I suppose that yesterday's idea needs to be made more explicit. A previous price is just a signal, one of many factors that help to clarify the real value of a product. Other obvious indicators to product value are the brand, the product model identifier, competitor prices, even the selling location.
For comparatively low-value interchangeable items, the sort that you see in a typical supermarket food isle, the money off one purchase is not changing your life. There the offer serves primarily as a "look-at-me" signal rather than a major financial incentive. But the key factors here are those adjectives, low-value and interchangeable. It does not substantially affect your life to substitute one product for another, and the use of the offer is to bring a different item to your attention.
And for higher value items, the previous price is becoming even less useful as an indicator because technology is advancing so rapidly, while because of competition and globalisation, many product prices need to decrease in real terms.
So if the previous price is just a signal of very little relevance then so is the offer.
I knew I'd be able to bring together economics, linguistics, mathematics, and semiotics :)