r/logic

[removed]

That’s a theorem.

true

Hi everyone,

I just recently made a video covering the history and development of proof theory in under 1 minute, and I’d really appreciate some honest feedback from this community.

As I am interested in mathematical logic, I’ve always been confused by what seems to be a neglect from the rest of the larger math community. I found that a lot of videos either skip over the history or get too bogged down in formalism. I tried making a good overview for the beginner that doesn't talk down to you.

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

Thank you all for your time.

With power comes responsibility.

The ridiculous nature of a proof.

Suppose someone sees structure, another person might not see that structure, so that person who cannot see it will ask for a step by step proof to prove the continuity of a structure. But continuity cannot be proven by discrete steps because we have shown that infinite discreteness cannot proxy for true continuity.

Diagonalization proves that a continuity has more real information than the discreetness. Every step-by-step proof is actually an illusion to satisfy the strange feelings. But every discreet example of a proof fails to show the actual continuity of the structure that one is claiming to exist..

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You might look at this and think to yourself " you're not showing enough discrete steps to prove the continuity of your results or structured"

If you think to yourself and say "nah this guy is a dumb ass" is it because you think im not reasonable or making sense? Is it possible that I'm not making sense because I'm failing to correctly unify ideas in a way that proves what I'm showing?

You can easily say I'm wrong because what I'm saying makes no sense. The sense of wrong comes from not detecting any relationship in the words that I'm saying to the truth of what I'm saying. Even if you think it might be possible that what I'm saying is true, you think that in its current form, it doesn't reveal enough structure that is corresponding to what I'm actually trying to say. You might say I need more evidence, more evidence is more discrete truth.

But the premise is that no matter how much discrete evidence I provide, I cannot actually prove the continuity of the structure I'm claiming to exist. The best I can do is add more discrete steps that get a little bit closer to proving the continuity. The only way you can accept that proof is if you think the discrete steps in my proof are actually sufficient to prove the continuity of the structure. So in reality there is no way that I can prove something like this, not how many discrete steps I take

The only way to accept this truth is just to accept the premise and not ask for why. That is called an axiom.

​

Proving: if every finite subgraph of G is k-colorable, then G is k-colorable.

For each vertex v, variables Pv,1,...,Pv,k ("v gets color i"). Axioms in Σ:

- Pv,1 ∨ ... ∨ Pv,k for each v

- ¬(Pv,i ∧ Pv,j) for i≠j

- ¬(Pu,i ∧ Pv,i) for each edge (u,v), each i

Σ satisfiable iff G is k-colorable. Every finite subset of Σ only mentions finitely many vertices/edges, and that induced finite subgraph is k-colorable by hypothesis, so every finite subset is satisfiable. By compactness, Σ is satisfiable, so G is k-colorable.

But isnt ropositional compactness is usually stated for countable languages? G could have uncountably many vertices, so Σ has uncountably many variables. Does compactness still hold as-is, or do I need the general version (via Zorn/ultrafilters) for uncountable Σ? If it still works, what's the justification? Thank you!

If an infinite number of proper classes can be formed by infinitely including or excluding sets from the class of all sets V, could that infinite number of proper classes be considered an infinite number of absolute infinities or just an infinite number of ways the only absolute infinity which would be the class of all sets V can be sliced (if of course a proper class can be considered an absolute infinity)?

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.

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.

2. 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.

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...

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")

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!

we are everything we‘re not. if x=x and x is what defines someone and makes them the person they are and y is what they dislike and hate, it‘s still something that defines this person
so x=x=y
for example, if i would dislike blueberrie, that would make me someone who hates blueberries, which would be part of me and my personality

for another example, imagine a picture of you in a certain surrounding like a forest. you are the main subject in the picture and the forest is in the background. you are x and the forest would be y. you are certainly not the forest but if there wouldn‘t be any forest or any background what would define the line between you and the background, there isn‘t a certain border. so the forest still defines you somehow.

i‘ve come to the conclusion that mathematics are just a metaphor for things others rather describe in words. variables are metaphors, as the human has always deeply felt a need to describe his environment.
and in the example of schroedinger‘s cat, it isn‘t really about the cat being dead or not, but rather about the paradoxon of life and x being y at the same time.

Greetings folks, there are about 1400 of you right now. But the sub had been locked down as restricted for about 3 years. So no posts have been accepted for all that time. Please do tell a friend, and invite your neighbors. Please take a look at the rules, and the related communities.

If there is something that people interested in analytic philosophy should be talking about or thinking about. Please do post it here.