Edna Maclean On Iñupiaq Counting

Introduction: The argument below can be found of page 831 of Edna Maclean’s Iñupiaq to English Dictionary.

Key Facts: N/A.

Text: Edna Maclean, Iñupiatun Uqaluit Taniktun Sivuniŋit: Iñupiaq to English Dictionary, Fairbanks: University of Alaska Press, 2014.

The decimal system is handy because the fingers can be used as counters. The Iñupiaq  base-20 system clearly extends this notion to the toes as well. The Iñupiat counted on one limb at a time, so there were 4 groups of 5, hence the sub-base 5 and the two-dimensional system. The human body may be considered the living model of the earliest abacus or counting board. Even the prototype of the Babylonian base-60 used points of the body to keep track of numbers. The majority of human counting systems are body-based. Some of the Iñupiaq number words clearly reflect their corporal origins. Tallimat, the word for five, for example, is related to the Iñupiaq word taliq, meaning ‘arm.’ The word for ten, qulit, means something like ‘top,’ suggesting that it refers to both of the arms  on the top half of the body. The word for eleven in most Inuit-speaking communities, including some Iñupiaq-speaking communities, means ‘it goes down,’ an indication that one is now counting on the toes. Further evidence is found in the word akimiaq, Iñupiaq for fifteen, which means something like ‘it goes across,’ implying that counting will now cross over an continue on the other foot.

The connection to the human body is most apparent in the Inuit words for twenty. Throughout the entire Inuit-speaking world, there is a clear human association. Most Inuit dialects use the same word for ‘person’ as for ‘twenty.’ The Iñupiaq word for twenty, iñuiññaq, is a word denoting a ‘complete person.’ Inuktitut dialects spoken in Eastern Canada use the word avatit, signifying ‘all the extremities’ of the body. Some have proposed that even the Iñupiaq word atausiq, for ‘one’ is probably also derived from a reference to the human body. Atusiq (or some close cognate variation, such as atauseq) is used almost universally where an Inuit dialect is spoken.

(Emphasis in original)

ANALYSIS

Comments: This is part of a larger discussion of numbers in Iñupiaq.

Statements: Okay, this is a long one (Sorry).

[1] The decimal system is handy because the fingers can be used as counters.

[2] The Iñupiaq  base-20 system clearly extends this notion to the toes as well.

[3] The Iñupiat counted on one limb at a time;

[4a] There were 4 groups of 5.

[4b] [This pattern of counting on one limb at a time explains] the sub-base 5 and the two-dimensional system.

[5a] The human body may be considered the living model of the earliest abacus or counting board.

[6] Even the prototype of the Babylonian base-60 used points of the body to keep track of numbers.

[5b] The majority of human counting systems are body-based.

[7] Some of the Iñupiaq number words clearly reflect their corporal origins.

[8] Tallimat, the word for five, for example, is related to the Iñupiaq word taliq, meaning ‘arm.’

[9] The word for ten, qulit, means something like ‘top,’

(suggesting that)

[10] it refers to both of the arms  on the top half of the body.

[11] The word for eleven in most Inuit-speaking communities, including some Iñupiaq-speaking communities, means ‘it goes down,’

an indication that

[12] one is now counting on the toes.

(Further evidence is found in)

[13] The word akimiaq, Iñupiaq for fifteen, which means something like ‘it goes across,’

(implying)

[14] counting will now cross over an continue on the other foot.

[15] The connection to the human body is most apparent in the Inuit words for twenty.

[16] Throughout the entire Inuit-speaking world, there is a clear human association [in words for twenty].

[17] Most Inuit dialects use the same word for ‘person’ as for ‘twenty.’

[18] The Iñupiaq word for twenty, iñuiññaq, is a word denoting a ‘complete person.’

[19] Inuktitut dialects spoken in Eastern Canada use the word avatit, signifying ‘all the extremities’ of the body.

[20] Some have proposed that even the Iñupiaq word atausiq, for ‘one’ is probably also derived from a reference to the human body.

[21] Atusiq (or some close cognate variation, such as atauseq) is used almost universally where an Inuit dialect is spoken.

[22] The Inupiaq Counting system is based on body parts.

Discussion: This example poses the following themes: Argument Recognition, Explanation, Missing Assertions, Redundant Assertions.

Argument Recognition: Insofar as the relationship between statement 3 and statement 4 is an explanation, it is important not to treat the former as an attempt to prove the latter. This gives us at least one interesting question about argument recognition.

Explanation: The words ‘so’ and ‘hence’ included in statement 4a and 4b is best interpreted as signaling an explanation rather than an inference. The author isn’t really using statements 1-3 to prove statement 4 so much as suggesting a systemic relationship between each of these elements. The wording of statement 4b has been altered to reflect this fact.

Missing Assertions: The final conclusion of this argument isn’t fully spelled out. It has been supplied as statement 22.

Redundant Assertions: These two statements do not exactly mean the same thing, but for purposes of the argument at hand, the differences do not appear significant. Hence, I have provided both with the same number [5].

[5a] “The human body may be considered the living model of the earliest abacus or counting board.”

[5b] “The majority of human counting systems are body-based.”

argargbigargyepDiagram: The diagram for this argument isn’t as difficult as it may seem. The author is presenting multiple pieces of information in favor of a general conclusion. Some of her points can be grouped into sub-themes with intermediate conclusions leading to the main point. She may be talking about the meaning of words, but Edna Maclean doesn’t make use of tricky semantics here. Her evidence is pretty straight forward.

One judgement call that I did make in preparing this diagram was spelling out a statement to represent the final conclusion of this argument. Although it does contain general statements about the role of the body in language in general, it does seem that Edna Maclean’s main point here is that the Iñupiaq counting system is body-based, as she might put it. Since there is no specific claim in the text that quite expresses that, I took the liberty to spell this out as a missing conclusion.

Although I am a little concerned about the semantics of the phrase ‘body-based,’ I thought it best to use her own vocabulary to express this main conclusion, not the least of reasons being that I wasn’t sure I could improve upon that language anyway.

I left two statements out the diagram, because I am not entirely sure how they fit in the overall argument. Statement 20 raises the prospect that the Iñupiaq  word for ‘one’ is derived from the human body and statement 21 says that all the Inuit languages seem to use a similar term. It seems that statement 21 could be used in conjunction with the general pattern which serves as the overall point of the argument to suggest that such consistent pattern must also be derived from body parts. This would suggest adding an argument that runs 21+[22] -> 20, but this would be a minor side point in relation to the arger argument ending at statement [22].  Since I’m not sure that I understood the point anyway, I think it best to leave these off to the side.

Evaluation: Most of these inferences are pretty straight forward. The author keeps providing empirical evidence in support of a range of observations about the role of the body in counting systems in general, within Inuit languages, and specifically in Iñupiaq. I think ‘moderate’ to ‘high’ ratings would be appropriate for most of these inferences, but I’m not going to break each of them down.

Final Thoughts: The basic question here is whether or not Edna Maclean has given us adequate reason to believe that Iñupiaq numbers exhibit a pattern touching on the practice of counting body parts. I believe she has done so.

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