Cantor abstractionist account of cardinal numbers has been discredited as a psychological theory of numbers which leads to contradiction – see Frege (1884) and Dummett (1991). The talk intends to resist these objections by arguing for the coherence and plausibility of Cantor's proposal. The defence of Cantorian abstraction will be built upon the set theoretic framework of Bourbaki (1968) – called BK – which is formulated in First-order Logic extended with the ε-operator. I will first introduce the axiomatic setting of BK and the definition of cardinal numbers. Then, I will present Cantor (1915) abstractionist theory, stressing the legacy with his early work of Cantor (1883), which will highlight two assumptions concerning the definition of cardinal numbers. I will argue that these assumptions are supported as well by the BK definition of cardinal numbers, which will be compared to the ones of Zermelo-von Neumann and Frege-Russell. Based on the similarities between the BK definition and Cantor (1915) abstractionist theory, I will characterize the BK abstractionist account of cardinal numbers by examining two objections originally made by Frege (1884) to Cantor (1915) proposal. A key ingredient in the defence of Cantorian abstraction will be played by reasoning about arbitrary sets, as denoted by the ε-operator in the definition of cardinal numbers.