Vincent F. Hendricks: Professor, Director | Center for Information and Bubble Studies | University of Copenhagen

The Convergence of Scientific Knowledge

The Convergence of Scientific Knowledge

– a view from the limit
Vincent F. Hendricks
Studia Logica Library, Kluwer Academic Publishers 2001, 410 pages




Reviews | Abstract | Keywords | Table of Contents | Cover


by Ryszard Wojcicki, Managing Editor, Studia Logica Library:

This book will be a rewarding reading for everybody who is interested in logical aspects of scientific knowledge acquisition. The presentation of the issues discussed in the book is exemplary. The author was able to present in parallel way three different perspectives under which the issues discussed in the book might be approached.

To begin with, this is the philosophical perspective. I hardly could mention another book in which various philosophical viewpoints on the nature of scientific inquiry are discussed in such a consistent but at the same time instructive and accurate way.

Another, perspective relevant to the considerations carried out by the author is logical. Again, the logical aspects of the problem are handled in a masterly way. That the problems of growth of science can be studied with the help of logical instruments is obvious. Both syntactical techniques being part of the development of various logical systems (the system of epistemic logic in the first place) and semantic techniques resulted from semantic studies of those systems are relevant for the area of studies covered by Hendricks. What those who go through the book will appreciate is the fact that Hendricks is able to show that the various logical tools he discusses form a coherent, completing one another whole. Needless to say that the fact that Hendricks was able to demonstrate that is one considerable advantages of the book.

Finally it is the perspective of the theory of learning. Again it is hardly surprising that the theory of learning might allow one to grasp in the right way various aspects of scientific growth … let me just notice that the idea of using the methods of the learning theory for the purposes of the studies carried out in the book has turned out extremely fruitful. I am quite sure that Hendricks’ approach to the problems he studies is of considerable interest for anybody who is interested in forming a good theoretical model of growth of science.

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It is popular view among epistemologists, methodologists and philosophers of science to hold that knowledge and science converge to the truth, or less ambitiously, converge to some adequate theory, in the limit. The former view characterizes scientific realism while the latter describes the general anti-realistic attitude. The aim, however, is not to say whether convergence will or will not occur. It is, rather, to investigate the proposal that such convergence, if it occurs, is constitutive of scientific knowledge: in brief to provide a (formal) epistemology of limiting convergence for scientific realism and anti-realism.

To investigate this proposal for epistemic convergent logics certain concepts from formal learning theory are applied. Learning theory is the formal study of inductive problems and their intrinsic solvability for both ideal and computationally bounded agents. Then together with a few topological concepts and classical modal, epistemic and tense logic the result is modal operator theory; modal simply refers to the fact that unary modal operators are used to represent epistemic attitudes like knowledge and belief. Modal operator theory can be used to answer a host of systematic issues like: What is/are:

  1. the role of background knowledge when engaged in scientific inquiry problems?

  2. the significance of temporally partitioning the set of hypotheses under scientific investigation – i. e. the spatio-temporal characteristics of laws of nature.

  3. the (truth-conducive) nature methodological canons placed on inquiry methods – their restrictive or permissive character?

  4. alethic simultaneity, i. e. the relation between empirical adequacy and truth.

  5. the strength of knowledge based on (1) discovery, (2) assessment methods in terms of the propositional modal epistemic systems corresponding to them?

  6. the relation between convergent knowledge and skepticism? 

  7. the relation between knowledge and the time over which it is acquired?

  8. the relation between scientific discovery and scientific assessment given inducement and transmissibility conditions?

  9. what is relation between scientific realism and anti-realism in the limit of inquiry.

Most of the results are genuinely new. One of the reasons is that the formal framework by default construction mixes the three classical logics of modal, epistemic and tense in order to investigate the fundamental proposal above. This is interesting in its own right because little attention has been paid to how the three types of logic interact with each other – and how the they interact with formal learning they.

Most importantly however, it is a systematic investigation concerning the prospects of limiting convergent scientific knowledge – both for scientific realism and anti-realism.


Epistemology, Methodology, Reliability, Scientific Inquiry, Knowledge as True Justified Belief, Skepticism, Justification Global and Local Underdetermination, Realism and Anti-realism, Scientific Rationality, Gettier-cases, Prologues, Induction, Problem of Induction, Laws of Nature, Scientific Methods, Assessment, Discovery, Logic, Possible Worlds, Branching Time, Formal Learning Theory, Epistemic, Tense and Modal Logic, Transmissibility, Forcing, KK-thesis, Limiting Convergence, Accessibility Relation, Relevant Possibilities of Error, Bayesianism, Probability Theory, Inducement, Methodological Recommendations, Epistemic Goals and Correctness.



List of Figures
List of Tables
Formal Prerequisites

Chapter 1. Introduction

Part I – The Philosophy of Convergence

Chapter 2. Epistemology, Methodology and Reliability
Chapter 3. Knowledge and Skepticism
Chapter 4. The Epistemology of Convergence

Part II – Modal operator theory

Chapter 5. The Ontology of Convergence
Chapter 6. Science and Setup
Chapter 7. Two Relations of Correctness
Chapter 8. Methods and Methodology
Chapter 9. Forcing
Chapter 10. Definitions of Knowledge
Chapter 11. Modal Formalization
Chapter 12. Systems for Convergent Knowledge
Chapter 13. Knowledge in Time
Chapter 14. Forcing and Convergence – and Method
Chapter 15. Transmissibility

Part III – Convergence in Sum

Chapter 16. Knowledge in the End


A. List of Axioms, Propositions and Theorems
Appendix B. Additional Proofs
Appendix C. Science and Relevance – and Philosophy