[tortoise]

But when I use the word "intelligence" in the context of this discussion I mean the capacity to acquire and apply knowledge; the faculty of thought and reason. As such, intelligence may be considered as necessary for producing objects that are designed and purposeful.

Let us assume all the above is true. Given that there is no objective measure for "design" and "purpose", as established previously and demonstrable mathematically, of what use is your definition in demonstrating intelligent design?

Remember, just because P implies Q does not make the assertion that Q implies P a valid construction. Elementary first-order logic.

[Fester Chugabrew]

Given that there is no objective measure for "design" and "purpose" . . .

There is no objective measure for "natural" and "supernatural" either. Be that as it may, the common definitions of "design" and "purpose" make the connection with intelligence to be a reasonable one. Not an irrefutable one, to be sure, but it is not a wild stretch by any means.