Online research in philosophy

Molecular biologists and biochemists often use diagrams to present hypotheses. Analysis of diagrams shows that their content can be expressed with linguistic representations. Why do biologists use visual representations instead? One reason is simple comprehensibility: some diagrams present information which is readily understood from the diagram format, but which would not be comprehensible if the same information was expressed linguistically. But often diagrams are used even when concise, comprehensible linguistic alternatives are available. I explain this phenomenon by showing why diagrammatic representation is especially well suited for a particular kind of explanation common in molecular biology and biochemistry: namely, functional analysis, in which a capacity of the system is explained in terms of capacities of its component parts.

Recent literature on the role of pictorial representation in the life sciences has focused on the relationship between detailed representations of empirical data and more abstract, formal representations of theory. The standard argument is that in both a historical and epistemic sense, this relationship is a directional one: beginning with raw, unmediated images and moving towards diagrams that are more interpreted and more theoretically rich. Using the neural network diagrams of Warren McCulloch and Walter Pitts as a case study, I argue that while in the empirical sciences, pictorial representation tends to move from data to theory, in areas of the life sciences that are predominantly theoretical, when abstraction occurs at the outset, the relationship between detail and abstraction in pictorial representations can be of a different character.

This article puts forward the notion of “evolving diagram” as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter “diagrams*”) in the context of “sketch theory,” a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively.

The received view in philosophical studies of quantum field theory is that Feynman diagrams are simply calculational devices. Alongside this view we have the one that takes virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of physics by Mario Bunge, Paul Teller, Michael Redhead, Robert Weingard, Brigitte Falkenburg, and others. In this article I present an alternative to the received view.

Seven years after Richard Feynman died, I visited Caltech for the first time. One reason for the visit was to give a talk about the transactional interpretation of quantum mechanics, which draws so strongly on Feynman's own unusual ideas about the nature of electromagnetic radiation, now more than half a century old. It was, to say the least, an unusual feeling to be talking not just from the spot where Feynman himself used to lecture, but about his own work. And when, during the question period at the end of the talk, the discussion moved on to QED, the dream-like quality of the occasion intensified -- an audience at Caltech, of all places, was asking me to explain QED to them!

A logical system is studied whose well-formed representations consist of diagrams rather than formulas. The system, due to Shin [2, 3], is shown to be complete by an argument concerning maximally consistent sets of diagrams. The argument is complicated by the lack of a straight forward counterpart of atomic formulas for diagrams, and by the lack of a counterpart of negation for most diagrams.

This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept formation as well as representations of proofs. In addition we note that 'visualization' is used in two different ways. In the first sense 'visualization' denotes our inner mental pictures, which enable us to see that a certain fact holds, whereas in the other sense 'visualization' denotes a diagram or representation of something.

Someone, let’s say, a baby, is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain. A speaker who is on the far end of this chain, who has heard about, say Richard Feynman, in the marketplace or elsewhere, may be referring to Richard Feynman even though he can’t remember from whom he first heard of Feynman or from whom he ever heard of Feynman… A certain passage of communication reaching ultimately to the man himself does reach the speaker. He then is referring to Feynman even though he can’t identify him uniquely… a chain of communication going back to Feynman himself has been established, by virtue of his membership in a community which passed the name on from link to link, not by a ceremony that he makes in private in his study: “By ‘Feynman’ I shall mean the man who did such and such…”. (p. 299).

Feynman diagrams: conceptual tools for theoretical physicists Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9580-y Authors Laurie M. Brown, Department of Physics and Astronomy, Northwestern University, Evanston, IL 60201, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.