Re: Readings in (some of the) foundations of mathematics --- tree of knowledge

[ Followup-To: set ]

In comp.theory olcott <[email protected]> wrote:
> On 7/4/2026 9:07 AM, Alan Mackenzie wrote:
> > In sci.math olcott <[email protected]> wrote:

> > [ .... ]

> >> A complete finite list of "atomic facts" of general
> >> knowledge tells us everything that can be expressed
> >> in language. This finite list also has all of the
> >> kinds of relations between these facts.

> > Seems doubtful.  Falsehoods can also be expressed in language, together
> > with that vast trove of expressions which are neither true nor false.  In
> > fact, when it comes to "everything that can be expressed in language", a
> > list of "atomic facts" would appear to be unhelpful, just as much as a
> > list of "atomic falsehoods" would be, whatever that might mean.


> A complete finite list of "atomic facts" of general knowledge
> only includes true truth bearers and only facts that cannot
> be derived from anything else. This excludes falsehoods and
> expressions that are neither true nor false. It is the axiomatic
> basis of knowledge of the world.

WHOOOOSHHH!  (The loud noise of you completely missing the point of my
post.)

Let's start again.  A complete list of "atomic facts", were such
possible, would tell you NOTHING about what can be expressed in language.
Your favourite nonsense quote about green thoughts sleeping furiously is
just as expressible as "Olcott is intelligent" or "the halting problem is
solvable".  Expressibility has no connection with truth or falsehood or
provability.

> -- 
> Copyright 2026 Olcott

-- 
Alan Mackenzie (Nuremberg, Germany).