An old puzzle: The average mother has 3.4 children. Yet the average
mother does not exist. So how can she have children? An old solution: She
doesn't. "The average mother has 3.4 children" is to be understood as
"the number of children divided by the number of mothers is 3.4". So
"average mother" is not a genuine predicate, but rather a meaningless part of
numerical predicates like "the average mother has ... children".
If this solution is correct, it is meaningless to say that average
mothers exist, that some of them influence others, and that all of them
are distinct. Which indeed it is.
I've just included automatic validation of each posting by the W3C HTML validator. To turn this on, you have to set
$blog->validateHTML = true;
in settings.inc.
Ab zum Eimer.
While I'm at it: some other things I've done recently are improving the Tree Proof Generator (in particular, the proofs are now drawn on a separate page, so that you can get back to the form by hitting your browser's back button), writing a summary of Frege's "Grundgesetze der Arithmetik" (in German), and finding a new flat.
I rewrote my blogger to make it more flexible. Among other features it now contains a pingback user agent (still no trackback support, though).
Postbote now automatically looks for new mails (there's a preference for how often it does that), lists only 20 mails simultaneously (there's another preference for changing this value), and creates popups for writing mails.
Email me if you have any problems with these features or anything else.
I've added another project to my list: Digital: A Frontend for Analog. Like most things I program, this is something many other people have made before, and most likely some of them did it much better.
I've spent some more time on the Tree Proof Generator. The algorithm is now a lot faster, more information is displayed during calculation, and there are new buttons to control the drawing.
This formula (the last one on the Examples page) is quite interesting: After the quantifiers have all been dealt with, there are 36 formulas on the tree that have to be broken down by the truth-functional rules. I let it run for several hours. When finally Mozilla ran out of memory it had developed just 25 of those 36 formulas, building a tree with 179797 nodes!
I've got that formula from David Bostock's very fine book "Intermediate Logic", where he says that "the tedium of writing out a completed tableau" for this formula would be "very considerable" (p.177).
Indeed.
Ich habe
Magdalenas Blogger ein bisschen weiter entwickelt und verwende ihn jetzt auch für diese Spalte. Vielleicht schaffe ich damit, hier ab und zu über Neuigkeiten zu berichten.