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Groups > comp.ai.philosophy > #34819
| From | olcott <polcott333@gmail.com> |
|---|---|
| Newsgroups | comp.theory, comp.ai.philosophy, sci.logic, sci.math |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Date | 2026-06-26 21:00 -0500 |
| Organization | A noiseless patient Spider |
| Message-ID | <111nard$vb4e$1@dont-email.me> (permalink) |
| References | (26 earlier) <111n567$u0m6$1@dont-email.me> <111n6lr$udqn$1@dont-email.me> <111n80h$u0m6$2@dont-email.me> <111n9jn$v2ar$1@dont-email.me> <111naal$u0m6$3@dont-email.me> |
Cross-posted to 4 groups.
On 6/26/2026 8:51 PM, dbush wrote: > On 6/26/2026 9:39 PM, olcott wrote: >> On 6/26/2026 8:11 PM, dbush wrote: >>> On 6/26/2026 8:48 PM, olcott wrote: >>>> On 6/26/2026 7:23 PM, dbush wrote: >>>>> On 6/26/2026 8:05 PM, olcott wrote: >>>>>> On 6/26/2026 6:18 PM, dbush wrote: >>>>>>> On 6/26/2026 6:58 PM, olcott wrote: >>>>>>>> On 6/26/2026 5:08 PM, dbush wrote: >>>>>>>>> On 6/26/2026 6:01 PM, olcott wrote: >>>>>>>>>> On 6/26/2026 2:55 PM, dbush wrote: >>>>>>>>>>> On 6/26/2026 3:38 PM, olcott wrote: >>>>>>>>>>>> On 6/26/2026 2:17 PM, dbush wrote: >>>>>>>>>>>>> On 6/26/2026 3:07 PM, olcott wrote: >>>>>>>>>>>>>> On 6/26/2026 1:51 PM, dbush wrote: >>>>>>>>>>>>>>> On 6/26/2026 2:48 PM, olcott wrote: >>>>>>>>>>>>>>>> On 6/26/2026 1:14 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>> On 2026-06-26 11:22, olcott wrote: >>>>>>>>>>>>>>>>>> On 6/26/2026 11:08 AM, dbush wrote: >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>>> the statement "no number is equal to its >>>>>>>>>>>>>>>>>> successor" is not provable.While this statement >>>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x). >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>>> Then to put things in words you can understand: >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> "I am driving to Walmart to buy a carton of >>>>>>>>>>>>>> Breyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>>> in PA. >>>>>>>>>>>>>> In both cases the semantics in not represented in PA. >>>>>>>>>>>>> >>>>>>>>>>>>> Not applicable, as that is not a sentence in PA. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> It is expressed in PA >>>>>>>>>>> >>>>>>>>>>> False. The above is not a sentence of PA. >>>>>>>>>>> >>>>>>>>>>>> to the same degree that G is expressed >>>>>>>>>>>> in PA has a huge natural number. The semantics of it and >>>>>>>>>>>> the semantics of G are neither expressible in PA. >>>>>>>>>>> >>>>>>>>>>> False. G is simply a sentence like ~∃x x>10 v x<5 but much >>>>>>>>>>> more complex. >>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>>> "No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>>> it, "out- of- scope"). >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>>> then it is not actually expressible in Q. >>>>>>>>>>> >>>>>>>>>>> "No number is equal to its successor" is a sentence in the >>>>>>>>>>> language of Q. More formally, it is this: >>>>>>>>>>> >>>>>>>>>>> ~∃x x=S(x) >>>>>>>>>>> >>>>>>>>>>> And this sentence is not provable from the axioms of Q (or, >>>>>>>>>>> in terms you would understand, the above is "out-of-scope" of >>>>>>>>>>> Q). >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> OK I checked the details so I need to make my >>>>>>>>>> language more precise. >>>>>>>>>> >>>>>>>>>> Within proof theoretic semantics any expression >>>>>>>>>> that cannot be proven in Q is not semantically >>>>>>>>>> grounded in Q. >>>>>>>>>> >>>>>>>>>> >>>>>>>>> >>>>>>>>> In your own words, what does it mean for a statement to be >>>>>>>>> "semantically grounded" in a formal system? >>>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>> I always do back-chained inference because the typical >>>>>>>> math way of doing forward chained inference may take >>>>>>>> an infeasibly long time. A finite set of back-chained >>>>>>>> inference steps from x to the axioms of Q. >>>>>>> >>>>>>> Back or forward chained doesn't matter, it's essentially the same >>>>>>> steps in a different direction. But in any case, you're saying >>>>>>> "semantically grounded" is just another synonym for unprovable. >>>>>>> >>>>>>> So to again put things in a way you'll understand, Godel proved >>>>>>> that any axiom system of arithmetic contains statements that are >>>>>>> not semantically grounded. >>>>>>> >>>>>> >>>>>> Not quite. G is not semantically grounded >>>>> >>>>> i.e. unprovable >>>>> >>>>>> in PA >>>>>> yet G is semantically grounded >>>>> >>>>> i.e. provable >>>>> >>>>>> in metamathematics. >>>>> >>>>> Which is exactly what Godel proved. >>> >>> Your lack of response indicates that you agree with Godel, but used >>> different words to do so. >>> >>>>> >>>>>> When an expression in PA only derives semantic >>>>>> meaning in PA when grounded in PA then G has no >>>>>> meaning in PA. >>>>> >>>>> i.e. if a statement is unprovable in PA then it's unprovable in PA. >>>>> >>>>> In other words, a meaningless tautology. >>>>> >>>>>> >>>>>>> That also means that, using your terminology, it has been proven >>>>>>> that the statement ~∃x x=S(x), i.e. "No number is equal to its >>>>>>> successor", is not semantically grounded in Q. >>>>>>> >>>>>> >>>>>> Thus is meaningless in Q and out-of-scope in Q. >>>>> >>>>> Which means the semantically valid statement in Q >>>> >>>> does not include ~∃x x=S(x) >>> >>> False, as it means "no number is equal to its successor", and the >>> concept of a successor and equality have semantic meaning in Q, as >>> does the concept of "all", "none", and "exists". >>> >> >> If there is no sequence of inference steps in Q from >> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >> ungrounded in the PTS atomic base of Q. > > In other words, ~∃x x=S(x) is unprovable in Q, as is commonly known. > > So once again, you agree with everyone else, but are using different > words to say so. > The big change is that undecidability is construed ether as semantic incoherence or as in the truth value of the Goldbach conjecture currently unknown. This is the best example that can possibly exist of proof theoretic semantics incoherent semantics. % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-24 15:26 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:21 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-25 11:14 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-26 09:39 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 08:10 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 09:20 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 08:45 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 09:57 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 09:24 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 12:08 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 12:22 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 13:25 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 12:39 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 13:42 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 12:53 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 14:02 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge André G. Isaak <agisaak@gm.invalid> - 2026-06-26 12:14 -0600
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 13:48 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 14:51 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 14:07 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 15:17 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 14:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 15:55 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 17:01 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 18:08 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 17:58 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 19:18 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 19:05 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 20:23 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 19:48 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 21:11 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 20:39 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 21:51 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 21:00 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-27 11:05 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:48 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:35 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 13:27 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 14:29 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 13:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 14:39 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:01 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 15:04 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:16 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 15:23 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:40 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 15:54 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:04 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:11 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:17 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:22 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:27 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:30 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:36 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:52 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:59 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 16:24 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 17:50 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:11 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:15 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:18 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:21 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:29 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:33 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:44 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:53 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 18:27 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 19:33 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 18:59 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 21:13 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 20:33 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 12:38 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 12:31 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-28 22:12 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:23 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-29 08:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-30 10:48 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-30 08:43 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:01 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-01 10:09 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:43 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-30 09:22 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:13 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-01 10:13 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:44 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-02 09:45 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-02 08:16 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-02 11:47 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:15 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-03 11:41 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-03 10:23 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-03 10:34 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-03 13:17 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-03 13:36 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-03 18:14 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:02 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-04 09:58 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-04 08:24 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:39 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-03 11:43 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:22 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-04 08:29 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Alan Mackenzie <acm@muc.de> - 2026-07-04 14:07 +0000
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-04 11:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Alan Mackenzie <acm@muc.de> - 2026-07-04 17:42 +0000
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:38 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge André G. Isaak <agisaak@gm.invalid> - 2026-06-27 13:40 -0600
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:46 -0500
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