It has been speculated that one explanation to the Fermi Paradox is that humans have been observed by extra-terrestrial life and it was concluded that we are not 'intelligent life', so no contact was made (in the same way that we don't try to 'contact' ants to teach them quantum physics).
If this was the case, what would intelligent life look like? What specific, scientific metrics could we use to quantify life as either intelligent or not?
There is no real defining line for "intelligent." Heuristically, we have defined intelligent as:
So pretty much, we define "intelligent" as "able to think in the way humans can but animals cannot." It's not a very satisfying definition, certainly not sufficient for exploring alien species.
We, of course, have IQ tests. Pattern matching tests like Raven's Progressive Matrices have been used to measure "intelligence" for quite some time. They do, of course, leave much to be desired, which is why few people put much stock into IQ tests.
However, I'm not sure of "intelligent" life is really what we're looking for in alien species. There's another class of words which I find more applicable: sentient, conscious, self-aware. If I was out looking for alien life, those are the adjectives I'd be looking for.
One metric you may find very interesting is the Phi function from Integrated Information Theory (IIT). IIT posits that consciousness can be measured in terms of how much information a system can process which cannot be explained simply by the sum of its parts. For example, the Phi of a block of RAM is basically 0, because RAM can't do any processing on its own. The Phi of a CPU is low, because it's heavily limited by its lack of space to store temporary values, but it can indeed do things which can't be explained simply as a sum of ALUs, caches, interrupt handlers, etc. Put them together, and the Phi of a computer, which is greater than 0 because it can do lots of things that can only be explained by the entire system. Break it up into its components, and it can't do much at all.
In IIT, a computer has some modicum of consciousness, because the metric IIT uses to define consciousness is one which is nonzero for a computer. However, the phi value for living animals is vastly higher than that of a computer, suggesting that animals are more conscious than computers. The Phi value for humans is presumed to be even higher than that of other animals, giving rise to the theory that we are the only conscious animal (IIT would argue that all animals are conscious, just to a lesser degree).
What's interesting about IIT is that that metric, Phi, is theoretically calculable for a system. Thus, if you came across an alien individual, you could theoretically determine a Phi for them, and use that to determine if your alien is "conscious" or not, by whatever line in the sand you want to separate "conscious" from "not conscious."
What I personally consider the boundary of "intelligence" (as used by OP, many animals show different degrees of intelligence, but that' another "kind" of intelligence) is invention and continuous usage of some language. This approach seems to be challenged here even more than it is in scientific world, be warned.
This given, the metric to establish "intelligence" of a completely foreign species goes through analysis of its language and communication patterns.
"some kind" of communication is present in many animal species (if not all) at all complexity levels, but (almost?) none of them rates as a full fledged Language.
By "Language" i mean some way to convey not only information of some kind, but also powerful enough to recursively describe objects/concepts unknown to the receiving end of communication.
In one word: a Language is the mean able to spread memes.
This capability seems restricted to humans (on this Earth) and seems to manifest itself naturally whenever a sufficiently high number of individuals are together (as demonstrated by insurgence of Nicaraguan Sign Language).
Any "intelligent" Alien would, most likely, have their own way to spread memes. This mean may be very different from our own, perhaps so much different they may fail to recognize our our message-passing infrastructure (and vice-versa, of course).
Anyways any search for intelligent beings goes through search for language, which is what SETI project is doing, trying to discriminate it from "natural patterns" clouding the background. Of course SETI is restricted to electromagnetic spectrum, bit any field research should take into account many more basic carriers (sound, visual patterns, short-range electromagnetic, chemical, whatever). This search is not trivial, especially if the main communication method is very different from ours.
Of course ability to build a wide range of artifacts should be a very strong hint a deeper analysis is needed, but it's possible to imagine "monkey-see-monkey-do" semi-intelligent species not really rating as "intelligent", but exhibiting a wide range of tools and artifacts.
OTOH any species having a rich Language and using it to communicate should be deemed as fully "intelligent" even if they elect to live in a "very natural" way minimizing artificial artifacts.
Considering your own premise that we (humans) do not qualify in the galactic (or universal) definition of "intelligent", asking the characteristics of an intelligent life form (read "alien") does not make sense at all. Since we are not intelligence, we can also not infer what true intelligence is (or would be).
This stems from the base argument that in order to perceive intellect, you must have some amount of intellect as a prerequsite. That is to say, the ants cannot know that humans are intelligent, since they are too dull and basal to understand what intelligence (of human levels) is at all.
Since we have been deemed unintelligent, all our assumptions and classification of galactic intelligence would also be equally unintelligent, making the whole discussion moot.
