> On 12 Dec 2015, at 10:54 , Martin Maechler <maechler at stat.math.ethz.ch> wrote: > > My conclusion: Breaking such a fundamental lemma of logic as > "the empty set is always true"Umm, that doesn't make sense to me. Surely you mean that "an AND-operation over an empty index set is TRUE"? A similar OR operation is FALSE, i.e. they behave like empty products and sums, respectively. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
On 12/12/2015 8:44 AM, peter dalgaard wrote:> >> On 12 Dec 2015, at 10:54 , Martin Maechler <maechler at stat.math.ethz.ch> wrote: >> >> My conclusion: Breaking such a fundamental lemma of logic as >> "the empty set is always true" > > Umm, that doesn't make sense to me. Surely you mean that "an AND-operation over an empty index set is TRUE"? A similar OR operation is FALSE, i.e. they behave like empty products and sums, respectively. >How about "the empty set is all true, and all false."
>>>>> "DM" == Duncan Murdoch <murdoch.duncan at gmail.com> >>>>> on Sat, 12 Dec 2015 09:05:04 -0500 writes:DM> On 12/12/2015 8:44 AM, peter dalgaard wrote: >> >>> On 12 Dec 2015, at 10:54 , Martin Maechler >>> <maechler at stat.math.ethz.ch> wrote: >>> >>> My conclusion: Breaking such a fundamental lemma of >>> logic as "the empty set is always true" >> >> Umm, that doesn't make sense to me. Surely you mean that >> "an AND-operation over an empty index set is TRUE"? A >> similar OR operation is FALSE, i.e. they behave like >> empty products and sums, respectively. >> DM> How about "the empty set is all true, and all false." or, what the I *meant* with the above: "All statements about elements of the empty set are true" ((and I still like the short form, even though it is not correct strictly logically/mathematically)) Of course, Peter is correct, and that any(logical(0)) is FALSE is really the only sensical way.