In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

This paper describes semantic communication as an arbitrary loss function. I reject the logical approach to semantic information theory described by Carnap, Bar-Hillel and Floridi, which assumes that semantic information is a logical function of Shannon information mixed with categorical objects. Instead, I follow Hirotugu Akaike’s maximum entropy approach to model semantic communication as a choice of loss. The semantic relationship between a thing and a message about the thing is modelled as the loss of information that results in the (...) impression contained in the message, so that the semantic meaning of a bear’s footprint is the difference between the actual bear and its footprint. Experience has a critical function in semantic meaning because a bear footprint can only be meaningful if we have some experience with an actual bear. The more direct our experience, the more vivid the footprint will appear. In this model, what is important is not the logic of the categories represented by the information but the loss of information that reduces our experiences of reality to functional communication. The hard problem of semantic communication arises because real objects and events do not come with categorical labels attached, so the choice of loss is necessarily imperfect and illogical. (shrink)

Philosophers and cognitive scientists alike have recently been interested in whether cognition extends beyond the boundaries of skin and skull and into the environment. However, the extended cognition hypothesis has suffered many objections over the past few decades. In this paper, I explore the option of control extending beyond the human boundary. My aim is to convince the reader of three things: (i) that control can be implemented in artifacts, (ii) that humans and artifacts can form extended control systems, and (...) (iii) that perhaps extended control ought to be preferred over extended cognition. Using the objections to extended cognition as constraints on my own extended theorizing and the example of autofocus systems in cameras, I decompose and localize the components of an autofocus system that realize the central properties of control from a plausible theory of control in the literature. I then provide criteria according to which control can be extended in a system. Finally, I consider how this theory of extended control ought to be preferred to theories of extended cognition. (shrink)

The objective of this thesis is to present a naturalised metaphysics of information, or to naturalise information, by way of deploying a scientific metaphysics according to which contingency is privileged and a-priori conceptual analysis is excluded (or at least greatly diminished) in favour of contingent and defeasible metaphysics. The ontology of information is established according to the premises and mandate of the scientific metaphysics by inference to the best explanation, and in accordance with the idea that the primacy of physics (...) constraint accommodates defeasibility of theorising in physics. This metametaphysical approach is used to establish a field ontology as a basis for an informational structural realism. This is in turn, in combination with information theory and specifically mathematical and algorithmic theories of information, becomes the foundation of what will be called a source ontology, according to which the world is the totality of information sources. Information sources are to be understood as causally induced configurations of structure that are, or else reduce to and/or supervene upon, bounded (including distributed and non-contiguous) regions of the heterogeneous quantum field (all quantum fields combined) and fluctuating vacuum, all in accordance with the above-mentioned quantum field-ontic informational structural realism (FOSIR.) Arguments are presented for realism, physicalism, and reductionism about information on the basis of the stated contingent scientific metaphysics. In terms of philosophical argumentation, realism about information is argued for primarily by way of an indispensability argument that defers to the practice of scientists and regards concepts of information as just as indispensable in their theories as contingent representations of structure. Physicalism and reductionism about information are adduced by way of the identity thesis that identifies the substance of the structure of ontic structural realism as identical to selections of structure existing in re to combined heterogeneous quantum fields, and to the total heterogeneous quantum field comprised of all such fields. Adjunctly, an informational statement of physicalism is arrived at, and a theory of semantic information is proposed, according to which information is intrinsically semantic and alethically neutral. (shrink)