Peer reviewers at many funding agencies and scientific journals are asked to score submissions both on individual criteria and overall. The overall scores should be some kind of aggregate of the criteria scores. Carole Lee identifies this as a potential locus for bias to enter the peer review process, which she calls commensuration bias. Here I view the aggregation of scores through the lens of social choice theory. I argue that, when reviewing grant proposals, it is in many cases impossible (...) to avoid commensuration bias. (shrink)

Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in defining (...) a new measure of truthlikeness which satisfies a number of desiderata. The resulting account has some interesting and surprising connections with other accounts on the market, thus shedding new light on current attempts of systematizing different approaches to verisimilitude. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

Truthlikeness is a property of a theory or a proposition that represents its closeness to the truth. We start by summarizing Niiniluoto’s proposal of truthlikeness for deterministic laws, which defines truthlikeness as a function of accuracy, and García-Lapeña’s expanded version, which defines truthlikeness for DL as a function of two factors, accuracy and nomicity. Then, we move to develop an appropriate definition of truthlikeness for probabilistic laws based on Niiniluoto’s suggestion to use the Kullback–Leibler divergence to define the distance between (...) a probability law X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X$$\end{document} and the true probability law T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document}. We argue that the Kullback–Leibler divergence seems to be the best of the available probability distances to measure accuracy between PL. However, as in the case of DL, we argue that accuracy represents a necessary but not sufficient condition, as two PL may be equally accurate and still one may imply more true or truthlike consequences, behaviours or true facts about the system than the other. The final proposal defines truthlikeness for PL as a function of two factors, p-accuracy and p-nomicity, in intimate connexion with García-Lapeña’s proposal for DL. (shrink)

Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability at the same time. For this purpose, this paper proposes the P–T probability framework, which is assembled with Shannon’s statistical probability framework for communication, Kolmogorov’s probability axioms for logical probability, and Zadeh’s membership functions used as truth functions. Two kinds of probabilities are connected by an (...) extended Bayes’ theorem, with which we can convert a likelihood function and a truth function from one to another. Hence, we can train truth functions (in logic) by sampling distributions (in statistics). This probability framework was developed in the author’s long-term studies on semantic information, statistical learning, and color vision. This paper first proposes the P–T probability framework and explains different probabilities in it by its applications to semantic information theory. Then, this framework and the semantic information methods are applied to statistical learning, statistical mechanics, hypothesis evaluation (including falsification), confirmation, and Bayesian reasoning. Theoretical applications illustrate the reasonability and practicability of this framework. This framework is helpful for interpretable AI. To interpret neural networks, we need further study. (shrink)

This is a response to the papers in the special issue Logical Perspectives on Science and Cognition—The Philosophy of Gerhard Schurz.

The notion of truthlikeness or verisimilitude has been a topic of intensive discussion ever since the definition proposed by Karl Popper was refuted in 1974. This paper gives an analysis of old and new debates about this notion. There is a fairly large agreement about the truthlikeness ordering of conjunctive theories, but the main rival approaches differ especially about false disjunctive theories. Continuing the debate between Niiniluoto’s min-sum measure and Schurz’s relevant consequence measure, the paper also gives a critical assessment (...) of Oddie’s new defense of the average measure and Kuipers’ refined definition of truth approximation. (shrink)

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.

Theories of truthlikeness (or verisimilitude) are currently being classified according to two independent distinctions: that between ‘content’ and ‘likeness’ accounts, and that between ‘conjunctive’ and ‘disjunctive’ ones. In this article, I present and discuss a new definition of truthlikeness, which employs Carnap’s notion of the content elements entailed by a theory or proposition, and is then labelled ‘Carnapian’. After studying in detail the properties and shortcomings of this definition, I argue that it occupies a unique position in the landscape of (...) different approaches to truthlikeness. More precisely, I show that it provides the only explication of truthlikeness which is both ‘conjunctive’ and ‘content-based’ in a suitably defined sense. (shrink)

Theories of verisimilitude have routinely been classified into two rival camps—the content approach and the likeness approach—and these appear to be motivated by very different sets of data and principles. The question thus naturally arises as to whether these approaches can be fruitfully combined. Recently Zwart and Franssen (Synthese 158(1):75–92, 2007) have offered precise analyses of the content and likeness approaches, and shown that given these analyses any attempt to meld content and likeness orderings violates some basic desiderata. Unfortunately their (...) characterizations of the approaches do not embrace the paradigm examples of those approaches. I offer somewhat different characterizations of these two approaches, as well as of the consequence approach (Schurz and Weingartner (Synthese 172(3):415–436, 2010) which happily embrace their respective paradigms. Finally I prove that the three approaches are indeed compatible, but only just, and that the cost of combining them is too high. Any account which combines the strictures of what I call the strong likeness approach with the demands of either the content or the consequence approach suffers from precisely the same defect as Popper’s—namely, it entails the trivialization of truthlikeness. The downside of eschewing the strong likeness constraints and embracing the content constraints alone is the underdetermination of the concept of truthlikeness. (shrink)

In this paper, we address the problem of truth approximation through theory change, asking whether revising our theories by newly acquired data leads us closer to the truth about a given domain. More particularly, we focus on “nomic conjunctive theories”, i.e., theories expressed as conjunctions of logically independent statements concerning the physical or, more generally, nomic possibilities and impossibilities of the domain under inquiry. We define both a comparative and a quantitative notion of the verisimilitude of such theories, and identify (...) suitable conditions concerning the (partial) correctness of acquired data, under which revising our theories by data leads us closer to “the nomic truth”, construed as the target of scientific inquiry. We conclude by indicating some further developments, generalizations, and open issues arising from our results. (shrink)

Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which (...) demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results. (shrink)

The expansion or revision of false theories by true evidence does not always increase their verisimilitude. After a comparison of different notions of verisimilitude the relation between verisimilitude and belief expansion or revision is investigated within the framework of the relevant element account. We are able to find certain interesting conditions under which both the expansion and the revision of theories by true evidence is guaranteed to increase their verisimilitude.

The paper sets up a general framework for defining the notion of verisimilitude. Popper’s own account of verisimilitude is then located within this framework; and his account is defended on the grounds that it can be seen to provide a reasonable structural or Pareto criterion, rather than a substantive criterion, of verisimilitude. Some other criteria of verisimilitude that may be located within the framework are also considered and their relative merits compared.

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in (...) agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic versus semantic formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence. (shrink)

Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in defining (...) a new measure of truthlikeness which satisfies a number of desiderata. The resulting account has some interesting and surprising connections with other accounts on the market, thus shedding new light on current attempts of systematizing different approaches to verisimilitude. (shrink)

The notion of truthlikeness or verisimilitude has been a topic of intensive discussion ever since the definition proposed by Karl Popper was refuted in 1974. This paper gives an analysis of old and new debates about this notion. There is a fairly large agreement about the truthlikeness ordering of conjunctive theories, but the main rival approaches differ especially about false disjunctive theories. Continuing the debate between Niiniluoto’s min-sum measure and Schurz’s relevant consequence measure, the paper also gives a critical assessment (...) of Oddie’s new defense of the average measure and Kuipers’ refined definition of truth approximation. (shrink)

The paper sets up a general framework for defining the notion of verisimilitude. Popper’s own account of verisimilitude is then located within this framework; and his account is defended on the grounds that it can be seen to provide a reasonable structural or Pareto criterion, rather than a substantive criterion, of verisimilitude. Some other criteria of verisimilitude that may be located within the framework are also considered and their relative merits compared.

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.