I understand that acidity is merely a reflection of how many free hydrogen ions are in water, and basisicity is just a reflection of the number of hydroxide ions, but I don’t understand how this definition holds true for acids and bases that don’t dissociate into hydrogen ions or hydroxide ions.

For example, how is sodium ethoxide, a very strong base, able to have such a high ph (14) if it doesn’t dissociate into hydroxide ions? I get how it’s called a base due to the Bronstead-Lowry definition, but I don’t get how it has such a high pH.

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• Sodium ethoxide does not have any pH at all. – Ivan Neretin Jul 5 '18 at 18:53
• When dissolved in water, shouldn’t it have a pH of 14, though? – user1939991 Jul 5 '18 at 18:59
• When dissolved in water, it will cease to exist. – Ivan Neretin Jul 5 '18 at 19:10

When discussing the strength of an acid/base we consider its dissociation constant, for bases this is its $K_\mathrm{b}$, or for easier comparison its $\mathrm{p}K_\mathrm{b}$. pH is a property specific to aqueous solutions of a specific composition / concentration / temperature, not any molecule itself.
$$\ce{OEt- +H2O\rightarrow HOEt +OH-}$$
I would strongly recommend reading up on Lewis acid-base theory, since it provides a more general/useful idea of acidity/basicity. Most reactions are in fact not done in water. Also you may be interested in knowing that it is impossible to have a base stronger than $\ce{NaOH}$ in water due to something called the leveling effect.