Emergence and singular limits

Abstract

Recent work by Robert Batterman and Alexander Rueger has brought attention to cases in physics in which governing laws at the base level "break down" and singular limit relations obtain between base-and upper-level theories. As a result, they claim, these are cases with emergent upper-level properties. This paper contends that this inferencefrom singular limits to explanatory failure, novelty or irreducibility, and then to emergence-is mistaken. The van der Pol nonlinear oscillator is used to show that there can be a full explanation of upper-level properties entirely in base-level terms even when singular limits are present. Whether upper-level properties are emergent depends not on the presence of a singular limit but rather on details of the ampliative approximation methods used. The paper suggests that focusing on explanatory deficiency at the base level is key to understanding emergence in physics.

What Is the Paradox of Phase Transitions?

“…Lebowitz 1999, S346;Liu 1999, S92;Morrison 2012, 143;Prigogine 1997, 45), which necessitate the development of new physical theory (Callender 2001, 550), and inducing a wide array of literature that argues to the contrary (e.g. Bangu 2009;Batterman 2005Batterman , 2011Butterfield 2011;Menon and Callender 2011;Norton 2011;Wayne 2009). …”

“…Authors such as Lebowitz (1999, S346), Liu (1999, S92), Morrison (2012, 143) and Prigogine (1997, 45) can be read as embracing tenet 3 and identifying PT as a kind of non-reductive emergent phenomena. Contrasting attitudes have been voiced by Wayne (2009), where Callender (2001 and Menon and Callender (2011) explicitly deny that phase transitions are irreducible and emergent phenomena by rejecting tenet 3. Butterfield (2011) can be read as both denying and embracing tenet 3, in an effort to reconcile reduction and emergence.…”

Emergence and Reduction in Physics

“…Ardourel, 2018;Butterfield, 2011aButterfield, , 2011bNorton, 2012Norton, , 2014Palacios, 2019;Wayne, 2012), singular limits can be explained away in favor of reduction. In this section, I will give an overview of this discussion by focusing not only on the case of phase transitions, but also on other cases of singular limits, such as the van der Pol nonlinear oscillator (Rueger, 2000;Wayne, 2012). I will take the side of the reductionists by adding some remarks on the notion of intertheoretic reduction and by defending a compatibility between reduction and emergence.…”

The structure of asymptotic idealization

“…Such idealizations, he claims dramatically, though they rest on infinities that do not exist in the physical world, are essential for explaining certain physical behaviors; they do this by revealing emergent qualitative features of the situation that dominate the relevant actual physics and so "constrain and largely determine" what happens, or at least those aspects of what happens that are to be explained.1 Other writers, such as Belot (2005), Wayne (2012), Pincock (2012), and Norton (2012), have disputed Batterman's views, arguing that asymptotic idealization is not the sole route to understanding the phenomena in question (Belot and Norton) or that idealization does not necessarily imply the emergence of new properties (Wayne and Pincock).…”