XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/7/2025 1:16 AM, Ross Finlayson wrote:   
   > On 12/06/2025 08:58 AM, olcott wrote:   
   >> On 12/6/2025 10:28 AM, Ross Finlayson wrote:   
   >>> On 12/05/2025 05:38 PM, olcott wrote:   
   >>>> Not one person can post a single date/time stamp   
   >>>> or Google groups link to show otherwise.   
   >>>>   
   >>>> The strongest of these fake rebuttals was:   
   >>>> "that is not how we memorized it".   
   >>>>   
   >>>   
   >>> "Overgeneralizations are generally un-sound."   
   >>>   
   >>>   
   >>> Now, as somebody who's interested in contrary opinions,   
   >>> yet not contrarians for contrarianisms sake,   
   >>> and somebody who's demonstrated that various widely   
   >>> held opinions in logical fields like logic are questionable,   
   >>> and both fraglich and fragwurdig (dubitable and question-raising),   
   >>> and indeed have some what may be "more true" implications,   
   >>> after something like Goedelian incompleteness some   
   >>> kind of super-Goedelian completeness,   
   >>> as somebody interested in rational contrary opinions   
   >>> for conscientious reasonings' sake, has that   
   >>> usual notions of the constructible vis-a-vis universal   
   >>> to be fair, are extra-ordinary.   
   >>>   
   >>> Don't get me wrong, there's the great hypocrisy of   
   >>> the ordinary Russell-ian retro-thesis that has readily   
   >>> demonstrable that adherence to it is an "inductively sound"   
   >>> yet "generally un-sound overgeneralization", so that   
   >>> there's a taint of guilt on any soi-disant logician   
   >>> who mistook "isolation and significance" for "completion   
   >>> and relevance".   
   >>>   
   >>>   
   >>> Or, as was written around here somewhere   
   >>> "hone-ey swah key maal ee ponce", yet,   
   >>> you know, "heal thyself".   
   >>>   
   >>>   
   >>> If you really want extra-Goedelian completeness then   
   >>> it demands a rather thorough account of theory and   
   >>> "the generally sound universal overgeneralization".   
   >>>   
   >>>   
   >>   
   >> I have never considered any kind of overgeneralization.   
   >> So I need much more elaboration before I can respond.   
   >>   
   >> My complete system would simply be the complete set of   
   >> atomic facts of the actual world and everything that   
   >> can be semantically entailed from them. Like Saul Kripke   
   >> already proved self-referential paradoxes cannot   
   >> be derived from such a system.   
   >>   
   >> https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/   
   >> files/2019/04/Outline-of-a-Theory-of-Truth.pdf   
   >>   
   >>   
   >> I try to as much as possible only form conclusions on   
   >> the basis of semantic logical entailment from   
   >> self-evidently true expressions of language.   
   >>   
   >   
   > A complete ontology sounds pretty general, ...,   
   > not much more general than that.   
   >   
   > First of all you need to eliminate the "material implication"   
      
   Yes I think that I discovered that.   
      
   A deductive argument is said to be valid if   
   and only if it takes a form that makes it   
   impossible for the premises to be true and   
   the conclusion nevertheless to be false.   
   Otherwise, a deductive argument is said to   
   be invalid. https://iep.utm.edu/val-snd/   
      
   This seems to stupidly allow false conclusions   
   to be drawn from false premises and still be   
   considered valid.   
      
   My first incremental change would require   
   a conclusion to be a necessary consequence of   
   all of its premises. I would use the modal   
   logic necessarily operator □ as a binary   
   operator.  H1,..., Hm □ C to adapt Mendelson.   
      
   The next change is much larger. I would use   
   Rudolf Carnap / Richard Montague Meaning   
   Postulates that can mathematically anything   
   that can be expressed in natural language   
   (such as English).   
      
   declarative   
   interrogative   
   imperative   
   exclamatory   
   The entire body of general knowledge would be stored   
   in a knowledge ontology as formalized natural language.   
   https://en.wikipedia.org/wiki/Ontology_(information_science)   
      
   We end up with something like this fully populated with   
   the set of basic facts and the relations between them.   
      
   Kurt Gödel in his 1944 Russell's mathematical logic gave   
   the following definition of the "theory of simple types"   
   in a footnote:   
      
   By the theory of simple types I mean the doctrine   
   which says that the objects of thought (or, in   
   another interpretation, the symbolic expressions)   
   are divided into types, namely: individuals,   
   properties of individuals, relations between   
   individuals, properties of such relations, etc.   
   (with a similar hierarchy for extensions), and   
   that sentences of the form: " a has the property   
   φ ", " b bears the relation R to c ", etc. are   
   meaningless, if a, b, c, R, φ are not of types   
   fitting together. Mixed types (such as classes   
   containing individuals and classes as elements)   
   and therefore also transfinite types (such as   
   the class of all classes of finite types) are   
   excluded. That the theory of simple types suffices   
   for avoiding also the epistemological paradoxes   
   is shown by a closer analysis of these.   
   (Cf. Ramsey 1926 and Tarski 1935, p. 399).".[24]   
      
   [24] page 455   
   https://lawrencecpaulson.github.io/papers/Russells-mathematical-logic.pdf   
      
   > or the "quasi-modal" logic more broadly, then what gets involved   
   > is the consideration of paradox-free reason _after_ confronting   
   > the paradoxes of logic,   
      
   Yes I have thoroughly done that, two different ways.   
   Paradox proves that our reasoning is somehow incorrect.   
   One of these ways is similar to Saul Kripke   
      
   https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/file   
   /2019/04/Outline-of-a-Theory-of-Truth.pdf   
      
   Here is my way of saying that. Paradox cannot be derived   
   by applying semantic logical entailment on the basis   
   of a complete and finite set of atomic facts.   
      
   Here is the other way the eliminates Paradox of self-reference   
   This short Prolog shows the error of the Liar Paradox   
   ?- LP = not(true(LP)).   
   LP = not(true(LP)).   
   ?- unify_with_occurs_check(LP, not(true(LP))).   
   false.   
      
   This means that the directed graph of the evaluation   
   sequence has a cycle meaning that the evaluation of the   
   Liar Paradox cannot possibly be resolved to a truth   
   value, thus never was a truth bearer or a proposition.   
      
   It expands to this: (and never terminates)   
   not(true(not(true(not(true(not(true(not(true(...))))))))))   
      
   > which are found simply results of competing   
   > rulialities in real mathematical structures, that mere inductive   
   > inference will always fail to find, while though that a wider, fuller   
   > dialectic of the deductive inference may relate to real mathematical   
   > structures of the continuous and infinite and about motion and time,   
   > then to arrive at the "extra-ordinary" of logic, "non-standard" as   
   > sometimes it's called, since otherwise it's just a retro-finitist   
   > retro-thesis.   
   >   
      
      
   [continued in next message]   
      
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