Mordechai, I too enjoy splitting hairs. I hope no one objects to my chiming in.
Breadcrumbs are a construct without a solid definition, from which I think much disagreement arises. Typically, they reflect the notional path to a page (the "path" according to where the user believes themselves to be), although often they reflect the logical path (where the file is in the directory structure) or the historical path (where the user had gone to get to where they are).
Historical paths are linear. The trouble with using ordered lists for them is not so much the semantics as programming: how do you recognize the difference between a click forward, then back to abort, then forward to the place the user intended, from an honest forward-back-forward to something else?
Well, those sorts of breadcrumbs I find tedious because I've already got a back button and Amazon certainly is trying to patent "The Page You Made" anyway.
Both logical and notional paths are derived from a hierarchal tree but are themselves linear. (Non-tree hierarchies are possible, with non-parent/child cross-linking, but why confuse the discussion more?) Between the current node (the page) and the greatest ancestor node (the home page) there exists only a single path of nodes in a specific order. This lineage is, by definition, linear and ordered. This makes it a prime candidate for an ordered list; this is what ordered lists are.
Many arguments in this thread used the words hierarchy and order and list to explain a problem that was really about completeness. Can an ordered list survive the removal of a member? Depends on the relationship between list items. A notional path certainly could survive such a removal; civilization does not collapse because our addresses on postal mail do not include the county even though they include the city and state. A logical path could not survive such a removal, any more than you could drive to California and enter Los Angeles before entering Los Angeles County.
Does your lineage denote the next ancestor/descendant (i.e., parent/child) relationship? Or does it merely indicate an ancestor/descendant relationship? Is it notional or logical? Is it complete? These answers are about personal style and the intent of the breadcrumbs as a solution. The nature of the solution depends on your answers.
However, the path is the order and not the items.
--
Ben Curtis
WebSciences International
http://www.websciences.org/
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