Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.

I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book

Abstract. Currently, the only discipline that has dealt with scientific representations— albeit non-structural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also deal with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an atomic “transforming ” event. This paper is conceived as a companion to [1], and is a revised version of [2]. Mathematics is the science of the infinite, its goal is the symbolic comprehension of the infinite with human, that is finite, means.

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.

Abstract. Currently, the only discipline that deals with scientific representations— albeit non-structural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also be dealing with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an elementary “transforming” event. Mathematics is the science of the infinite, its goal is the symbolic comprehension of the infinite with human, that is finite, means.

I argue that the evolutionary rationale for the brains of organisms was not representation nor reactive parallelism as is generally proposed, but was specifically an internal operational organization of blind biologic process instead. I propose that our cognitive objects are deep metaphors of primitive biological response rather than informational referents to environment. A concise operational organization was an evolutionary necessity to enable an adroit functioning of profoundly complex metacellular organisms in a hostile and overwhelmingly complex environment. It was, however, antithetical to a representative role. This hypothesis, in concert with ancillary logical and epistemological hypotheses, opens the very first real possibility for an actual and adequate solution of the problem of "consciousness".

We first examine Howard's analysis of the Bell factorizability condition in terms of 'separability' and 'locality' and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of 'non-separability' rather than 'non-locality' and that 'non-separability' implies the failure of space-time as a principle of individuation for quantum-mechanical systems. And I find his arguments for both claims to be lacking.

Abstract not found

In this paper I will propose the conceptually simplest, (but technically most difficult), part of a three part hypothesis for a solution of the problem of consciousness. {1} I propose that the evolutionary rationale for the brains of complex organisms was neither representation nor reactive parallelism as generally presupposed, but was specifically an internal organization of blind biologic process instead. I will propose that our cognitive objects are deep operational metaphors of primitive biological response. They are not informational referents to environment. They are the organizational tools of the megacellular colossus. I will argue that a pointedly operational organization was an evolutionary necessity to enable an adroit functioning of profoundly complex metacellular organisms in a hostile and overwhelmingly complex environment. I argue that this organization was antithetical to a representative role however because the latter ignores the crucial factor of urgency, (i.e. danger / risk)! I have argued elsewhere {2} that this hypothesis, (in concert with ancillary logical and epistemological hypotheses), opens the very first real possibility for an actual and adequate solution of the problem of "consciousness".

During the period of approximately 1570-1790 the first metamorphosis of science transformed the operational foundations of science, that were largely the heritage from the time of Aristotle, into its modern form. These new foundations consisted of the use of (1) Physical Experiments and the use of (2) Mathematical Models, involving di#erential equations. This metamorphosis was largely due to Brahe, Kepler, Galileo, Newton, Leibniz, Euler, and Lagrange. These operational methods were accompanied by the development of several philosophical attitudes and beliefs. One attitude (an implicit but operative frame of mind) arose from the loss of concern about the limitations of the encoding and decoding of information between experiments and mathematics; that is, an increased identification of the physical world with the mathematical models used to make very limited predictions of that world. The more overt philosophical beliefs related to the fundamental character of reductionistic methods in science. Among these beliefs was the idea that it is possible to synthesize this reductionistic knowledge, thereby obtaining a theory of the universe, capable of predicting all phenomena in nature. The idea that there is indeed any such thing as one set of laws which govern the behavior of the universe has its origins in antiquity, where the laws often referred to the desires of a god. This belief was immeasurably reinforced within Science by the success of Newton's `universal law' of gravitation. The blending of these persuasions was perhaps captured best, intended or not, in Einstein's famous remark, "I shall never believe that God plays dice with the world." Over the past century the character and structure of science has been going through a second process of fundamental change which...