Tolerance and Chance

This chapter explores Tolerance Puzzles in which the operative modality is that of objective chance. We show that a principle of ‘Chance Fixity’, according to which facts about the chances at a given time are not themselves matters of chance at that time, is deeply embedded in ordinary and scientific reasoning about chance and rules out Iteration-denial for the relevant chance operators. We also develop a new ‘Robustness Puzzle’ in which the analogue of Hypertolerance completely untenable. This puzzle turns on strengthenings of Tolerance claims to claims about high (conditional) chance, as opposed to mere positive chance.

Tolerance Puzzles

This chapter provides a general schema for regimenting a broad family of puzzles of modal variation. These puzzles begin with a ‘Tolerance’ premise according to which an objects (or a certain kind of object) can differ in any small way along a certain parameter. This is supplemented with a ‘Non-contingency’ premise according to which the Tolerance premise is necessarily true if true at all, an ‘Iteration’ premise according to which anything possibly possible is possible, and a ‘Persistent Closeness’ premise according to which what counts as a ‘small difference’ is modally constant. These premises jointly imply the conclusion, ‘Hypertolerance’, that the object or objects in question can differ arbitrarily along the relevant parameter. We show how this schema is general enough to subsume puzzles involving time or objective chance, and discuss some difficulties that arise in trying to formulate compelling instantiations of the schema involving variation in originating matter.

Reconciling Meticulous Divine Providence with Objective Chance

Randomness can be defined in terms of objective probability: an event is random just in case its objective probability (in the circumstances) is other than zero or one. There is a tension between objective probability and divine providence: if God has arranged for E to occur, then its objective probability would seem to be one. I will first show that this tension creates problems for six models of how to combine worldly chance with divine providence: determinism, Molinism, Thomism, divine luck, the multiverse, and van Inwagen’s theory of chance. I will then develop two new solutions to this problem.

Ambiguity aversion, modern Bayesianism and small worlds

The central question of this paper is whether a rational agent under uncertainty can exhibit ambiguity aversion (AA). The answer to this question depends on the way the agent forms her probabilistic beliefs: classical Bayesianism (CB) vs modern Bayesianism (MB). We revisit Schmeidler's coin-based example and show that a rational MB agent operating in the context of a "small world", cannot exhibit AA. Hence we argue that the motivation of AA based on Schmeidler's coin-based and Ellsberg's classic urn-based examples, is poor, since they correspond to cases of "small worlds". We also argue that MB, not only avoids AA, but also proves to be normatively superior to CB because an MB agent (i) avoids logical inconsistencies akin to the relation between her subjective probability and objective chance, (ii) resolves the problem of "old evidence" and (iii) allows psychological detachment from actual evidence, hence avoiding the problem of "cognitive dissonance". As far as AA is concerned, we claim that it may be thought of as a (potential) property of large worlds, because in such worlds MB is likely to be infeasible.

Two Senses of “Probability”

The word “probability” has long been used in (at least) two distinct senses. One sense has to do with a rational agent’s degree of belief, commonly called credence in the philosophical literature. The other sort of probability is thought to be characteristic of a physical system, such as a roulette wheel; these are “in the world” rather than in our heads. This concept is called chance. It would be a mistake to think of these as rivals for the title of the single correct interpretation of probability. Rather, they are both useful concepts, with different roles to play. This chapter is an introduction to these concepts and their relations. It includes a discussion of the proper formulation and justification of a principle that links the two concepts, the Principal Principle. It is argued that neither of these concepts is dispensable. This raises the question of whether there is a notion of probability that can play the role of objective chance and is compatible with deterministic laws of physics.

Multi-objective chance-constrained blending optimization of zinc smelter under stochastic uncertainty

<p style='text-indent:20px;'>Considering the uncertainty of zinc concentrates and the shortage of high-quality ore inventory, a multi-objective chance-constrained programming (MOCCP) is established for blending optimization. Firstly, the distribution characteristics of zinc concentrates are obtained by statistical methods and the normal distribution is truncated according to the actual industrial situation. Secondly, by minimizing the pessimistic value and maximizing the optimistic value of object function, a MOCCP is decomposed into a MiniMin and MaxiMax chance-constrained programming, which is easy to handle. Thirdly, a hybrid intelligent algorithm is presented to obtain the Pareto front. Then, the furnace condition of roasting process is established based on analytic hierarchy process, and a satisfactory solution is selected from Pareto solution according to expert rules. Finally, taking the production data as an example, the effectiveness and feasibility of this method are verified. Compared to traditional blending optimization, recommended model both can ensure that each component meets the needs of production probability, and adjust the confident level of each component. Compared with the distribution without truncation, the optimization results of this method are more in line with the actual situation.</p>

Surrealism, Chance and the Extended Mind

This chapter discusses how the Surrealists engaged with techniques like automatic drawing, the exquisite corpse, collage, frottage and decalcomania, and how this might be interpreted in the context of theories of distributed cognition, enactivism, embodiment, and the extended mind. The Surrealists’ use of ‘objective chance’ was driven by a belief in the existence of an unconscious state of mind which could only be accessed obliquely, by using techniques which bypassed both artistic skill and conscious thought. ‘Where does the mind stop and the rest of the world begin?’. This question is posed by Clark and Chalmers (1998) as an introduction to the concept of the extended mind, but it could just as well be the very question the Surrealists were trying to address in their search for a universal truth, the key to which they believed to be the unconscious mind as defined by Freud.