The Logic of Say's Law
Say's law in essence means that there can never be deficient aggregate demand, something which also means that there can't be general overproduction. The reason for that is we always have unfulfilled desires, and thus always want more goods and services. That is essentially always true, and is if anything even more true during recessions when people are compelled to cut back on their purchases because of lower income. The only possible context where this would not be the case would be in some hypothetical world where everyone already has what they want, either because of super abundance or the spread of some anti materialist philosophy. But in that case it wouldn't really be a problem, so even then aggregate demand wouldn't be deficient.
This however, does not mean that there can't be any economic crisis, of course. While aggregate demand can't be too low, demand for certain products are often too low. And when there is a significant mismatch between the structure of production (supply) and the structure of demand, then recessions or depression will be the result. But that does not in any way contradict Say's law.
Keynesians often retort that during deep slumps all industries suffer problems (Actually, this is not strictly true, there are some goods and services that boom during recessions and depressions). Doesn't this prove that aggregate demand is deficient? No, this is in fact the result of inadequate supply of goods that people want. Inadequate supply is another way of describing falling income resulting from the overproduction in selected cyclical industries (which is to say capital goods and consumer durables). That means that the workers and capitalists in those industries don’t produce anything which workers and capitalists in relative non cyclical industries want. It is a decline in aggregate supply (income) which causes a decline in aggregate demand.
Some critics have further argued that Say's law assumes no hoarding, or at least no increase in hoarding, and that if people decide to increase hoarding of money, then Say's law will not hold. But what hoarding means is in effect that people want higher real cash balances, which in turn is a desire for higher future demand for goods. That means that there is a relative overproduction of current consumer goods and a relative underproduction of investment goods that will enable that higher future demand for goods. The relative overproduction is in turn a sign that prices are too high and need to come down. People still want these things, but at current prices, they provide less value than future goods, meaning that prices must come down in order to raise real cash balances that way and begin the adjustment process. But again, this is simply another example of a mismatch between the structure of supply and the structure of demand in accordance with Say's law.