It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a complete one (...) are established. (shrink)

This paper tries to extend Hintikka's inductive logic so that we can confirm a causally necessary statement. For this purpose, a joint system of inductive logic and logic of causal modalities is constructed. This system can offer a plausible explication of the distinction between nomic and accidental universality, as well as a good formulation of a causal law. And the transition from actuality to causal necessity is construed, in this system, as essentially probabilistic; i.e. no statements about actuality can entail (...) a necessary statement, but certain statements about actuality can single out a most probable causal law. (shrink)

In this paper, (1) I argue that Sherlock Holmes was a good logician according to the standard of his day, and (2) I try to show what his method of reasoning was. Now, (2) is a harder task than (1), because we have to identify the essential features of his method of reasoning. In order to show this, I have not only to examine what Holmes says he is doing, but also to look at the methods of scientific reasoning recommended (...) by several distinguished philosophers of science in the 19th century. I want to examine Holmes's method of reasoning in a historical setting; and this has something to do with the philosophy of science in the 19th century, and hopefully with the philosophy of science today. I will examine whether such methods are similar or dissimilar to Holmes's method. Logicians and philosophers I wish to examine are, John Herschel, John Stuart Mill, William Whewell, Augustus de Morgan, and William Stanley Jevons; however, since the space is limited, I cannot do justice to all of them. My conclusion is this: Sherlock Holmes was distinctly different from Herschel or Mill or Whewell who may be called a classical methodologist; but he was very close to de Morgan or Jevons who were an advocate of the new symbolic logic and the probabilistic theory of induction. But what is the point of showing all this? The rise and development of statistical method in the19th century had a great impact on the theories of scientific reasoning, and de Morgan's or Jevons's theory is a newer theory of induction in this century. And such a change of methodology is clearly reflected in the popular stories of Sherlock Holmes, which were written in the late 19th century and early 20th century. (shrink)

In this paper, I will try to exploit the implication of Leibniz's statement in Monadology (1714) that "there is a kind of self-sufficiency which makes them [monads] sources of their own internal actions, or incorporeal automata, as it were" (Monadology, sect.18). Leibniz's monads are simple substances, with no shape, no magnitude; but they are supposed to produce the phenomena resulting from their activities, which for us humans look as the whole world, the nature. The activities of a monad are characterized (...) by mental terms, perceptions (internal states) and appetites (which change the internal state). By means of perceptions, a monad becomes a "perpetual living mirror of the universe"; it can receive the information of other monads and it can send its own, in turn, to others. The communication and interconnection thus produced result in the physical and the psychical phenomena observed by us, humans. According to Leibniz, all monads are governed by the teleological law given by the God, and the world of phenomena are governed by the causal and mechanical law. Leibniz argues that there is a pre-established harmony among the monads so that this double character is no problem. Now, I will propose an informational interpretation of monadology, which regards the monads as an automaton governed by the God's program and arranged appropriately; and I will argue that Leibniz's scenario can be defended in terms of this interpretation. The crucial part of this interpretation is that the God's program and the monads' activities are related with the phenomenal world by means of a coding by God. This interpretation is also defended on the textual basis, with a special reference to Leibniz's distinction between primitive and derivative forces. Drawing on R. M. Adams's careful reading of Leibniz's texts (Leibniz: Determinist, Theist, Idealist, 1994), I will argue that his rendering is quite in conformity with my interpretation, although he does not seem to be aware of the notion of coding. (shrink)

Do you know the Japanese equivalent for "philosophy"? That word, "tetsugaku", was coined after the Meiji Revolution. Do you know when the standard philosophy of science, in the form of the logical empiricism, was introduced into Japan? After the World War II, around 1950. Do you know whether or not the philosophy of science, especially its "hardcore", is studied seriously in Japan? Very few people are studying the philosophy of space and time, the philosophy of quantum mechanics, the philosophy of (...) evolution, the philosophy of probability, or the philosophy of social sciences. Do you know how many HPS departments exist in Japan? Only three, one is founded in 1951 and its graduate program was extended in 1970, and the other two were founded around 1993. Now, with these preparations, you are beginning to understand what I am going to talk about---Is Philosophy of Science alive in Japan? I will briefly outline the history of the philosophy of science in Japan, and discuss some of its peculiarities. And from this discussion, I wish to point out what is needed for the philosophy of science in Japan. Here is an Outline: " 1. Three Basic Facts 2. Taketani's Doctrine of the Three Stages 3. Logical Empiricism 4. Scientists and Philosophers 5. "New" Philosophy of Science 6. What is needed for Japanese Philosophy of Science? ". (shrink)

Leibniz coined the word “dynamics,” but his own dynamics has never been completed. However, there are many illuminating ideas scattered in his writings on dynamics and metaphysics. In this paper, I will present my own interpretation of Leibniz’s dynamics and metaphysics. To my own surprise, Leibniz’s dynamics and metaphysics are incredibly flexible and modern. In particular, the metaphysical part, namely Monadology, can be interpreted as a theory of information in terms of monads, which generate both physical phenomena and mental phenomena. (...) The phenomena, i.e., how the world of monads appears to each monad must be distinguished from its internal states, which Leibniz calls perceptions, and the phenomena must be understood as the results of these states and God’s coding. My distinctive claim is that most interpreters ignored this coding. His dynamics and metaphysics can provide a framework good enough for enabling Einstein’s special relativity. And finally, his dynamics and metaphysics can provide a very interesting theory of space and time. In Part 1, we will focus on the relationship between metaphysics and dynamics. Leibniz often says that dynamics is subordinated to metaphysics. We have to take this statement seriously, and we have to investigate how dynamics and metaphysics are related. To this question, I will give my own answer, based on my informational interpretation. On my view, Leibniz’s metaphysics tries, among others, to clarify the following three: How each monad is programmed. How monads are organized into many groups, each of which is governed by a dominant monad ; this can be regarded as a precursor of von Neumann’s idea of cellular automata. And how the same structure is repeated in sub-layers of the organization. This structure is best understood in terms of the hierarchy of programs, a nested structure going down from the single dominant program to subprograms, which again controls respective subprograms, and ad infinitum. If we may use a modern term, this is a sort of recursion, although Leibniz himself did not know this word. And one of my major discoveries is that the same recursive structure is repeated in the phenomenal world, the domain of dynamical investigations. Recursion of what, you may ask. I will argue that it is elastic collision. For Leibniz, aside from inertial motions, dynamical changes of motion are brought about by elastic collisions, at any level of the infinite divisibility of matter. This nicely corresponds to the recursive structure of the program of a monad, or of the program of an organized group of monads. This is the crux of his claim that dynamics is subordinated to metaphysics. Moreover, the program of any monad is teleological, whereas the phenomenal world is governed by efficient cause of dynamics. And it is natural that the pre-established harmony is there, since God is the ultimate programmer, as well as the creator. (shrink)

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s paper, and J. A. Cover’s (...) improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1- to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (shrink)

Darwin argued for the biological basis of morality in his Descent of Man (1871). Beginning with the thesis of the continuity of man and animals, he tried to explain the origin of the moral sense, or conscience, as understood as an ability to discern right and wrong, and to feel guilty if one realizes to have done wrong. His argument is that, in any animal with social instincts and sufficient intellectual powers, a moral sense would be developed. Although Darwin's argument (...) had some missing links, I try to show that his argument can be consistently reconstructed, in view of the recent development of evolutionary biology and behavioral ecology. As I understand, Darwin's basic tenet is reductionism via evolutionary processes (natural selection, in particular): morality can be reduced to a combination of non-moral factors, each of which can be shared with other animals; you do not have to assume that morality is sui generis. (shrink)

Darwin's famous book, is not an easy book for the reader. Especially, the central part of his doctrine addressing the problem of how a small difference between varieties of a single species may become larger and larger and become a large difference between two distinct species or between two genera etc. is often confusing. Darwin brings in the "principle of divergence" in order to answer this central question, but the problem is: what is the status (...) of this principle of divergence? Is it an independent principle from that of natural selection? How does it work, and how, exactly, does Darwin explain the diversification of organic beings? In this paper, I will give a logical analysis of Darwin's whole reasoning on this problem, based on the text of as well as as of . (shrink)

I have developed an informational interpretation of Leibniz’s metaphysics and dynamics, but in this paper I will concentrate on his theory of time. According to my interpretation, each monad is an incorporeal automaton programed by God, and likewise each organized group of monads is a cellular automaton governed by a single dominant monad. The activities of these produce phenomena, which must be “coded appearances” of these activities; God determines this coding. A crucially important point here is that we have to (...) distinguish the phenomena for a monad from its states. Both are a kind of representation: a state represents the whole world of monads, and phenomena for a monad “result” from the activities of monads. But the coding for each must be different; R for the first, Ph for the second, where W is a state of the monadic world. The reason for this is that no monadic state is in space and time, but phenomena occur in space and time. Now, the basis of the phenomenal time must be in the timeless realm of monads. This basis is the order of state-transition of each monads. All the changes of these states are given at once by God, and these do not presuppose time. The coded appearances of this order occur in time, and its metric must depend on God’s coding for phenomena. For humans, in particular, this metric time is derived from spatial distance via the laws of dynamics. Thus there may well be an interrelation between spatial and temporal metric. This means that the Leibnizian frame allows relativistic metric of space-time. I will show this after outlining Leibniz’s scenario. (shrink)

This is a short summary of my new interpretation of Leibniz’s philosophy, including metaphysics and dynamics. Monadology is the core of his philosophy, but according to my interpretation, this document must be read together with his works on dynamics and geometry Analysis Situs, among others. Monadology describes the reality, the world of monads. But in addition, it also contains a theory of information in terms of the state transition of monads, together with a sketch of how that information is transformed (...) into the phenomena via coding. I will argue that Leibniz’s program has a surprisingly wide range, from classical physics to the theories of relativity, and extending even to quantum mechanics. (shrink)

In this paper, I will present an analogy between Leibniz’s Monadology and musical works. A musical work is usually written down in a score. It is divided into many voice parts, and for every part, it gives all musical information necessary for performance. Now, since any such score specifies all notes of that musical work, at once, it can be regarded as atemporal; musical time does not flow in a score. And it does not specify spatial relations among the voice (...) parts. Thus, the musical work described in a score exists as an informational entity. A score is a kind of “program” for playing. This program contains invariant structures, and such structures define the identity of the work. On the other hand, it allows freedom for performers. Any performer has to “interpret” the work, and his or her performance is an expression of that interpretation. Any such interpretation may be regarded as a kind of “coding” for transforming the specified invariant structures into actual sounds in space and time. This dual aspect of musical works is the basis of my analogy. It should be conducive to improving our interpretation of Monadology. (shrink)

Drawing on my previous paper “Monadology and Music”, I will further pursue the analogy between Monadology and music. I wish to emphasize that good examples of “pre-established harmony” can be extracted from this analogy. Also, a good illustration of “Leibniz’s Demon” can be obtained. This Demon is such that it can tell, given a piece of matter, the whole history of the world, past, present, and future. In terms of finite examples of musical pieces and their performances, Leibniz’s point of (...) this Demon can be better understood. (shrink)

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s paper, and J. A. Cover’s (...) improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1-to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (shrink)

In Part 3, I will discuss the problems of inertia and gravity in Leibniz, and present three conjectures: If Leibniz were really ready to insist on relativity, he would have to assert the relativity of inertial motion. In Leibniz’s theories of dynamics and geometry, there was a struggle between his predilection for straight line and his adherence to an optimality principle. Gravity, as well as inertia, can be considered as a universal feature of the world, so that the foundation of (...) both may have a common root. Further, drawing on the results in Part 1 and Part 2, I will argue for the need of a unified interpretation of Leibniz’s metaphysics and dynamics. My three conjectures as regards Leibniz’s possible treatment of inertia and gravity are proposed along a unified interpretation, in terms of my informational reconstruction of Leibniz’s philosophy. Finally, the most important features of the informational interpretation are summarized. The synopsis of the whole paper is added. (shrink)

In Part 3, I will discuss the problems of inertia and gravity in Leibniz, and present three conjectures: If Leibniz were really ready to insist on relativity, he would have to assert the relativity of inertial motion. In Leibniz’s theories of dynamics and geometry, there was a struggle between his predilection for straight line and his adherence to an optimality principle. Gravity, as well as inertia, can be considered as a universal feature of the world, so that the foundation of (...) both may have a common root. Further, drawing on the results in Part 1 and Part 2, I will argue for the need of a unified interpretation of Leibniz’s metaphysics and dynamics. My three conjectures as regards Leibniz’s possible treatment of inertia and gravity are proposed along a unified interpretation, in terms of my informational reconstruction of Leibniz’s philosophy. Finally, the most important features of the informational interpretation are summarized. The synopsis of the whole paper is added. (shrink)

Deborah Mayo propounded the epistemology of experiment in her Error and the Growth of Experimental Knowledge (1996), and the notion of severity plays an essential role in her epistemolgy. In the following two notes, I wish to point out a defect of her definition of severity, and to argue that she must revise this definition in conformity with what she actually does in her book (Note 1). The revision has some important consequence: in order to apply Mayo's severity consideration to (...) experimental tests, we have to know all alternative hypotheses, in a given experimental situation, in advance. Mayo does not seem to recognize this, and her analysis of Perrin's experiment seems to be affected by this defect. I will present what I regard as the correct way to reconstruct Perrin's argument (Note 2). (shrink)

In this paper, I will show that Sherlock Holmes was a good logician, according to the standard of the 19th century, both in his character and knowledge (sections 2 and 3). Holmes, in all probability, knew William Stanley Jevons’ clarification of deductive reasoning in terms of “logical alphabets” (section 4). And in view of his use of “analytic-synthetic” distinction and “analytic reasoning,” I will argue that Holmes knew rather well philosophy too, as far as logic and methodology are concerned (section (...) 5). Further, I have argued that Holmes introduced new twists (presumably, following Jevons) into analytic reasoning: application to reasoning as regards causal sequences, and probabilistic elimination of hypotheses (sections 6 and 7). Also, in this context, I will clarify the significance of Holmes’ metaphor of the “little attic”: without fine assortment in your brain, it is hard to devise promising hypotheses (section 8). Finally, presenting a simple model of probabilistic inference, which became prevalent in the 19th century (section 9), I claim that the essence of Holmes’ reasoning consists of probabilistic inferences, “balance probabilities and choose the most likely,” which is nothing but probabilistic elimination of hypotheses in the light of evidence. I also argue that my claim fits in well with the text of Holmes stories (section 10). (shrink)

(1) Darwin inherited Lyell’s methodology and applied it to the animate beings. This led him, eventually, to the principle of natural selection. This principle enabled him to expel God from biology. (2) Darwin diverged from Lyell on Man and Morality, presumably because of his experience in Tierra del Fuego. This led him to the thesis of continuity of man and animals, and he noticed the function of morality. (3) The process of Darwin’s theory construction may be likened to gradual evolution. (...) Each element of his theory, by itself, is not revolutionary. But taken together and combined, these elements produced a revolutionary change. (shrink)

The problems of the social responsibility of the scientist became a subject of public debate after the World War II in Japan, thanks to the activities and publications of Yukawa and Tomonaga. And such authors as J. Karaki, M.Taketani, Y. Murakami, and S. Fujinaga continued discussion in their books. However, many people seem to be still unaware of the most important source of these problems. As I see it, one of the most important treatments of these problems was the Franck (...) Report (June 11, 1945) submitted to the US government by James Franck (chairman) toward the end of the war. This Report contains many important ideas and suggestions as regards the responsibility of the scientist, the morality of the use of atomic bombs, the prospective nuclear armaments race, and the possibility of international control of nuclear power. However, I should like to concentrate only on the first topic in this paper. Why did Franck and his committee at Metallurgical Laboratory of the University of Chicago feel the urgent need for writing and submitting this Report? According to the Report, "in the past, scientists could disclaim direct responsibility for the use to which mankind had put their disinterested discoveries. We cannot take the same attitude now because the success which we have achieved in the development of nuclear power is fraught with infinitely greater dangers than were all the inventions of the past." (I. Preamble) This passage seems to contain the crux of our problem: These scientists clearly recognize the "new" responsibility for them, and the ground of this responsibility is also clear enough; i.e., when a new scientific discovery or invention turns out to have grave bearings on human interests, the scientists who became aware of that are responsible for notifying people of this and advise to look for suitable means for avoiding prospective dangers. In the rest of the paper, I elaborate the reasoning behind the preceding passage, and confirm that basically the same idea and reasoning has been repeated and developed in Russell-Einstein Manifesto (1955), by Pugwash Conferences (first in 1957), by Tomogana, and by Rotblat (the long-time Secretary of Pugwash, who received the Nobel Peace Prize together with the Conference in 1995). (shrink)

It is often said that the kinetic theory of gases is one of the best examples of the reduction of one theory into another; that is, the classical theory of thermodynamics [or to be more exact, a significant portion of it] is alleged to be reduced to the kinetic theory, which is based on the Newtonian mechanics and the atomistic view of the matter. But what is the nature of this alleged "reduction"? If you want to know the right answer (...) to this, the best way is to examine the historical development of the kinetic theory. The kinetic theory is a theoretical attempt to explain the nature of gases and heat processes, in general, in terms of the movements of numerous molecules constituting a gas. Its major advocates were James Clerk Maxwell (1831-79) and Ludwig Boltzmann (1844-1906); in the course of their work on the kinetic theory, they had to struggle with several conceptual problems, as well as with many empirical problems, and these conceptual problems have something to do with our question of theory reduction. And you will see that these problems center on the concept of probability. Drawing on Dr. Shin'ichiro Tomonaga's examination, I will argue that their case was not a reduction to, but an extension of, the Newtonian mechanics. (shrink)