The purpose of this paper is to make clear the difference between Heyting, who was a representative scholar of the intuitionist school and who first introduced the intuitionistic formal logic and arithmetic, and Gentzen, who was a representative scholar of the Hilbertian finitist school, by a close look at their constructive interpretations of logical connectives. We show that although both Gentzen and Heyting proposed very similar constructive interpretations for logical connectives of intuitionistic logic mathematically, their interpretations were based on very different standpoints philosophically: Gentzen used the logical positivist way of verification theory of meaning, while Heyting emphasized the Husserlian phenomenological way of verification theory of meaning. In addition, we shall point out that although both Heyting and Gentzen emphasized similar forms of constructive interpretation for the intuitionistic implication in terms of "proof-construction" , the notion of "proof" here was taken very differently by Gentzen and Heyting, resulted in the different attitudes towards the intuitionistic logic.
Kripke's monumental work on Wittgenstein made it possible to think about the global structure of Philosophical Investigations (P.I.) and to suppose the existence of systematic thinking in that book by emphasizing the importance of so called rule following considerations for later Wittgenstein. On the other hand, however, Kripke's work seems to have misled us to a wrong assumption that the central theme in these considerations is not the concept of rules but that of meaning. I learned from my past systematic investigation of Wittgenstein's texts, including both P.I. and his other texts that reveal us the specific contexts in which his huge considerations concerning rules were conducted in 1930's and 1940's, that the problems concerning rules play the central role in the formation of matured philosophy of later Wittgenstein exhibited in P.I. In this paper, I would like to show 1) Wittgenstein faced not one but three problems concerning the concept of 'rules of a language game' in the initial 188 sections of P.I., one of which is the paradox of rules, 2) he solved these problems in §§ 198-243 of P.I. by presenting a new concept of 'following a rule', which is supposed to be prior to any explicit rules with respect to both existence and meaning, 3) 'following a rule' is a generic name for primitive linguistic practices such as counting or ordering, out of which all our linguistic practices or language games are constructed, 4) according to Wittgenstein's new understanding of human linguistic practices based on the concept of 'following a rule', any forms of Platonism as well as formalism in mathematics cannot be correct.
This paper presents a theory of akrasia that draws essentially on the notion of time preference. When we make a decision over which course of action to pursue, it often happens that what can be obtained in the near future motivates us more strongly than what lies temporally further afield, although we are aware that the latter is to be evaluated more highly than the former. This is the effect of time preference, and I will argue that it plays a crucial role if we are to understand how our behaviour can exhibit weakness of will.
Recently philosophers of biology have debated over the status of evolutionary theory; is it interpreted as realistic or anti-realistic? I discuss this issue by using Fisher's formula of natural selection as an example. In generalizing evolutionary phenomena, we need only partial information. So I compare the formula of natural selection with information theory, which gives us a reasonable tool of inference on the basis of partial information, and show that the formula of natural selection may be regarded as a part of information theory. I conclude that there is the mixture of realistic and anti-realistic factors in the formula of natural selection, and that the aim of evolutionary theory is rational prediction or explanation of phenomena on the basis of partial information, not complete description of it on the basis of full information.
Living systems have to maintain a particular relationship with the environment by continuing trans-boundary interactions with the environment. To understand how living systems have evolved their ability to manage the uncertainty of the environments, it is needed to formalize the probabilities of events occurring to an internal entity, not to an external, meta-observer, in relation to objective properties of the entity and the environment. I argue that major philosophical interpretations are not sufficient to explain the relationship between objective properties of living systems and probabilities of events occurring to the systems, and propose an alternative interpretation and theory of probabilities of events, named internal probability theory, to apply probability concept to the explanation of the evolution of life. In the internal probability theory, the probability of an event is interpreted as the degree of the uncertainty of events occurring to an internal material entity, not to an external epistemic observer. A mathematical model shows that the probabilities of events that a given subject entity experiences are not simply determined by the degrees of discrimination between different states of the environment by the entity, but determined by the interaction between the subject and the environment, arising from their cognitive properties, such as selectivity and discrimination ability. With the aid of the internal probability concept, the probability of survival can be realized in terms of objective properties of the subject entity and the environment, which may lead us to an understanding of how living systems manage the uncertainty of the environment.
The objective of this paper is to analyze the argumentation of evolutionary psychology often referred to as 'evolutionary functional analysis' and to point out some of its inherent problems from a methodological point of view. The conclusion to be drawn is this: although evolutionary functional analysis can be considered to be a scientific practice since it fits into the formula of hypothetico-deductive method, there still remain enormous elements of unfounded speculation in it. This becomes especially evident in the process of identifying the adaptive problems in the Environment of Evolutionary Adaptedness(EEA) as well as in the presuppositions implicit behind the thesis of the ancient origin of our current mind.
Experimental endeavor addressing the emergence of life faces two different frameworks of space and time. While the space-time framework applicable to the experimentalist who is designing the setup is classical in accepting both space and time being homogeneous with infinite extension, the framework intrinsic to atoms and molecules moving around inside the setup is quantum-mechanical and accordingly nonlocal though limited in its extension. A descriptive access to those atoms and molecules carrying quantum nonlocality with limited extension can be made with use of the corresponding demonstrative pronouns. One advantage of referring to demonstrative pronouns instead of ordinary nouns rests upon the ease with which one can avoid an unnecessary theoretical burden of sticking to the classical space-time framework with infinite extension all the time. Once the empirical fact of quantum non-locality with limited extension is duly focused upon, atoms and molecules as quanta can become cohesive between themselves if they happen to interact with each other. Quantum non-locality makes material interactions cohesive in precipitating synchronization between the mutually interacting bodies. Assimilation as a material capacity grounded upon the cohesiveness latent in the act of coming into synchronization, which is totally absent in the classical framework, can underlie the synthetic chemical reactions which may have been relevant to the emergence of life.
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