The classical dichotomy is the division between real money, which is measured in physical terms and is usually supposed to be a better indicator of money value due to its stability, and nominal money, which is measured in terms of a currency and hence is susceptible to inflation. It was a term coined by the early 20th century classical writers. According to Milton Friedman, who is commonly referred to as the father of monetary economics, different forces influence real and nominal variables (money value here) and changes in the money supply affect nominal variables but not real variables. This irrelevance of monetary changes for real variables is called monetary neutrality.
Patinkin (1954) challenged the classical dichotomy as being inconsistent, with the introduction of the 'real-balance effect' of changes in the nominal money supply. The early clasical writers postulated that money is inherently equivalent in value to that quantity of real goods which it can purchase. Therefore, in Walrasian terms, a monetary expansion would raise prices by an equivalent amount, with no real effects (employment, growth). Patinkin postulated that this inflation could not come about without a corresponding disturbance in the goods market, through the 'real balance effect'. As the money supply is increased, the real stock of money balances exceeds the 'ideal' level, and thus expenditure on goods is increased to re-establish the optimum balance. This raises the price level in the goods market, until the excess demand is satisfied, at the new equilibrium. He thus argued that the classical dichotomy was inconsistent, in that it did not explicitly allow for this adjustment in the goods market - the price adjustment was assumed to be immediate - the 'invisible hand'.
Later writers (Archibald & Lipsey, 1958) argued that the dichotomy was perfectly consistent, as it did not attempt to deal with the 'dynamic' adjustment process, it merely stated the 'static' initial and final equilibria.