Schaffner's model of theory reduction has played an important role in philosophy of science and philosophy of biology. Here, the model is found to be problematic because of an internal tension. Indeed, standard antireductionist external criticisms concerning reduction functions and laws in biology do not provide a full picture of the limits of Schaffner's model. However, despite the internal tension, his model usefully highlights the importance of regulative ideals associated with the search for derivational, and embedding, deductive relations among mathematical structures in theoretical biology. A reconstructed Schaffnerian model could therefore shed light on mathematical theory development in the biological sciences and on the epistemology of mathematical practices more generally.

Kuhn made two attempts at providing an evolutionary analogy for scientific change. The first attempt, in The Structure of Scientific Revolutions, is very brief and unstructured; in this article I discuss some of its weaknesses. Alexander Bird takes this attempt more seriously and provides a criticism based on oversimplified evolutionary assumptions. These assumptions prove to be inadequate for the second, more articulate, evolutionary analogy suggested by Kuhn in “The Road since Structure.” I argue, however, that this second Kuhnian attempt is undermined by his inadequate view of biological progress and by his misunderstanding of the concept of ecological niche.

This article explores the relation between the concept of symmetry and its formalisms. The standard view among philosophers and physicists is that symmetry is completely formalized by mathematical groups. For some mathematicians however, the groupoid is a competing and more general formalism. An analysis of symmetry that justifies this extension has not been adequately spelled out. After a brief explication of how groups, equivalence, and symmetries classes are related, we show that, while it's true in some instances that groups are too restrictive, there are other instances for which the standard extension to groupoids is too unrestrictive. The connection between groups and equivalence classes, when generalized to groupoids, suggests a middle ground between the two.

We maximally extend the quantum-mechanical results of Muller and Saunders (2008) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite-dimensional Hilbert spaces. This confutes the currently dominant view that (A) the quantum-mechanical description of similar particles conflicts with Leibniz's Principle of the Identity of Indiscernibles (PII); and that (B) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We take sides with Muller and Saunders (2008) against this currently dominant view, which has been expounded and defended by many.

We have argued elsewhere that natural selection is not a cause of evolution, and that a resolution-of-forces (or vector addition) model does not provide us with a proper understanding of how natural selection combines with other evolutionary influences. These propositions have come in for criticism recently, and here we clarify and defend them. We do so within the broad framework of our own ‘hierarchical realization model’ of how evolutionary influences combine.

Because contemporary scientific research is conducted by groups of scientists, understanding scientific progress requires understanding this division of cognitive labor. We present a novel agent-based model of scientific research in which scientists divide their labor to explore an unknown epistemic landscape. Scientists aim to find the most epistemically significant research approaches. We consider three different search strategies that scientists can adopt for exploring the landscape. In the first, scientists work alone and do not let the discoveries of the community influence their actions. This is compared with two social research strategies: Followers are biased toward what others have already discovered, and we find that pure populations of these scientists do less well than scientists acting independently. However, pure populations of mavericks, who try to avoid research approaches that have already been taken, vastly outperform the other strategies. Finally, we show that, in mixed populations, mavericks stimulate followers to greater levels of epistemic production, making polymorphic populations of mavericks and followers ideal in many research domains.

The claim that a functional kind is multiply realized is typically motivated by appeal to intuitive examples. We are seldom told explicitly what the relevant structures are, and people have often preferred to rely on general intuitions in these cases. This article deals with the problem by explaining how to understand the proper relation between structural kinds and the functions they realize. I will suggest that the structural kinds that realize a function can be properly identified by attending to the context of functional explanation.