Donald Gillies

Intersubjective Probability and Confirmation Theory

This paper introduces what is called the intersubjective interpretation of the probability calculus. Intersubjective probabilities are related to subjective probabilities, and the paper begins with a particular formulation of the familiar Dutch Book argument. This argument is then extended, in Section 3, to social groups, and this enables the concept of intersubjective probability to be introduced in Section 4. It is then argued that the intersubjective interpretation is the appropriate one for the probabilities which appear in confirmation theory whether of a Bayesian or a Popperian variety. The final section of the paper states and tries to answer an objection due to Putnam.

The evidence that evidence-based medicine omits

According to current hierarchies of evidence for EBM, evidence of correlation (e.g., from RCTs) is always more important than evidence of mechanisms when evaluating and establishing causal claims. We argue that evidence of mechanisms needs to be treated alongside evidence of correlation. This is for three reasons. First, correlation is always a fallible indicator of causation, subject in particular to the problem of confounding; evidence of mechanisms can in some cases be more important than evidence of correlation when assessing a causal claim. Second, evidence of mechanisms is often required in order to obtain evidence of correlation (for example, in order to set up and evaluate RCTs). Third, evidence of mechanisms is often required in order to generalise and apply causal claims. While the EBM movement has been enormously successful in making explicit and critically examining one aspect of our evidential practice, i.e., evidence of correlation, we wish to extend this line of work to make explicit and critically examine a second aspect of our evidential practices: evidence of mechanisms.

A Falsifying Rule for Probability Statements

MY AIM in this paper is to discuss a problem raised by Popper in chapter vIII of the Logic of Scientific Discovery. This problem can be simply explained. According to Popper a scientific theory should be capable of being falsified by evidence. Now statistical theories appear in much reputable science; yet they are not, strictly speaking, falsifiable by the frequency evidence which is used in practice to test them. As Popper himself puts it ([8], p. 146):

Bayesianism and the Fixity of the Theoretical Framework

Bayesianism is a powerful current of thought in quite a number of different areas, which include: artificial intelligence, decision theory, economics, philosophy of science, and statistics. In the present paper, I will deal only with Bayesianism in statistics. In fact since the beginning of this century, the principal controversy within statistics has been between Bayesianism and the so-called classical statistics. I will begin therefore by attempting to characterise, in outline at least, these two approaches to statistics.

An action-related theory of causality

The paper begins with a discussion of Russells view that the notion of cause is unnecessary for science and can therefore be eliminated. It is argued that this is true for theoretical physics but untrue for medicine, where the notion of cause plays a central role. Medical theories are closely connected with practical action (attempts to cure and prevent disease), whereas theoretical physics is more remote from applications. This suggests the view that causal laws are appropriate in a context where there is a close connection to action. This leads to a development of an action-related theory of causality which is similar to the agency theory of Menzies and Price, but differs from it in a number of respects, one of which is the following. Menzies and Price connect ‘A causes B’ with an action to produce B by instantiating A, but, particularly in the case of medicine, the law can also be linked to the action of trying to avoid B by ensuring that A is not instantiated. The action-related theory has in common with the agency theory of Menzies and Price the ability to explain causal asymmetry in a simple fashion, but the introduction of avoidance actions together with some ideas taken from Russell enable some of the objections to agency accounts of causality to be met. 1. Introduction2. Russell on causality3. Preliminary exposition of the action-related theory4. Differences between the action-related theory and the agency theory of Menzies and Price5. Explanation of causal asymmetry6. Objections to the action-related theory7. Extension of the theory to the indeterminate case Introduction Russell on causality Preliminary exposition of the action-related theory Differences between the action-related theory and the agency theory of Menzies and Price Explanation of causal asymmetry Objections to the action-related theory Extension of the theory to the indeterminate case

Intersubjective probability and economics

The aim of this article is to analyse the role of probability and uncertainty in economics. A distinction is made between interpretations of probability in which probability is regarded as objectivei.e., a property of the external world, and those in which probability is regarded as epistemologicali.e., as a measure of belief, or rational belief, or knowledge. A new epistemological interpretation, the intersubjective is introduced and then applied to three examples from economics. Two of these are micro - namely pricing under conditions of oligopoly, and collective wage bargaining. The third is macro - namely the question of levels of investment in the light of long-term expectation. To analyse these examples, the article introduces the concept of strategically relevant uncertaintyThe article concludes by arguing in general terms that the objective interpretation of probability is appropriate for the natural sciences, while the epistemological one is appropriate for economics.

Causality, Propensity and Bayesian Networks

This paper investigates the relations between causality and propensity. Aparticular version of the propensity theory of probability is introduced, and it is argued that propensities in this sense are not causes. Some conclusions regarding propensities can, however, be inferred from causal statements, but these hold only under restrictive conditions which prevent cause being defined in terms of propensity. The notion of a Bayesian propensity network is introduced, and the relations between such networks and causal networks is investigated. It is argued that causal networks cannot be identified with Bayesian propensity networks, but that causal networks can be a valuable heuristic guide for the construction of Bayesian propensity networks.

An Aristotelian approach to mathematical ontology

The paper begins with an exposition of Aristotle’s own philosophy of mathematics. It is claimed that this is based on two postulates. The first is the embodiment postulate, which states that mathematical objects exist not in a separate world, but embodied in the material world. The second is that infinity is always potential and never actual. It is argued that Aristotle’s philosophy gave an adequate account of ancient Greek mathematics; but that his second postulate does not apply to modern mathematics, which assumes the existence of the actual infinite. However, it is claimed that the embodiment postulate does still hold in contemporary mathematics, and this is argued in detail by considering the natural numbers and the sets of ZFC.

Logicism and the Development of Computer Science

This paper argues for the thesis that ideas originating in the philosophy of mathematics have proved very helpful for the development of computer science. In particular, logicism, the view that mathematics can be reduced to logic, was developed by Frege and Russell, long before computers were invented, and yet many of the ideas of logicism have been central to computer science. The paper attempts to explain how this serendipity came about. It also applies Wittgensteins later theory of meaning to human-computer interaction, and draws the conclusion that computers do understand the meaning of the symbols they process. The formal language of logic is suitable for humans trying to communicate with computers.

Problem-Solving and the Problem of Induction

In his 1972 book: Objective Knowledge, Popper devotes Chap. 1 to the problem of induction. Elsewhere in the book (in Chaps. 3, 4, 6 and 8), he presents a general schema of problem solving. The aim of this paper is to bring these two strands of thought together. The initial problem (P1) is here the traditional philosophical problem of induction. Popper proposes a tentative solution (TS) to this problem. The paper then proceeds with the problem solving schema by adding error elimination (EE), i.e. criticisms of the tentative solution. These are concerned with computer induction, and with the claim that corroboration is in some sense inductive. This discussion leads in turn to the emergence of a new problem (P2). A suggestion is made about how this new problem might be tackled. The approach involves Neuraths principle, but applied to methods rather than theories.