The truth is built of true facts and untrue facts: facts that are not based on a system of observation yet are true anyway. Nevertheless, Wittgenstein seems to disagree with Gödel’s incompleteness theorem. Food for a lasting scientific debate. Anyway, Wittgenstein was looking at language and philosophy, not at mathematics.
Final remarkable mathematical truth for now from Cantor.
As an example, Cantor proved that real numbers are more numerous than the set of natural numbers. While both are infinite. He also invented a way to operate on infinite sets.
Cantor ended up in a mental hospital, which seems to be viewed as as heroic achievement among mathematicians—an opinion I do not share.
I recall reading The Mystery of the Aleph by Amir D. Aczel about Cantor. Unfortunately, I have lost my notes and the book. This book was very accessible, I do recall that.
In the 30th anniversary edition of ‘The Selfish Gene’ (2006) Richard Dawkins writes a vile but correct comment on Fred Hoyle‘s misrepresentation of Darwinism in an endnote (pp. 277-278). He ends his note:
‘Publishers should correct the misapprehension that a scholar’s distinction in one field implies authority in another. And as long as that misapprehension exists, distinguished scholars should resist the temptation to abuse it’.
Very true, though on the same page, in the note referenced on this page (page 59 of the 30th Anniversary edition), Dawkins almost falls into his own trap, saving himself with one little sentence.
Richard Dawkins
The note’s text to the main text is so incredibly incorrect that it is quite funny, given he does this on the same page as his scolding on Hoyle.
In the note, Dawkins wants to explain Daniel Dennett‘s theory of consciousness. Although Dennett has tried to explain his ideas in several books, Dawkins wants to summarize Dennett’s work in this two-page note for unclear reasons.
Daniel Dennett
Dawkins takes two technical ideas from the world of computers to illustrate his ideas: the concept of a virtual machine and the ‘the distinction between serial and parallel processors’. Dawkins starts out by explaining completely incorrectly what a virtual machine is. He mentions the Macintosh User Interface as an example of a virtual machine. The Mac is a great machine, but the Macintosh User Interface has very little to do with a virtual machine, and the connection with consciousness remains very unclear. Dawkins could have simply relied on the Wikipedia article for a correct description of virtual machines.
The story derails entirely when Dawkins turns to his description of ‘serial and parallel processors’. The piece is so incorrect that highlighting the individual errors here does not make sense. Since Dawkins fails to see the distinction between processors and processes, he starts wrong and worsens things in every sentence. And it’s not like this was rocket science at the time of writing. Parallel processing has been known and applied in computing since our ownEdsger Dijkstra and others invented concepts like the semaphore and the indivisible instruction.
More linkages to Dennett’s work and that of his friend Douglas Hofstadter on page 59, where Dawkins discusses self-awareness and rejects ideas of self-awareness because
So, can we conclude that Dawkins has fallen into the trap of asserting that a scholar’s distinction in one field implies authority in another?
As I said, almost. On page 280 Dawkins saves himself, on the edge, with this little remark:
‘The reader is advised to consult Dennett’s own account when it is published, rather than rely on my doubtless imperfect and impressionistic – maybe even embellished – one.’ How true.
I have never had such fun with academic footnotes.
