> On 19 Jun 2019, at 12:57, Philip Thrift <[email protected]> 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] <javascript:>> >> 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/ > <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 > > @ > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/84b359a5-8239-4030-9c58-79800b360882%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/84b359a5-8239-4030-9c58-79800b360882%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/CA76C743-255D-4F23-9948-82CD9667A5F9%40ulb.ac.be.
