There are many alternative ways that a mind or brain might represent that two of its representations were of the same object or property, the 'Strawson' model, the 'duplicates' model, the 'synchrony' mode, the 'Christmas lights' model, the 'anaphor' model, and so forth. I first discuss what would constitute that a mind or brain was using one of these systems of identity marking rather than another. I then discuss devastating effects that adopting the Strawson model has on the notion that (...) there are such things as modes of presentation in thought. Next I argue that Evans' idea that there are 'dynamic Fregean thoughts' has exactly the same implications. I argue further that all of the other models of thought discussed earlier are in fact isomorphic to the Strawson model. a search for the source of these difficulties reveals the classical notion of modes of presentation as resting on two assumptions, neither of which I recommend. It depends on denying that the way the mind reacts to or understands the thoughts or ideas that it harbours has any bearing on their intentional contents. And it depends on an internalist view of thought content, in particular, on denying that the natural informational content carried or potentially carried by a thought has any bearing on its intentional content. (shrink)
Chancy modus ponens is the following inference scheme: ‘probably φ’, ‘if φ, then ψ’, therefore, ‘probably ψ’. I argue that Chancy modus ponens is invalid in general. I further argue that the invalidity of Chancy modus ponens sheds new light on the alleged counterexample to modus ponens presented by McGee. I close by observing that, although Chancy modus ponens is invalid in general, we can recover a restricted sense in which this scheme of inference is valid.
To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate tradeoffs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. (...) While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps. (shrink)
The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...) approximations to Solomonoff prediction do not always converge. (shrink)
In its broadest sense, "universality" is a technical term for something quite ordinary. It refers to the existence of patterns of behavior by physical systems that recur and repeat despite the fact that in some sense the situations in which these patterns recur and repeat are different. Rainbows, for example, always exhibit the same pattern of spacings and intensities of their bows despite the fact that the rain showers are different on each occasion. They are different because the shapes of (...) the drops, and their sizes can vary quite widely due to differences in temperature, wind direction, etc. There are different questions one might ask about such patterns. For instance, one might ask why the particular rainbow... (shrink)
How can we study bounded rationality? We answer this question by proposing rational task analysis —a systematic approach that prevents experimental researchers from drawing premature conclusions regarding the rationality of agents. RTA is a methodology and perspective that is anchored in the notion of bounded rationality and aids in the unbiased interpretation of results and the design of more conclusive experimental paradigms. RTA focuses on concrete tasks as the primary interface between agents and environments and requires explicating essential task elements, (...) specifying rational norms, and bracketing the range of possible performance, before contrasting various benchmarks with actual performance. After describing RTA’s core components we illustrate its use in three case studies that examine human memory updating, multitasking behavior, and melioration. We discuss RTA’s characteristic elements and limitations by comparing it to related approaches. We conclude that RTA provides a useful tool to render the study of bounded rationality more transparent and less prone to theoretical confusion. (shrink)
Ramsey (1926) sketches a proposal for measuring the subjective probabilities of an agent by their observable preferences, assuming that the agent is an expected utility maximizer. I show how to extend the spirit of Ramsey's method to a strictly wider class of agents: risk-weighted expected utility maximizers (Buchak 2013). In particular, I show how we can measure the risk attitudes of an agent by their observable preferences, assuming that the agent is a risk-weighted expected utility maximizer. Further, we can leverage (...) this method to measure the subjective probabilities of a risk-weighted expected utility maximizer. (shrink)
The argument of this article is that the Albert Memorial acted as a catalyst for some of Collingwood's most well known ideas in the philosophy of history and aesthetics. It was not, however, the exclusive source of those ideas, and indeed they had philosophical expression elsewhere. One may view his contemplations, then, as work in progress. For example, the logic of question and answer promoted by the Memorial was also prompted by Collingwood's reading of Bacon and Descartes. This was a (...) reflection of his determination to depart from the realism of his philosophical teachers. Similarly, the Memorial directs Collingwood's thought forward. The Memorial acts as a facilitator of his thought on history, which in the course of its formulation undergoes many transformations. The logic of question and answer also finds a place in Collingwood's early thinking about art, but even here it is in the process of constant transition. Collingwood's reaction to the Memorial helps us to conclude that there is nothing ironic about the fact that Collingwood loathed the structure that was also the instigator of one of his most influential philosophical doctrines. (shrink)