This paper aims to elucidate how the meaning of words would change by the experience in using figurative expressions on the basis of later Wittgenstein's considerations. The various figurative expressions he investigated can be divided into three categories, metaphors in thinking, metaphors in perception, and “the secondary meaning”. I insist that all of these are brought about by the notice or forefeel of resemblances which is also needed in aspect-switching and conclude that the experiences of meaning could be the driving forces for changes of language games.

One of the most influential approaches to understanding the nature of genetic information is by the etiological theory of function, its most sophisticated exemplar being teleosemantics. Such discussions are largely focused on genetic information carried by the genes. Although the concept of gene itself has been a target of intense arguments, most of the earlier arguments had adopted rather simple and naive ones. By considering the arguments regarding the concept of gene more seriously, the current study aims to investigate the philosophical consequences of teleosemantic analysis of genetic information and shows that the nature of genetic information can differ depending on which concept of gene we adopt.

Since Gödel's Incompleteness Theorems were published in 1931, not a few mathematicians have been trying to do mathematics in a framework as weak as possible to remain in a “safe” terrain. While the Incompleteness Theorems do not offer any direct motivations for exploring the terrae incognitae of the alarmingly general and consistency-wise strong settings like the full ZFC or even ZFC with large large cardinals etc., Gödel's Speedup Theorem, a sort of a variant of the Incompleteness Theorems, in contrast, seems to provide positive reasons for studying mathematics in these powerful extended frameworks in spite of the peril called the (in)consistency strength.

In this article of purely expository character, we will examine a version of the Speedup Theorem with a detailed proof and discuss the impact of the Speedup Theorem on the whole mathematics.