Barry Loewer

Determinism and Chance

Abstract It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as ‘ignorance’ probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role of probability in explanation and laws. This is the ‘paradox of deterministic probabilities’. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics.

David Lewis’s Humean Theory of Objective Chance

The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual “interpretations of probability” give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper “A Subjectivist’s Guide to Objective Chance” he described a framework for representing single case objective chances, showed how they are connected to subjective credences, and sketched a novel account what they are within his Humean account of scientific laws. Here I will describe these contributions and add a little to them.

Wanted Dead or Alive: Two Attempts to Solve Schrodinger's Paradox

We discuss two recent attempts two solve Schrodingers cat paradox. One is the modal interpretation developed by Kochen, Healey, Dieks, and van Fraassen. It allows for an observable which pertains to a system to possess a value even when the system is not in an eigenstate of that observable. The other is a recent theory of the collapse of the wave function due to Ghirardi, Rimini, and Weber. It posits a dynamics which has the effect of collapsing the state of macroscopic systems. We argue that the modal interpretation cannot account for non-accurate measurements and that both accounts have the consequence that in ordinary measurement situations (including the situation of Schrodingers cat) the observables that ends up well defined are not quite the ones that we want to be well defined.

Tails of Schrödinger’s Cat

IN HIS FAMOUS THOUGHT EXPERIMENT, Schrodinger (1935) imagined a cat that measures the value of a quantum mechanical observable with its life. Adapted to the measurement of x-spin of an electron, the experiment is this. If at the start of the measurement interaction the state of the cat is |R〉 (the ready to measure state), and the state of the electron is |↑〉 (the electron’s x-spin is up), then at the conclusion of the measurement the state of the cat and electron is |↑〉|Alive〉. And if at the start of the measurement interaction the state of the cat is |R〉 and the state of the electron is |↓〉 (the x-spin of the electron is down) then at the conclusion of the measurement the state of the cat and electron is |↓〉|Dead〉 The cat records the x-spin of the electron in its state of aliveness.

From information to intentionality

Arabella believes that her cat, Glendower, wants to go out. Her belief has representational and semantic features. It is about Glendower; it represents him as wanting to go out, and it has truth conditions. Her belief also has causal and rationalizing powers. She opens the door because she believes Glendower wants to go out. If we think that Arabella and other believers are physical entities we are led to wonder how it is possible for a physical thing, whether it is composed of cells or micro chips, to have beliefs, desires and other propositional atti tudes. This is the problem of intentionality. It has proved to be a very difficult problem. The source of the difficulty is that intentional and semantic concepts, reference, truth conditions, meaning etc. make no appearance in biological or physical theory. Additionally, beliefs have a normative dimension. They are assessible as correct or incorrect, rational or irrational. But the descriptions which occur in physical theory apparently are nonnormative. How can states which not only can represent but also misrepresent be captured in physical theory? The challenge for a philosopher who holds that intentionality is part of the natural order is just this: To show how it can be that certain physical states are capable of representation and misrepresenta tion and then to show how such states enter into the causation of behavior.

Non-ideal measurements

We have previously objected to modal interpretations of quantum theory by showing that these interpretations do not assign outcomes to non-ideal measurements. Bub and Healey replied (in this journal) by offering alternative accounts of non-ideal measurements. In this paper we argue, first, that our account of non-ideal measurements is correct and, second, even if it is not correct, it is overwhelmingly likely that interactions satisfying our characterization of non-ideal measurements actually occur and that such interactions possess outcomes. A successful defense of the modal interpretation must assign outcomes to these interactions or show that they do not have outcomes or show that in fact they never occur. Bub and Healey show none of this.

Why is there anything except physics

In the course of defending his view of the relation between the special sciences and physics from Jaegwon Kim’s objections Jerry Fodor asks “So then, why is there anything except physics?” By which he seems to mean to ask if physics is fundamental and complete in its domain how can there be autonomous special science laws. Fodor wavers between epistemological and metaphysical understandings of the autonomy of the special sciences. In my paper I draw out the metaphysical construal of his view and argue that while in a sense it answers Fodor’s question it is immensely implausible.

Cotenability and counterfactual logics

There are two accounts of the truth conditions of counterfactual statements which have been developed. According to David Lewis’s’ formulation of the possible world account “if A were the case then B would be the case” is true if there are possible worlds in which A and B are true which are more similar to the actual world than any possible world in which A is true and B is false. The other approach is the metalinguistic theory which counts a counterfactual as true if its antecedent together with certain auxiliary statements and laws of nature implies its consequent. Nelson Goodman* has developed this account and it is his version of it which we will investigate in this paper. Lewis has argued that the metalinguistic theory is compatible with his, while other? have claimed that the two approaches are fundamentally different. In this paper we seek to clarify the relationship between the two accounts particularly with respect to the logics which they determine. In order to state the two approaches with precision we will formulate them for a propositional language JZ with finitely many atoms to which the binary connective > is added. Lewis semantics for JZ are fomulated in terms of the concept of a system of spheres. A system of spheres is a three-tuple (IV, w*,

A conditional logic for defeasible beliefs

) where IV is a set of possible worlds, W* E IV is the act.ual world, and

Deontic Logics of Defeasibility

is a function which assigns to each ZJ G IV a subset of the power set of IV, P(W), which is totally ordered by set inclusion and which has {uj as its minimal member. Lewis suggests that we think of the members of