Probability,Approximate Truth,and Truthlikeness: More Ways out of the Preface Paradox

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including a recent one advanced by Hannes Leitgeb (Analysis 74.1).     

Point-Free Geometry and Verisimilitude of Theories

A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions of verisimilitude.     

Verisimilitude and the Dynamicsof Scientific Research Programmes

Some peculiarities of the evaluation of theories within scientific research programmes (SRPs) and of the assessing of rival SRPs are described assuming that scientists try to maximise an ‘epistemic utility function’ under economic and institutional constraints. Special attention is given to Lakatos' concepts of ‘empirical progress’ and ‘theoretical progress’. A notion of ‘empirical verisimilitude’ is defended as an appropriate utility function. The neologism ‘methodonomics’ is applied to this kind of studies. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Need for a Revolution in the Philosophy of Science

There is a need to bring about a revolution in the philosophy of science, interpreted to be both the academic discipline, and the official view of the aims and methods of science upheld by the scientific community. At present both are dominated by the view that in science theories are chosen on the basis of empirical considerations alone, nothing being permanently accepted as a part of scientific knowledge independently of evidence. Biasing choice of theory in the direction of simplicity, unity or explanatory power does not permanently commit science to the thesis that nature is simple or unified. This current ‘paradigm’ is, I argue, untenable. We need a new paradigm, which acknowledges that science makes a hierarchy of metaphysical assumptions concerning the comprehensibility and knowability of the universe, theories being chosen partly on the basis of compatibility with these assumptions. Eleven arguments are given for favouring this new ‘paradigm’ over the current one. This revised version was published online in August 2006 with corrections to the Cover Date.     

Accuracy,Verisimilitude, and Scoring Rules

Suppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis [2016] have given an argument that, if sound, rules out many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in part by noting that the argument fails to account for verisimilitude—that certain false hypotheses might be closer to the truth than other false hypotheses are. Oddie [forthcoming], however, has argued that no member of a very wide class of scoring rules (the so-called proper scores) can appropriately handle verisimilitude. I explain how to respond to Oddie's argument, and I recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie.