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
- What is the most primitive notion in mathematics? May 30, 2023I had a recent conversation with a professional mathematician about the status of relations, functions and predicates. I was arguing that it seems intuitive (to me at least) to classify them in this hierarchy (as to which is more primitive): All predicates are functions. All functions are relations. The obvious problem here is that it […]daegontaven
- Who invented a way to measure the consistency of logical statements using cosine distance? May 30, 2023It seems as if the consistency of logical propositions is amenable to being measured using cosine distance. let $\ell$ be such a metric. For any proposition $P$, it is the case that $P$ is consistent with itself, so $\ell(P, P) = 1$ For any proposition $P$, it is the case that $P$ is not consistent […]Lisramic
- Using Fitch proof system to for: Given ¬q, (¬p⇒(¬q⇒¬r)), (s∨r), (s⇒t), and (p⇒t), prove t. May 30, 2023I've been tasked with using the fitch proof system to do the to complete the following proof: Given ¬q, (¬p⇒(¬q⇒¬r)), (s∨r), (s⇒t), and (p⇒t), prove t. I'm experiencing difficulty getting this done. I've tried by assuming ¬t, proving a contradiction and thereby deriving ¬¬t, and then using negation elimination to get t. I've also tried […]JCKing87
- Is there an efficient algorithm for finding rows that have the same sum of column values up to a threshold value? May 30, 2023I have a table like this (more specifically a nested dictionary) img a b c d e 1 img 0 0 1 0 1 2 img 3 1 0 0 2 3 img 4 0 0 0 1 4 img 2 2 0 0 0 5 img 0 0 0 0 2 6 img 2 […]Jeni
- For JJ Smith's propositional logic trees, why is the negated biconditional used for equivalence instead of simply α and ¬β? May 30, 2023The tree tables are testing for satisfiability, and in this case we are testing if two formulas α and β are equivalent. The negated biconditional ¬(α ↔ β) represents a contradiction if the two formulas are equivalent, therefore all paths will close on the tree. However, if the two formulas are equivalent, would doing a […]salparadis0
- Is "$(\exists z)$ the sky is blue" a proposition? May 30, 2023Is "$(\exists z)$ the sky is blue" a proposition? I am unsure as this sentence certainly states something which could be either true or false; however the $(\exists z)$ seems meaningless here- I am unsure if the fact that $z$ is unused after it has been quantified is relevant here. ThanksGod
- Are "∀x ∈ R" and "∃x ∈ R" propositions? May 30, 2023Is the proposition which consists solely of "∀x ∈ R" considered true because x does not fail to satisfy any conditions we lay out? Or is it not a proposition? Is the proposition which consists solely of "∃x ∈ R" considered true because we are asserting the existence of a real number? Or is it […]God
- Who is the "$\Pi_2$-soundness" version of the first incompleteness theorem due to? May 30, 2023I'm trying to remember who is responsible for the following well-known weak version of the first incompleteness theorem: Suppose $T$ is a c.e. consistent $\Pi_2$ extension of Robinson's $\mathsf{Q}$ (or any c.e. consistent theory which interprets such). Then $T$ is incomplete. Proof: we can computably enumerate the indices of $T$-provably-total computable functions, and then diagonalize […]Noah Schweber
- In consecutive statements, are conjunctions implicit? May 30, 2023Is it fine to abbreviate $∃x [P(x)∧Q(x)]$ as $∃x P(x)Q(x)$?God
- prove that the models are equivalent May 29, 2023Let $L$ be a lexicon given by $L = \{R^2\}$, where $R$ is a binary relationa7777
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