• solid — the category FinSet

  

  , a sack of wheat

  

  , a bag of marbles; atoms; axiom of choice; individuation. The urelemente or wheat-kernels are interchangeable although they’re technically distinct. Yet I can pick out just one and it has a mass.
• liquid — continuity; probability mass; Lewis’ gunky line; Geoff Hellman; the pre-modern, “continuous” idea of water; Urs Schreiber; Yoshihiro Maruyama; John L Bell; dynamical mixing models like stirring a soup
• gas — Lebesgue measure theory; sizing Wiener processes

  

  or other things in other “smooth” categories; here I mean again the pre-atomic vision of gas: in some sense it has constant mass, but it might be so de-pressurised that there’s not much in some sub-chamber, and the mass might even be so dispersed not only can you not pick out atoms and expect them to have a size (so each point of probability density has “zero” chance of happening), but you might need a “significant pocket” of gas before you get the volume—and unlike liquid, the gas’ volume might confuse you without some “pressure”-like concept “squeezing” the stuff to constrain the notion of volume.