Øystein Linnebo

I defend the view that our ontology divides into categories, each with its own canonical way of identifying and distinguishing the objects it encompasses. For instance, I argue that natural numbers are identified and distinguished by their positions in the number sequence, and physical bodies, by facts having to do with spatiotemporal continuity. I also argue that objects belonging to different categories are ipso facto distinct. My arguments are based on an analysis of reference, which ascribes to reference a richer structure than it is normally taken to have

Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, the method is poorly behaved unless the background second-order logic is predicative

In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties

In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal language, and we show that the two approaches are equivalent.

Fixing Frege is one of the most important investigations to date of Fregean approaches to the foundations of mathematics. In addition to providing an unrivalled survey of the technical program to which Frege's writings have given rise, the book makes a large number of improvements and clarifications. Anyone with an interest in the philosophy of mathematics will enjoy and benefit from the careful and well-informed overview provided by the first of its three chapters. Specialists will find the book an indispensable reference and an invaluable source of insights and new results. Although Frege is widely regarded as the father of analytic philosophy, his work on the foundations of mathematics was for a long time rather peripheral to ongoing research. The main reason for this is no doubt Russell's discovery in 1901 that the paradox now bearing his name can be derived in Frege's logical system. But recent decades have seen a huge surge of interest in Fregean approaches to the foundations of mathematics. A variety of consistent theories have been discovered that can be salvaged from Frege's inconsistent system, and foundational and philosophical claims have been made on behalf of many of these theories. Burgess claims quite plausibly that the significance of any such modified Fregean theory will in large part depend on how much of ordinary mathematics it enables us to develop. His book is accordingly 'a survey of various modified Fregean systems, attempting to determine the scope and limits of each'. The book's agenda is thus predominantly technical, and its spirit open-minded and experimental.

It is sometimes suggested that criteria of identity should play a central role in an account of our most fundamental ways of referring to objects. The view is nicely illustrated by an example due to (Quine, 1950). Suppose you are standing at the bank of a river, watching the water that floats by. What is required for you to refer to the river, as opposed to a particular segment of it, or the totality of its water, or the current temporal part of this water? According to Quine, you must at least implicitly be operating with some criterion of identity that informs you when two sightings of water count as sightings of the same referent. For unless you have at least an implicit grasp of what is required for your intended referent to be identical with another object with which you are presented, you have not succeeded in singling out a unique object for reference.