Breakthrough technologies are technologies that introduce radically new capabilities or a performance increase of at least an order of magnitude. Examples are the turbojet, inertial navigation, and autonomous driving. However, a remarkable pattern for these technologies is that their feasibility seems to have been initially contested. Existing approaches for technology assessment such as the Technology Readiness Levels do not seem to be adequate for capturing the subtle dimension of assessing the potential of breakthrough technologies, as they rather focus on technological maturity. Important aspects such as performance, enabling systems, and contextual factors are not taken into account. This paper addresses the principle feasibility of breakthrough technologies by looking at what arguments for and against principle feasibility were/are used and how the feasibility question was resolved. For this purpose, we reconstruct past and ongoing principle feasibility debates of four exemplary breakthrough technologies using a technology conceptual model and argument maps. For the four technologies analysed, we conclude that sufficient expected performance was a key issue debated in all cases, whereas physical effects and working principles were issues for breakthrough technologies with a relatively low maturity. Principle feasibility issues for breakthrough technologies seem to be resolved by introducing new component technologies and working principles. For future work, we propose the use of case and field studies in order to explore contextual feasibility criteria for breakthrough technologies such as injection into existing system architectures, enabling systems, and market readiness.