In this paper, I try to defend Presentism. First of all, I explore how Presentism diverges to its versions and show that none of them, which include the currently standard Presentism that invokes tense logic, are tenable. Next, I point out that some philosophers argue that by replacing the Quinean criterion of existence with the Truthmaker Principle, another version of Presentism, which invokes tensed properties, can emerges. However, this version has a highly implausible conclusion. Finally, I argue that it can be avoided by taking the evidences of the past or future truths to be typical truthmakers of them.

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In [Kachi 2002a] I made comparison between several definitions of validity in Simple Partial Logic (SPL) and adopted two of them as most appropriate. In this paper, after elaborating more on these two definitions than in my previous paper and considering the characteristics of Partial Semantics, in which these definitions are given, I construct a tableau proof theory and prove its soundness and completeness. Then, based on the characterization of Partial Semantics, I will show that we can regard SPL as a logic of extensional alethic modality.

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The modern psychology and the positivism as a methodology of science in general both emerged hand in hand in the middle of 19th century. At the beginning, they regarded human consciousness as the absolute basis of knowledge, i. e. the “consciousness worship”. The misunderstanding that the consciousness is evidently known led to a false conviction that they could know all that should be known in the world. Meanwhile, natural sciences continued researches in their own way upon their own material evidences. With the decline of introspectionist psychology, the material evidences unnoticedly succeeded the overconfidence in the old evidence of the consciousness. The process opened the way to a belief that the being in the world is exhausted within the realm of positivistic science, i. e. “onto-delusion”. However, the “consciousness worship” is still in effect, because even the positivism based on material evidences cannot avoid depending upon “normal” human consciousness as a premise of objectivity. Psychology has played the central role in this delusional process. We have no right to demand universal validity from the beginning in any method of science.

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Enormous development of physics in the early 20th century brought about a prospect for Unified Science. However physics itself is now loosing its identity, as seen in a lively study of quantum information. What is happing now is a specification into parts rather than a unification of parts.

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D. Hilbert raised the problem to prove consistency of formalized mathematics. In this paper I will expound its background and the status quo of the consistency proofs. First let me explain the intended significance of proving consistency, and a background idea to divide mathematical objects in two, i. e., transfinite/finitary objects. Next I will discuss impacts of the incompleteness theorems to the problem and their interpretation. Finally let me give sketches of the practice of the consistency proofs due to G. Gentzen et al. and their significance, and the present state of the consistency proofs.

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