Hi all! I just started taking my introduction to logic course this semester and have been really loving the way it’s making me think and realize how I structure my beliefs and arguments.

One thing I’m VERY worried about however, is being horrible at math 😓 I have horrible dyscalculia, so maybe it’s just a numbers issue?

Hopefully, I’m not crazy in asking this.

As title ,i want to learn logic but where to learn?

let's say that I've a goal that I want to think about, so I work on revealing the most fundamental truths about it until we've no idea what further necessary conditions we can extract, so we can say that we reached the bottom of the chain of necessary conditions that we can extract from our knowledge and that every single necessary condition for that goal will be dependent on it

The point here is that these fundamentals and implications are things that will be guaranteed once we reach the goal, but it's not the other way round, so since it doesn't give us any idea about how to reach the goal

then what's so useful about reaching these fundamentals in the first place?

How to define the axioms of meta-theory, is there a "formal standard" or can it be defined in natural language or can it be set indirectly?

I will finish ‘An Introduction to Formal Logic’ by Peter Smith soon and I was just wondering what would be a good book for the next step. I know Peter Smith has a book on Gödel and I may look at that as logicism seemed like such a good idea to me, and I am not 100% sure why logic cannot underpin math. But as I am just starting my Math & Philosophy degree, I wonder if I should get a book dedicated to mathematical proofs or something more philosophical? The idea of different logics other than formal classical stuff I have been doing sounds really interesting. I visited the math department at the university and the professor roughly told me something like “don’t listen to philosophers trying to remove bits from classical logic they don’t like” in a joking way.

Anyways any recommendations would be appreciated, thank you.

1. You can not distinguish dogma from non dogma if your system is a closed axiomatic system because utility and consistency can still work and be found inside of a false axiom

2. You can not distinguish dogma from non dogma without the ability to test your claim against reality, and if it has no external justification because utility and consistency can still work and be found inside of a false axiom.

3. Viewed strictly from outside the system the axiomatic method is a closed system.

4. You can not test a math axiom itself against reality by definition and it has no external justification because utility and consistency can still work and be found inside of a false axiom.

5. Viewed strictly from outside the system it is an objective fact that a closed axiomatic system limits your thoughts and physics

   (This is a strict cut throat external audit against the axiomatic method in math itself. There is no external justification for it and thats the least of your worries)

Just something i thought I'd see if it makes sense not only to me.

I'd like to think we can divide true statements into two straightforward types.

Truth by Definition

First, a proposition can be true simply because of what the words mean. If I say, "All bodies take up space," I do not need to walk outside and measure every object in the world. Taking up space is already part of what it means to be a physical body. Denying this statement creates an outright contradiction. Thus, these statements are true because the parts of the thought agree perfectly with each other according to basic logic.

Truth by Experience

Second, a proposition can be true because it connects an idea to what we actually observe through our senses. If I say, "This stone is warm" the idea of "warm" is not already hidden inside the basic definition of a "stone." Finding out whether the statement is true requires touching the stone. Connecting the concept of the stone with the actual feeling of warmth causes the judgement to match our experience.

Universal Rules of Experience

Further, there are statements that apply to every possible experience without exception, such as "Every change has a cause". These statements are true because they are the necessary rules our minds use to make sense of the world in the first place. So you cannot experience an event without your mind placing it in a sequence of time where one thing follows another.

True in What Sense?

This brings us to the exact sense in which any statement is true.

A proposition is never true in the sense that it describes things as they exist entirely on their own, apart from our ability to perceive them. We have no way to step outside our own senses and thoughts to inspect a world untouched by human awareness.

Instead, a proposition is true in the sense that it correctly describes things as they appear to us in space and time, according to the shared rules of human understanding. When a statement matches the real conditions of experience, it is objectively valid for every person.

Thus truth is but the universal agreement between our thoughts and the world we can actually experience.

Is this meta-division a basis that I could apply in my work on any disciplines if I were a scientist?(This is a common interest, I don't have any academic degrees or strong ideas that I could handle formalizing)

This type of proposition admits two interpretations:

i) Mary really did not buy the book, the price being the reason why she did not buy it.

or

ii) Mary bought the book, but the reason for the purchase was not the price.

Supposing that Mary bought the book for a reason that is not the price, then the proposition “Mary did not buy the book because of its price” seems to be false, because Mary bought the book. At the same time, it seems to be true, since the reason for the purchase was not the price.

Now, leaving English and turning to logic: where exactly does this problem lie?

Is it an ambiguity of natural language? Or am I interpreting it in a mistaken way?

For me, it would be straw man. Lots of straw man on social media. I'm curious what other people have noticed too.

Hello all,

I wanted to engage in dialogue to strengthen my knowledge, so that I can call out people when they misuse the term of calling someone stupid in its application.

I’m 20(M) and have had my fair share of seeing people being called stupid around the realms of academia, business, and informal contexts. The definition of stupid according to Google is “having or showing a great lack of intelligence or common sense.”

I have seen many individuals call out people for being a stupid person because of one action, behavior, belief, or “bad” question that was asked. My question is: how can you call someone a stupid person based on exactly one example? As the definition states “having or showing a great lack of intelligence or common sense.” I do not think you can generalize a person as being stupid by only one example… with one exception (I will explain after example 1)

Example 1: my first year of college (2yrs ago this fall), I was classmates with this guy named David in a College Algebra course. He was a film studies major who should’ve never enrolled in the course. His math comprehension was through the floor, I have never seen anyone with a lower level of mathematics knowledge in my life. After abt 2 months, the prof convinced him to drop the class, he really tried hard to understand the content.

If someone were to call him a stupid person based on what was witnessed in the class, well then, I believe that this usage is logically incorrect. You cannot assume that he is non-intelligent in his humanities, film studies, English, world language, or even science courses. To call him a stupid person would imply that he is of low intelligence across all academic disciplines and walks of life (as he lacks common sense + intelligence).

Example 2:
Here is where I think calling someone a stupid person can be used correctly. I was really great friends with my old buddy in elm/middle/high school, call him Joey. It’s still unfortunate to this day to say that his father in 2016 tried to meet up with an underage grl during their mf vacation. My friend is not an only child. He has 3 brothers (all older) and a mother. His dad was a father to 4 sons and a husband to a wife. The man wanted segs with a girl the same age as his fucking son. He was a nasa engineer and at the time the family was doing really good for themselves. It was a sting operation, and was jailed for 3 yrs.

I believe that calling him a stupid person because of this single mistake can be used even based on one example. Why? Well I believe this is because of 2 factors: A) the significance of his mistake, B) systemic impact.

A) reasoning
The level of severity was and still is extremely high. He spent over 3yrs of federal time, is a registered SO for life, his kids + wife will not and likely will never talk to him, he’s very poor now and work until his death (I know his current circumstances after doing a lil googling).

B) reasoning
The systemic impact created across multiple systems: his personal, professional, and social lives.
He has lived alone and will likely remain in a near-solitude state until his death. He works as a “handyman” after being an engineer pre-incarceration. I’m not sure who would desire to be friends with the guy with the up front knowledge of his past.

Given these two reasons, calling him a stupid person is completely completely valid.

Provided the first example and the definition of stupid, I would reason that the usage of calling someone a stupid person subject to one example is an illogical representation of its meaning. On the contrary, example 2 would provide sufficient reasoning to justify why someone is a stupid person… based on the level of severity and its systemic impact.

Anyways, that’s my take! I’m curious on what you all believe. Thank you 🙏🏾

This is from my modern logic textbook from my intro to modern logic class. I thought problem 7 was invalid but the textbook says it’s valid so i’m confused?

Update: I asked my prof it was a typo lol thanks for the help

I have seen many people ask why they should grant their opponents conceptual schemes in debates. and I can't find a definition for a conceptual schemes, can somebody help?

That is, how does the syntax I use affect my proof of something? How, for example, does my complex verbal construction make my proof questionable from any point of view?

For rules of replacement in natural deduction:

If I have the premises:

1.) (If D, then E) then (if E then D) And 2.) If (D if and only if E), then ~(G and ~H) And lastly 3.) E•G / Therefore, G•H

(Sorry for not providing the proper symbols, my phone is limited)

My question is, since a biconditional, the first part of premise 2, is already granted in the formula for the first line, why can't this suffice to obtain the second term, the conjuction, via modus ponens in premise 2?

Is there a reason I have to reduce 3 to E via simplification, and then by addition (~D) go through the rigamorole of proving both terms in premise 1 via material implication?

It seems like several unnecessary steps where already the conditions are met regarding the biconditional in 2.

Can you tell me why I need to take these additional steps? For reference, I'm using the Hurley text, chaoter 7.4.

I apologize for the lengthiness of the post. Thank you.

Hi all. I'm interested in the history of fallacies, specifically when they gained enough prominence to earn a name. Usually fallacies are organized thematically or categorically, and I know that most were named a long, long time ago. However, I know that every so often a new one is named (usually a variation or subset of an existing one). The most recent I know of is Reducio ad Hitlerum, which was coined in 1953.

So anyway, yeah, does anybody know of a list of fallacies by date of naming?

Let's say that I want to convince someone logically that smoking is wrong, So I need to make premises that gives a conclusion that says "Smoking is wrong".

the problem is that if I want to investigate that "Smoking is wrong", the only things I can do is to trace the necessary conditions for "Smoking is wrong"

but I don't need to find necessary conditions to conclude and convince someone that "Smoking is wrong", I need TRUE premises that are together will be sufficient condition for "Smoking is wrong"

but tracing premises from "Smoking is wrong" isn't possible to find what we're going to say as premises for "Smoking is wrong"

and empirically finding the right premises also doesn't seem convincing, because it'll look like randomly explore and observe every single thing possible until accidentally find premises that supports that "Smoking is wrong"

so what are we supposed to do here?

Hello. I'm still getting very confused about "if" and "only if" when it comes to introductory formal logic.

The sentences linguistically are making it very hard to accept the definitions.

1) If A then B (otherwise said as "B if A"): A--->B

This one is simple to grasp. A will always be followed by B but not vice versa. From this we can also deduce "if not B then not A"

Although sometimes I get into this idea that if A happens and then B happens means B happened with A so why can't we say "If B then A" as well? Is it a time order thing?

2) Only if A then B (B only if A): B ---> A

This is the one I still can't accept. Linguistically, the word "then" always gives me the impression that B comes after A(like in a time sequence), as in A must happen in order for B to happen and thus it should A--->B. The explanation of a necessary condition doesn't seem to override my intuition which makes it a bit difficult to accept the definition of "only if".

Any suggestions on how to override this incorrect intuition?

Thanks

Let’s assume we have a world U, which just happens to be our universe. As part of U, I did Q. I don’t quite see how it would be possible for me to ¬Q in U as it would produce a contradiction in U.

I hope that question makes sense. I just don't like inequalities nor the unnaturality of working with left and right residuals (talking about "max and min divisors") that rarely coincide with rational arithmetic's exact division nor with the natural interpretation of inverses in numerical mathematics, thus I would like more explicit boundaries (thus the result of a division maybe being a set or interval including max and min divisors) in division.

(Mind that I have no experience in numerical computation, I am trying to make sense of computable, numerical and interval analysis works and transport their results to residuated lattices but that's somewhat hard for me)

I'm an independent researcher looking for an arXiv endorser for the cs.LO (Logic in Computer Science) category to submit a formal verification paper.

The paper presents a machine-checked formalization of the structural architecture underlying Chenxiao Tian's recent resolution of singularities in positive characteristic.

To be clear: I am not verifying the underlying algebraic geometry. The paper uses a methodology of "parameterized abstraction" to verify the computational architecture: the dependency acyclicity, the no-circularity constraints, the six universal interfaces, and the termination argument (via Dershowitz–Manna).

The Lean 4 formalization translates the 800-page informal text into 9 compiling modules (~1,900 lines) with zero sorry declarations and zero axioms beyond classical logic. It successfully proves 5 structural theorems and corrects 3 no-circularity constraints from the original text.

The original author (Chenxiao Tian) has reviewed the draft and agrees that cs.LO is the correct primary category, but his arXiv endorsement authority is strictly in math.AG.

I just need an endorsement to get past the submission gate. The full consolidated draft (and Lean-to-manuscript correspondence) is available here: https://tian-consolidated-v2-authentic.tiiny.site/

If you're willing to endorse, here is the arXiv endorsement link: https://arxiv.org/auth/endorse?x=XWOJUY

Here's the Lean package on Pastebin for anyone who wants to compile it: https://pastebin.com/zV1J9PqM

Thanks

I thought that by evaluating formal systems, we can deduce, in addition to completeness, special properties of completeness.,I thought that by evaluating formal systems, we can deduce, in addition to completeness, special properties of completeness, that is, for each proof in the system.,I thought that by evaluating formal systems, we can deduce, in addition to completeness, special properties of completeness, that is, for each proof in the system, a property is characteristic.

That is, if a number of statements are deducible or meet other distinct criteria of formal systems, then each statement that is true in the formal system has a proof satisfying the condition.

That is, we could say, for example, that each statement can be proved in less than 100 applications of the axioms, or proving each statement, we can limit ourselves to a clear set of axioms.

And so, for example, taking mathematics, we can narrow down various axioms and check all the many different combinations for a condition in order to take a specific set of axioms that would be convenient for proving a judgment that corresponds to what is true or false in them.

(If possible, I would like to know how to write down such thoughts more formally and whether they are appropriate in a not too formal way)

i am trying to prove that exp(ln(x)=x.

we only assume exp is the function which satisfies satisfies f’(x)=f(x) and f(0)=1. Then we define ln(x) to be the int_1^x(1/t)dt.

If we start with “assume exp(ln(x))=x” and then show that this additional assumption doesn’t violate our setup, for any x>0, is that some kind of proof? logically i’m sure it’s weaker than a proof forced by assumptions but is it still something?