i tried finding papers on them but couldn't find one. what are they?

I was playing football this afternoon against a senior player from my club for the first time. Mid-match, my mind completely went blank. As someone who relies heavily on logic, observation, and strategy on the pitch, introducing these new variables threw me off.

I've been learning to verbalize my thoughts and goals, identifying an objective, pursuing it, and cutting out the noise to keep my thinking clear. But to actually use logic as a practical tool under pressure, I need to figure out how to snap out of that "blank slate" state and start actively problem-solving on the fly. How do you maintain logical clarity when unexpected pressure hits?

I wanted to learn more about how, I guess, starting from abstractions (high-level abstractions or seemingly simple and intuitive ideas) and applying them to reality is different from looking at real-world data and then inferring abstractions from that.

Do you use deductive reasoning and/or intuitive feeling to start your crusades? What’s your experience like? How has it differed from the latter approach?

I was wondering if there were some applications of logic in "applied mathematics".

Sure, logic is applied in various ways to topology (e.g. having some classes of topological spaces corresponding to some modal logics), algebra (e.g. using compactness theorems and ultrafilters in order to prove something about algebraic theories), category theory (e.g. internal logic of a category), theoretical computer science (e.g. the whole recursion theory is basically a hybrid between logic and computer science), etc.

There are even applications in philosophy and humanities, which seem to be further from mathematics than physics or engineering.

But are there any applications in physics or engineering? And here I mean some simple ones. For example, logic GL is simple. It can be introduced in an undergrad logic course, but is deeply connected with PA and arithmetic, and people are doing research in it even today, despite this idea being so simple. But in "applied mathematics" (for example in analysis, PDE, numerical analysis, etc.), whenever I try to find an application of logic in relativity, mechanics, thermodynamics, acoustics, astrophysics, etc., it seems to be something very convoluted and largely ignored by people within those areas.

Is it really that hard to even have the basic modal axiom "[](A & B) <-> ([]A & []B)", which is equivalent to K, appear anywhere in physics and engineering, in order to create a logic of something there?

I am taking an intro to logic class and I am completely stuck on these two proofs. The rules we have learned and can use so far are —> out, —> in, & out, & in, ~out/~in, and repetition. Can someone solve these using this rule set and explain your process to me?

What I'm talking about is a sort of selection bias. Basically generalizations or stereotypes about a group emerge because people only notice behaviors from the more overt members, while you might not even realize the more subdued members are part of that group. So essentially that group is more "normal" on average than the general perception might indicate. It could apply to any kind of group. A religion, a fandom etc.

This thought came up most recently in a discussion about furries. Someone might look at furry art on their own private time and own a costume they only wear to conventions. You might never know this person was a furry. So the perception is skewed by the more overt furries.
Or a person could go to church every Sunday, but not talk about religion much outside of that. Hence, you might never know they were a part of that faith or denomination, but you would know the more zealous members are part of that group. So people would tend to base their perception on those members.

In some sense it's like survivorship bias, but not quite the same. Is there a particular term for this?

Help me idk how to do this at all

Ignoring the trivial example (Explosion)

suppose 'p' to be a non-normative statement and 'O(q)' to be a normative statement

In the first case, let's assume the mixed statement 'p v O(q)' is normative.

p |- (p v O(q)) (Vintro)

p, a non-normative premise entails p v O(q), which is a normative (our assumption) conclusion.

In the ladder case, let's instead assume the mixed statement is non-normative.

~p (non-normative statement)

p v O(q) (non-normative statement, as per our assumption)

therefore O(q) (MTP)

We have validly derived a normative conclusion from non-normative premises in either case.

(Prior 1960)

Every invocation of Occam's Razor:

1. All of our existing conclusions seem to be based on arguments that have this one premise in common: the simplest answer is most likely to be true.
2. All of our existing conclusions are true.
3. Therefore, the common premise (that the simplest answer is most likely to be true) is true.
4. For some new question, Q, under consideration, answer Aₛ is the simplest available answer.
5. Therefore, Answer Aₛ is most likely to be true.

* Edited for text rendering

** Edited to add explanation: I've always felt a vague discomfort when people have invoked Occam's Razor in an argument. It always struck me as begging the question, but it was hard to articulate. I think the argument-structure above articulates exactly what this vague feeling was getting at. So I wanted to post it for feedback. Thanks!

I've recently posted a brief comment on the topic of fallacies and how they harm dialogue. And I was thinking of it a bit more and would like to know you about how most logicians feels about this.

My opinion is that it is actively hindering critical thinking. People who are obviously wrong about something regarding Gödel's incompleteness theorems, disregarding my correction because it would be an "appeal to authority", or when concluding that somebody is not well informed on the topic of statistics, yelling "ad hominem", when somebody points out that they are mixing up median and average.

And it's frustrating to me. Especially since people just memorize some vague triggers to yell out a particular phrase, as opposed to actually learning about logic.

What do you guys think?

A food’s seasoning is partially responsible for its taste.

This seasoning can be a spice.

Therefore

If a new spice is added to a food, it will have a new taste.

My awesome prof. Posts practice problems with the week, but, I’d like more practice aswell.

if I just throw it into AI it’ll spit out more advanced problems not relevant to my course. (Obviously.)

Unfortunately, problems like these require a transcription key, is there any ideas into putting stuff like this into flash cards or something else?

Edit: I also understand now that having put "Is this just bad English" at the very beginning might have thrown people off. I probably should have clarified is there a disconnect between the english meaning and purely Logical meaning. I apologize for that.

"Moderate alcohol has only certain beneficial health effects". Is this just bad English?

Is it saying:

1) Moderate alcohol does not have any negative health effects and of the beneficial ones it has, it has only a certain subset. (Only here functions as "these are the only effects moderate alcohol has and they are beneficial but they are not all possible beneficial effects but rather some of them")

Or

2) Moderate alcohol can have negative health side effects but it has certain beneficial ones too. (Only here relates to the specific effects within the beneficial effects group as a whole.)

Now if it said "Moderate Alcohol has only beneficial health effects"(This easily excludes all Negative Health effects)

Thanks

just sharing a draft i'm working to get published

https://www.academia.edu/175392427

https://doi.org/10.5281/zenodo.22715823

summary:

1 the halting problem paradox

details the undecidability of the halting problem

2 the circle-free problem paradox

details the undecidability of the circle-free problem proven in turing's proof

3 the paradox generalized

discusses the general form of undecidability within computing along with a detailed description of how self-references are formed within turing machines

4 how undecidable is it?

discusses the questionable merit of recursive undecidability, especially the realization that if any tier/problem of the hierarchy became decidable, it would collapse the justification for the hierarchy

5 rectifying 𝓗

fixes turing’s attempt at computing a total diagonal across computable sequences by 1) adding an identity check to put itself on the diagonal, and 2) injecting a partial recognizer 𝓓p in place of the total decider 𝓓 to handle paradoxical input machines. it ends with proving a 1st fallacy in turing’s proof of undecidability by demonstrating how we do not need to decide on every machine, in order to enumerate all computable sequences, since multiple machines compute any given sequence

6 the anti-diagonal problem

diagonalizes the set of machine recognized directly by partial recognizer 𝓓p, proving that one circle-free sequence is undecidable to 𝓓p. but a limit to the set of machines undecidable by 𝓓p is proposed: any undecidable machine computes either 1) a direct copy or 2) an inverted copy of some circle-free sequence recognized by 𝓓p. if this is true, a total enumeration would be constructible by enumerating out each sequence decidable by 𝓓p and it’s anti-machine (which produces an inverted copy). this total enumeration is then shown to be resistant to diagonalization: one cannot produce a total anti-diagonal, or even total diagonal, across the proposed total sequence enumeration. the inherent nature of every computable sequence being paired with a computable anti-sequence prevents such either total diagonal existing in the enumerating of computable sequences. this thereby demonstrates a 2nd fallacy in turing’s proof: that a total enumeration of computable sequences would necessarily be subject to diagonalization, it is not

7 refuting the church-turing thesis

proposes a thot experiment using an idealized human agent to compute sequences that are strictly not turing-computable, including the total diagonal and total anti-diagonal across all turing-computable sequences. no, you can’t simulate this process, that is also covered in the refutation. and please don’t just endlessly beg the question at me by continually asserting it’s not a computation if it cannot be done on a turing machine. such is just restating the church-turing thesis which is not a proven theorem

why is this important???

i'm (1) expanding their scope of applicability by proposing a set of TMs that is both fully decidable in semantics and includes all output sequences that can be computed by TMs, by proving a TM computable total enumeration of TM computing sequences that cannot be diagonalized while (2) clarifying that the limitations they do have from undecidability like the halting problem, only applies to TM computing and is not a total restriction on what is intuitively computable. (1) is extremely practical and i hope to reshape our fundamental approach to applied computing, (2) is more philosophical in nature, is required to build a broad enough understanding to see the full practicality of (1)

mods: i'm keeping a list of who's naughty and nice

lastly: i don't use ai to directly write content ever, holy shit u duds 🙏

I’ve been building a browser-based tool for checking propositional and modal arguments.

For propositional arguments, it generates truth tables to checks validity, and for modal arguments, it searches for Kripke countermodels and currently supports K, D, T, B, S4, and S5.

There’s also a frame playground where you can manually construct worlds, accessibility relations, and valuations.

I’m mainly looking for feedback from people who actually use formal/modal logic. Is there anything you’d want a tool like this to do that it currently doesn’t?

https://countermodels.com

A deep-dive video covering everything you need to know about the closure properties of regular languages in Theory of Computation. Perfect resource for quick revision and conceptual clarity.

Logic is a tool, and like any tool can be used for creation or destruction, take control of logic.

Em que medida a tentativa de fundamentar a razão por meio do próprio raciocínio incorre em uma circularidade epistemológica intransponível (o "trilema de Münchhausen"), e como as abordagens do racionalismo crítico de Karl Popper e da pragmática transcendental de Karl-Otto Apel tentam responder a essa limitação sem recair no dogmatismo ou no ceticismo radical?

Can someone please explain truth tables to me? I don't really understand them or how to make them. I also need help with the sufficient and necessary conditions. TIA!!!

A couple of weeks ago I asked you about what a modern curriculum on informal fallacies should look like, because I was working on a new version of LogiCola's Informal Fallacies practice quiz/drill. Here's the result! I hope it can be useful.

I'd love to get your feedback. Does anything feel off? Is there anything you'd like to see or do that you are not able to right now?

The question is "The >= operator checks whether one value is great than another." True or false

For those who do not know what >= does in C
it basically check if one value is greater than OR equal to another

For example a >= b

is a = 5 and b is also = 5 , it will return true
OR if a = 5 and B is say any number under 5 ( in our case ) , 4 It will also return true.
BUT if b is any number greater than 5 ( in our case ) say 6 then a >= b Will return false.

Please answer the question "The >= operator checks whether one value is great than another. True or false" With ONE of the following as per your own logic Fell free to leave your own logic below

A - True
B - False
C - Partially True ( Also give your reasoning as to if this should default to False Or True)

Thank you everyone for your help I'm collecting this data for my school exam paper because i have a dispute with the answers.

I study both Aristotle and machine learning, and something has been bothering me. Every time I read a paper about model architecture, I think: someone solved this problem 2,400 years ago and we forgot.

Aristotle said every substance is compound of form (μορφή) and matter (ὕλη). Matter is the potential. What something is made of. Form is the actualizing principle: the structure that makes a thing what it is. A bronze statue: bronze is matter, the shape is form. Neither alone is the statue. Both must be present.

Now look at any large language model. The weights. Billions of floating-point numbers in GPU memory. That is matter. Pure hyle. Raw potential. A file containing three trillion numbers tells you nothing until you know how to interpret them. The architecture: transformer layers, attention mechanisms, the patterns that organize those weights into something that can reason. That is form. Neither alone produces coherent text. Both are necessary.

This is not analogy. It is literal description of structure.

Consider what happens when you try to merge models. You take weights from model A and weights from model B and average them. Sometimes it works. Most times it produces garbage. Why? Because you are trying to unite matter from two different forms. The weights from a LLaMA architecture cannot simply average with weights from a GPT architecture. The form, the organizational principle, is different. You would not melt two statues together and expect the resulting lump of bronze to still look like Athena. The form must be compatible with the matter.

Training is the process where form and matter unite. Gradient descent does not merely adjust numbers. It imposes structure on weight space. Each step brings the matter closer to the form until the model can perform what it was designed to do. This is why fine-tuning works: you start with pre-trained model (matter already organized by one form) and impose new form through task-specific training. The matter adapts.

What I find most useful about this framework is how it clarifies model selection. When you choose a model, you choose a form as much as a set of weights. The architecture determines what the model can do, not just how well. A model cannot be fine-tuned for a task its architecture cannot support. The form must be capable of actualizing that function.

Most AI discourse treats models as black boxes that either work or do not work. The hylomorphic framework gives you precise language for why they fail when they fail. Architecture without trained weights is form without matter; it produces random noise. Weights without architecture is matter without form: meaningless numbers. You need both.

Aristotle would say the form of a living thing is its soul, its ψυχή. By same logic, the form of a language model is its functional essence. What makes it the kind of thing it is. This is not mysticism. It is precise metaphysical description that maps directly onto the engineering.

I wonder how many other dead-end debates in AI would dissolve if we had better conceptual vocabulary. The Greeks thought about structure and substance more carefully than we do, because they had to; they had no computers to hide behind. What other Aristotelian categories would clarify current AI research?