Implicit Knowledge (nursery edition)

We earlier shared an anecdote of implicit or “chrysalis-enclosed” knowledge, from an introspective five-year-old of our acquaintance:

https://worldofdrjustice.blogspot.com/2013/09/implicit-vs-active-knowledge.html

Compare this childhood reminiscence of a boy growing up on the Upper East Side:

I remember my grandmother’s house quite well.  It was a very cold formal place.  There was an enormous marble entrace hall …

We behaved extremely well.  We knew the rules inside out  without knowing the rules.

Jeff Kisseloff, You Must Remember This:  An Oral History of Manhattan  from the 1890s to World War II (1989), p. 120

Implicit vs. Active Knowledge

I greeted the young mother next door, and noted  with approval  the locomotive progress of the heir and baby, Master Jack.   “It’s Mr Crawlies!” I observed colloquially, as he busied himself amid the bugs and flowerbeds. He is actually capable of walking “six steps”, his mother assured me;  but he prefers to crawl (lazy fellow) “because it’s easier”.  I noticed that his cotton onesie was fitted with leather soles, which might  more realistically  have been applied at the knees.

Then up skipped his elder sister, my little friend Marya, who lately has marched into kindergarten.  With scarcely a glance at her young sibling, for whose quaint ways  she shows indulgence but no doting,  in a half-whisper  she informed me:

“Today is my first day to write.   I knew how to write before, but I kept it in my head,”, she said, indicating the noggin in question  with a well-informed forefinger, “and didn’t let it out.”

What exactly that might mean, I leave for the elves to interpret.  She herself, when grown to womanhood, will no longer know.   But years later (after I am gone), she might happen to read this, and wonder, then smile at a dim remembered light ….

Platonism is not the problem

Thomas Tymoczko, introduction to New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. xiii:

To account for the indubitability, objectivity  and timelessness of mathematical results,  we are tempted to regard them as true descriptions of a Platonic world outside of space-time.  This leaves us with the problem of explaining how human beings can make contact with this reality.

Well, yes, that is indeed a question;  but not a new one.   The same conundrum confronts us in the Mind-Body problem; the problem of Free Will; and more simply, the problem of how you and I can communicate at all.  There are even puzzles at the level of mid-level objects.  The thesis of Mathematical Realism may or may not be valid, but it does not introduce a problem which we might otherwise avoid.