Holger Andreas

The concept of measurement is fundamental to a whole range of different disciplines, including not only the natural and engineering sciences, but also laboratory medicine and certain branches of the social sciences. This being the case, the concept of measurement has a particular relevance to the development of top-level ontologies in the area of knowledge engineering. For this reason, the present paper is concerned with ontological aspects of measurement. We are searching for a list of concepts that are apt to characterize measurement methods in a general manner. To establish such means of characterization, we will primarily deal with the semantics of measurement values.

In this paper, we develop a non-reductive variant of the regularity theory of causation proposed in Andreas and Günther (Pacific Philosophical Quarterly 105: 2–32, 2024). The variant is motivated as a refinement of Lewis’s (Journal of Philosophy 70:556–567, 1973) regularity theory. We do not pursue a reductive theory here because we found a challenge for Baumgartner's (Erkenntnis 78:85–109, 2013) regularity theory which applies to our previous theory as well. The challenge is sidestepped by a framework of law-like propositions resembling structural equations. We furthermore improve the deviancy condition of our previous theory. Finally, we show that the present theory can compete with the most advanced regularity and counterfactual accounts.

The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory relations. We show that our final analysis captures the presumed asymmetry between explanans and explanandum much better than Rott’s original analysis.

In this paper, a solution to the problem of theoretical terms is developed that is based on Carnap’s doctrine of indirect interpretation of theoretical terms. This doctrine will be given a semantic, model-theoretic explanation that is not given by Carnap himself as he remains content with a syntactic explanation. From that semantic explanation, rules for the truth-value assignment to postulates, i.e. sentences that determine the meaning of theoretical terms, are derived. The logical status of postulates will be clarified thereby in such a way that the problem of theoretical terms disappears.

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science.

According to Woodward’s influential account of explanation, explanations have a counterfactual structure, and explanatory counterfactuals are analysed in terms of causal relations and interventions. In this paper, we provide a formal semantics of explanatory counterfactuals based on a Ramsey Test semantics of conditionals. Like Woodward’s account, our account is guided by causal considerations. Unlike Woodward’s account, it makes no reference to causal graphs and it also covers cases of explanation where interventions are impossible.

We put forth an analysis of causation. The analysis centers on the notion of a causal model that provides only partial information as to which events occur, but complete information about the dependences between the events. The basic idea is this: an event causes another just in case there is a causal model that is uninformative on both events and in which the first event makes a difference as to the occurrence of the other. We show that our analysis captures more causal scenarios than the other counterfactual accounts to date.

We define a formal semantics of conditionals based on _normatively ideal worlds_. Such worlds are described informally by Armgardt (Gabbay D, Magnani L, Park W, Pietarinen A-V (eds) Natural arguments: a tribute to john woods, College Publications, London, pp 699–708, 2018) to address well-known problems of the counterfactual approach to causation. Drawing on Armgardt’s proposal, we use iterated conditionals in order to analyse causal relations in scenarios of multi-agent interaction. This results in a refined counterfactual approach to causal responsibility in legal contexts, which solves overdetermination problems in an intuitively accessible manner.

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated.

In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all admissible interpretations of the Peano axioms. Moreover, we compare this application with the modal structuralism by Hellman (Mathematics without numbers: towards a modal-structural interpretation. Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic.

In this book we present a collection of papers on the topic of applying paraconsistent logic to solve inconsistency related problems in science, mathematics and computer science. The goal is to develop, compare, and evaluate different ways of applying paraconsistent logic. After more than 60 years of mainly theoretical developments in many independent systems of paraconsistent logic, we believe the time has come to compare and apply the developed systems in order to increase our philosophical understanding of reasoning when faced with inconsistencies. This book wants to be a first step toward an application based, constructive debate to tackle the question which systems are best applied for which kind of problems and which philosophical conclusions can be drawn from such applications.

The present paper aims to complement causal model approaches to causal explanation by Woodward [15], Halpern and Pearl [5], and Strevens [14]. It centres on a strengthened Ramsey Test of conditionals: α ≫ γ iff, after sus- pending judgment about α and γ, an agent can infer γ from the supposition of α. It has been shown by Andreas and Gu ̈nther [1] that such a conditional can be used as starting point of an analysis of ‘because’ in natural language. In what follows, we shall refine this analysis so as to yield a fully fledged account of causal explanation.

In this book we present a collection of papers on the topic of applying paraconsistent logic to solve inconsistency related problems in science, mathematics and computer science. The goal is to develop, compare, and evaluate different ways of applying paraconsistent logic. After more than 60 years of mainly theoretical developments in many independent systems of paraconsistent logic, we believe the time has come to compare and apply the developed systems in order to increase our philosophical understanding of reasoning when faced with inconsistencies. This book wants to be a first step toward an application based, constructive debate to tackle the question which systems are best applied for which kind of problems and which philosophical conclusions can be drawn from such applications.

A central topic in the logic of science concerns the proper semantic analysis of theoretical sentences, that is sentences containing theoretical terms. In this paper, we present a novel choice-semantical account of theoretical truth based on the epsilon-term definition of theoretical terms. Specifically, we develop two ways of specifying the truth conditions of theoretical statements in a choice functional semantics, each giving rise to a corresponding logic of such statements. In order to investigate the inferential strength of these logical systems, we provide a translation of each truth definition into a modal definition of theoretical truth. Based on this, we show that the stronger notion of choice-semantical truth captures more adequately our informal semantic understanding of scientific statements.

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected].

This paper aims to set forth Carnapian structuralism, i.e., a syntactic view of the structuralist approach which is deeply inspired by Carnap’s dual level conception of scientific theories. At its core is the axiomatisation of a metatheoretical concept AE(T) which characterises those extensions of an intended application that are admissible in the sense of being models of the theory-element T and that satisfy all links, constraints and specialisations. The union of axiom systems of AE(T) (where T is an element of the theory-net N) will allow us to present scientific theories in an axiomatic fashion so that deductive reasoning in science can be formalised. Thereupon defeasible and paraconsistent means of reasoning will be introduced. The logical study of scientific reasoning is the key motivation of Carnapian structuralism. A further motivation is to help overcome the syntactic-semantic split in the philosophy of science.

Some scientific theories are inconsistent, yet non-trivial and meaningful. How is that possible? The present paper aims to show that we can analyse the inferential use of such theories in terms of consistent compositions of the applications of universal axioms. This technique will be represented by a preferred models semantics, which allows us to accept the instances of universal axioms selectively. For such a semantics to be developed, the framework of partial structures by da Costa and French will be extended by a few elements of the Sneed formalism, also known as the structuralist approach to science.

In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back to Carnap but has been advanced until the present day without a proper semantic explanation.

This article concerns the split between syntactic and semantic approaches to scientific theories. It aims at showing that an axiomatic representation of a scientific theory is a precondition of comprehending if the models of contain infinite entities. This result is established on the basis of the proposition that the human mind—which is finitely bounded for all we know—is not capable of directly grasping infinite entities. In view of this cognitive limitation, an indirect and finite representation of possibly infinite components of the models of a scientific theory proves to be indispensable. Sets of axioms and sets of axiom schemes provide such a representation. These considerations will be cast into an argument for an axiomatic conception of scientific theories. The article concludes with a case study of the ideal gas model.