On a Wrong Picture of Knowing: On Certainty and Wittgenstein's Conception of Philosophy1

My procedure in this paper will be to arrange remarks from Wittgenstein's own later writings, especially On Certainty, often in the form of a dialogue between a Wittgensteinian voice and an interlocutor. My hope is to provide an arrangement of materials that brings out how they hang together and how they show us what's wrong with a picture of knowing that has motivated much of our epistemology.     

Private Announcements on Topological Spaces

In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information \(\varphi \), while all the other agents observe that group G is informed, but are uncertain whether the information provided is \(\varphi \) or \(\lnot \varphi \). This article follows up on our prior work (van Ditmarsch et al. in Proceedings of the 15th TARK. pp 95-102, 2015) where the dynamics were public events. We provide a complete axiomatization of our logic, and give two detailed examples of situations with agents learning information through semi-private announcements.     

Visual search for dimensionally redundant pop-out targets: Evidence for parallel-coactive processing of dimensions

In two visual search experiments, the detection of singleton feature targets redundantly defined on multiple dimensions was investigated. Targets differed from the distractors in orientation, color, or both (redundant targets). In Experiment 1, the various target types were presented either in separate blocks or in random order within blocks. Reaction times to redundant targets significantly violated therace model inequality (Miller, 1982), but only when there was constancy of the target-defining dimension(s) within trial blocks. In Experiment 2, there was dimensional variability within blocks. Consistent with Experiment 1, constancy of the target-defining dimension(s), but this time across successive trials (rather than within blocks), was critical for observing violations of the race model inequality. These results provide evidence for parallel-coactive processing of multiple dimensions, consistent with thedimension-weighting account of Müller, Heller, and Ziegler (1995).     

Converting between measures of slope of the psychometric function

The psychometric function’s slope provides information about the reliability of psychophysical threshold estimates. Furthermore, knowing the slope allows one to compare, across studies, thresholds that were obtained at different performance criterion levels. Unfortunately, the empirical validation of psychometric function slope estimates is hindered by the bewildering variety of slope measures that are in use. The present article provides conversion formulas for the most popular cases, including the logistic, Weibull, Quick, cumulative normal, and hyperbolic tangent functions as analytic representations, in both linear and log coordinates and to different log bases, the practical decilog unit, the empirically based interquartile range measure of slope, and slope in a? representation of performance.     

ELEPHANTS, MICROSCOPES AND FREE BEAUTY: REPLY TO DAVIES

According to Stephen Davies, there is no such thing as free beauty. Using actual and imaginary examples, he tries to show that our aesthetic evaluations of objects inevitably pay heed to the kinds to which they belong or in which we judge them to belong. His examples are not as compelling as he thinks, however. Furthermore, nature looked at through a microscope (or a telescope) provides us with a particular class of counter-examples which have not been dealt with by Davies and which put considerable pressure on his account.     

Introspective forgetting

We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs not involving the forgotten atom(s) remain true. The work for this publication was mainly carried out while Hans van Ditmarsch was associated to: Institut de Recherche en Informatique, Université Paul Sabatier, France.