Question about None

Steven D'Aprano steven at REMOVE.THIS.cybersource.com.au
Mon Jun 15 06:50:27 CEST 2009


On Sun, 14 Jun 2009 19:14:10 -0400, Terry Reedy wrote:

> Steven D'Aprano wrote:
>> 
>> So-called "vacuous truth". It's often useful to have all([]) return
>> true, but it's not *always* useful -- there are reasonable cases where
>> the opposite behaviour would be useful:
[...]
> It seems to me that the absurd conclusion implied by the theorem
> invalidates the theorem rather than supporting your point.

I wouldn't go so far as to say the vacuous truth theorem ("empty 
statements are true") is invalidated. The Wikipedia article discusses 
various reasons why it's more correct (or at least more useful) to treat 
vacuous statements as true:

http://en.wikipedia.org/wiki/Vacuous_truth

But it's not without difficulties -- however those difficulties are 
smaller than those if you take vacuous statements as false in general.

[...]
> Try finding another 'reasonable case'.

Any time you do something like:

if not x and all(x):
    process(x)


instead of just:

if all(x):
    process(x)


I can't think of a real world example off the top of my head, but here's 
a contrived example demonstrating that vacuous truths imply both a fact 
and it's opposite:


def startswith(s, chars):
    """Return True if s starts with any of chars."""
    for c in chars:
        if s.startswith(c): return True
    return False


if all([startswith(w, "aeiou") for w in words]):
    print "All the words start with vowels."

if all([startswith(w, "bcdfghjklmnpqrstvwxyz") for w in words]):
    print "All of the words start with consonants."


If words is empty, this code claims that all of the words start with 
vowels as well as starting with consonants.

There are, of course, ways to work around that other than rejecting 
vacuous truths. One is to simply use an "elif" for the second test.



-- 
Steven



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