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Proximity ferroelectricity has recently been reported as a new design paradigm for inducing ferroelectricity, where a non-ferroelectric polar material becomes a ferroelectric by interfacing with a thin ferroelectric layer. Strongly polar materials, such as AlN and ZnO, which were previously unswitchable with an external field below their dielectric breakdown fields, can now be switched with practical coercive fields when they are in intimate proximity to a switchable ferroelectric. Here, we develop a general Landau-Ginzburg theory of proximity ferroelectricity in multilayers of non-ferroelectrics and ferroelectrics to analyze their switchability and coercive fields. The theory predicts regimes of both "proximity switching" where the multilayers collectively switch, as well as "proximity suppression" where they collectively do not switch. The mechanism of the proximity ferroelectricity is an internal electric field determined by the polarization of the layers and their relative thickness in a self-consistent manner that renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier. Further reduction in the coercive field emerges from charged defects in the bulk that act as nucleation centers. The application of the theory to proximity ferroelectricity in Alx-1ScxN/AlN and Zn1-xMgxO/ZnO bilayers is demonstrated. The theory further predicts that multilayers of dielectric/ferroelectric and paraelectric/ferroelectric layers can potentially result in induced ferroelectricity in the dielectric or paraelectric layers, resulting in the entire stack being switched, an exciting avenue for new discoveries. This thawing of "frozen ferroelectrics", paraelectrics and potentially dielectrics, promises a large class of new ferroelectrics with exciting prospects for previously unrealizable domain-patterned optoelectronic and memory technologies., Comment: 42 pages including 7 figures and 4 Appendices. To be submitted to Physical Review