The question 'What is the criterion of identity for directions?' might be construed as asking either 'When do lines have the same direction?' or 'When are directions identical?'. Frege's answer 'When they are parallel' fits the former question, not the latter, for it specifies a relation other than identity between lines, not directions. Jonathan Lowe thinks the latter question more fundamental, and claims that Frege's criterion can be reformulated to answer it: 'When some line with one is parallel to some (...) line with the other'. At p. 147 of Identity and Discrimination I make three points against this view: Lowe's construal does not permit a principled rejection of an intuitively unacceptable answer to the original question, On pain of circularity, Lowe's answer uses conceptual resources beyond those of Frege's, and thus is not a mere reformulation, Lowe's question seems to make the hopeless demand for something more basic than 'x = y Lowe's reply 'One-level versus two-level identity criteria' does not address or . I shall follow him in discussing only. (shrink)

Standardly, a one-level criterion of identity 1 is given in the form: ∀ x∀ y )where ‘ K’ denotes the kind of thing for which the criterion is being given and ‘ R’ denotes the criterial relation.Thus, we have, for example, the criterion of identity for sets: ∀ x∀ y))and for composites: ∀ x∀ y))and for events: ∀ x∀ y)). is equivalent to the conjunction of: ∀ x and ∀ x )),which just give two necessary 2 conditions for application of (...) the predicate ‘ K’. 3Consider now the reading of ‘ Kx’ as ‘ x is a member of the Theology Department’ and ‘ Rxy’ as ‘ x admires y and y admires x’. On this reading says that every theologian admires himself and admires no other member of the department. In other words it tells us that the theologians are a bunch of narcissists bound together only by mutual contempt or indifference . Suppose that this is 4 true of the theologians. It might also be …. (shrink)

It has long been debated whether objects are ‘sortally’ individuated. This paper begins by clarifying some of the key terms in play—in particular, ‘sortal’, ‘individuation’, and ‘object’. The term ‘individuation’ is taken to have both a cognitive and a metaphysical sense, in the former denoting the singling out of an object in thought and in the latter a determination relation between entities. ‘Sortalism’ is defined as the doctrine that only as falling under some specific sortal concept can an object be (...) successfully singled out in thought. It is argued that such a view is too strong, but that a weaker one, ‘categorialism’, can be defended, this implying that a thinker cannot successfully single out an object in thought without having at least an implicit grasp of the criterion of identity that the object satisfies. (shrink)

E. J. Lowe; One-level versus two-level identity criteria, Analysis, Volume 51, Issue 4, 1 October 1991, Pages 192–194, https://doi.org/10.1093/analys/51.4.192.

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

A lot of people believe that distinct objects can occupy precisely the same place for the entire time during which they exist. Such people have to provide an answer to the 'grounding problem' – they have to explain how such things, alike in so many ways, nonetheless manage to fall under different sortals, or have different modal properties. I argue in detail that they cannot say that there is anything in virtue of which spatio-temporally coincident things have those properties. However, (...) I also argue that this may not be as bad as it looks, and that there is a way to make sense of the claim that such properties are primitive. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...