On Thursday, June 20, 2019 at 5:27:06 AM UTC-5, Bruno Marchal wrote: > > > On 19 Jun 2019, at 12:57, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Wednesday, June 19, 2019 at 5:13:57 AM UTC-5, Bruno Marchal wrote: >> >> >> On 18 Jun 2019, at 12:49, Philip Thrift <[email protected]> wrote: >> >> >> >> On Tuesday, June 18, 2019 at 4:55:01 AM UTC-5, Bruno Marchal wrote: >>> >>> >>> On 13 Jun 2019, at 20:12, Philip Thrift <[email protected]> wrote: >>> >>> >>> Feyerabend wrote of scientific fundamentalism, being indoctrinated into >>> a particular theory as being TRUTH. >>> >>> >>> People seriously claiming truth are con artist only. It is scientism or >>> outright crackpotery. >>> >>> Bruno >>> >>> >>> >>> >> >> >> But what of "The Church-Turing Thesis holds unquestionably”? >> >> >> ? >> >> Everything ( thesis, hypothesis, axioms, … their consequences) is >> questionable. >> >> That is why we make clear our assumptions, so that if and when we find a >> contradiction (internal, external) we can debate which axioms to change, >> which part of the theory to improve, etc. >> >> What is not easily questionable is the validity of the reasoning. The >> fact that CT implies incompleteness, is not seriously questionnable, even >> if we can always suspect a systematic error unseen by anybody, but that is >> true for all knowledge/belief. >> >> Bruno >> >> >> > All "reasoning" (and its "validity") is questionable. > > > Not in first-order logic, and its effective extension, as long as the > length of proofs is human manageable. > > But provably so in the full second-order logic. > > Validity is “mechanically checkable” and this makes sense even without CT! > > That is why logic exist, to separate the notion of validity (checkable) > and notion like proof and truth. > > > > > There is *inconsistent mathematics.* > > > > There are inconsistent theories. Mathematics is a reality, out of the > category of things on which the adjective “consistent” applies. > > > > As an applied mathematician, I relate to it: > > *inconsistent mathematics can have a branch which is applied mathematics* > - https://plato.stanford.edu/entries/mathematics-inconsistent/ > > > The notion of consistency is just related a little bit, using weak logic. > Incompleteness explains why all machines have to do that when they apply > math. > > <>t -> <>[]f. Consistency entails the consistency of inconsistency. > > > > > > > "Incompleteness" arguments have their place, but are not holy writ. > > > Yes. It is just a reality that we have to take into account, and with > mechanism, it is the motor of (dream) creation, somehow. > > Bruno > > >
*Logic is mere heuristics.* It is not Holy Writ the LORD God wrote into Stone Tablets. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3a1264a2-3086-456c-9861-54ca623df0bd%40googlegroups.com.
