[Top] [All Lists]

[ontolog-forum] On dyads and triads

To: Steven Ericsson-Zenith <steven@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Hassan Aït-Kaci" <hassanaitkaci@xxxxxxxxx>
Date: Thu, 28 Mar 2013 11:11:27 +0100
Message-id: <5154174F.4000303@xxxxxxx>
On 3/21/2013 9:34 AM, Steven Ericsson-Zenith wrote:

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.


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


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):


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.


Attachment: hak.vcf
Description: Vcard

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (01)

<Prev in Thread] Current Thread [Next in Thread>