Reductionism is a philosophical position which states that all of that field can be reduced to a common foundation.

This contrasts with emergentism, which says that the entire field cannot be reduced to a common foundation.

Note that this is different from the pluralism/monism distinction: monist reductionists believe there is only one way to reduce a field down to a common foundation, while pluralist reductionists would believe that there are multiple ways to reduce a field down to a common foundation.

Reductionism in the foundations of mathematics

Reductionism is inherent in the foundations of mathematics, because it posits that everything in mathematics can be reduced down to the foundations of mathematics.

On how ontological reductionism is problematic in the philosophy of science:

Daniel C. Dennett (1987) “True Believers.“ The Intentional Stance. Cambridge, MA: MIT Press.

Jimmy Aames (2019) Patternhood and Generality: A Peircean Approach to Emergence. European Journal of Pragmatism and American Philosophy, XI (2). (pdf, web)