Historically, the theory of probability emerged from the efforts of Pascal and Fermat in the 1650s to solve problems posed by a gambler, Chevalier de Méré (Rényi, 1972; Devlin, 2008), and reached its current form in Kolmogorov, 1933. Remarkably, not even highly experienced gamblers can extract high precision probability estimates from observed data: one of de Méré's questions concerned comparing the probabilities of getting at least one 6 in four rolls of one die (p 0.5177) and getting at least one double-6 in 24 throws of a pair of dice (p 0.4914). Four decades later, Samuel Pepys is asking Newton to discern the difference between at least two 6s when 12 dice are rolled (p 0.6187) and at least 3 6s when 18 dice are rolled (p 0.5973). In this paper we make this phenomenon, the very limited ability of people to deal with probabilities, the focal point of our inquiry. These limitations, we will argue, go beyond the well understood limits of numerosity (Dehaene, 1997), and touch upon areas such as cognitive limits of deduction (Kracht, 2011) and default inheritance (Etherington, 1987). We will offer a model of the naive/commonsensical theory of probability. In Section 2 we discuss likeliness, which we take to be a valuation of propositions on a discrete (seven-point) scale. In Section 3 we turn to the inference mechanism supported by the naive theory, akin to Jeffreys-style probability updates. In Section 4 we briefly sketch the background theory and discuss what we take to be the central concern, learnability.

A standard model of how brains produce natural cognition would provide a framework for organizing cognitive neuroscience research. A recent effort (Laird et al., in press) to build on consensus views of cognitive operations and produce a standard model of natural cognition started with common aspects of well-established cognitive architectures ACT-R, Sigma, and SOAR. The model captures scientific consensus on “how” the brain works, but it does not offer a coherent story for “why” the component modules (i.e., working memory, long-term memory, visual and motor areas) exist and interact in the ways described. This manuscript starts with background information on a well-cited theory of action selection, and extends that theory to a fuller explanation of decision-making, action and perception that includes a framework for the elements of cognition.

Jerome Feldman DRAFT 1/10/17 Introduction Science is a crowning glory of the human spirit and its applications remain our best hope for social progress. But there are limitations to current science and perhaps to any science. The general mind-body problem is known to be intractable and currently mysterious. This is one of many deep problems that are universally agreed to be beyond the current purview of Science, including quantum phenomena, etc. But all of these famous unsolved problems are either remote from everyday experience (entanglement, dark matter) or are hard to even define sharply (phenomenology, consciousness, etc.). In this note, we will consider some obvious computational problems in vision that arise every time that we open our eyes and yet are demonstrably incompatible with current theories of neural computation. The focus will be on two related phenomena, known as the neural binding problem and the illusion of a detailed stable visual world.