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On 3/21/2013 9:34 AM, Steven
Ericsson-Zenith wrote:
Indeed.
On Mar 21, 2013, at 1:29 AM, "Hassan Aït-Kaci" <hassanaitkaci@xxxxxxxxx> wrote:
But I'm sure my ignorance of such "deep" issues explains my silly comment ... ;-)
Dear Steven,
I must confess that I mulled a long time over whether or not to
reply to your swift and terse kick-in-the-groin reaction to my
tongue-in-cheek comment re. dyads vs. triads... In fact, the very
terseness of your swift slap was, as condescending as it did sound
("why bother trying to teach a chimp how to speak?"), amusing to me
while satisfying me as well (it confirmed the futility of any
further interaction).
But you went on ... and on ... and thus broke the spell (so to
speak).
As the French say (and they say many things I admit), "La culture
est comme la confiture : moins on en a, plus on l'étale." [Culture
is like jelly: the less you have the more you spread.] And, to
pursue with some untranslatable double-meaning punny thought of my
own, "Je préfere une petite tartine bien beurrée à un gros pain
sec." [I prefer a small well-buttered toast to a big dry loaf.]
So I too, like Ed (Barkmeyer), have been getting headaches trying to
follow your arguments and understand your explanations.
Pulling Peirce out of your purse every other paragraph reminds me of
preachers predicating to proselytes invoking their prophets and
quoting from a holy book. As if it was a given that the cryptic
words of such prophets and their books were the final and definitive
argument.
So let me indulge in spreading some minor toast with some (admitted
less deep) culture of mine in response to your heavy-duty dry
philosophical loaves - not that I care so much about dyads, triads,
or other shmyads ... no. You see, I am not a philosopher - just a
(would-be) computer scientist with a bent for formal justifications
when appropriate, and only when they clarify things rather than
making everything more confused and murkier than ever. I am neither
competent, nor interested, in discussing at length how many triadic
or dyadic angels can dance on the head of a pin. You may try adding
to your tirades on triads. But I'd die adding to my diet on dyads.
Haskell Curry and Robert Feys proposed Combinatory Logic and showed
that all lambda-definable functions (in the sense of Alonzo Church),
and thus all computable sets (in the sense of Turing) [the two being
equivalent as shown by Stephen Kleene in his thesis on Recursion
Theory done under Church's supervision in 1934], can be expressed as
some combination of only two basic combinators S and K where:
K = \lambda x.\lambda y. x
S = \lambda x.\lambda y. \lambda z. (x z (y z))
In that sense, all that is computable is fundamentally dyadic. Now,
you may argue that there is a third hidden meta-operator (the
combination - or functional application). I grant you that - and
this is what John Sowa alluded to in his comments. Indeed, all you
need are unary functions since the types A x B -> C and A -> B
-> C are isomorphic ("Currying"). This is in fact the same as the
logical equivalence A & B => C with A => B => C (using
the well-known functor of categories between types and formulae).
John added that this is not really dyadic because Currying will
produce partial results of non-ground types. But I beg to differ,
since such ground types (such as the natural numbers) and operations
thereon (such as addition, multiplication, etc., ...) are all
expressible and encodable as non-ground functional expressions. So
all you need are (non-ground) functions. Be that as it may, for any
pair of entities to interact, there must be a third (meta) entity -
viz., the interaction. So we're back after all to the holy trinity:
the father, the son, and the holy spirit.
This rambling of mine is not to say that I'm right and you're wrong
- nor vice versa. It simply means that there are varying schools of
thoughts, and that I prefer those that are closer to my needs,
mathematically and computationally crisper and using plain
contemporary language rather than 19th-century philosophical musings
making no sense to me as a humble 21st-century computer scientist.
All else is Greek to me. But, if I had to choose one ancient Greek
statement that a fully adhere to, I would favor Socrates's « ἕν οἶδα
ὅτι οὐδὲν οἶδα » (hén oȋda hóti oudèn oȋda) - in Latin « scio me
nihil scire » - "The only thing I know is that I know nothing"...
Finally, since we are at quoting holy books, my all-time favorite
is, "In the beginning was the Word..."
Your response to my comment was such a beginning ... Indeed! ;-)
Yours, cordially.
-hak
PS/ BTW, all these religious allusions by no means alter my
atheistic convictions. :-)
PPS/ I can't help adding this 17th-century poetic quote as a post
post-scriptum (in French - translation follows):
Il est certains esprits dont les sombres pensées
Sont d'un nuage épais toujours embarrassées ;
Le jour de la raison ne le sauroit percer.
Avant donc que d'écrire apprenez à penser.
Selon que notre idée est plus ou moins obscure,
L'_expression_ la suit, ou moins nette, ou plus pure.
Ce que l'on conçoit bien s'énonce clairement,
Et les mots pour le dire arrivent aisément.
...
Et, pour finir enfin par un trait de satire,
Un sot trouve toujours un plus sot qui l'admire.
Nicolas Boileau Despréaux (1636-1711)
L'Art poétique
My translation:
There may be certain minds cluttered with murky thought
In a thick cloud always embarrassed to see naught;
No daylight of reason could make out anything.
Before starting writing you ought to learn to think.
Whether our idea is more or less obscure,
Expressing it may thus be less sharp or more pure.
What is so well conceived shall be spoken clearly,
And the words to say it will come up easily.
...
And, to conclude at last with a dash of satire,
A fool always shall find more fool to be admired.
Nicolas Boileau Despréaux (1636-1711)
The Art of Poetry
(http://lucmonnin.net/332/Boileau.html)
PPPS/ Oh well, while I'm at it, might as well... I warmly recommend
this delightful essay by Freeman Dyson entitled "Birds and Frogs" on
the history of mathematical thinking (but that surely applies to
other disciplines, philosopy in particular):
http://www.ams.org/notices/200902/rtx090200212p.pdf
A few thinkers are birds soaring high in the sky seeing far in the
abstract and without limits, while others are frogs on their lily
pads aware of all the concrete nooks and crannies of their swamps.
But, IMHO, most of the rest of us are but flies in a confused
Brownian motion, each on a continuous though nowhere-differentiable
random path, buzzing in a shapeless cloud at mid-height only to be
gobbled up by birds and frogs alike.
--
-hak
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