I would not be so reductionist. Intelligence doesn't seem to be an universal thing, even IQ (a human invented metric) is measured in terms of some statistics. If you have an IQ of ~60 you have intelligence but a completely different one from an IQ >85.
> But humans are intelligent, human languages have a universal grammar and can be indefinitely extended with new words. I think this puts us in the intelligence species club, and all species in that club can all discuss any idea.
Humans have different intelligences. You can be intelligent (per the human intelligence definition) but a math ignorant. Again, this implies intelligence as we know it is not an universal thing at higher levels: not all people can have a physics Ph.D. as not all people could be a good artist where good techniques are recognizable, same for music, etc.
Yes, a cockroach is in another level of intelligence (or non-intelligence) but that does not mean there is not a super-intelligence that makes us relative cockroach.
Also, without any intention of talking about religion or "intelligent design", we can theorize that the Universe is supersmart because it creates intelligent creatures, even if it is not conscious about that. I would be very catious to define intelligence in an universal way.