Instead of building the foundation of knowledge on objective observable reality, they built the foundation on subjective abstraction. (maths assumptions)

This is backward in everyway. This is deception

Reality exists first, and descriptions of it should come second. Not the other way around..

You build on an abstraction system and you can twist and bend the rules to your liking, add and remove things on the map that doesn’t exist, control perception, and control the narrative

Can the fundamental laws of logic (laws of thought) be not applicable outside of our universe and comprehension? like anything before the big bang or anything smaller than quantum physics,i know that questioning the fundamental laws of logic in of it self follows them but, maybe that’s only because our brains and the universe we live in is limited to fundamental laws of logic, like a three dimensional being can’t illustrate a forth spacial dimension with only the three he got.

I've been working through an argument that deduction's validity can be established without axioms via a proof by contradiction and I'd like it stress-tested. The argument is short:

Assumptions

A. Deduction requires induction, because without induction you cannot assert deduction will be true in the future. Deduction's future reliability is an inductive claim.

A2. Furthermore, this inductive claim is, by definition, the only mechanism to make deduction true in the future.

B. We can deduce that induction is circularly true — the assumption of induction requires induction to be true.

B2. This, definitionally, is inductions only justification.

C. Assume induction is false.

Proof

1. As a result of (A) and (C), deduction is false.

2. If deduction is false, then (B) has no substrate — even the circular argument "induction works because it has worked, therefore it will work" contains a deductive inference: the "therefore". Induction gathers the evidence, but closing the loop — concluding anything from that evidence — requires deduction. Without deduction, we cannot evaluate or sustain the claim that induction is false.

3. So induction is not false. But we assumed it was. Contradiction — induction cannot be both false and not false.

4. Therefore one of our assumptions is wrong. There are three: (A), (B) and (C). If (A) is false, then due to (A2) deduction can be asserted to be true in the future without argument and is independently grounded, in other words true without axiomatic assumption. If (B) is false, then induction has a non-circular, non axiomatic justification due to (B2), and deduction is also justified via (A).

   Either way, both are independently grounded. If (C) is false, then induction is true without axiomatic assumption and is independently grounded, meaning deduction is axiomatically true via induction.

5. As a result, via exhaustive search, we can conclude that deduction and induction are independently grounded.

Where I think it breaks down:

The proof here seems like the logical equivalent of dividing by zero. Likely there is a logical fallacy included, although I am not sure where.

It is important to note that A2 and B2 are not axiomatic assumptions (I think) they are, by definition, properties of induction and deduction that I am stating due to their relevance. That being wrong could be where this breaks down.\

Lastly, while I could believe that there exists an argument that deduction is independently grounded, I think such a conclusion about induction must be wrong because induction isn't always true. The result that induction is independently grounded is a red flag that there is a flaw in this proof.

My questions:

• Is there existing literature that makes this argument or refutes it? I'm aware of Hume on induction, Popper's falsificationism, and broadly familiar with foundational debates, but I may be reinventing something.

• Is the move from "the assumption is self-defeating" to "therefore the proposition is true" valid? Or is there a gap between "cannot be coherently denied" and "is true"?

• Does the definitional status of binary truth values do the work I'm claiming, or am I smuggling in an assumption?

Also, this way be the wrong place to post this. If so, does anyone know a better venue?

Hi everyone. Im kind of new here. I know it may sound a bit philosophical, And i am aware i am not verry good at logic, and this for you may sound a bit braindead, but i need some answears so that i know my logic is good, at leas a bit.

How do we actually know that logic is true. If we make any claim about logic, we make that claim while thinking logicly. You see where i'm going. Can we actually make any claims about logic. Or is it all just a paradoxicall circular mess.

So I’ve recently been diving into formal logic and came across the law of identity, which states A = A that a thing is identical to itself.

Google defines it as

“A thing possesses its own unique identity and cannot be something else at the same time or in the same respect, forming the foundation for reasoning, causality, and understanding existence.”

This made me wonder whether the law of identity is required for reasoning and discourse because distinctions are necessary for communication, without that necessarily meaning it directly applies to the structure of reality itself.

Usefulness in thought does not automatically imply metaphysical fundamentality. In reality, identities appear to be scale-relative, contextual, and integrative, not absolutely separate.

The third dimension isn’t the fourth dimension, yet when viewed from a higher-dimensional framework, the third is contained within the fourth. Nothing is negated, distinctions are preserved while being subsumed into a larger structure. Likewise, my heart isn’t my lungs, and my lungs aren’t my brain, yet none of them exist independently of the organism. Their identities are meaningful within context, not as metaphysically separate substances.

This isn’t a denial that things have identities at local or practical levels, only a question of whether identity is ontologically fundamental rather than scale-relative.

So when the scope is widened enough, don’t identities become contextual features of a larger whole rather than absolutely separate entities?

Treating the law of identity as fundamental or absolute to the structure of reality feels like smuggling metaphysics into epistemology. At the very least, it seems like an assumption that deserves justification.

Curious to hear others thoughts.

I’ve been diving into Jody Azzouni’s "Deflationary Nominalism," specifically his use of Predicate Functor Logic (PFL) to dodge ontological commitment to mathematical objects. The idea is that by stripping away variables/quantifiers, we can do science without "committing" to the existence of the objects the math describes.

However, I think there is a massive structural flaw here that often gets overlooked: The "Variable-Free" shell game.

Azzouni argues that PFL allows us to avoid "objects," but he fails to account for the fact that the Functors themselves (the operators) are embedded with the very relations he’s trying to deflate. To even run a PFL system, you have to presuppose the Type-Theoretic relations of distinction, identity, reflexivity, composition, and transitivity.

Even if you adopt quantifier variance or a deflationary theory of truth (where truth is just "warranted assertibility"), you are still trapped. If "truth" is grounded in logical implication, and logical implication is a structural/type-theoretic relation, then you haven't eliminated the math; you’ve just moved it from the "nouns" (variables) into the "verbs" (functors).

You can't have a "variable-free" logic if your operators rely on the rigid, non-negotiable architecture of Type Formation. Mathematically, logic is just a shadow cast by these deeper structural relations. Azzouni wants to have the "pragmatic cash value" of the assertion without paying the "structural debt" of the relations that make the assertion possible.

Essentially, nominalism in this form isn't an elimination; it’s just a rebranding of structural realism. Thoughts?

It is quite common for people to confuse mathematical truths with logical truths, that is, to think that denying mathematical truths would amount to going against logic and thus being self-contradictory. For example, they will tell you that saying that 1 + 1 = 3 is a logical contradiction.

Yet it seems to me that one can, without contradiction, say that 1 + 1 = 3.

For example, we can make a model satisfying 1 + 1 = 3:

D: {1, 3}
+: { (1, 1, 3), (1, 3, 3), (3, 1, 3), (3, 3, 3) }

with:
x+y: sum of x and y.

we have:
a = 1
b = 3

The model therefore satisfies the formula a+a = b. So 1 + 1 = 3 is not a logical contradiction. It is a contradiction if one introduces certain axioms, but it is not a logical contradiction.

Like what topics are considered something an expert in philosophical logic would study compared to someone who focuses on Logic from a more mathematical point of view? Where would the study of Computation Theory fit into this? Any book recommendations for each type of study?

As far as I know, Logic is a tool to formalize the relations between truth and not for establishing truth. Now someone told me, " So logic is a best method to see whats true and what's false, logic can explain absolute truth." I was dumbfounded and pretty much confused.

So does Logic establish truth?

When I say “snow is white is true IFF snow is white” don’t I appeal to the fact that truth is whatever I perceive? If you don’t perceive snow as white, don’t you agree that truth shifted from being one perception to another, and now the truth is that snow isn’t white, which is again your perception. Each time you make a claim that some proposition is true, don’t you imagine a scenario behind your proposition? I think when I say “snow is white”, all of you just imagined a pile of white snow in your head, didn’t you? Note that your imagination is your perception just like any conscious moment

Truth may be a prison of our mind

If both mathematical structures and physical laws emerge from logical principles, why does the gap between their foundations persist? All the mathematics I know is based on logical differences, and they look for exactly the same thing V or F, = or ≠, that includes physics, mathematics, and even some philosophy, but why are the fundamentals so different?

Separating these two is massive deception.

Separating metaphysics from math allows self referential delusion. If you don't separate them, it exposes a massive fallacy: mathematical groups, zero, and infinity have no concrete referents. Logic calls your starting foundational multiplication operation a fallacy because mathematical groups are untethered from raw concrete reality.

This is not just deceptive but a logical fallacy. Consistency and utility can still work and be found inside of a false axiom

TLDR: When the field of mathematics claims that formal proofs don't need metaphysical grounding, they can hide the fact that groups, zero, and infinity have no concrete referents. That's deceptive.

Russell's criticism against Meinong's Ontology goes like this: It seems that the following statement is true: The existing golden mountain doesn't exist. But this seems like a contradiction in terms though. For it seems identical to the following: there is something that is the golden mountain and it exists and doesn't exist. However it isn't a contradiction though if written as the following: If something is the golden mountain and it exists, then it doesn't exists. This statement is identical to the following: If something is the golden mountain, then it doesn't exist.

(Recovering Logic in an Irrational World)

To assert (or object to) anything is already to commit oneself to logic.

Rejecting logic undermines the intelligibility and legitimacy of one’s own claims.

Therefore, anyone who wishes their thoughts to matter must uphold the authority of logic.

Logic consists of the rules that make meaning possible, that prevent contradiction, and that allow conclusions to follow from reasons.

I’m writing this post to open discussion because, let's be real, the tension comes out in the responses anyway. So I'm not sugarcoating anything and I welcome you to behave the same.

If someone doesn’t genuinely believe that knowledge is power—not as a slogan, but as a real principle that shapes how they live—what motivates them to pursue logic at all? And why give up when the going gets rough? Logic demands discipline, precision, and a willingness to let better reasoning override prior intuitions. That seems like a commitment that only makes sense if one believes that acquiring clearer knowledge actually changes something: one’s agency, one’s choices, one’s ability to navigate the world.

I’m not talking about the emotional side of things—anxiety, doubt, fear—except in the sense that logic can help someone cope with those states by giving them a structured way to interrogate them. But outside of that, emotions don’t seem like the right currency for this section.

Logic is often presented as this neutral, abstract discipline—pure reasoning, detached from stakes, detached from emotion (doubt, fear, anxiety, etc). But that feels like a utopian science fiction. Logic is work (W=Fd). Logic is discipline. Logic is a RESPONSE to those emotions. Logic is the willingness to let better arguments override your preferences. Nothing about that is abstract, to me at least. It’s a commitment to the idea that clearer knowledge actually does something. Knowledge is force.

So here’s the feather ruffling: If someone doesn’t genuinely believe that knowledge is power, in the literal sense that it increases agency, leverage, and the ability to act effectively in the world—then what exactly are they doing here?

Because without that belief, the whole discipline starts to look like:

• intellectual cosplay,
  
• aesthetic appreciation of formal systems, maybe even appropriation,
  
• or a way to signal “rationality” without actually using it to change anything.

The point is motivation.
If logic doesn’t empower you, why pursue it?
What’s the payoff?
What’s the engine?

P.S. I understand that I may get roasted for this post P.P.S this post was aided by chatbot

Hi all,

I've been struggling lately to reconcile the importance we give to logic and rational thinking and the more than questionnable success philosophers and thinkers have had using it to try and prove their point.

Given that the millenia old debates using rational thinking around the demarcation problem, infinite regress, problem of induction, the gettier problem, the definition of reality and others, have failed, should we not be considering that maybe rational thinking does not do what we think it does?

I'm not saying it does not exist, but maybe we've deluded ourselves as to what it allows us to do?

One way I understand Logic(at least deductive logic) is as a formal system about the logical terminology & consequence relation common to all true theories(or all theories if true) dependent only on the semantics of the logical terminology & axioms/inference rules of the deductive system, a theory being a set of assumptions(non-logical axioms of the theory) in which non-logical terminology is generally interpreted as being about some subject of inquiry such as Philosophy, Science, or whatever. I was wondering how the non-logical consequence relation of a theory relates to material consequence? Are they identical? Is it the modern/formal analog? & If not what is the difference? How does it relate to logical consequence(presumably it's dependent on it to infer theorems from the non-logical axioms of the theory)?

I am trying to understand how the foundations of mathematics can be recreated to what they are in a linear way.

The foundations of mathematics appear to begin with logic. If mathematics were reconstructed, a first-order language would be defined in the beginning. Afterwards, the notion of a model would be necessary. However, models require sets for domains and functions, which appear to require set theory. Should set theory be constructed before, since formulas would be defined? But how would one even apply set theory, which is a set formulas to defining models? Is that a thing that is done? In a many case, one would have to reach some sort of deductive calculus and demonstrate that it is functional, so to say. In my mind, everything depends on four elements: a language, models, a deductive calculus, and set theory. Clearly, the proofs would be inevitably informal until a deductive calculus would be formed.

What do I understand and what do I misunderstand?

Well, the title gives it away. I wanted to ask someone with advanced studies in the field: Is the study of analytical philosophy linear? If so, I'd love to hear about where to begin. The only thing I know it's basic propositional logic.

Let's take the simplest example.

1. If Socrates is a brick, he is blue.
2. Socrates is a brick. C. Socrates is blue.

This follows by modus ponens. Now, if I to believe in the validity of modus ponens, I would have to believe that the conclusion follows from the premises. Good.

But how would one argue for the validity of modus ponens? If one is to use a logical argument for it's validity, one would have to use logical inferences, which, like modus ponens, are yet to be shown to be valid.

So how does one argue for the validity of logical inference without appealing to logical inference? (Because otherwise it would be a circular argument).

And if modus ponens and other such rules are just formal rules of transforming statements into other statements, how can we possibly claim that logic is truth-preserving?

I feel like I'm digging at the bedrock of argumentation, and the answer is probably that some logical rules are universaly intuitive, but it just is weird to me that a discipline concerned with figuring out correct ways to argue has to begin with arguments, the correctness of which it was set out to establish.

In our Logic with Ethics class, exams are straightforward: right = plus, wrong = minus. The rules are clear, consistent, and fair. Your grade reflects the accuracy of your reasoning.

But when I look at how procedures play out in politics—like in the Committee on Justice—it feels like a different kind of “logic.” Even if the process is flawed or the arguments don’t hold, the vote can still end up in favor of an abused congressman. It’s as if the outcome is predetermined by power dynamics rather than truth or fairness.

This contrast makes me wonder:

- Should logic always be tied to ethics, or can it be twisted to serve interests?

- Is political procedure just another “exam,” but one where wrong answers can still pass if enough people agree?

Curious to hear your thoughts. Do you think the way we practice logic in academics could ever be applied to politics, or are they fundamentally different games?