Written work – None.
WeBWorK – Assignment #5, due Tuesday, October 9th, at midnight.
OpenLab – OpenLab #4, due Thursday, October 11th, before class.
Logic on Math StackExchange
- How to construct a propositional logic formula to enforce a certain relation? December 11, 2024Disclaimer: this is a question from a homework but i am really struggling with it and would like to get some help. I have a set of students $S$, set of Time-slots $T$,set of cookies $P$ and the relation $M \subseteq (S\times P)$ where each tuple means that the student likes that cookie type. now […]fady abo swees
- What is wrong with my Prenex normal form? December 11, 2024I had this equation $$∃yG(y)→¬(∀xF(x,y)↔G(y)).$$ Then I turned it to $$∀y(¬G(y)) \lor ∀x(F(x,y))\land ¬G(y) \lor ∃x(¬F(x,y))\land G(y).$$ Then I turned it to Prenex normal form: $$∀k∀s∃m(¬G(k) \lor F(s,y)\land ¬G(y) \lor ¬F(m,y)\land G(y)).$$ My professor says that something is wrong with my last equation. She said that I used too many quantifiers and changed the meaning […]Пчеловод
- The definition of inconsistency in a logical theory [duplicate] December 11, 2024A classical definition of inconsistency is the theory leads to contradictory statements Shoenfield: Mathematical Logic defines this on page 42 that A theory T is inconsistent if every formula of T is a theorem of T I guess this is because in classical logic there's the ex falso quodlibet rule, from false implies everything, which […]Gergely
- Unsure about soundness of proof about transitivity. December 11, 2024sorry in advance for any imprecision, missing tags etc but this is my first question. I'm reading Daniel J. Velleman 'How To Prove It' and i'm having a hard time understanding how to write a sound proof. I encountered an exercise that i think can help me understand a lot and since there is no […]Luca
- Would solving the Liar's Paradox allow for self-meta-logics? December 11, 2024By self-meta-logic, I mean a logic that is its own meta-logic; a logic that can talk abouts its models. If I understand correctly, this is impossible (for "interesting" logics at least) due to Tarski's Undefinability Theorem. Any "interesting" logic will derive this theorem, which means that if that logic contains a truth predicate, it would […]user110391
- Is there a "tree of derivations" construction? December 10, 2024My question stems from the following observation: in Logic we construct a series of finitary syntactical structures by means of trees. First we have the base constants, variables, and function symbols, from which we make terms through chains (i.e. trees). From there we construct formulas as trees whose nodes are our previously constructed terms + […]Sho
- Maximum cardinality of a collection of sets of integers with pairwise finite intersections [duplicate] December 9, 2024Let $\mathcal{C}$ be a collection of subsets of $\mathbb{N}$ such that any two distinct $U,V\in\mathcal{C}$ have finite intersection $U\cap V$. Then what can be said about the cardinality of $\mathcal{C}$? I have a construction showing $|\mathcal{C}|=\aleph_1$ is possible, but I don’t know if $|\mathcal{C}|=|\mathbb{R}|$ is possible. My construction uses transfinite recursion and the axiom of […]SmileyCraft
- Is there a syntactic "higher-up" to derivations? December 9, 2024The question is likely to be illposed, but I was wondering whether there was some known syntactic "higher-up" to the notion of derivation of semi-exoteric use. By this I mean: when working in $\mathsf{PA}$, we make use of digitalization so as to encode finite structures such as: lists, trees, and —on the syntactic side of […]Sho
- "You cannot engage in argument unless you rely on the principle of non-contradiction" December 9, 2024A very good SEoP article "Aristotle on Non-contradiction" by Paula Gottlieb makes two interesting claims, one after the other: Claim 1: "Anyone asking for a deductive argument for PNC [the principle of non-contradiction], as Aristotle points out, is missing the point, or, rather, is asking for something that is impossible without using PNC." Claim 2. […]logiclearner
- Why does "p⊃q" instead of "q⊃p" mean "if p then q"? [closed] December 9, 2024The “if-then” sentence is called a conditional and will be symbolized as (p ⊃ q). The part to the left of the horseshoe is called the antecedent (what comes before), and the part to the right of the horseshoe is called the consequent (what comes after). So why does "p⊃q" instead of "q⊃p" mean "if […]陈海斌
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