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- What counts as an argument, technically speaking? [closed] November 15, 2025Lets say there is one premise and one concslusion. Initially I assumed thats an invalid deductive argument. But now I am not so sure, is it an argument at all? Is there a formal definition for an argument / deductive argument, some structure it has to follow to be considered as such? A := It […]Loki
- Combinatorics and logic Olympiad Problem (Requires Proper Proof). I have been thinking this problem for quite a while, looking for the best method. [closed] November 14, 2025Put 77 Chocolate Bars into as few bags as possible such that you can give either 11 children 7 candy bars each with bags or 7 children 11 candy bars each with bags again.Tanish Agrawal
- Is there a complete proof system for deriving some axiom schema from others? November 14, 2025Say that an axiom schema is an algorithm $A$ that produces a family of first-order statements (I believe we can recursively enumerate all the algorithms that produce well-formed sentences). Given axiom schemas $A_1$ and $A_2$, say that $A_1\models A_2$ if any model $\mathcal{M}$ of all the statements enumerated by $A_1$ is also a model of […]Pineapple Fish
- What is Gödel's argument for why his proof for a single system applies to all systems November 13, 2025I'm having trouble understanding how Gödel extrapolates from a consistent formal system to any formal system. For reference, his First Incompleteness Theorem states: Any consistent formal system $F$ within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of $F$ which can neither be […]Ben
- Ordinal definability of a minimal witness in L(R, Hom) November 13, 2025Recall that for a transitive set $X$, $L(X)$ is class of sets constructible from $X\cup\{X\}$. For some reason I need to show that every element of $L_\alpha(X)$ is ordinal definable over $L_\alpha(X)$ using parameters from $X$ [1]. I am proving this by induction on $\alpha$, but given limit $\alpha$, if $x\in L_\beta(X)$, then we only […]Akira Satou
- Relation between Tarski's conception of truth and (implicit) Axioms November 11, 2025I am trying to understand the original paper of Tarski Concept of Truth in the formalized languages, as printed in his collected works. I have read introductory texts from Shoenfield Mathematical Logic (only first 5 chapters thoroughly) and Ebbinghaus, Flum, Thomas Introduction to mathematical logic, as well as early graduate course in logic. but other […]Alexander Wagner
- What does $\forall x\exists x P(x)$ mean? [duplicate] November 10, 2025Is this even a valid formula syntactically? Implies "for all $x$ there is an $x$" that the $\forall x$ is redundant, because obviously there is an $x$? Or is the variable in the new context (after $\forall x$) an other entity and treated like a differently named variable (let's call it $y$)? So basically is […]Janek
- The necessity of introducing CwF for the categorical semantics of Martin-Löf theories? November 10, 2025This question involves two simple subquestions regarding the intuition of necessity of introducing CwF (Category with families) as categorical semantics of Martin-Löf theories. (Note that I'm not familiar with categorical logic and type theory so some questions may not even make sense.) First of all I want to know what does the coherent problem break, […]Westlifer
- Empty Set question from Terence Tao's Analysys I [closed] November 9, 2025Axiom 3.2 (Empty set). There exists a set ∅, known as the empty set, which contains no elements, i.e., for every object x we have x ∈ ∅. The empty set is also denoted {}. Note that there can only be one empty set; if there were two sets ∅ and ∅` which were both […]g0r
- Guessing the outcome of a coin toss with a probability greater than 0.5 November 9, 2025I stumbled across an answer about The envelope paradox which states that: Let Player 1 write two different numbers on two slips of paper. Then player 2 draws one of the two slips each with probability $\frac{1}{2}$ and looks at its number $x$ and has to guess wether $x$ is the larger or the smaller […]math_survivor
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