The truth of Say's Law seems evident once we think about it. When a good or service is sold, it represents income for the seller. The raw materials or supplies used by the seller to produce a good or service previously resulted in income for the producer of the raw materials or seller of the supplies, and so on down the line. Thus, everything that is sold in the aggregate generates the aggregate demand to purchase it. Say's Law of Markets can therefore be expanded by saying that "supply generates its own demand, and demand its own supply."
As Jean-Baptiste Say put it in response to the criticisms leveled against his economic theories by the Reverend Thomas Malthus (author of the 1798 Essay on Population),
All those who, since Adam Smith, have turned their attention to Political Economy, agree that in reality we do not buy articles of consumption with money, the circulating medium with which we pay for them. We must in the first instance have bought this money itself by the sale of our produce.This is, admittedly, a lengthy quote to get through. It is, however, important. It highlights most effectively an essential difference between Keynesian economics and a more rationally structured approach such as binary economics. That is, the way to stimulate demand and get an economy going, or to maintain a stable economy is not, as Keynes supposed, to redistribute income (effective demand) through the tax system or by inflating the currency.
To a proprietor of a mine, the silver money is a produce with which he buys what he has occasion for. To all those through whose hands this silver afterwards passes, it is only the price of the produce which they themselves have raised by means of their property in land, their capitals, or their industry. In selling them they in the first place exchange them for money, and afterwards they exchange the money for articles of consumption. It is therefore really and absolutely with their produce that they make their purchases: therefore it is impossible for them to purchase any articles whatever, to a greater amount than those they have produced, either by themselves or through the means of their capital or their land.
From these premises I have drawn a conclusion which appears to me evident, but the consequences of which appear to have alarmed you. I had said — As no one can purchase the produce of another except with his own produce, as the amount for which we can buy is equal to that which we can produce, the more we can produce the more we can purchase. From whence proceeds this other conclusion, which you refuse to admit — That if certain commodities do not sell, it is because others are not produced, and that it is the raising produce alone which opens a market for the sale of produce.
I know that this proposition has a paradoxical complexion, which creates a prejudice against it. I know that one has much greater reason to expect to be supported by vulgar prejudices, when one asserts that the cause of too much produce is because all the world is employed in raising it. — That instead of continually producing, one ought to multiply barren consumptions, and expend the old capital instead of accumulating new. This doctrine has, indeed, probability on its side; it can be supported by arguments, facts may be interpreted in its favor. But, Sir, when Copernicus and Galileo taught, for the first time, that the sun, although we see it rise every morning in the east, magnificently pass over our heads at noon, and precipitate itself towards the west in the evening, still does not move from its place, they had also universal prejudice against them, the opinions of the Ancients, and the evidence of the senses. Ought they on that account to relinquish those demonstrations which were produced by a sound judgment? I should do you an injustice to doubt your answer.
Besides, when I assert that produce opens a vent for produce; that the means of industry, whatever they may be, left to themselves, always incline themselves to those articles which are the most necessary to nations, and that these necessary articles create at the same time fresh populations, and fresh enjoyments for those populations, all probability is not against me. (Letters to Malthus, 1821, p. 2)
The sound method of stimulating demand is to enable people to produce a marketable good or service. Only production of marketable goods and services generates sustainable effective demand as well as the supply of goods and services to meet that demand. Because production = income, this avoids the twin evils of inflation and deflation — as well as confiscatory taxation to redistribute wealth.
This seems to answer the question about what to do when there is insufficient demand in the economy: produce more, don't artificially stimulate demand. It also, unfortunately, raises another question: how are people to produce when they have only their labor to sell, and advancing technology and cheaper foreign labor is depriving them of the existing market for their labor, or driving the price of it below the level necessary to generate an adequate and secure income for the worker and his or her dependents?