Abstract
This book deals with a basic problem arising within the Bayesian approach to scientific methodology, namely the choice of prior probabilities.1 The problem will be considered with special reference to some inference methods used within Bayesian statistics (BS) and the so-called theory of inductive probabilities (TIP).2 In this study an important role will be played by the assumption — defended by Sir Karl Popper and the supporters of the current verisimilitude theory (VT) — that the cognitive goal of science is the achievement of a high degree of truthlikeness or verisimilitude.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Notes
After World War II the Bayesian approach has gained increasing support among statisticians and epistemologists. In particular, in the last fifteen year the Bayesian approach to epistemology has been developed by several authors such as Rosenkrantz (1977,1981), Horwich (1982), Levi (1980), Howson and Urbach (1989). Although the contention between the Bayesian approach and other statistical and epistemological approaches is an intriguing topic (see, for instance, Barnett (1973), Howson and Urbach (1989), Earman (1992)) it is not my topic since my concern in this book is with problems arising within the Bayesian approach.
The theory of inductive probabilities (developed by Carnap and other epistemologists) deals with certain types of inductive inferences, such as prediction of future events, which are also typical subjects in philosophical research on induction. In particular, the problem of assessing the probability of a future event - which had already been considered by Hobbes (1650) - has received much attention after it was studied by Hume (1739): see Hacking (1975, p. 48 and 178).
Following a common epistemological usage, here “hypothesis” refers to whatever factual statement, from specific predictions to highly general theories. On the contrary, in statistics “hypothesis” is typically used with a much narrower meaning. Unfortunately, many other terminological conflicts occur between epistemology and statistics. Although I tried to make the text sufficiently clear to readers with a background in any of the two fields, a bias towards the epistemological jargon was inevitable given my own background. Hence, some tolerance is requested to those readers who will find familiar terms employed with a unfamiliar meaning (or vice versa).
This term is used, among others, by Swinburne (1973) and Skyrms (1966).
Of course scientists qua human beings pursue non-cognitive goals even within their scientific activity. For instance, “many people called scientists regard science as some battlefield where `being regarded as clever and correct’ is more important than `really having done all the work”’ (Prof. W. Schaafsma, private communication).
The notion of cognitive context is borrowed from Levi (1967).
Empiricist philosophers such as Francis Bacon and rationalist philosophers such as Descartes, although holding different views about the nature of scientific method, shared the same infallibilistic view - which Watkins (1978, p. 25) calls the “Bacon-Descartes ideal” - about the goal of science. The infallibilistic ideal was also advocated by scientists and philosophers such as Boyle, Locke and Newton.
Here “the truth” is intended in the sense of the correspondence theory of truth suggested by Aristotle and accepted, more or less explicitly, by most infallibilists: a statement is true if and only if it corresponds with reality, i.e., with the way things really are. According to the infallibilistic view the scientific method, if properly used, infallibly guarantees the discovery of true theories (see Laudan, 1973, p. 277).
Indeed certainty about a given statement may be seen as the maximum degree of belief in the truth of the statement.
For instance, Descartes (ca. 1628) maintains that we should “reject… merely probable knowledge and make it a rule to trust only what is completely known and incapable to be doubted.”
A fascinating inquiry into the `emergence of probability’ in modern thought is made by Hacking (1975).
The origins of the concept of verisimilitude and, more generally, the fallibilistic methodologies are traced by Niiniluoto ( 1987, Ch. 5).
It would appear that in the last century a number of philosophers had already recognized that the probabilistic and verisimilitude views are not incompatible (see Laudan, 1973, pp. 285–286 and 295). However, according to Laudan (ibid.,p. 286) “these two approaches did… represent different emphases, and were to give rise in the twentieth century to two very different strains in philosophy of science (Carnap and Keynes being the descendants of the progress by probabilification school, and Popper and Reichenbach focusing primarily on progress by self-correction)”.
Another example of a co-ordinated development of the Bayesian approach and the verisimilitude theory is given by the notions of expected verisimilitude and probable verisimilitude which can be defined using the concepts of epistemic probability and verisimilitude (see Chapter 4.3).
Following a common epistemological usage, here “inference” is employed in the sense “argument”. This conflicts with the more frequent statistical usage of “inference” in the sense of “conclusion” (cf. note 3).
The conclusion of an inductive inference, indeed, is frequently termed “hypothesis” because of its conjectural character.
As pointed out by Hacking ( 1975, Chapter 2), since its emergence in the Western thought probability was essentially dual, on the one hand having to do with degrees of belief (epistemic probability), on the other, with devices tending to produce stable long-run frequencies (physical or objective probability).
See Chapter 2.1 and Chapter 11, note 4.
The term “Generalized Carnapian (GC-)systems” is borrowed from Kuipers (1978).
See Chapter 7, note 18.
Gini diversity is a measure of the degree of disorder of a population or process (for a more detailed description see Chapter 10). Contrary to what one might believe at first sight, Est[G(q)] is different from Gini diversity G(y°) of the prior vector y°: see formula (8.7) and Chapter 8, note 5.
On the other hand idealizations - which play a basic role in empirical sciences - may be very useful also in methodological analysis. This basically depends on the possibility of finding interesting generalizations and `concretization’ of the proposed idealizations (cf. Chapter 11 where some possible extensions of the present approach to EPO are suggested).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Festa, R. (1993). Introduction. In: Optimum Inductive Methods. Synthese Library, vol 232. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8131-8_1
Download citation
DOI: https://doi.org/10.1007/978-94-015-8131-8_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4318-4
Online ISBN: 978-94-015-8131-8
eBook Packages: Springer Book Archive