Saturday, 31 January 2015

Inuit and the notion of "number"

Sometimes, in my quieter moments, I think about Kant's decidedly mathematical assertion that space and time are primal elements of human consciousness and cognition. That Kantian philosophy would be "decidedly mathematical" is neither surprising nor remarkable, but what is remarkable (if obscurantist) about his philosophical treatment of space and time is that he went beyond the merely empirical (and, therefore, naive) and pared everything down to the absolutely essential elements of human consciousness—Descartes appears rather parochial compared to Kant:

Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind's nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally. (Kants gesammelte Schriften, Ak 2: 403)

Ditto, for our notion of time (ie, subjective, ideal, etc.).

What blew my mind (as a linguist) is that Kant was able to link these two primitive elements of human consciousness to the structure of language—ie, as forming the foundations of grammar, no less! I invite you to consider our notions of "proximity", and not only our notions of "past, present and future" but additionally what are called irrealis moods of "perfective past, present, and future"—ie, "will have had..."—and swat them away as you would annoying flies. What you're left with are things and actions without context (adverbs and adjectives having been swatted away along with space and time), and therefore completely meaningless (Saussurean) cats and dogs (let alone, jumps and sittings).

Georg Ferdinand Ludwig Philipp Cantor was a German mathematician who invented the set theory in mathematics. At its core, set theory is a realization that our notion of counting is a secondary, emergent activity arising only after we realize (discern) that we can collect and organize like objects into sets.

To quote the incomparable David Berlinski (Infinite Ascent, 2005):

From the first, working mathematicians turned gratefully to set theory because of its immense, its obvious, usefulness. It comprises a series of ideas, and language, and a technique, its serviceability in this regard an especially ironic circumstance just because sets are not themselves obviously mathematical objects, sets serving perfectly well to collect kiwis and kangaroos, as well as numbers and points. (Berlinski 2005, p. 128)

I would contend that the Inuit notion of "number" is exactly like how set theory treats a collection of things (ie, numbers and/or points on a plane or line). The lexicalized root itself, naasaut (number), may be analysed as:

[naa-] + [-saq-] + [-ut(i)-] or,

[completion] + [working to achieve a desired state] + [instrument]

In a typically particularized context/definition an Inuktitut dictionary, Uqausiit Tukingit (2000), defines a notion of:

naajijuq: ullunik imannanik aullaqsimaniaqĊ‚ungi, ullut taakkua naangmata naajivuq

or, translated:

naajijuq: in having planned to be away (hunting) for a set number of days, when these days have past (the hunter) returns home

and, here is the entry on naasaut itself:

naasaut: nalunaiqsiniq kisutuinnait qassiuninginnik

which may be translated as:

naasaut: the act of giving an indication of how many things are

The Inuit notion of "completion" (or, "achieving an end") is uncannily anticipatory of set theoretic notions of number. The notational conventions of set theory indicate "number" in terms of a series of what are called "empty sets" {∅} embedded between {}—as per Peano's axiom that zero is a number—belies the simplicity and elegance of its subject. The concept of number is rather more abstract and ineffable for the precise reason that it is more primitive than the act of counting.

Number, then, may be described precisely in terms of Kant's notions of space and time: it is a primitive element necessary to achieve consciousness and cognition, and, more importantly, to gain competence and mastery over grammar.

The bias that it is only the Western Mind that has achieved the pinnacle and sophistication of capturing the whys and wherefores of human consciousness is really a "tilting at windmills": as Kant adumbrates, all human consciousness has space, time and number at its foundations. It is from these that any scaffolding (ie, culture) is only possible. As the Kant quotation above implies, consciousness/self-awareness is not an achievement by effort; it is a commonality belonging to all sentient beings. It is an axiom upon which all things that we can perceive, imagine and articulate are based.


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