Robert Hansen (RH) posted Nov 28, 2012 7:26 AM (GSC's remarks interspersed): > > On Nov 27, 2012, at 5:51 PM, Joe Niederberger > <firstname.lastname@example.org> wrote: > > > Your war against common sense though,... > > I have no war against common sense. That would be > like having a war against taste or smell. My claim is > simple. Common sense just isn't synonymous with > mathematics, or more precisely, with reasoned thought > and analysis. In fact, the two domains share nothing > in common, no pun intended. Regardless of the fact > that reasoned thought can explain common sense and > fathom its examples, it acts entirely in spite of > common sense. And "commonplace" is certainly not > synonymous with "common sense". That has a different > meaning altogether. > As so often, RH's claims arise out of a total misunderstanding of just what he is writing about, in this case, about what 'common sense' may be; and just what its derivates, such as 'reasoned thought and analysis' (and 'synthesis'; and, for that matter, 'mathematics') are. Reasoned thought and analysis (and synthesis' and for that matter, mathematics) in fact all *grow out* of 'common sense'. It is true enough that one person's 'common sense' may be another's 'nonsense' - the great human adventure, in which 'language' has played a crucial role, has always been to try and arrive at an adequate mutual understanding of each others' 'common sense'.
A little reasoned thought and analysis will show that the above is inescapably true in all circumstances. It is a fact that reasoned thought and analysis (and synthesis) can often lead us to results that may seem counter-intuitive (i.e. against 'common sense') - but that does not negate their origins. > > Common sense is the perception of the concrete world > that we all share. > True enough. > > Common sense is devoid of reasoned > thought and analysis. > Ridiculous. > > That is my definition and in > the context of this discussion, neither unfair nor > unwarranted. > It's a 'definition' arising out of a ridiculous misunderstanding. > > Mathematics on the other hand is > analysis. It is a reasoned and imagined theory about > abstract and imagined entities, most significantly, > the real numbers. When we attempt to teach this > imagined theory and its imagined elements to the > unaware student, we use concrete examples (common > sense) as an aid in that task but not as a substitute > for that task and not as a substitute for the goal of > the task, reasoned analysis and thought. > See all of above.
GSC ("Still Shoveling Away!" - with apologies if due to Barry Garelick for any tedium caused; and with the observation that there is a SIMPLE way to avoid such tedium)