There are two numbers that people commonly say as one thing but I've seen mentioned as another: number of senses and number of states. Neither are technically formally defined, but each has a number that people generally accept as true, 5 and 4 respectively. I like to go with the other numbers. I've seen as high as 23 for the number of senses, that classification divided touch into contact and thermal, added things like time, balance, and proprioception, the ability to know where the body is in space without looking i.e. being able to catch a ball behind your back. It basically defined a "sense" as any method of perception of the world by means of a specifically designed structure of system. So by that definition, taste buds define the sense of taste, the olfactory bulb defines the sense of smell, rods and cones define sight, etc. Wikipedia classifies some of them by type here.

As for the number of states of matter, that is less subjective than senses. The four that people usually know, solid, liquid, gas, and plasma, are the four most common states, there are several more and sometimes the common four are subdivided into several different states. Bose_Einstein condensates are used in some experiments, the one that comes to mind is the creation of sonic black holes, or "dumb" holes. There are others like fermionic condensates and photonic matter. Neutron stars are comprised of degenerate matter, sometimes called neutronium or element zero coughMass Effectcough. Helium at temperatures near 0K becomes a superfluid, supersolids exist as well. The state of superconductivity is sometimes referred to as a state of matter. Then there are theoretical states like the quark-gluon plasma, a state with so much energy that it is able to overcome the strongest of the fundamental forces, the nuclear strong force, and dissociate particles into individual quarks. Then there's the dropleton, a state which has been discovered since I last looked at this list.

Doesn't really answer your question, but you mentioned pedantry so I thought I'd take it to an extreme.