The Three Worlds Theory outlined by Karl Popper in the 1960s has gained enthusiastic supporters, but many problems with the theory have also been pointed out. Among these problems, in this paper I will focus on the growth of knowledge, which is one of the key concepts in the Three Worlds Theory. First, I will reply to a criticism that is often made on the basis of a comparison between Popper's world 3 and Plato's world of ideas. Second, I will consider the relationship between the growth of knowledge and the autonomy of world 3. Finally, I will suggest that a study of a metaphysical evolutionary theory is necessary.

Humean compatibilists argue that determinism is compatible with leeway freedom. They refute one of the premises of the consequence argument that we have no choice about the laws of nature, and they do this by arguing that the laws of nature does not prevent us from doing otherwise by necessity since the laws of nature are just regularities. One of the humean compatibilists, Bernald Berofsky, starts off his critique of this premise by pointing out that the standard consequence argument fails to deal with the relationship between the physical and the mental. In order to overcome this deficit, he builds the expanded consequence argument, and argues that even this expanded argument has a corresponding false premise, namely that no matter what we do, the sentences representing the laws of nature are true. At the same time, he accepts two supervenience theses: (i) humean supervenience about laws and (ii) physicalism, especially the thesis that mental properties strongly supervene on physical properties. In this article, I argue that these two theses, together with the reasonable premises and inference rules, entail that no matter what we do, we cannot choose otherwise than we actually do. I conclude that Berofsky's defense of humean compatibilism fails because humean compatibilism would not succeed without abandoning either humean supervenience about laws or physicalism.

Electronic Theory of Organic Chemistry is one of the most characteristic theories in chemistry. This theory continues to be taught in current chemical education, despite its incompatibility with quantum theory and its clearly recognized limitations. How can this be explained? I will try to answer this question using the concept of explanatory understanding, which has recently been discussed in the philosophy of science. In doing so, I intend to use De Regt's approach (2017) to scientific understanding as a kind of explanatory understanding. By looking at it from the perspective of scientific understanding, I will be able to defend electronic theory of organic chemistry in this sense, as it provides organic chemists with an understanding of the phenomenon of organic synthesis.

McLaughlin and Miller (1992) provided a novel framework for resolving Zeno's paradox by employing Nelson-style nonstandard analysis. The following two principles play the key roles in their model of motion.The first is the ontological principle that every point in space-time is described as a vector of hyperreals. The second one is epistemological: one cannot distinguish two points in space-time that are infinitely close to each other. In this paper, we extract the topological essence from their argument. More precisely, we argue that the above principles correspond to introducing two topologies on the hyperreals, called Q-topology and μ-topology. We also consider Hellman-Shapiro's account of nonstandard analysis in the context of philosophy of continua.