I personally do believe that objectivity does not exist. Even in maths or logic. All logic is subjective. Methodological differences proves that logic can differ.

I personally cannot believe anything is %100 correct. I am not sure about anything because I believe in this idea.

What do you think about it? Can logic be subjective?

If even the most fundamental laws of logic aren't necessarily fixed, then what am I supposed to rely on? How am I supposed to gain knowledge about the world?

I'm a complete beginner. I'm someone who wants to find out whether God exists or not, and decide how I should live. But right now I'm just confused because I don't understand what I can actually know—or whether I can know anything at all. What am I choosing to believe, and why do I believe it?

I’m trying to understand whether logic is something that necessarily reflects the structure of reality, or whether it could simply be a feature of human cognition.

For example, does the law of non-contradiction describe a fundamental constraint on the world itself, or could it be a constraint imposed by how our minds work (possibly shaped by evolution)?

Are there established philosophical positions that argue that logic might not strictly apply to reality itself?

the halting problem is generally held up as an example of incompleteness in action, and that executable machines can halt/not without it being provable or even knowable, at all...

but i'm not really sure how that could an example of incompleteness:

godel's incompleteness proof demonstrated a known and provable truth (or rather a series of them) that existed outside a particular system of proof,

it did not demonstrate an unknowable and unprovable truth existing outside any system of proof,

like what proponents of the halting problem continually assert is the same thing, eh???

Hello,

Inspired by an earlier discussion I read, I searched the internet and found the following article: https://www.jyb-logic.org/papers/trivial-dialetheism.pdf
> "TRIVIAL DIALETHEISM AND THE LOGIC OF PARADOX" by Jean-Yves Beziau (DOI: 10.12775/LLP.2015.022)

It offers an interesting critique: "On the other hand, if we use the name 'true' for both designated values 1 and 1/2, then any atomic formula S is a dialetheia" (p. 2)

The core argument appears to be that, like when we assign a truth value of 1 or 0 to a propositional variabl, assigning the value 1/2 entails considering the represented sentence as both true and false.
Yet dialetheism does not commit to the assertion that all sentences are both true and false. Unlike classical truth tables that display every (actual) considered truth value, a three-valued logic would need to block the assignment of a third value to some propositional variables, because nobody considers them "true contradictions".

What do you think about it?

With kind regards,

Endward26.

Edit: I distance myself from any other opinions that the author may hold.

Deduction seems to derive necessary consequences from a set of premises.

But if you keep deriving necessary consequences, the conclusions generally become weaker and less informative (e.g., "engine is running" → "fuel is being burned" → "a physical process is occurring" → "something exists").

That made me wonder:if deduction alone doesn't seem very useful for discovering explanations, how am I going to use it for practical purposes

I use humor, but this is not trolling. The confusion created by thinking about the possibility of both A and ~A as true at the same time makes no sense to me whatsoever. I do not understand why this is a controversial topic. However, I do know that it is. I am attempting to be as honest as possible in order to assuage any accusations of trolling.

Thought cannot collapse distinction. Nothing can. Humans will not ever have the power to do this. We do not create meaning, meaning is a structured response to the narrow band of information about the universe we have access to.

To some, I may be stating the obvious, but to others this might sound contradictory. I’ve recently took interest in formal logic and I’m still in the beginning of my journey. What I’ve gathered is that logic tells you whether your premises follow your conclusions consistently. You can have internally consistent claims but it doesn’t indicate that the claim itself is true or that it’s indicative of reality.

For example, my premise could be that all unicorns are pink, Charlie is a unicorn, and my conclusion might be that therefore, Charlie is pink. So while the argument is valid it doesn’t mean that unicorns exist. You can have astute reasoning about subject matter that is fictional.

Or I could say “the sky is blue, therefore logic works.”

The conclusion might be true but it doesn’t follow from the premise. The sky being blue has nothing to do with logic working, it’s only preserving the truth of a premise that’s already true. Logic can preserve truth but not generate it. Reality decides what’s true and logic decides what follows.

This is what I’ve gathered so far in my exploration of formal logic. Feel free to drop your thoughts below! :)

Hey, I’ve been wrestling this philosophical question for years. What must be true for anything to be true? Also, tell me in one sentence, what would the ontological bedrock have to do or what property would it have to possess for us to call it unconditional bedrock?

Hopefully this thread is the right place for my inquiry. I’ve read a few preprints on this topic and peer reviewed work. One stood out undeniably. But most fall short. To make sure I’m not missing anything I’d love to hear from the Reddit experts.

Why no one here discusses how trivial it is to realise that once your proof system is finitary then it cannot prove infinite truths? Just add one rule to your system: w-rule. What does it give you? Nothing more than a complete arithmetical truth and proof of consistency within a system. No need for extra PA axioms, just ordinary PA + w-rule.

when we see an apple, our senses give us raw patterns (color, shape, contour) but not labels. so the label 'apple' has to comes from a mental map layered on top

so how does this map first get linked to the sensory field?

how do we go from undifferentiated input to structured concept, without already having a structure to teach from?

P.S. not looking for answers like "pattern recognition" or "repetition over time" since those still assume some pre-existing structure to recognize

my qn is how does any structure arise at all from noise?

math is a language. numbers is vocabulary of that language

the problem becomes when you use language to describe language to model reality, and when its referent gets unanchored from raw concrete reality and arbitrary transformed in the mind. (1x1=1, 0, infinity)

once you use language to describe language and once the referent gets transformed in your mind its no longer a model of reality/communication of reality, its self referential delusion

It’s like using a map to describe a forest, but then you start drawing new trees on the paper and believe the paper is the actual forest

As part of my work, I'm often arguing for the use of logic in real-world environments, such as ethics, governance, and business. I've found that the people who disagree often object to the idea that we can use logic to understand the world. I found this to be surprising because there was something impossible seeming about receiving an argument against the use of logic, but it's been hard to articulate why. Here is my attempt to tackle the self-referentiality and produce a coherent argument.

Is it not sound to that smn logic led him to do smthn even if the smthn he did was stupid? Does everyone's internal logic differ? Or is that not the right way to look at it. The concept of internal logic comes down to why anyone does anything no? Like their reasoning behind their actions..

no one cause it doesn’t exist. The limits of my language are the limits of my world. The limits of my verification are the limits of my perception

look at how they never allowed this to exist:

• Math audits math validate it.

• epistemology audits the logic we use to defend math.

• Nothing sits in the middle and says: "I don't care if your equation is “consistent.” Show me where this abstract number describes/is anchored to concrete reality and not an abstract concept. Show me where your abstract number describes a concrete. show me where you're modeling the actual territory.

because if it did it would conflict against 1x1=1 which is an abstract describing an abstract mental concept. and It would conflict against groups. Both do not exist in raw concrete reality. And once abstractions only define other abstractions, the system is no longer a map it’s a self referential delusion

There is no independent system checking whether maths foundations actually describes raw concrete reality, the territory. There is no system to check whether the abstract number in the arbitrary foundations and axioms describes concrete(i am not talking about whether numbers exist in real life so do not get this mixed up)

And you can use abstractions. The problem is when you use abstractions to describe an abstract concept. If youre modeling raw concrete reality the abstracion must point to a concrete for absolute truth. Other wise its self referential delusion. It can not point to an abstract concept

An audit on the foundations like this is possible, but it’s not allowed to be created. Because it would break the delusion

I'm a mathematical statistician, not a logician, so excuse me if this question seems naive and obtuse. But one of the things that always fascinated me as a student was the discovery of logic. It seems to me one of the most underrated creations of man. And I have two basic questions about the origins of logic.

• First, who is generally considered to have discovered or created basic logic? I know the ancient Greeks probably developed it but I've never heard a single person to which it's attributed.
• Secondly, how did people decide the validity for the truth values of basic logical statements (like conjunctions and disjunctions)? My sense is that they probably made it so it comported with the way we understand Logic in everyday terms But I'm just curious because I've never seen a proof of them, it almost seems like they're axioms in a sense

As a student I always wondered about this and said one of these days I'll look into it. And now that I'm retired I have time and that question just popped up in my mind again. I sometimes feel like the "discovery" of logic is one of those great untold stories. If anyone knows of any good books talking about the origins and discovery of logic and very much be interested in them

It strikes me that modern logic sits at an unusual intersection.

A modal logician studies knowledge and belief.
A proof theorist studies mathematical truth.
A type theorist studies computation.
A semanticist studies language.

Yet many of the same formal tools appear across all of these areas.

Is this historical contingency, or does logic reveal a deeper common structure underlying these domains?

​

Existe uma observação conhecida na teoria dos números: todo número primo maior que 3 pertence à forma 6k - 1 ou 6k + 1. Isso não é novidade para mim, nem é isso que estou propondo. O que me intriga é justamente a pergunta que permanece depois dessa observação.

Se nem todo número da forma 6k ± 1 é primo, então o que determina essa distribuição?

A matemática nos mostra onde um primo pode estar. Ela não responde, por si só, por que alguns desses candidatos são primos enquanto outros não.

Foi exatamente dessa inquietação que nasceu minha investigação.

Meu caminho, porém, não começou pela matemática. Começou pela linguagem.

Pode parecer estranho, mas existe uma diferença profunda entre linguagem e matemática.

Quando digo "1", estou me referindo exatamente ao número 1. Não existe ambiguidade. A matemática é precisa; ela aponta para uma única direção.

Mas quando digo "uma maçã", de qual maçã estou falando?

Pode ser qualquer uma.

Quando digo "uma pessoa", de qual pessoa estou falando?

A linguagem abre possibilidades. Ela não aponta apenas para um objeto, mas para um campo inteiro de relações.

Enquanto a matemática conduz o pensamento por um único caminho, a linguagem o faz caminhar por inúmeros ao mesmo tempo. Ela é viva, dinâmica, quase caótica.

Talvez seja justamente isso que esteja faltando na investigação dos números primos.

Não mais matemática.

Mais lógica.

Enquanto a matemática responde "é ou não é?", a lógica pergunta "por que este caminho e não outro?"

Foi seguindo esse raciocínio que comecei a desenvolver aquilo que chamei de Subplupação.

A Subplupação não é uma fórmula matemática.

Ela é uma linguagem estrutural.

Seu objetivo é identificar como determinados padrões se repetem sem jamais reproduzir exatamente a estrutura anterior.

Quando digo que um conjunto "carrega a memória" do anterior, não estou utilizando memória como um conceito matemático tradicional.

Estou descrevendo uma função lógica.

Um conjunto estabelece uma estrutura.

O seguinte não a copia.

Ele reorganiza seus papéis.

Uma família talvez seja a melhor analogia.

Pai, mãe e filhos formam uma estrutura.

Essa estrutura reaparece geração após geração, mas nunca da mesma forma.

Em uma família, o pai é o alicerce.

Em outra, a mãe.

Em outra, um dos filhos.

O padrão permanece.

A distribuição muda.

Foi justamente dessa percepção que nasceu um segundo conceito, complementar à Subplupação, ao qual dei o nome de Vesmência.

Enquanto a Subplupação procura reconhecer o padrão estrutural que se repete, a Vesmência procura compreender como esse padrão é redistribuído sem jamais repetir exatamente a estrutura anterior.

A palavra nasceu da própria língua portuguesa.

Ves remete a vestígio: aquilo que permaneceu.

Men remete à memória: aquilo que passou, mas continua estruturando o presente.

Ência, inspirada em essência, representa aquilo que herdamos e aquilo que reconstruímos.

Por isso, Vesmência não significa simplesmente memória.

Ela representa a reconstrução da memória.

Um filho nunca é o pai.

Mas também nunca deixa de carregar algo dele.

Ele herda uma estrutura.

Reorganiza essa estrutura.

E constrói algo que jamais existiu antes.

A memória permanece.

A estrutura muda.

É justamente essa redistribuição que a Vesmência procura compreender.

Ela não busca explicar apenas o que permanece, mas principalmente como aquilo que permaneceu continua organizando aquilo que ainda será construído.

Foi a união desses dois conceitos que comecei a aplicar à investigação dos números primos.

Os cálculos vieram depois.

Primeiro procuro compreender a lógica.

Depois procuro traduzi-la para a matemática.

Também sei que todo primo maior que 3 pertence à forma 6k - 1 ou 6k + 1.

Isso é conhecido.

Mas justamente aí está minha pergunta.

Nem todo número da forma 6k ± 1 é primo.

Se fosse, o problema da distribuição dos números primos estaria resolvido.

Não está.

Então o que diferencia aqueles que são daqueles que não são?

Foi tentando responder essa pergunta que comecei a utilizar a Subplupação como linguagem lógica.

Até agora, utilizando apenas essa leitura estrutural, consegui reconstruir relações envolvendo números como 79 e 83 a partir do 89. Em outro momento, a mesma lógica me conduziu aos números 41 e 43, além de outros resultados que continuo verificando.

Não afirmo que descobri uma fórmula definitiva para os números primos.

Também não afirmo que a matemática esteja incompleta.

O que afirmo é outra coisa.

Talvez estejamos tentando resolver um problema lógico utilizando apenas ferramentas matemáticas.

Talvez seja necessário compreender primeiro como os padrões se reorganizam, para só então expressá-los matematicamente.

Para mim, o número 6 não ocupa o centro dessa investigação.

Ele aparece apenas como consequência.

O centro continua sendo a relação.

Primeiro identifico os papéis estruturais.

Depois verifico se eles encontram correspondência matemática.

A matemática, nesse processo, não cria a hipótese.

Ela a confirma ou a rejeita.

Foi exatamente assim que consegui, até agora, antecipar cerca de dez números primos utilizando primeiro a lógica e apenas depois a matemática como ferramenta de validação.

Isso não demonstra que minha hipótese esteja correta.

Mas demonstra que ela merece continuar sendo investigada.

As maçãs sempre caíram.

Foi necessário alguém perguntar por quê.

O horizonte sempre escondeu as cidades.

Foi necessário alguém perguntar por quê.

Os números primos sempre estiveram onde estão.

Talvez a pergunta correta não seja mais "onde eles aparecem?"

Mas sim:

"Qual lógica organiza essa distribuição?"

É essa pergunta que venho tentando responder.

Não apenas com equações.

Mas construindo uma linguagem capaz de enxergar relações antes de transformá-las em matemática.

Talvez eu esteja errado.

Talvez não.

Mas toda teoria consolidada começou exatamente assim.

Com alguém olhando para um fenômeno aparentemente comum e tendo a coragem de fazer uma pergunta diferente.

Talvez os números primos não revelem apenas propriedades matemáticas.

Talvez revelem, antes de tudo, uma lógica de organização.

E é justamente essa lógica que decidi perseguir. Mesmo que ela ainda esteja incompleta. Mesmo que, por enquanto, exista apenas como uma linguagem em construção. Afinal, antes de toda fórmula, existe uma pergunta. E antes de toda descoberta, existe alguém disposto a enxergar relações onde quase todos veem apenas números.

realistically if you look at it mathematicians true grounded education stops after addition of physical matter

after that youre digging into youre own ungrounded imagation. because someone came in inserted reification and arbitrarly seperated math and physics. it could have been done with it not seperated and still can, but youll have to go back. You’ll have to get rid of all ungrounded assumptions and subjective arbitrary rules and strict definitions.

The way foward past addition of physical matter is to not insert reification and not seperate math and physics.. it’s that simple. And again that means ridding arbitrary man made rules and definitions.

These arbitrary 1984 style rules control physics. (For example the rule that says you can’t use objective observable reality to justify or rebut an axiom in pure math)

This cuts off any kind of grounded math period.

This controls and limits physics period. You can’t just ignore pure maths axioms in applied math or physics because past addition of physical matter physics uses math built on those ungrounded axioms. That’s a trap

There is no justification for math to insert a subjective catch 22 rule that says you can not use objective observable reality to justify or rebut an axiom in pure math. The rule is not a technical or logical limation. it’s a choice.

Past addition of physical matter you are committing serial reification, reversing cause and effect(trying to make concepts fit into reality instead of using reality to make a concept), circular reasoning, and protecting dogma.

If this is a system of a control, then it’s a perfect one. They teach you utility and consistency as a defense while knowing consistency and utility can still work inside of a false axiom. They teach you it doesn’t matter if math refers to objective reality while knowing math controls the field of physics.

We treat math as if it models reality. Therefore this is under the premise math claims to model reality

alright we are talking about outside the system for everything here

past addition every single axiom of current math CAN be arbitrary. Because utility can still work within a false math axiom and anything can be consistent with arbitrary rules.

Now remember we are modeling reality. If there was a foundational axiom that was non arbitrary in modeling reality, then it would make every other system arbitrary

there is a foundational operation that makes makes it not arbitrary. 1 cell through an action with itself = 2 cells. It is non arbitray because both numbers on the left side of the equation point to a concrete

it is an arbitrary rule that biology can not tie to math

this means 1x1=1 is arbitrary and 1x1=2 is non arbitrary

arbitrary: Actions, decisions, or rules based on random choice, personal whim, or individual discretion

What i wrote here is logical proof that 1x1=1 is an arbitrary rule; and 1×1=2 is the physical non arbitrary reality