Week 2 Assignments
Written work – none
WeBWorK – Assignment #1 and #2, due Tuesday, September 6th, at midnight.
OpenLab – OpenLab #2, due Thursday, September 8th, at the start of class.
Logic on Math StackExchange
- functions inheriting structure from the structure of the codomain December 5, 2023This question is kind of vague and I'm just asking for a reference. I have noticed the following 'behaviour' in many instances in mathematics. Example 1. Let $ (M,+,*)$ and $(N,\hat{+},\hat{*} $ be $R$-modules, then $\text{Hom}_R(M,N)$ is an abelian group and this is only due to the fact that $(N,\hat{*})$ is an abelian group. Example […]El Ruño
- Assuming a theory is a set of logic sentences, what makes a theory weaker than another in propositional logic? December 4, 2023I've come across the term "weaker set" when studying logic. I'd like to know what makes a set A of logic sentences "weaker" than a set B. Is it because A is smaller than B or is it because the set of every consequences of A is smaller than the set of every consequences of […]Jonas
- Prove that the following formula is a theorem using general resolution. December 4, 2023This is the formula. Prove it is a theorem using general resolution. A∨(B→C)→(A∨B)→(A∨C) I'm going to be completly honest, I tried solving it using ChatGPT but the results were unreliable. I don't know how to solve it because I haven't been to class. Please help.KillHorizon23
- Context where people either always lie or always tell the truth : which question to ask? December 4, 2023The problem takes place on an island where all the inhabitants are either “knights” who always tell the truth or “knaves” who always lie. What one question might be asked of an islander to find out where a road leads-to the city of knights or to the city of knaves? I have tried multiple random […]DIVYANSH SHANKAR
- propsitional logic exersice December 4, 2023Show that [(p ∨ q) ∧ (r ∨ ¬q)] → (p ∨ r)] is a tautology by making a truth table, and then again by using an argument that considers the two cases “q is true” and “q is false” I need help on this one .maryam
- Laws of Form: Reformulation or New Mathematics? December 3, 2023I was recently made aware of Spencer-Brown's work (see his book) on what is known as Laws of Form (LoF) or Calculus of Indications. I did find some very sparse literature on the subject, including a well written draft by Kauffman. I am naturally skeptical of relatively unknown theories that make grandiose claims, so mathematical […]Pellenthor
- Does logical consequence in classical logic assume finitely many premises/conclusions? December 3, 2023In logic one often reads $\Gamma \vdash$ A or $\Gamma \vDash$ A. Can one assume in classical logic (PL, FOL, Higher Predicate Logic, Modal Logic) that $\Gamma$ always is a set of finitely many statements, i.e. $\Gamma$ = {$p_{1}, …, p_{n}$} (as well as A if A stands for a set of statements)? I think […]God
- How to prove that $\lnot(a \neq b)$ doesn't imply $a=b$ in intuitionistic logic? December 3, 2023I tried to prove that $\lnot(a \neq b)$ doesn't imply $a=b$ in intuitionistic logic. I used LEM for this proof: $\lnot(a \neq b)$ : $a=b$ $\lor$ $a \neq b$ Let $a=b$. Then statement $a \neq b$ is false and we use statement $\lnot(a \neq b)$. For this statement we don't have that $a=b$ but we […]Mike_bb
- Is there any logic system which ENTIRELY rejects non-contradiction of any kind for any sentence (i.e. all contradictions are true)? Is this possible? December 3, 2023I've recently learned about paraconsistent and intuitionistic logic, and dialetheism. According to the Stanford Encyclopedia of Philosophy's page on Dialetheism, it states: Dialetheism is the view that some contradictions are true. Likewise, it also states: Dialetheic paraconsistency has it that some inconsistent but non-trivial theories are true. As per the following answer on Math StackExchange, […]setszu
- Proof that LEM is equivalent to the well-ordering of $\Bbb{N}$ December 3, 2023John L. Bell's Intuitionistic Set Theory contains an exceedingly slick demonstration that the law of excluded middle is equivalent to the well-ordering of the natural numbers $\Bbb{N} := \{ 0, 1, 2, ... \}$ - a demonstration so slick, I find myself doubting it. His logic runs as follows: let $p$ be some logical proposition, […]Rivers McForge
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