more on this theme | more from this thinker
Full Idea
Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789.
Gist of Idea
Why is arithmetic hard to learn, but then becomes easy?
Source
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2)
Book Ref
-: 'Philosophical Review 114' [Phil Review 2005], p.198
A Reaction
His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects.
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |