In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all those (...) convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

Recent philosophy of measurement has emphasized the existence of both diachronic and synchronic “loops,” or feedback processes, in the epistemic achievements of measurement. A widespread response has been to conclude that measurement outcomes do not convey interest-independent facts about the world, and that only a coherentist epistemology of measurement is viable. In contrast, I argue that a form of measurement realism is consistent with these results. The insight is that antecedent structure in measuring spaces constrains our empirical procedures such that (...) successful measurement conveys a limited, but veridical knowledge of “fixed points,” or stable, interest- independent features of the world. (shrink)

This thesis considers the following problem: What methods should the epistemology of science use to gain insight into the structure and behaviour of scientific knowledge and method in actual scientific practice? After arguing that the elucidation of epistemological and methodological phenomena in science requires a method that is rooted in formal methods, I consider two alternative methods for epistemology of science. One approach is the classical approaches of the syntactic and semantic views of theories. I show that typical approaches of (...) this sort are inadequate and inaccurate in their representation of scientific knowledge by showing how they fail to account for and misrepresent important epistemological structure and behaviour in science. The other method for epistemology of science I consider is modeled on the methods used to construct valid models of natural phenomena in applied mathematics. This new epistemological method is itself a modeling method that is developed through the detailed consideration of two main examples of theory application in science: double pendulum systems and the modeling of near-Earth objects to compute probability of future Earth impact. I show that not only does this new method accurately represent actual methods used to apply theories in applied mathematics, it also reveals interesting structural and behavioural patterns in the application process and gives insight into what underlies the stability of methods of application. I therefore conclude that for epistemology of science to develop fully as a scientific discipline it must use methods from applied mathematics, not only methods from pure mathematics and metamathematics as traditional formal epistemology of science has done. (shrink)

The chapter argues from an ethology-inspired internalist perspective that ‘colour’ is not a homogeneous and autonomous attribute, but rather plays different roles in different conceptual forms underlying perception. It discusses empirical and theoretical evidence that indicates that core assumptions underlying orthodox conceptions are grossly inadequate. The assumptions pertain to the idea that colour is a kind of autonomous and unitary attribute. It is regarded as unitary or homogeneous by assuming that its core properties do not depend on the type of (...) ‘perceptual object’ to which it pertains and that‘colour per se’ constitutes a natural attribute in the functional architecture of the perceptual system. It is regarded as autonomous by assuming that it can be studied in isolation of other perceptual attributes. More generally, the chapter argues on the bases of corresponding empirical and theoretical evidence that perception cannot be understood as the ‘recovery’ of physical world structure from sensory structure by input-based computational processes. Rather, the sensory input serves as a kind of sign for biologically relevant aspects of the external world that activates biologically given conceptual forms with their internal parameters. Although the sensory input is a causally necessary requirement for the activation of conceptual forms, the perceptual computations triggered are under the control of an internal programme based on a set of conceptual forms. (shrink)