What is the actual paradox in the Paradox of Thrift?
The Wikipedia article has several different quotations over time, though I would state the claimed paradox as a variant of (2), possibly something like 


  an increase in the rate of saving can lead to lower total savings


perhaps illustrated with a graph something like 



which suggests that the paradox seems to depend on the the combined relationships between income and savings and between investment and output, together with some macroeconomic tautologies.  If the relationships were different, or if the tautologies did not cause changes in equilibria, there might not be a paradox