Table of contents

Book info

Foreword

Part One: The Prelude

Chapter 1. From Antiquity to Pascal and Fermat

1. Gambling in antiquity and afterwards

2. “What happens, does not happen always, perforce, or the most often”

3. From chance to contingency

4. Precursors

5. The geometry of chance

Chapter 2. Small and high stakes

1. Port-Royal Logic

2. Inspirations and content

3. The wager

4. Huygens – how to expect winning?

Chapter 3. Theology versus probability

1. Posthumous work by Jacob Bernoulli

2. God’s omniscience and the law of large numbers

3. Probability

4. Moral disputes

5. Bernoulli and Leibniz. The logic of contingent events

6. Political arithmetics

Chapter 4. Chance and how the world is organised

1. The principle of least action

2. The polemics of an academic

3. How does the Universe work?

4. The case of Samuel König

5. The principle of least action in contemporary physics

6. Is the integral more mysterious than the differential?

7. Chance versus Intelligence

Chapter 5. The taming of chance

1. Why does chance need taming?

2. Random events versus the strategy of creation

3. Experimenting with chance

4. Morality versus probability calculus

5. Theology – science – theology

6. Perspectives

Part Two: The Fugue

Chapter 6. The probabilistic revolution

1. Introduction

2. Probability and astronomy

3. Towards measure theory

4. Statistical mechanics

5. Brownian motion

6. Kolmogorov

7. Interpretations – von Mises

8. Interpretations – de Finetti

9. Probability as measure

10. Probabilistics versus mathematical structuralism

11. After Kolmogorov

Chapter 7. What is chance?

1. Introductory remarks

2. Preliminary definitions

3. Subjective sources of probabilities

4. Objective sources of probabilities

5. Instability versus ignorance

6. The strategy of nature

7. Chance and sufficient reasons

8. Concluding remarks

Chapter 8. Generalised probability calculi

1. Introduction

2. A bit of history

3. A bit of mathematics: some properties of von Neumann algebras

4. Von Neumann’s agenda

5. A bit of probability calculus

6. A noncommutative probability theory

7. Free probability calculus

8. Consequences

Chapter 9. Probability in the structure of the Universe

1. Probability – from applications to theory

2. Measure and probability

3. Interpretations

4. The structure of chance

Part Three: The Coda

Chapter 10. A short history of anti-evolutionary fundamentalism

1. The beginnings of fundamentalism

2. Monkey trials

3. Intelligent Design

4. God or pure chance?

Chapter 11. The Temptation of Manichaeism

1. Previous disputes in new guises

2. Gnostics or ‘those who know’

3. Mathematics against gnosis

4. Is God the Lord of all?

Chapter 12. Ex casu et fortuna

1. Against the pagans

2. How comes evil?

3. Contingency and the free will

4. A meeting in the market

5. St Augustine’s warning

Chapter 13. The God of probabilities

1. The ontology of probability

2. The problem of low probabilities

3. The problem of high probabilities

4. The indifference principle

Chapter 14. One of the strands of cosmic evolution

1. A basket of problems which have attracted insufficient attention

2. A sink for disorder

3. The natural history of carbon

4. Dynamical systems

5. The dynamics of life

6. Natural selection

Chapter 15. Intelligent Design or the Mind of God?

1. Two strategies

2. Necessity and chance

3. Should biology arouse metaphysical emotions?

4. The Mind of God

5. The game of chance called life

6. The Great Matrix

Footnotes

Translated by: RAFAŁ ŚMIETANA

Editing & proofreading by: AEDDAN SHAW

Cover design: MARIUSZ BANACHOWICZ

Layout: MIROSŁAW KRZYSZKOWSKI

Typesetting: Byfflo Books

The cover uses a fragment of Vincent Van Gogh’s „The Starry Night” © Bridgeman/BE&W

© Copyright by Michał Heller & Copernicus Center Press Kraków 2012
© Copyright for the English translation by Copernicus Center Press

Originally published in Polish as Filozofia przypadku by Copernicus Center Press, Krakow 2011

ISBN 978-83-7886-024-2

Publication supported by The John Templeton Foundation Grant „The Limits of Scientific Explanation”

Copernicus Center Press Sp. z o.o.
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Foreword

If I were to dedicate this book to someone, it would be to Richard Dawkins and William Dembski. They are worlds apart, yet they have even more in common. They stand divided by their views on the theory of evolution. Dawkins considers it to be a „blind watchmaker” who explains everything, while in Dembski’s view it is full of „irreducibly complex situations” that testify to Intelligent Design. They are linked by their passion in the promotion of their respective views, by a willingness to stake everything on a single card. In the book that I now submit to the Reader, I put forward my own position, equally distant from the views of one and the other. However, I do not wish to join the club of zealots in preaching my own ideas, therefore I attempt to consider the issue from a broader perspective and in a broader context, while treating the discussion with both above-mentioned authors only marginally, by way of exemplifying their relevance to the problems at hand.

My broader context is constituted by the „philosophy of chance” not only (or perhaps, not principally) in the theory of biological evolution, but also in the structure and evolution of the entire Universe, and my broader perspective is the historical perspective. Even though I do not intend to write a history of the concept of chance (if I did, it would have to be a work of considerably greater length), I wish, however, to focus on at least some episodes in the history of science and philosophy, namely those that have played a more important role in the formation of the concept and its transformations. History explains a number of problems, including those with which we struggle even today, often only because it never occurred to us that we should have examined their development through the ages.

Looking at the evolution of the concepts connected with probability and chance, at the very outset we can see why we tend to associate the concept of chance (at this stage understood only intuitively) with the collapse of rationality. This association has made the process of domesticating random events considerably more difficult. After all, how one can understand something that is not rational? Help – yet over a long timeframe – arrived from two sources: from theological considerations – because chance may not break free from the embrace of Providence, and from the practice of gambling – because if one wants to win, one must somehow learn to control the randomness of chance. Thanks to the human passion for gambling, the exchange of letters between Pascal and Fermat constituted the foundations for what became later known as probability calculus, but soon this current was joined by theological strands at a key juncture: the notion of probability itself drifted in from theological disputes of Spanish casuists to the nascent probability calculus. The pace of events has since accelerated. Although in his seminal work Jacob Bernoulli still writes a lot about games of chance and hazard, they are more and more clearly replaced by purely mathematical theorems. Moreover, the practical applications of probability calculus testify to its maturity. For instance, mortality statistics have allowed the problem of epidemics in large cities to be overcome (since it was mostly there that reasonably accurate registers of the dead were maintained), and the application of statistical methods to the system of annuities began to bring profits to bankers. Thus ended the first stage of domesticating chance and thus ends the first part of this book.

Then there is a gap. If I wanted to write a history of probability calculus, I would have to add here several chapters detailing what happened between Laplace (inclusive) and the beginning of the 20th century. No doubt, this would be interesting and might even shed quite a lot of light on a number of detailed issues, but would distance me from the main objective of this book – the philosophy of chance. For this very reason, I decided to jump straight to the 20th century. The beginning of the previous century saw the emergence in mathematics of processes with a fundamental impact on the understanding of chance and related concepts. Probability calculus quickly transformed from a collection of statements and rules useful in various applications into a theory of modern mathematics. Thanks to Andrey Kolmogorov, who noticed the relationship between probability and the mathematical measure theory, and his formalisation of probability calculus, the concept of probability was at last liberated from intuitive associations and became an effective tool for conducting formal analyses. Thanks to this development, probability theory as a special case of measure theory, entered into fruitful interactions with other mathematical theories, rising to the role of one of the key branches of contemporary mathematics. Interpretative problems, so important for the ‘philosophy of chance’ did not disappear, but even here formalisation proved to be helpful in that it made it easier to perceive the boundary between the purely formal structure and its interpretative circumstances.

Progress in mathematics usually leads to generalisations. The fact that probability appeared in quantum mechanics in a new role, so to speak, not only intensified interpretative disputes, but also became a harbinger (or even a preliminary stage) of a generalisation of this concept. The process, once initiated, continued apace. Today, we have at our disposal a number of generalisations of probability theory (or, more accurately, probabilistic measure) of which the most spectacular include the so-called noncommutative probabilistic measures. Their particular beauty consists in that generalised concepts of probability possess a host of properties which are completely surprising from the vantage point of our mental habits.

The concept of chance is evidently connected with the notion of probability. An event is called random if we believe that its a priori probability of occurrence is small (at any rate, less than one). If we agree to adopt this intuition as the basis for a definition of chance, then we are immediately confronted by a question: What kind of probability are we talking about? In day-to-day situations, we are in no doubt that we mean standard probability, more or less as defined by Kolmogorov. But in philosophical and worldview discussions it is impossible to avoid descending to the basic level (below the Planck threshold), because there – in our opinion – the issue of the structure of the Universe ‘is decided.’ If this level is indeed probabilistic, as all signs appear to indicate, in what sense is it probabilistic? After all, there are many probabilistic measures. Both the understanding of chance and its part in the structure of the Whole depend on our answer to this question.

In this way, almost imperceptibly, we have moved on to the third part of the book where the problem of the ‘philosophy of chance’ is brought to the fore. We thus return to the clash between Dawkins and Dembski, which will help us outline our own solution. Let us formulate the problem in a contrasting manner, as is done by the proponents of Intelligent Design: God or pure chance? This time, however, we approach the question armed with a substantial dose of information concerning probability calculus and equipped with an understanding of chance in its context. We must, naturally, supplement our knowledge with a certain quantum of information from the history of theology, for it turns out that the former masters, even though their knowledge in many domains did not match ours, had a keen theological intuition (which we have, to a large extent, squandered somewhere along the way). We will try to link one with the other – our knowledge with a theological sense drawing on tradition.

The existence of chance events in the structure of the Universe is an irrefutable fact. They are not exceptional. They are interwoven into the cosmic fabric. But their distribution in this structure is not accidental. They constitute an essential part of ‘the matrix of the Universe.’ They appear as initial conditions for certain laws of physics and as fluctuations that attack different dynamic processes occurring throughout the Universe. Without initial conditions, the laws of nature would not be able to operate, moreover, without external fluctuations, non-linear dynamic processes would be in no position to generate authentic new developments. Biological evolution is such a dynamic process, with natural selection, one of its basic mechanisms, consisting in an interaction between internal sensitivity of an evolving system with small fluctuations of the environment. Biological evolution constitutes one of the strands of cosmic evolution.

This extraordinary symphony of cosmos can be approached from different points of view. Like Dawkins, we may attempt explain everything by referring to pure chance. Like Dembski, we may try to discern the interventions of the Intelligent Designer in the exceptionally intricate details of the cosmic structure. Nevertheless, both of these attempts are unsuccessful and require fairly extensive intellectual acrobatics to maintain. Chance occurrences explain nothing, because they themselves demand an explanation. They are so subtly intertwined with the cosmic structure that without it they lose their import and cannot exist. And the reference to special places in the structure of the Whole as traces made by the Designer is, for this Designer, an insult exactly for the same reason for which the explanatory power of pure chance must be rejected. In the Cosmic Matrix there are no special places (regardless of whether we call them effects of chance or results of an extraordinary intervention); everything is part of the one Great Matrix. I would call it Intelligent Design, but this beautiful name has been compromised, therefore I prefer to use a phrase so often used by Einstein: „the Mind of God”. And the purpose of science is nothing else but to decipher this „Mind of God”.

***

I wish to express gratitude to my friend Jan Jaworowski, professor emeritus of mathematics at Indiana University, Bloomington, for his willingness to read a computer printout of this book. His precious comments permitted me to eliminate a number of inaccuracies, even errors. Those that remain notwithstanding, are my sole responsibility.

Every book consists of matter and form. Matter is the content, whilst the form is comprised of the words and sentences that are used to convey it. An ideal translation should preserve the content, while endowing it with a new form. And yet form shapes content, in a manner somewhat reminiscent of the philosophy of Aristotle, where it is the former that determines the heart of the matter. How is one, then, supposed to create something new while remaining faithful to the original? This challenge was faced by my translator, Rafał Śmietana, and his assistant Aeddan Shaw. I would like to express my heartfelt gratitude to them for meeting the challenge with such skill.

Tarnów, May 17, 2011

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