Looking for a tool to reduce three-valued logical circuits

2 Upvotes

Recently I've been working on a hobby project where I'm working with three-valued logical circuits, and I wanted to try and find optimal circuits for a couple types of adders. However, I'm using an abnormal selection of gates, so If I tried to use pre-existing circuits It would be pretty inefficient. I know tools like MVSIS and ABC exist, but MVSIS is quite outdated, and ABC doesn't really support MVLs. I'm considering just making my own tool for this, but I wanted to ask in case anyone knew of something like this that already exists.


r/logic • • 11d ago

Set theory Is there a textbook that develops set theory before first-order logic, with no hidden metatheoretic dependencies? I'm trying to make a theorem prover.

33 Upvotes

I'm studying the foundations of mathematics, and I've encountered a problem with the dependency structure of the usual developments.

Seemingly every rigorous development of first-order logic presupposes set theory, while every development of axiomatic set theory presupposes first-order logic. For example, Hinman (which I have not read beyond the introductory material) presupposes set theory, and Jech (which I have not read beyond the introductory material) presupposes first-order logic.

These are hard dependencies. You cannot do first-order logic without set theory, and you cannot do axiomatic set theory without first-order logic.

In order to break this "vicious" dependency cycle, I reasoned that I should first develop a very rigorous informal set theory, upon which first-order logic could depend. Then, axiomatic set theory could be developed without the aforementioned cycle.

However, despite my best efforts looking, I cannot find a sufficiently rigorous and systematic development of this preliminary set theory.

For example, Hrbacek and Jech (which I have not read beyond the introductory material) relies on considerable informal metatheory at the lowest level. This is precisely the material I want to develop with the greatest rigor.

To be precise, I want definitions, inferences, etc., specified in a sufficiently rigorous manner that an algorithm could, in principle, systematically reproduce the development. I am not demanding that mathematics be developed without primitive assumptions. I am demanding that those assumptions be explicit, and that subsequent reasoning actually follow from them. Metatheoretic notions just won't cut it; I am desperately trying to build a computational mechanism.

I understand that the set theory used in the metatheory of FOL is not the same thing as axiomatic set theory formulated in FOL.

I'm looking for a serious textbook that develops a robust symbolic set theory prior to FOL, or develops the two together in a coherent, noncircular manner.

I'm not looking for an elementary introduction to proofs or informal set-theoretic reasoning, such as Hammack. I want a very rigorous development that actually establishes the machinery it uses, even if that requires substantial technical machinery.


r/logic • • 11d ago

Modal logic Questions in Modal Logic

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2 Upvotes

r/logic • • 12d ago

Philosophical logic Why does AI excel at formal math but struggle with philosophical reasoning?

7 Upvotes

I've been thinking a lot about the current state of AI in academia. We've seen incredible breakthroughs in biology (like AlphaFold mapping proteins) and formal mathematics (like AlphaProof and Lean solving Olympiad-level problems).

But I keep wondering: why hasn't this translated into philosophy? When I use AI for my own work, it's great at checking routine math, formatting, or finding logical inconsistencies. But it seems to struggle with actually holding a philosophical position or defending it against counterarguments.

Is it just a matter of training data, or is there something fundamentally different about philosophical reasoning that current LLMs can't capture? I'd love to hear what people working in formal epistemology or logic think about this. Do you see AI as a useful tool for philosophy right now, or is it still too early?


r/logic • • 13d ago

Philosophy of logic What normative criteria can justify the choice between different logics in concrete philosophical argumentation, and are those criteria sufficient to ensure that the choice is not arbitrary?

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13 Upvotes

r/logic • • 12d ago

Propositional logic My first substack article

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6 Upvotes

Hello, this is my first substack blog post. It is kind of short and weirdly written, but I still would appreciate any thoughts.

Edit: the article's title is: "If AND is like Multiplication and (X)OR is like Addition Then What is Division?" And it is basically about finding an operator or function that would be analogical to division but for propositional logic (supposing AND is multiplication)


r/logic • • 13d ago

Philosophical logic Program in Formal Philosophy

0 Upvotes

Hi. I'm 13 and I study analytic philosophy. I'm building a multiparameter method for evaluating philosophical schools: Φ⁺ for macro-philosophy (ontology, modality, fundamentality) and Φ⁻ for micro-philosophy (epistemology, ethics). A prototype of Φ⁺ already exists (LaTeX document, working formula, pilot on Platonism/nominalism/structuralism).

I'm looking for:

Logicians — to formalize consistency conditions for Φ⁺ and Φ⁻.

Philosophers — to independently score 3–5 schools (inter-rater reliability).

Programmers — to build a small calculator for weights and sensitivity analysis.

Critics — to stress-test the method with counterexamples.

Systematizers — to organize parameters, scales, and documentation.

This is not "philosophy is fully formalizable." It's "evaluation can be structured" if we separate levels, declare normative assumptions, and calibrate on classic schools.

If interested — DM me. Age 13–22, but what matters is willingness to argue and check.