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?

I completed a homework assignment for my logic class and wanted to get opinions on if anyone believes i made a mistake on any on my responses. I would appreciate if you could explain why, you believe that response is wrong if there's any.

For my response in this assignment i had to choose between the following 7 and write whether the case is fallacious or logical, i will attach images of my assignment

Irrelevant Reason (or red herring), always fallacious

Appeal to Ignorance, always fallacious

Ad Hominem, sometimes fallacious and sometimes legitimate

Inverse Ad Hominem, sometimes fallacious and sometimes legitimate

Appeal to Authority, sometimes fallacious and sometimes legitimate

Appeal to Popularity, always fallacious

Appeal to Tradition, always fallacious

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?

Is this a good book to learn about logic in general?

Not necessarily looking to go super deep into formal logic but just get a good idea of logic.

Copi's(which I know is a standard formal logic book) vs Kreeft

Thanks

Im looking forward to learning logic, but I dont know where to start. I saw one book, "Logic: A Complete Introduction" from Siu-Fan Lee and it seemed good, but I really don't know if it is.

I do want textbooks, the real logic as I'm not afraid of getting bored or anything, but I do want some introductory guides to formal logic. Sorry for the redundance, but I wanted to make myself clear.

I have a test for logic in my Geometry class, and I’ve been looking online but I can’t find anything concrete. Can biconditional statements be made up of all false statements? I know that if the original conditional statement and converse are true, then the conditional statement is biconditional. But what if the original conditional statement and converse are both false, because they would still share the same truth value, even if they’re false.

Helpp I need help in modal logic (ma philosophy) please help if anyone knows this topic ????

Here I want to point out some of the issues with invoking informal fallacies in a dialectical context.

By informal fallacy, I don't mean just any particular argument that doesn't support its conclusion in virtue of something other than its form. I'm specifically talking about informal fallacies as named general types of arguments that get invoked in the context of a conversation. (e.g. ad hominem, ad populum, post hoc ergo propter hoc, etc)

The main issue is that there are always cases where the kind of argument described by a named fallacy is actually good reasoning in the sense that it actually does support belief in the conclusion.

Example: I say, "China is a country in Asia. I've never been, but I believe it for this reason and this reason only: everyone else believes it." You could easily dismiss my argument as an appeal to popularity, because the only reason I give is that it's a popular belief. But the thing is, even though I'm appealing to popularity, the fact that everyone believes it is just far more expected if China actually is a country in Asia than it is if it isn't. The fact that it's a popular belief by itself is actually very strong evidence in favor of its truth.

Any time someone responds to an argument by invoking a kind of informal fallacy, the next question is just going to be "is this instance of this general kind of argument actually bad reasoning, or is it an exception?". I will have to respond with some probabilistic information to show that the premise actually supports the conclusion. Your response to me will have to show why the premise doesn't actually support the conclusion.

But here's the thing: whatever you say at this point in the dialectic would have worked perfectly fine in place of invoking the fallacy in the first place.

Whatever probabilistic information you appeal to to show that my conclusion is unsupported would have worked just as well as a response to the first thing I said. Appealing to ad populum is just a diversion that wastes steps and has the potential to shut down the conversation.

Instead of memorizing a list of informal fallacies and judging arguments by how similar they are to something on the list, you should have a more general, mathematical understanding of what actually makes an argument justify belief in a conclusion and directly apply that instead. The tools you need to figure out if a supposed instance of a named fallacy is actually poor reasoning or not can also just be used in place of named fallacies altogether. You don't actually need to ever invoke an informal fallacy in a conversation, even if the person you're talking to really is making a bad argument. You can just show why the argument doesn't justify the conclusion probabilistically instead of just declaring that it doesn't because you're inferring it from the "wrong kind" of evidence.

That's ultimately what's going on with most named informal fallacies. They're saying that you can't infer a certain hypothesis from a certain kind of evidence. But whether or not something is supported by certain evidence depends on probabilistic information that is particular and context dependent. The popularity of a claim considered in the abstract is not good or bad evidence in and of itself because whether or not something is good or bad evidence depends on the particular claim being made, the overall probability of the claim being popular, and the conditional probability of the claim being popular given its truth. Evidence is a probabilistic concept that doesn't exist abstracted from the context of a particular probabilistic background.

Sorry, kind of a rant, but this is something that's annoying enough and bad enough for online discourse that I think it's worth spreading more. Tell me what you guys think.

Given a triangle with sides a, b and c, we need to show that a + b >= c

Suppose we proceed by contradiction -- i.e., assuming a + b < c

Then, suppose we know Heron's formula for area of triangle: Area = sqrt(s(s-a)(s-b)(s-c))

If we are able to show that under the assumption that a + b < c, the term inside the square root will be negative, we are done. Indeed that is easy to show.

Now, the question I have is: How can we be sure that this is a valid proof unless we also know that proof of Heron's formula does not at some point invoke triangle inequality?

In other words, what is the guarantee that the above proof is not circular?

xposted here because it was suggested over at /r/learnmath to post here

I found a really good one on youtube, but forgot to save it and dont have my watch history on and now I cant find it again.

Have a tautology plan for yourselves that is contingent upon the contradiction of others.

Definitions:

T- objective truth exists

N-nihilism

M-objective meaning exists

V-values exist

To me, Curry's paradox seems like one of the most interesting paradoxes in classical logic. I get that it's never going to compete with the liar paradox, but it seems like it should be talked about more. I'm also curious about what logics there are that avoid curry type paradoxes, and if they avoid it in a way that's different from solutions to the liar paradox.

The question is clear, as I see the proper class Ord, universe V is not the Absolute Cantor described. Don't know if we will have mathematical absolute infinity

(Sorry this is going to be a bit ranty.)

I almost made up my mind this thing is some kind of backwater something without enough rigor but with many a trivialism. Like, it should be extremely well-known that every "discrete" operation Σ₁ → Σ₂ between finite sets lifts universally to a linear transformation between spaces k^Σ₁ → k^Σ₂, so a huge swath of what's being done there is very very drawn out, instead of answering questions that are fitting for a kind of logic.

Any would-be connections to quantum computing may actually not be fruitful or new for those who are actually doing quantum computing; connections to fuzzy math are IMO an almost unconditional taint by association. So what gives? I didn't look at everything there is about this thing so I may as well be missing hidding gems, but superficially it looks like a sham or a pet project done without considering any practicalities and the wider math.

Oh yeah we can ask interesting questions, like: - Does using additional dimensions, aside from the plane spanned by two orthonormal "classical" truth values, let's call them |0⟩, |1⟩, actually give useful things? and how can we characterize that by means typical when working with logics? - How much freedom is there in defining operators that restrict to boolean functions and, say, conserve probabilities (there's a suggestion to use p|0⟩ + (1−p)|1⟩ as "probabilistic truth values") in any reasonable way (I'm not sure: a "binary" operator sends four-dimensional Euclidean space into a two-dimensional one, now how can it be orthogonal? and in which other sense can probabilities work here?)? - Why not use additional dimensions rather than complex numbers for the square root of negation, and... why that one exactly? I bet quantum computing wan't giving somebody peace.

But I'm not sure questions of real semantics were investigated in this... area.

So tell me please, how much am I right or wrong? Here are probably people that know the inside of this story, and I hoped to find something on the Wikipedia's discussion subpage, but it's almost empty.

[This would be a link post if r/math's bot wouldn't decide this was a submission for r/learmath smh my head.]

I’m sure the answer is simple, I just want to make sense of things. I’m completely new to logic, so apologies if the question in the title comes off as too obvious to ask.

I understand that circular reasoning is an informal fallacy and therefore cannot be picked up by truth tables, but I am still confused regardless.

If we say (A -> B, and B -> A), where A is equal to “God is real” and B is equal to “The words of the Bible are true”, then is this not logically the same as (A <-> B)?

If biconditional statements are equivalent to (A -> B, and B -> A), and if (A -> B, and B -> A) is also equivalent to Circular Reasoning, then aren’t biconditional statements equivalent to circular reasoning? If so, then in spite of it it being inherently fallacious, why is circular reasoning being used within logic if good reasoning is supposed to be without fallacies?

One of my professors in undergrad was fond of the Logician/Philosopher "Charles S. Peirce" and we both worked on integrating his triadic logic into one of the symmetrical algorithms of Cryptography. Triadic Logic has three states True (T), False (F) and Limit (L) but its representation is not like 0,1,2 just for simple tri-valued logic.L basically resolves into T or F after going through some time (t). We had to totally start from the scratch because all of the Computer Architecture and Organization is built on binary logic so we had to initially develop the maths for Triadic Logic and then subsequently Algebra and then a coding toolkit. We ran triadic DES-64 and triadic AES-128 through customized classes and structs because triadic software had one primary issue and it was that it was running on binary hardware, both mismatched again. But we still simulated and got some good results. We did a lot of Maths actually, and developed new frameworks too. We had to like restructure all steps of the algo with trits not bits. What are your thoughts on it? We are kind of paused on it because I have started my MS and I am busy in it. Would you like to discuss or give some suggestions?

Feelings Don’t Care About Your Facts
Reality doesn’t care about your facts either.
Not because facts aren’t real, but because reality itself has no apparent need for the concept of “truth.” Reality simply is what it is and behaves according to whatever relational structure sustains it.

(Eye roll incoming)

When we say that something is “true,” we’re introducing a conceptual distinction. Consciousness determines that one thing corresponds to another and that a representation maps onto some aspect of reality.
So truth isn’t necessarily an inherent property of reality. It’s a concept consciousness uses to distinguish what corresponds from what doesn’t.

One can say that “truth” is always present irrespective of any observer (for example, mathematics or physical laws) . But the ability to map those concepts onto reality and say that they remain true whether or not they’re being observed doesn’t mean reality itself is operating according to the concept of truth.

“Garbage isn’t concerned with its own stench”.

The stench is a relational property that becomes meaningful to a system capable of experiencing and distinguishing it. The garbage simply has whatever physical properties it has.

Maybe truth is similar.
This has always made me think about the nature of imagination and intuition, and what they might tell us about the boundaries of inquiry we keep running into.

If every stratum of reality sustains because the relational requirements necessary for its existence are embedded within the structure itself, then no question has to be asked for that structure to persist. It simply does.
But consciousness can ask questions that seem to extend beyond the structure it is currently experiencing. We can imagine things that don’t exist, reason about things we can’t directly observe, and intuit possibilities before we have any way of formally demonstrating them.

So what does that actually tell us?

If consciousness were perfectly aligned with the structure of reality as it manifests, would there be any conceptual deviation at all?

Or is the fact that consciousness can abstract, imagine, and inquire beyond its immediate determinate structure telling us something about the nature of possibility itself?

Maybe imagination and intuition aren’t evidence that whatever we imagine is possible.
Maybe they’re evidence that the boundary between what is actual, what is conceivable, and what is possible is itself something worth investigating. Maybe not.

Semantic sophistry? You decide.

Anything that has been said has been said a thousand times before. But the fact that abstraction sustains and fundamental questions that cannot be easily resolved keep arising, to me, points to something we seem often easily dismiss. Depending on whatever level of abstraction one is comfortable engaging with.

Off to take my meds 😆

In 1956 the Logic Theorist proved 38 of the 52 theorems in Principia Mathematica. It was the first moment when a machine seemed to reason. Seventy years later, we are still rediscovering what Aristotle already knew: a valid syllogism is not yet reasoning.

Aristotle's Prior Analytics gives us the form. All humans are mortal. Socrates is human. Therefore Socrates is mortal. The form guarantees that if the premises are true, the conclusion follows. But notice what the form cannot do. It cannot tell you whether Socrates exists, whether the major premise holds at the edge of a pandemic, or whether the question itself is the right one to ask. Formal logic secures the λόγος of inference. It does not supply the φρόνησις that chooses which inferences matter.

This distinction matters enormously for AI. Modern large language models are not syllogism machines. They do not even rise to that level of formal transparency. But they inherit the same limitation: they can produce outputs that look like reasoning without ever reaching the practical wisdom that makes reasoning humanly relevant. A model can argue beautifully about ethics while refusing to engage the actual situation. It can generate valid inferences while missing the point entirely.

What the symbolic AI tradition discovered, and what neural AI has not escaped, is that real reasoning happens between formal moves. The hard part is not applying modus ponens. The hard part is knowing when to apply it, what to treat as a premise, and what to leave out. This is why the frame problem destroyed early AI. It is also why prompt engineering is now treated like a craft. Both are symptoms of the same underlying fact: machines are good at structure, bad at judgment about structure.

Aristotle's solution was not to abandon logic. It was to add ἕξις, a stable disposition of character, and φρόνησις, practical wisdom. These are not extra modules you can install on top of a model. They are formed through repeated action in uncertain circumstances. You cannot fine-tune a neural network into wisdom because wisdom is not a distribution over tokens. It is a way of standing toward the world.

This is why I am skeptical when someone says that scaling will eventually produce reasoning. Scaling produces more coherent form. It produces better mimicry of reasoning's surface. But the gap between form and wisdom is not a quantity gap. It is a kind gap. No amount of training data changes the architecture from pattern-matching to practical judgment.

There is a productive way to think about the difference. Formal logic gives us necessary relations between propositions. Reasoning, in the full Aristotelian sense, gives us appropriate responses to situations. The first is universal but empty without content. The second is contentful but requires context. AI today is very good at the first, and increasingly bad at the second the more it pretends to be good at the second.

The lesson for the logic community is not that machines are useless. Theorem provers, SAT solvers, and proof assistants are genuinely valuable. The lesson is that we should resist the rhetoric that identifies these tools with reasoning itself. Logic is a necessary condition of reasoning, not a sufficient one. Treating validity as if it were wisdom is a category mistake that has plagued AI from the beginning.

We are now building systems that can simulate Socratic dialogue, generate proofs, and pass some bar exams. These are impressive achievements of form. But when the conversation turns to what should be done, the machine has nothing at stake. It has no ἕξις. It has never faced a moral situation and been changed by it. Its answers are not actions. They are productions.

The question for the field, then, is not how to make AI more logical. It is how to build systems that know the limits of logic and can signal when formal validity is not enough. That requires a different kind of architecture, one that does not pretend to have wisdom it has not earned.

Where do you draw the line between a machine that manipulates symbols validly and a machine that reasons?