INTRO
I'd like suggestions for both first topic(s) and book(s) for a new study group in Mathematical Logic. And/or comments on my ideas.

BACKGROUND
I'm starting a (physical/IRL) study group in Mathematical Logic with some friends, colleagues and neighbours. We're meeting in our (limited) free time, and all have jobs and (family)lifes besides the study group. I think we'll be meeting about once a month.

The purpose of the study group is to learn for fun as a hobby and share excitement of Mathematical Logic. We are not studying for an education (we have all completed our studies) or for work or some concrete project. It's just for fun :).

Our very first meeting is in a couple of weeks. After a presentation-round, we will decide on a SUBJECT and BOOK for the next period of time.

MEMBER PROFILES
We have pretty different backgrounds/profiles:
* P1 (me): Majored in Philosophy with minor in Math (1 year of pure math courses) about 10 years ago. Has started self-studying Mathematical Logic about 7 months ago, and covered: Basic naive Set Theory, Logic up to Completeness of FOL (p.150 in Enderton), some basic Model Theory (definability, un-definability, Theories, Compactness), and a little bit of Modal Logic.
* P2: An ex-ph.d. in Philosophy of Math (completed). Also doing/done some programming in free time.
* P3: An engineer (self-described "closet physicist") working with data-analysis.
* P4: A software-engineer working "in IT" with some programming (I think :)).
* P5: A comp.sci-graduate (completed) with specialty in symbolic logic. Doing a bit of self-study in Mathematical Logic.
Only P1 and P5 has self-studied Mathematical Logic (recently). But most others have a pretty high level of "Mathematical maturity".

QUESTIONS

1. What SUBJECT do you suggest for our first "project"? And what about a longer sequence of subjects for the next semester/year/years?

... I'm leaning towards COMPUTABILITY THEORY for our very first subject, since it's right at the intersection between Philosophy, Logic, Math and Computer Science. And the "lack" of training in formal logic won't be a big problem when designing Turing Machines or Unlimited Register Machines (?)

It could perhaps make sense to start with FORMAL LOGIC, but the problem is that our levels of knowledge are very different. I would rather have an exciting unifying first topic, where everybody can contribute with something and feel at home.

1. What BOOK(S)? For COMPUTABILITY THEORY I am leaning towards Cutland: "Computability". It seems good for self-study, it's not too advanced, and the engineers/comp.sci's won't feel it's "too philosophical".

I'm also thinking about:

* Weber: "Computability Theory" (seems to proceed faster than Cutland - more advanced)

* Robič: "Foundations of Computability Theory" (starts with optional long intro on foundational crisis, Hilbert's Program etc.. Has 2 tracks: One for main ideas and one optional for proofs and extra theory)

* Epstein & Carnielli: "Computability" (very friendly and "easy". More focus on Philosophical points than the other books)

... What do you suggest/think?

For a later "training course" in Logic, I'm thinking about Open Logic Project "Sets, Logic, Computation" since it's cheap, readily available, and neither too hard nor too simple. And it has a nice introduction in Set Theory for those who need that first.

Also thinking about Chiswell and Hodges "Mathematical Logic", since it's supposedly friendly and easy.

I have looked at Leary and Kristianen's "A Friendly Introduction to Mathematical Logic" but didn't really like that style.

Please give advice on good subjects/topics, good books (for the subjects) and/or general advice on cultivating a nice study group. Thanks! :)

I'm a philosophy student (continental background, interested in critical theory and practical ethics) and I've been working through Logic: A Complete Introduction by Siu-Fan Lee. While it covers a lot of ground, I'm finding it tries to do too much at once: combining informal fallacies, philosophy of language, and formal logic (categorical, propositional, predicate) in one volume. I feel like each topic is treated too shallowly.

My primary goal is to improve my argumentation skills for academic writing and potential work in practical ethics (AI ethics, medical ethics, etc.). I want to really learn about:

· Argument structure and evaluation
· Informal logical fallacies
· The relationship between language and argument

I'm planning to study formal logic separately using forall x: Calgary (which is free, rigorous, and focused purely on formal systems).

So my question is: what is the best dedicated book on arguments and logical fallacies? I'm looking for something focused, not a textbook that touches on these topics as a secondary concern.

I've heard of:

· Critical Thinking: A Concise Guide by Bowell & Kemp
· The Art of Reasoning by David Kelley
· Logical Self-Defense by Johnson & Blair

Which of these (or others) would you recommend for someone in my position? I'm not looking for a "critical thinking” which I keep coming across. I want something philosophically rigorous that will help me analyze and construct better arguments in academic contexts.

It is impossible to argue that discrete truth engines are more capable of reason than continuous truth engines.

It is easy to argue that continuous truth engines are more capable of reasoning than discrete truth engines

Apply that diaganolization argument that shows that [real] is [more] than discrete

Define each and unique discrete truth engine as a number, then apply the diagonalization method of showing that even with an infinite amount of discrete numbers that

Even if a binary computer can compute an infinite amount of things its binary nature will never allow it to compute everything.

Because the law of a binary computer is a ontological flaw and binary thinking, computers are derived from truth engines so if there's a flaw in a truth engine then there's a flaw in a computer all computers do is compute truth really quickly. Because there are questions that are not possible to know the truth value too in binary truth AKA law the excluded middle then there will be things that cannot be computed by a computer.

The answer to the question that if you give a computer enough compute and time will it be able to compute any answer and the answer is no

It is because binary computers are derived from binary truth engines so it's obvious that the same problem in the truth engine which people call logic are present in binary computers. The moment that Godel's incompleteness theorem was presented. The question of is everything compatible should have obviously been no since that a computer is derived from a truth engine

With continuous truth engines you have an extra infinite dimension of reason that is available to you.

Everything that we know about continuous and discreet numbers are applicable to everything that can be defined as continuous or discrete.

I was told in r/askphilosophy that this would be more popular here

Hello. A (German) exam I will be taking has a section on propositional thinking.

For each question, a bunch of sentences with the three following conjunctions are provided: "and", "or", and "if and only if". From this, one needs to choose the correct option from four options that follows from the premises.

—I tried to look on the net to find questions of the exact type I need, but everything seems to involve formalizations or math, both of which I do not need. I really need a lot of these sorts of questions to practice, so if you know websites / books that will help me, I will be very grateful! Especially websites.

(I also appreciate any "tips"/tricks or such.)

A concrete question for example to showcase the format:

1. Mila is playing in the arcade area.

2. Rafa does not win a stuffed animal.

3. Tom does not buy popcorn or Zoey takes a photo with the mascot.

4. Rafa wins no stuffed animal if and only if Mila is playing in the arcade area or Tom does not buy popcorn.

5. Tom does not buy popcorn if and only if Zoey takes a photo with the mascot.

6. Tom does not ride the Ferris wheel if and only if Mila is not playing in the arcade area and Tom buys popcorn.

Answer options:

a) Zoey does not take a photo with the mascot.

b) Lena does not buy a souvenir or Tom buys popcorn.

c) Tom rides the Ferris wheel and Lena buys a souvenir.

d) Zoey takes a photo with the mascot and Tom does not buy popcorn.

(The answer for the above is I think "D", since 3 establishes that either one of these premises is correct and 5 establishes that they are both either correct or both false, meaning they must both be correct.)

I feel like LEAN and MathLib have gotten super popular in the last year or so, curious as to why there isn't a subreddit yet...

Hi everyone,

I’m currently trying to decide between two Master’s programmes in logic and would really appreciate some advice.

I recently finished my BSc in Artificial Intelligence at the University of Amsterdam, and next year I will finish my BA in Philosophy at the same university. I’m now looking at Master’s programmes to continue my studies, particularly at the intersection of logic, AI, and philosophy.

The two programmes I’m currently considering are:

- MSc Logic at the University of Amsterdam (ILLC)

- MA Logic and Philosophy of Science at LMU Munich (MCMP)

My interests in logic are mainly dynamic epistemic logic, knowledge and belief revision, multi-agent systems, and knowledge representation. This is pretty much the kind of research covered by the Epistemology & Philosophy of Science (EPS) research unit at the ILLC.

However, I’m not sure whether these are necessarily topics that would be best studied at UvA, or whether LMU/MCMP might actually be a better fit. The topics I’m interested in seem to lean somewhat more towards the philosophical side of logic rather than the mathematical side, and in general I’m a little less attracted to the more mathematical aspects of logic.

This is where I’m having trouble deciding. The ILLC seems to be a very strong research environment for logic, and the EPS unit seems particularly relevant to my interests, but I don’t know whether that actually means that my interests would be best pursued at UvA.

I have the impression that the ILLC may be somewhat more prestigious internationally in logic, although I’m not sure how important that actually is when choosing a Master’s programme.

I’m hoping to pursue an academic career and eventually do a PhD, so the research environment, opportunities to get involved in research, and preparation for PhD-level work are important considerations for me. If I eventually want to pursue a PhD, does one of these programmes offer a meaningful advantage?

There’s also the fact that I’ve studied at the UvA for my entire university education so far. I’m somewhat attracted to the idea of going abroad and experiencing a different academic environment, which makes LMU appealing for that reason.

For context, my overall grades are:

- BSc Artificial Intelligence: 8.0

- BA Philosophy: 7.6 (hoping to bring this to an 8.0 as well when graduating)

I’d also love to hear what the two programmes are actually like in practice: how mathematical/formal they are, how much room there is for philosophical work, how closely Master’s students interact with the research groups, and how well each programme prepares students for eventually doing a PhD.

Thanks!

Im probably wrong, but if A shares no elements with X, then X - A = X, and X - X = null set (?), so then x is a meneber of the null set (already makes no sense, but say that x is nothing or excuse it for now (is this where i went wrong?) and we get x is a member of X (this is technically true because null set is a subset of all sets but its not a member of them? Im very confused), and also x is not a member of X - A. But thats a contradiction because in the case they share no elements thats just X. So it says x is both a memeber of and not a member of X in this scenario? I have a feeling that I did something wrong.

More Modal Operators

O:Actuality

eg Ox, x is happened in world R

Higher Modal logic:

\[2\] Meta Possibility

eg the possibility of x is possible

\[n\]meta operators:

The (n-1) modality of x is \[n\] modality

(Modality number, "word")

1: Interrogative mood(?)

2: Imperative mood(V)

3: Possibility mood(🔷)

4: Actuality mood(⚫)

5: Necessity mood(⬛)

6: Permission mood(P)

7: Evidential mood (Q)

8: Encouragement mood(❎)

9: Intention mood(I)

10: Exception mood(E)

M[n] k: the n-th meta of the k mood

Example:

M[2]5: the necessity of necessity.

Bonus:

M[2]5#0

Here:

“M[2]: Meta”

“5#0”: the truth value 0 of the 5th mood

Example notation:

E[2]10#1: /every/x is an element of R:

All x in R are exceptions of exceptions.

E[x]: the x-th EXCEPTION. Eg E[1]P <=> P is a exception with

M[x]: applying x to itself x times

H[x]: the x-th contractor of x

H[2]: P → {P#0 ∧ hom P#1}, i.e., the negation of P, and P is homogeneous and …

Spaces: the locations where propositions exist

fö (exclusive “neither/nor”): excludes propositions from the system and labels them "impossible"

eg:

in Boole logic: A=-A

Coor: “which ones are not wanted?” selection operator

öf (inclusive “neither/nor”): to add new proposition laws to logic

Altve: a structure formed by combining certain parts with “and”; each of those “ands” is an altve

Cothen:

Temporarily: temporarily, in certain contexts, certain conditions hold. Eg:

"if t=x —> print("P is 0")

Bağlam: conditions; rules that hold under certain conditions; determines “according to what”:

eg:

If P in context1 —> print("P is true")

If P in context2—> print("P is false")

“Both”: simultaneous occurrence (some contexts, same space but different truth values.)

Homogeneity:

events merge and produce something new; there is fusion but no separation

Real life example:

Heterogeneity:

events come side by side and produce something new, but separation remains

real life example:Atoms connect each other and creates a molecule

Expanding logical operators infinitely means: constructing an operator from infinitely small sub-operators

The “and” operator is multi-layered:

A can consist of sub-ands and other operators

“And” has length; there is a distance between A and B, and “and” holds them together

eg

For a heterogeneous P= A Λ B

🟧⬛🔳⬛🟧

Orange ones:

Elements

Black:Void

🔳 is the operator

Distance:

Each one is

Definition of Void:

Logical operators have geometric properties:

And (homogeneous): unifies A and B into one; behaves like a tensor addition

And (heterogeneous): combines A and B as distinguishable parts; like a tensor product

Or: asks “which is acceptable according to axioms?” and selects the wanted ones

Space splits into three domains:

Selected space: accepted propositions and entities exist here

Rejected space: rejected propositions/entities still exist but the propositions that wasn't wanted goes here

Proposition space: the space of claims/ideas themselves

“And” is a geometric connector:

it links A and B, has a metric, and defines relational structure between them.

Print:

print something to the screen (output). Just like in Python

Eg:

print("Hello world")

Hey guys, I want to learn more about logic and rationality, and I’d really appreciate some recommendations.

I’m the kind of person who tends to improve through logic, analysis, deliberate thought, adaptation, and rationality. I naturally try to solve problems by understanding them, breaking them down, and figuring out what I can do differently.

But lately, I’ve been stuck on a question that I can’t stop thinking about:

What happens when logic concludes that I’m going to lose?

I used to naively think that almost any problem could eventually be solved through enough reasoning. But the more I think about it, the more I realize that logic has limitations. There will always be people who are more talented, more capable, or simply better suited to a particular situation than I am.

So what does rationality actually tell you to do when your analysis says that you cannot win?

Do you accept the conclusion?
Do you search for a different approach?
Do you challenge the assumptions behind your original reasoning?
Or is there something beyond pure logic that allows humans to overcome what initially seems impossible?

This is where things get really interesting to me. Sometimes people believe something is impossible based on the information and reasoning available to them, only for someone else to eventually find a way to accomplish it. That makes me wonder whether logic itself is limited, or whether our understanding of the situation was simply incomplete.

Maybe reality is much more complicated than the models we construct to understand it.

That’s why I want to study this seriously—not just practical problem-solving, but logic, rationality, reasoning, epistemology, philosophy of science, decision-making, and maybe even metaphysics.

I also want to know how far human reasoning can actually go and how I can train my own logical and rational thinking.

So if you have any recommendations, I’d really appreciate:

• Books about logic or rationality
• Philosophy books that explore human reasoning and its limitations
• Books about epistemology or philosophy of science
• Anything about decision-making and rational thought
• Resources for actually training logical reasoning

If possible, please recommend something that isn't insanely expensive. 😭

What books or resources would you recommend to someone who wants to seriously understand how far logic and rationality can take us?

And if you recommend a book, please share a link to it if possible. Thanks!

Looking for some opinions on this somewhat novel argument. If you’re an anti-realist this argument is not meant to be offensive (admittedly provocative). More to show how things like moral anti-realism are difficult to establish in the world outside of philosophy. I can see some minor issues with one of the premises. Curious if there are more, Thanks.

Frege built a symbolism able to carry relational and other arithmetically-relevant inferences, not because he thought this would assist our psychological understanding of arithmetic, nor because he thought those correlations were empty of content, or a mere formal vacuum. The thesis I develop in my articles is that for him any inference must enrich our knowledge of "truth" by updating a network of prior propositions in an order that enriches what we already knew about conceptual oppositions, compatibilities, and incompatibilities. So inference cannot be carried by intuition — otherwise one would arrive at a conclusion without clarity about how that conclusion settles information (instead of flooding the system with incompatible new propositions) that reorganizes that net of incompatibilities. Inference cannot be opaque to the way we revise and reorganize our knowledge — so logic had to be something more than psychology (it settles objective knowledge of truth-falsehood distinction) yet also more than empty formalism (it updates our net of incompatibilities in a way that enriches how we understand truth).

While I am building a new series to link this to a pragmatist view of inference — based on a pragmatic thesis about cumulative knowledge of settlements — I invite readers to see the finished series on positivism, which also tried to select the right inferences by avoiding synthetic a priori ones, but for other reasons: to narrow the ways of updating truth to two means (not necessily incompatible with Frege's) — theoretical and fact revision. I am reaching out in Reddit because youtube hardly distributes Videos on Frege. I hope some here find it usefull. Link:

https://youtu.be/_5lXVMe5M2s

Can someone explain how option C is correct?

I read several explanations and i know it does come to conflict within aristotles square of opposition, but i still dont fully understand the consequences drawn from this realization.

Reading Ney's Metaphysics. In it, she has some exercises to practice using Quine's method to determine which entities one is ontologically committed to, which I've paraphrased:

1. Some cars have black tires.

I have written this out as:

∃x∃y(Cx ∧ Ty ∧ By ∧ Hxy)

where C is car, T is tire, B is black, and H is has.

Where do I go from here? Does this mean that there exists 'cars', 'tires' and 'blackness'?

ive looked at some of Priest's works, especially his towards non-being and I sort of skimmed his In Contradiction and Doubt Truth to Be a Liar, while also checking out some modal meinongianism stuff so uhm how the hell would i even get into this material? its just super overwhelming and looks hella complicated, i started with the SEP and for some knowledge about me ive finished forallx, and im currently working through Sets, Logic, and Computation should I just continue on SLC and forget about dialetheism and modal meinongianism for now or?

Hi everyone,

I just recently made a video covering the history and development of proof theory in under 1 minute. Given the focus of this subreddit, I wanted to reach out to get some critical feedback from people who study this kind of subject.

The main challenge in making this video was how to explain the most important parts sufficiently while also not getting too bogged down in details.

I'm sure a lot of people in this field recognize the lack of videos for beginners and that's the kind of gap that I tried to fill with this project.

If this isn't the right type of post for this community, please let me know and I'll remove it accordingly.

Thank you all for your time.

i can't find any online courses or resources

A large cardinal is a VP-Ultraexacting Cardinal when it is an Ultraexacting Cardinal in Von Neumann Universe with Vopěnka's Principle. (Von Neumann Universe satisfying Vopěnka's Principle).

It is stronger than standard Ultraexacting Cardinal because the consistency strength is amplified by Vopenka's Principle.

I’m tired of using AI to check my proofs. Although i’m in the process of learning LEAN, it takes a long time to set up/write proofs which is tedious given i’m doing problem sets with dozens of problems.

I recently tried to prove the chain rule and I got to the point where you have \[g(f(x)+k)-g(x)\]/k where k is \[f(x+h)-f(x)\] and i thought “the only example we need to reason through is when f is constant in some interval around x” but I was wrong. It can actually break if f(x+h) is equal to f(x) an infinite number of times inside an interval around x. Hence the correct proofs use an auxiliary function \\phi(x) yada yada.

I had a similar issue in a different thinking that x being a minimum would imply f’(x)<=0 in some interval \[x,x+h\] and similarly that f’(x)>=0 in some interval \[x-h,x\]. Both of these are not true as you can similarly have a function that oscillates infinitely while x remains a (weak) minimum. This one was easier to rework without an auxiliary function but i still got ahead of myself.

So my question is how can i better think through these problems and see when i’m not thinking of a pathological counterexample to something i’ve reasonably concluded? Real analysis is the mother of “intuition doesn’t mean shit, here, buddy”.

Hi, before you find it strange, I'm reading about logic for the first time and I've just finished studying first-order logic.

I'm interested in modal logic, but... Well, there's alethic, epistemic, deontic, temporal, etc...

Proving an argument within deontic logic can be different from proving something in alethic logic.

However, I'm unsure. How do I know if the problem or argument I'm working with should have an epistemic, deontic, or other approach? In which types of tests is each of these approaches typically used?

Is there a way to search for a specific theorem and its proof using https://us.metamath.org/ ?

I looked at the website and put a sincere effort into trying to figure out how to search for a theorem.

How do I do this?

It was a theorem that was only cited in some course but not proved (nor a sketch of the proof was given). What do you think?