No one of them seems to confuse terms (words, labels, names, tags) with categories.

I would actually be close to claiming that all tags are (used as) category names, unless they are assigned on the basis of some process that either picks them randomly, or with no connection with the content or form of the tagged item whatsoever (and thus randomly from the point of view of tagging the item).
If one reads (watches, tastes (?), whatever) an item and assigns to it a tag based on that experience, it reflects some sort of categorizing, unless the tag is intended to be a proper name. (But who tags items on the web with proper names? Well, in principle not impossible, but unlikely.)

Consider the tags ‘poor’, ’super!’, ‘me’, ‘dogs’, ‘ghrrr’, etc. Unless used as proper names for items on the web (e.g., this picture has the name ‘poor’), they seem to name categories — those of poor items (in whatever sense), of super items (…), of dogs (perhaps rather of representations of collections of dogs, rather than of individual dogs, such as a picture of two dogs, but not a picture of one dog), of whatever makes the author make the sound ‘ghrrr’, etc. ‘Me’ is an indexical, and while you could claim that it is used as a proxy for a name (it names an individual), in the context of items on the web it would rather name a category of, e.g., pictures of the author (thus ‘me’ is actually shorthand for ‘picture of me’).

What do you mean by ‘property’? How can a tag — a syntactic element — be a property? You seem to use the term ‘property’ with a non-standard way. There is hardly an agreement in philosophy as to what properties are (see, e.g., http://plato.stanford.edu/entries/properties/; they speak of property words, words denoting properties, but not of words as properties), but there seems to be no confusion of words with properties, at least.

vQ

On the other hand, I am not as convinced about the strong distinction between “categories” and “names for categories”, as you are. There is of course A LOT of work done on this subject by cognitive psychologists (and philosphers, if you insist!)

One of my favourites is Ellen Markman. Another is Paul Bloom. What do you think of this:
http://faculty.virginia.edu/childlearninglab/research_interests.php
http://links.jstor.org/sici?sici=0009-3920(199010)61%3A5%3C1461%3ANMCRTA%3E2.0.CO%3B2-N

And of course:
http://www.bbsonline.org/documents/a/00/00/04/32/bbs00000432-00/index.html

In a system with a controlled, unambiguous dictionary, you could identify tags with categories. This would still be a simplification, though.

The questions are (among others):
1. When we tag items on the web, do we do so with some categorization in mind, or not? That is, does tagging reflect categorizing?
2. Does the fact that we mine interesting patterns from popular tags prove that tagging reflects categorizing?

As for 1., it may be hard or even impossible to judge in general, but I would guess that tagging does reflect categorizing. At least when I assign a tag, it is because I find the item in question belonging to some particular category.
But we can’t exclude that there are some who assign tags based on some obscure motivation not related to categorizing.

As for 2., it appears to me that even if tags were assigned completely randomly, without any categorizing in mind, we could still mine some interesting patterns, just by chance. On the other hand, that we do not see any interesting pattern emerging for some tag, does not mean that there is no categorizing intended; it may be that the way we (the miners) categorizes is so different from the way they (the taggers) categorize that we are simply not able to see the pattern which is there.

This is of course philosophizing, and it seems plausible that most people do categorize while tagging. My major concern with tagging flows from that tags themselves are not categories, but rather names, and that synonymy and homonymy seem to unnegligibly interfere, in some cases, with the use of tags for practical purposes.

vQ