Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does (...) exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”. (shrink)

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

Two different concepts of iconicity compete in Peirce's diagrammatical logic. One is articulated in his general reflections on the role of diagrams in thought, in what could be termed his diagrammatology — the other is articulated in his construction of Existential Graphs as an iconic system for representing logic. One is operational and defines iconicity in terms of which information may be derived from a given diagram or diagram system — the other has stronger demands on iconicity, adding to the (...) operational criterion a demand for as high a degree of similarity as possible and may be termed optimal iconicity. Peirce himself does not clearly distinguish these two iconicity notions, a fact that has caused some confusion. By isolating them, we get a clearer and more refined conceptual apparatus for analyzing iconic signs, from pictures to logic. (shrink)

Charles Sanders Peirce (1839-1914), the founder of pragmatism, is generally considered the most significant American philosopher. Popularized by William James and John Dewey, pragmatism advocates that our philosophical theories be linked to experience and practice. The essays in this volume reveal how Peirce developed this concept.

Since its inception in 1869, the periodic system — icon of modern chemistry — has suffered from the problematic accommodation of the rare-earth elements. The substance of this paper intends to retrace Mendeleev’s shifting attitudes with regard to the rare-earth crisis during the period 1869–1871. Based on a detailed examination of Mendeleev's research papers from that period, it will be argued that the rare-earth crisis played a key role in inducing a number of important changes in Mendeleev’s philosophical viewpoints with (...) regard to the epistemological concept of a chemical element and the nature of elementary groups. Many of Mendeleev's most cherished beliefs got endangered by the nature of these elements. Their mystifying properties forced him to revise his ideas about primary and secondary groups, the elements as basic and simple substances, and the use of short and long form tables. They made him question the validity and universality of the periodic law, and led him into hypothesizing about the internal structure of matter and constitution of atoms. (shrink)

This essay explores the connection between representation and explanation in the sciences. I suggest that scientific representation schemes be viewed as pragmatic tools for acquiring the sort of articulated awareness that is the hallmark of nontrivial knowledge. Crystal field theory in chemistry illustrates this perspective. Certain representations achieve the status of being paradigmatically explanatory, thereby shaping models of intelligibility. In turn, these explanatory preferences serve largely to define and differentiate disciplinary communities by implicitly endorsing particular epistemic aims and values. In (...) this way, the pragmatic nature of explanatory discourse effectively grants its intellectual utility. (shrink)

In this paper, I develop Mauricio Suárez’s distinction between denotation, epistemic representation, and faithful epistemic representation. I then outline an interpretational account of epistemic representation, according to which a vehicle represents a target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target, which would allow them to perform valid (but not necessarily sound) surrogative inferences from the model to the system. The main difference between the interpretational conception I (...) defend here and Suárez’s inferential conception is that the interpretational account is a substantial account—interpretation is not just a “symptom” of representation; it is what makes something an epistemic representation of a something else. (shrink)

Models such as the simple pendulum, isolated populations, and perfectly rational agents, play a central role in theorising. It is now widely acknowledged that a study of scientific representation should focus on the role of such imaginary entities in scientists’ reasoning. However, the question is most of the time cast as follows: How can fictional or abstract entities represent the phenomena? In this paper, I show that this question is not well posed. First, I clarify the notion of representation, and (...) I emphasise the importance of what I call the “format” of a representation for the inferences agents can draw from it. Then, I show that the very same model can be presented under different formats, which do not enable scientists to perform the same inferences. Assuming that the main function of a representation is to allow one to draw predictions and explanations of the phenomena by reasoning with it, I conclude that imaginary models in abstracto are not used as representations: scientists always reason with formatted representations. Therefore, the problem of scientific representation does not lie in the relationship of imaginary entities with real systems. One should rather focus on the variety of the formats that are used in scientific practice. (shrink)