The paper questions the validity of the speculative method of Quentin Meillassoux as presented in his main work After Finitude. An Essay on the Necessity of Contingency. His book is considered to have initiated a new philosophical current in continental philosophy, called Speculative realism, which is supposed to go beyond the division analytical-continental in philosophy and to revive the interest in metaphysics. Meillassoux calls his position “speculative materialism” and he wants to prove, with some sophisticated philosophical arguments, the existence of the material (it means non-subjective) Absolute. He claims that his approach falls outside of the pitfalls of dogmatic metaphysics, which tries to prove the existence of some necessary entity, and of so called “correlationism”, which imprisons the thought in subjectivity or culture. Meillassoux pretends to prove out of facticity: 1) the only nondogmatic necessity: the necessity of contingency, 2) the necessity of contingent things, 3) the principle of unreason, 4) the ontological foundation of the principle of non-contradiction, 5) the existence of omnipotent hyper-Chaos, 6) the validity of mathematics in the description of the objective world. The article tries to prove systematically the inconsistency of the arguments that serve Meillassoux in the construction of his speculative and purportedly non-metaphysical system.