Tuesday, April 5, 2011

Remarks 8 & 9

Five red apples

Recall that in Remark 1, a number word is used in a way that relates loosely - if at all - to numbers as a measure of quantity. In essence, the shopkeeper simply recites in order the words in a sequence until reaching the word written on the list, taking an apple from the drawer while reciting each word. The fact that the resulting numerical quantity of apples on the counter or in a bag is what an English speaker calls "five" is irrelevant. In the simple language of Remark 1, "five" is merely the word that terminates the process.

The builder

The point is made even more forcefully in Remark 8. In this Remark, each number word used in the scenario of Remark 2 is replaced by the corresponding letter of the alphabet. Now the process stops when the helper - who is reciting the alphabet as he picks up stones to take to the builder - gets to a letter of the alphabet that the builder has shouted. Of course, in either language the specific sound used in counting is irrelevant. The sequence {a,b,c,d,...} works just as well as the sequence {one, two, three, four, ...} - as would any sequence of sounds that was agreed upon by the builder and the helper.

Also added to the language are the words "there" and "this". The first added word is used in commands of the form "d-slabs-there", in which the builder points to the place to which the helper is to bring the "d" slabs as he says "there". The second added word is used in commands of the form "this-there", in which the builder points to a stone while saying "this" and to the location in which the stone is to be placed while saying "there".


In Remark 9, the role of ostensive teaching in such a system is addressed. There will certainly be Augustinian type teaching in which the teacher points at a type of stone and says the word for that type - eg, "slab" - for the purpose of naming. But the discussion of the use of ostensive teaching with respect to counting seems at best confusing, perhaps even wrong. The example given seems to suggest that the teacher says "a,b,c slabs" while pointing at a different slab while saying each letter. But that isn't consistent with the description of how counting words are to be used in the simple language assumed in Remark 8 in which the slabs are direct objects of an action - being removed from a pile. Pointing involves a direct object - say, a finger - pointing to an indirect object. It isn't obvious that using the latter to teach the former would work.

Also in the discussion, the role of pointing at slabs for naming is analogized to pointing during ostensive teaching at different sized groups of objects with the intent to associate a word with each such group, not for counting but for naming. This seems an aside irrelevant to these Remarks since no application in the context of the simple language of Remark 8 is suggested.

Ostensive teaching of "there" seems conceptually straightforward. For example, the teacher could point at objects removed from a box while saying the words {a,b,c,d}, then point to a table top while saying "there", and finally move the objects to the table top.

Teaching "this" is trickier because its role is more subtle. While "there" indicates a location, "this" can be viewed as indicating the content of a location. (Analogous to pointers in the C programming language.) For example, if an apple is placed on a table and the teacher points to the apple while saying "apple", the intent is for the student to associate the word "apple" and the apple itself. But if the teacher were to point at the apple while saying "this", the intent would be for the student to associate the word "this" with whatever object happened to be on the table, ie, with the content of the location pointed to. One can imagine ways of trying to achieve that association, but it is not obvious which - if any - would work.

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