Hard and Blind: On Wittgenstein's Genealogical View of Logical Necessity

My main aim is to sketch a certain reading (‘genealogical') of later Wittgenstein's views on logical necessity. Along the way, I engage with the inferentialism currently debated in the literature on the epistemology of deductive logic.publishedVersio

How to think about informal proofs

This document is the Accepted Manuscript version of the following article: Brendan Larvor, ‘How to think about informal proofs’, Synthese, Vol. 187(2): 715-730, first published online 9 September 2011. The final publication is available at Springer via doi:10.1007/s11229-011-0007-5It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the fieldPeer reviewedFinal Accepted Versio

A Place to Rest Your (Burnt) Bones? Mortuary Houses in Early Anglo-Saxon England

This is an Accepted Manuscript of an article published by Taylor & Francis in Archaeological Journal on 5th October 2017, available online: doi: 10.1080/00665983.2017.1366704This article presents a fresh interpretation of square and rectangular mortuary structures found in association with deposits of cremated material and cremation burials in a range of early Anglo-Saxon (fifth-/sixth-century AD) cemeteries across southern and eastern England. Responding to a recent argument that they could be traces of pyre structures, a range of ethnographic analogies are drawn upon, and the full-range of archaeological evidence is synthesized, to re-affirm and extend their interpretation as unburned mortuary structures. Three interleaving significances are proposed: (i) demarcating the burial place of specific individuals or groups from the rest of the cemetery population, (ii) operating as ‘columbaria’ for the above-ground storage of the cremated dead (i.e. not just to demarcate cremation burials), and (iii) providing key nodes of commemoration between funerals as the structures were built, used, repaired and eventually decayed within cemeteries. The article proposes that timber ‘mortuary houses’ reveal that groups in early Anglo-Saxon England perceived their cemeteries in relation to contemporary settlement architectures, with some groups constructing and maintaining miniaturized canopied buildings to store and display the cremated remains of the dead

The Unity of a Tractarian Fact

It is not immediately clear from Wittgenstein’s Tractatus how to connect his idea there of an object with the logical ontologies of Frege and Russell. Toward clarification on this matter, this paper compares Russell’s and Wittgenstein’s versions of the thesis of an atomic fact that it is a complex composition. The claim arrived at is that whilst Russell (at times at least) has one particular of the elements of a fact – the relation – responsible for the unity of the whole, for Wittgenstein the unity of a fact is the product of copulative powers inherent in all its elements. All kinds of constituents of Tractarian facts – all kinds (forms) of object – are, to use Fregean terminology, unsaturated.Articl

“Till at last there remain nothing”

In A Treatise of Human Nature, David Hume presents an argument according to which all knowledge reduces to probability, and all probability reduces to nothing. Many have criticized this argument, while others find nothing wrong with it. In this paper we explain that the argument is invalid as it stands, but for different reasons than have been hitherto acknowledged. Once the argument is repaired, it becomes clear that there is indeed something that reduces to nothing, but it is something other than what, according to many, Hume had in mind. Thus two views emerge of what exactly it is that reduces. We surmise that Hume failed to distinguish the two, because he lacked the formal means to differentiate between a rendering of his argument that is in accordance with the probability calculus, and one that is not

The structure of idealization in biological theories: the case of the Wright-Fisher model.

In this paper we present a new framework of idealization in biology. We characterize idealizations as a network of counterfactual and hypothetical conditionals that can exhibit different “degrees of contingency”. We use this idea to say that, in departing more or less from the actual world, idealizations can serve numerous epistemic, methodological or heuristic purposes within scientific research. We defend that, in part, this structure explains why idealizations, despite being deformations of reality, are so successful in scientific practice. For illustrative purposes, we provide an example from population genetics, the Wright-Fisher Mode