The article aims to determine whether it is possible to build the reliably practiced classical philosophy, understood as a metaphysical research, directed towards the nature of objective reality. The purpose of this kind of philosophizing is knowledge and truth. Moreover, the practice of such philosophizing and its results should meet some of the characteristics of science. The paper establishes a set of conditions that have been imposed on the science of metaphysics by Kazimierz Twardowski. Among the conditions of such philosophizing (...) are anti-dogmatism, criticism, inter-subjectivity of philosophizing and its results, proper epistemic justification of philosophical beliefs, application of the analysis method, rigorous language and reasoning, the use of experience and scientific knowledge. The paper considers these conditions to be correct in most cases and argues that metaphysics can meet them. The existing cases of analytical metaphysics show that metaphysics is possible as a science. Next, the article argues that the late Twardowski failed to substantiate his claim that metaphysical positions which he classified as a world-view philosophy could not be scientifically justified, which could have been possibly done with differentiating ways of understanding what such a scientific justification should be. The article argues that he did not take into account a reductive conception of the metaphysical philosophy, which even though it allows the plurality of metaphysical explanations and does not force anyone to accept one position as the only possible and correct explanation, would have an objective value, if such metaphysics were elaborated indeed. (shrink)