Global supervenience without reducibility

Does the global supervenience of one class on another entail reductionism, in the sense that any property in the former class is definable from properties in the latter class? This question appears to be at the same time formally tractable and philosophically significant. It seems formally tractable because the concepts involved are susceptible to rigorous definition. It is philosophically significant because in a number of debates about inter-level relationships, there are prima facie plausible positions that presuppose that there is no such entailment: standard versions of non-reductive physicalism and of normative non-naturalism accept global supervenience while rejecting reductionism. I identify a gap in an influential argument for the entailment, due to Frank Jackson and Robert Stalnaker, and draw on the model theory of infinitary languages to argue that some globally supervening properties are not reducible

Supervenience, Logic, and Empirical Content: Commentary on Hans Halvorson, The Logic in Philosophy of Science

Halvorson’s book’s real achievement is that it is both a source and a challenge, and not just for philosophers of science. I will begin with some notes to add to Halvorson’s discussion of supervenience and definability. Then secondly I will engage the book’s way of dealing with empirical content. Extension of formal methods to the relation of theory to world, as mediated by experiment and measurement, seems to me crucial to its value, and I will make three suggestions for this. Then thirdly I will turn to the tantalizing hints Halvorson gives us of an overall view of logic and language, and speculate about how that would answer questions about scientific representation and more specifically about the object language / metalanguage relation

Supervenience, Logic, and Empirical Content: Commentary on Hans Halvorson, The Logic in Philosophy of Science

Halvorson’s book’s real achievement is that it is both a source and a challenge, and not just for philosophers of science. I will begin with some notes to add to Halvorson’s discussion of supervenience and definability. Then secondly I will engage the book’s way of dealing with empirical content. Extension of formal methods to the relation of theory to world, as mediated by experiment and measurement, seems to me crucial to its value, and I will make three suggestions for this. Then thirdly I will turn to the tantalizing hints Halvorson gives us of an overall view of logic and language, and speculate about how that would answer questions about scientific representation and more specifically about the object language / metalanguage relation

Structural problems for reductionism

Universal reductionism—the sort of project pursued by Carnap in the Aufbau, Lewis in his campaign on behalf of Humean supervenience, Jackson in From Metaphysics to Ethics, and Chalmers in Constructing the World—aims to reduce everything to some specified base, more or less austere as it may be. In this paper, I identify two constraints that a promising strategy to argue for universal reductionism needs to satisfy: the exhaustion constraint and the chaining constraint. As a case study, I then consider Chalmers’ Constructing the World, in which a priori implication, or “scrutability”, plays the role of reduction. Chalmers first divides up the total vocabulary of our language into different families, and then argues, for each family separately, that truths involving expressions in that family are scrutable from the putative base. He does not systematically address the question whether “cross-family sentences”—sentences involving expressions from more than one family—are scrutable. I shall argue that this lacuna cannot be filled, since scrutability does not allow for the exhaustion constraint and the chaining constraint to be jointly satisfied. I further suggest that Carnap’s account, in which definability plays the role of reduction, has better prospects of meeting these constraints

Supervenience among classes of relations

This paper extends the definition of strong supervenience to cover classes of relations of any adicity, including transworld relations. It motivates that project by showing that not all interesting supervenience claims involving relations are global supervenience claims. The proposed definition has five welcome features: it reduces to the familiar definition in the special case where the classes contain only monadic properties; it equips supervenience with the expected formal properties, such as transitivity and monotonicity; it entails that a relation supervenes on its converse; it classifies certain paradigms correctly; it makes distinctions even in the realm of the non-contingent, as witnessed by the fact that identity does not supervene on any class of relations. Finally, the paper applies the defined concept, and the related concept of orthogonality, to the study of internal and external relations

What Makes a Computation Unconventional?

A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.Comment: Based on an invited lecture for the 'Symposium on Natural/Unconventional Computing and Its Philosophical Significance' at the AISB/IACAP World Congress 2012, University of Birmingham, July 2-6, 201

On the Emergence of Time in Quantum Gravity

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time (Section 2). We then introduce the search for a quantum theory of gravity (Section 3); and review some general interpretative issues about space, time and matter Section 4). We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach (Section 5). Section 6 concludes.Comment: To appear in ``The Arguments of Time'', ed. J. Butterfield, Oxford University Press, 199

Supervenience, Reduction, and Translation

This paper considers the following question: what is the relationship between supervenience and reduction? I investigate this formally, first by introducing a recent argument by Christian List to the effect that one can have supervenience without reduction; then by considering how the notion of Nagelian reduction can be related to the formal apparatus of definability and translation theory; then by showing how, in the context of propositional theories, topological constraints on supervenience serve to enforce reducibility; and finally, how constraints derived from the theory of ultraproducts can enforce reducibility in the context of first-order theories

Ramsey equivalence

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following observation: if a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used

Ramsey equivalence

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following observation: if a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used