A model-theoretic account of representation (or, I don't know much about art … but I know it involves isomorphism)

Discussions of representation in science tend to draw on examples from art. However, such examples need to be handled with care given a) the differences between works of art and scientific theories and b) the accommodation of these examples within certain philosophies of art. I shall examine the claim that isomorphism is neither necessary nor sufficient for representation and I shall argue that there exist accounts of representation in both art and science involving isomorphism which accommodate the apparent counterexamples and, moreover, allow us to understand how ‘‘impossible’’ artistic objects and inconsistent scientific theories can be said to represent

Quantum objects are vague objects

[FIRST PARAGRAPHS] Is vagueness a feature of the world or merely of our representations of the world? Of course, one might respond to this question by asserting that insofar as our knowledge of the world is mediated by our representations of it, any attribution of vagueness must attach to the latter. However, this is to trivialize the issue: even granted the point that all knowledge is representational, the question can be re-posed by asking whether vague features of our representations are ultimately eliminable or not. It is the answer to this question which distinguishes those who believe that vagueness is essentially epistemic from those who believe that it is, equally essentially, ontic. The eliminability of vague features according to the epistemic view can be expressed in terms of the supervenience of ‘vaguely described facts’ on ‘precisely describable facts’: If two possible situations are alike as precisely described in terms of physical measurements, for example, then they are alike as vaguely described with words like ‘thin’. It may therefore be concluded that the facts themselves are not vague, for all the facts supervene on precisely describable facts. (Williamson 1994, p. 248; see also pp. 201- 204) It is the putative vagueness of certain identity statements in particular that has been the central focus of claims that there is vagueness ‘in’ the world (Parfit 1984, pp. 238-241; Kripke 1972, p. 345 n. 18). Thus, it may be vague as to who is identical to whom after a brain-swap, to give a much discussed example. Such claims have been dealt a forceful blow by the famous Evans-Salmon argument which runs as follows: suppose for reductio that it is indeterminate whether a = b. Then b definitely possesses the property that it is indeterminate whether it is identical with a, but a definitely does not possess this property since it is surely not indeterminate whether a=a. Therefore, by Leibniz’s Law, it cannot be the case that a=b and so the identity cannot be indeterminate (Evans 1978; Salmon 1982)

Theories, models and structures: thirty years on

Thirty years after the conference that gave rise to The Structure of Scientific Theories, there is renewed interest in the nature of theories and models. However, certain crucial issues from thirty years ago are reprised in current discussions; specifically: whether the diversity of models in the science can be captured by some unitary account; and whether the temporal dimension of scientific practice can be represented by such an account. After reviewing recent developments we suggest that these issues can be accommodated within the partial structures formulation of the semantic or model-theoretic approach

On representing the relationship between the mathematical and the empirical

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London’s analysis of the superfluid behavior of liquid helium in terms of Bose-Einstein statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London’s model