On 6/3/2015 7:16 AM, Brian Tenneson wrote:
On Wednesday, June 3, 2015 at 2:16:31 AM UTC-7, Bruno Marchal wrote: On 02 Jun 2015, at 20:10, Brian Tenneson wrote:Grammatical systems just might be the type of thing Tegmark is looking for that is a framework for all mathematical structures... or at least a large class of them. I am still exploring the idea of grammatical system induction.I am not sure what you mean by grammatical induction. Is that not equivalent with the omega-induction principles, like with PA? It is described in this document: https://docs.google.com/document/d/1amDb4Yti4egpKfcO2oLcnGAH8UpC8_tKb7ivuH3AT7A/edit?usp=sharing
A couple of points I don't understand. First, G is a set of sentences. I'm not sure what "any" means. Does it mean G is all grammatical sentences? Is G assumed finite, or countable? Second, why is H defined as an element of G^n (Cartesian product of sets) instead of just a subset of G? Third, if [H->G] is a function doesn't that implies that T(H) ends with a unique G, which is not generally true of inferences.
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