Robert Hansen (RH) posted May 29, 2013 4:25 PM: (I regret I have brought this up after so long - but one statement in RH's response to Lou Talman had [probably subconsciously] been troubling me - and it struck me just now that I should express my objections. I am here responding to that single statement only. I do have some reservations [not that serious] about various other parts of RH's arguments). > > On May 28, 2013, at 4:43 PM, "Louis Talman" > <email@example.com> wrote: > > > I don't know what is. And Robert acquiesces, <snip> > > The only door to algebra is algebra. > MOST EMPHATICALLY NO! The only doorway to (beginning) algebra is common sense. Common sense has to be (I claim) the doorway to beginning anything at all (even quantum physics, for example) - though later many things in any field may *appear* to be 'counter to common sense'. There are, I believe, some quite deep philosophical issues involved in this - though I've not examined these issues adequately.
The doorway to (further) algebra is (beginning) algebra + common sense. (These claims can be readily demonstrated if we were able to use what I call 'prose + structural graphics' [p+sg] here. In 'pure prose' such a demonstration is extremely difficult, perhaps impossible).
RH and I have had some other discussions on 'common sense' (at this very thread or another - I don't have those postings to hand). He has claimed that something in some list of his (not clarified to me) "nullifies common sense".
In one sense, RH's statement is nonsense; in another sense, he may be speaking a very profound truth indeed (though he does not realise that).
I suspect, from our discussions, that what RH means by 'common sense' may be somewhat (perhaps significantly) different from what I mean by it - but I've not tried at all to trace the source(s) of our differences on 'common sense'.