Philosophical questions about minds and computation need to focus squarely on the mathematical theory of Turing machines (TM's). Surrogate TM's such as computers or formal systems lack abilities that make Turing machines promising candidates for possessors of minds. Computers are only universal Turing machines (UTM's)—a conspicuous but unrepresentative subclass of TM. Formal systems are only static TM's, which do not receive inputs from external sources. The theory of TM computation clearly exposes the failings of two prominent critiques, Searle's Chinese room (...) (1980) and arguments from Gödel's Incompleteness theorems (e.g., Lucas, 1961; Penrose, 1989), both of which fall short of addressing the complete TM model. Both UTM-computers and formal systems provide an unsound basis for debate. In particular, their special natures easily foster the misconception that computation entails intrinsically meaningless symbol manipulation. This common view is incorrect with respect to full-fledged TM's, which can process inputs non-formally, i.e., in a subjective and dynamically evolving fashion. To avoid a distorted understanding of the theory of computation, philosophical judgments and discussions should be grounded firmly upon the complete Turing machine model, the proper model for real computers. (shrink)

Why do people create extra representations to help them make sense of situations, diagrams, illustrations, instructions and problems? The obvious explanation— external representations save internal memory and com- putation—is only part of the story. I discuss seven ways external representations enhance cognitive power: they change the cost structure of the inferential landscape; they provide a structure that can serve as a shareable object of thought; they create persistent referents; they facilitate re- representation; they are often a more natural representation of (...) structure than mental representations; they facilitate the computation of more explicit encoding of information; they enable the construction of arbitrarily complex structure; and they lower the cost of controlling thought—they help coordinate thought. Jointly, these functions allow people to think more powerfully with external representations than without. They allow us to think the previously unthinkable. (shrink)

In this paper I argue that much of the confusion and mystery surrounding the concept of "self" can be traced to a failure to appreciate the distinction between the self as a collection of diverse neural components that provide us with our beliefs, memories, desires, personality, emotions, etc (the epistemological self) and the self that is best conceived as subjective, unified awareness, a point of view in the first person (ontological self). While the former can, and indeed has, been extensively (...) studied by researchers of various disciplines in the human sciences, the latter most often has been ignored -- treated more as a place holder attached to a particular predicate of interest (e.g., concept, reference, deception, esteem, image, regulation, etc). These two aspects of the self, I contend, are not reducible -- one being an object (the epistemological self) and the other a subject (the ontological self). Until we appreciate the difficulties of applying scientific methods and analysis to what cannot be reduced to an object of inquiry without stripping it of its essential aspect (its status as subject), progress on the "self", taken as a pluralistic construct, will continue to address only one part of the problems we face in understanding this most fundamental aspect of human experience. (shrink)

Four Basic Logical Issues: The paper addresses what we see as the four major issues in logic. The overriding issue is that of the choice of logic. We start with some discussion of the preliminary issue of whether there is such a 'one true logic,' but we reserve the main discussion for the first issue of 'classical logic versus nonclassical logic.' Here, we discuss the role of meaning and truth, the relation between classical logic and classical negation, and whether and, (...) if so, how classical logic should reside at the base world. Given the argument in favor of an overall use of nonclassical logic, the second issue is that of the choice of nonclassical logic. Brady's logic MC of meaning containment is argued for, with some comparison made with other relevant logics. For the remaining two issues, we make a case for relevant deduction, in comparison with classical deduction, and we explore possibilities for the appropriate metalogic, comparing classical and nonclassical approaches. (shrink)

Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model (...) of self-recognition and the conception(s) of self based on that capacity. (shrink)

Cognitivism in psychology and philosophy is roughly the position that intelligent behavior can (only) be explained by appeal to internal that is, rational thought in a very broad sense. Sections 1 to 5 attempt to explicate in detail the nature of the scientific enterprise that this intuition has inspired. That enterprise is distinctive in at least three ways: It relies on a style of explanation which is different from that of mathematical physics, in such a way that it is not (...) basically concerned with quantitative equational laws; the states and processes with which it deals are in the sense that they are regarded as meaningful or representational; and it is not committed to reductionism, but is open to reduction in a form different from that encountered in other sciences. Spelling these points out makes it clear that the Cognitivist study of the mind can be rigorous and empirical, despite its unprecedented theoretical form. The philosophical explication has another advantage as well: It provides a much needed framework for articulating questions about whether the Cognitivist approach is right or wrong. The last three sections take that advantage of the account, and address several such questions, pro and con. (shrink)

The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...) a computer. In Emperor I go further than this and suggest that the outward manifestations ofconscious mental activity cannot even be properly simulated by calculation. To support this view, I use various arguments to show that the results of mathematical insight, in particular, do not seem to be obtained algorithmically. The main thrust ofthis work, however, is to present an overview ofthe present state of physical understanding and to show that an important gap exists at the point where, quantum and classical physics meet, as well as to speculate on how the conscious brain might be taking advantage ofwhatever new physics is needed to fill this gap to achieve its nonalgorithmic effects. (shrink)

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the (...) intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand. (shrink)

This multifaceted essay emerges from a host of sources within diverse academic settings. Its central thesis is guided by physicist John A. Wheeler's thoughts on the quantum enigma. Wheeler concludes, following Niels Bohr, that we are co-participants within the universal self-organizing process. This notion merges with concepts from Peirce's process philosophy, Eastern thought, issues of topology, and border theory in cultural studies and social science, while surrounding itself with such key terms as complementarity, interdependence, interrelatedness, vagueness, generality, incompleteness, inconsistency, and (...) mestizaje. Ultimately, a sense of semiosic process pervades in light of combined homogenous and hetergenous tendencies. (shrink)

The subjectivism of the Austrian school of economics is a special case of Dewey's transactional philosophy, also known as pragmatism or pragmatic epistemology. The Austrian economists Carl Friedrich Menger (1840-1921) and Ludwig von Mises (1881-1973) adopted an Aristotelian deductive approach to economic issues such as social behavior and exchange. Like Menger and Mises, Friedrich A. Hayek (1899-1992) viewed scientific knowledge, even in the social sciences, as asserting and aiming for objective certainty. Hayek was particularly critical of attempts to apply the (...) empiricism of the natural sciences in the social sciences. Though Hayek was not a positivist in the sense ascribed to Milton Friedman (1912-), because he accepted the possibility of final, objective certainty, Hayek's view of scientific knowledge was closer to that of the logical positivists of the Vienna circle than to Dewey's pragmatism. Mises' a priorism, asserting and aiming for apodictic certainty, represented a more extreme form of objectivism even than Hayek's. Mises was similar in this regard to non-Austrian axiomatists such as Gerard Debreau (1921-2005), though he joined Hayek in eschewing mathematical formalism. In Dewey's contrasting view, the scientist commends new, alternative ways of knowing to the scientific community, offering more profound insight or more efficacious practical applications. Alternative ways of knowing which do not offer practical or intellectual benefits are to be rejected. Both the radical subjectivism of the Austrian school and Dewey's transactional strategy justify rejection of the mirage of social justice. Dewey's knowledge as ways of knowing suggests a broader and more fundamental critique of the socialist position in the calculation debate. The arguments presented by the Austrian school can be reformulated in terms of Dewey's pragmatic philosophy. (shrink)

Between World War I and World War II, the students of Columbia University's John Dewey and Frederick J. E. Woodbridge built up a school of philosophical naturalism sharply critical of claims to value-neutrality. In the 1930s and 1940s, the second-generation Columbia naturalists and their students who later joined the department reacted with dismay to the arrival on American shores of logical empiricism and other analytic modes of philosophy. These figures undermined their colleague Ernest Nagel's attempt to build an alliance with (...) the logical empiricists, accusing them of ignoring the scholar's primary role as a public critic. After the war, the prestige of analytic approaches and a tendency to label philosophies either???analytic??? or???Continental??? eclipsed the Columbia philosophers??? normatively inflected naturalism. Yet in their efforts to resist logical empiricism, the Columbia naturalists helped to construct a sturdy, canonical portrait of???American philosophy??? that proponents still hold up as a third way between analytic and Continental approaches. (shrink)

The conceptual framework of behaviorism is reconstructed in a logical scheme rather than along chronological lines. The resulting reconstruction is faithful to the history of behaviorism and yet meets the contemporary challenges arising from cognitive science, psycholinguistics, and philosophy. In this reconstruction, the fundamental premise is that psychology is to be a natural science, and the major corollaries are that psychology is to be objective and empirical. To a great extent, the reconstruction of behaviorism is an elaboration of behaviorist views (...) of what it is for a science to be objective and empirical. The reconstruction examines and evaluates behaviorist positions on observation and the rejection of introspection, the behavioral data language, theory construction, stimulus-response psychology, the organization of behavior, complex processes, agency, and the interpretation of mentalistic language. The resulting reconstruction shows behaviorism to be a pragmatic psychological version of positivism based on a behavioral epistemology. (shrink)

We propose that the sudden emergence of metazoans during the Cambrian was due to the appearance of a complex genome architecture that was capable of computing. In turn, this made defining recursive functions possible. The underlying molecular changes that occurred in tandem were driven by the increased probability of maintaining duplicated DNA fragments in the metazoan genome. In our model, an increase in telomeric units, in conjunction with a telomerase-negative state and consequent telomere shortening, generated a reference point equivalent to (...) a non-reversible counting mechanism. (shrink)

Derrida's key concepts or pseudo-concepts of différance, the trace, and the undecidable suggest analogies to some of the most significant results of formal, symbolic logic and metalogic. As early as 1970, Derrida himself pointed out an analogy between his use of ‘undecidable’ and Gödel's incompleteness theorems, which demonstrate the existence, in any sufficiently complex and consistent system, of propositions which cannot be proven or disproven (i.e., decided) within that system itself. More recently, Graham Priest has interpreted différance as an instance (...) of the general metalogical procedure of diagonalisation. In this essay, I consider the extent to which Derrida's key terms and the essential operations of deconstruction can be formalised. I argue that, if formalisation is indeed the technique of writing par excellence, then the formalisation of deconstructive concepts tends to show how the auto-deconstruction of total systems arises from the problematic possibility of writing itself. For instance, since diagonalisation permits the ‘arithmetisation of syntax’ whereby a formal system is able to formulate claims about its own logico-grammatical properties, we can understand its potential to inscribe the undecidable within the systematicity of language as simply one instance of the potential of writing, in figuring itself, to render inscrutable the trace of its own origin. (shrink)

. The question of whether or not our universe is deterministic remains of interest to both scientists and theologians. In this essay I argue that this question can be solved only by metaphysical decision and that no scientific evidence for either determinism or indeterminism will ever be conclusive. No finite being, no matter how powerful its cognitive abilities, will ever be able to establish the deterministic nature of the universe. The only being that would be capable of doing so would (...) be one that is at once transcendent and immanent. Such a being is compatible with the God of the Christian tradition, which yields that a deterministic worldview is compatible with a deterministic worldview. A more important point is that because science is never able to establish the determinism of our universe, it can never definitely rule out divine action except on metaphysical grounds. (shrink)

In applied problems mathematics is used as language or as a metalanguage on which metatheories are built, E.G., Mathematical theory of experiment. The structure of pure mathematics is grammar of the language. As opposed to pure mathematics, In applied problems we must keep in mind what underlies the sign system. Optimality criteria-Axioms of applied mathematics-Prove mutually incompatible, They form a mosaic and not mathematical structures which, According to bourbaki, Make mathematics a unified science. One of the peculiarities of applied mathematical (...) language is a variety of dialects: a problem can be presented in terms of various mathematical notions. Another peculiarity is polysemy: a problem can be presented in the framework of one dialect by a set of various models with equal right to exist. The pragmatic sense of distinction between applied and pure mathematics must lead to specific training in each case. (shrink)