The limits of abstraction

  title={The limits of abstraction},
  author={Roy T. Cook and Philip A. Ebert},
The Limits of Abstraction, Kit Fine, Oxford: Clarendon Press, 2002, pp.216. ISBN 9780191567261 
Ineffability within the limits of abstraction alone
The purpose of this article is to assess the prospects for a Scottish neo-logicist foundation for a set theory. The gold standard would be a theory as rich and useful as the dominant one, ZFC,Expand
Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume's Principle
ion and Epistemic Entitlement: On the Epistemological Status of Hume’s Principle
In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I findExpand
Toward a Trivialist Account of Mathematics
The aim of this chapter is to defend mathematical trivialism—the view that the truths of pure mathematics have trivial truth-conditions and the falsities of pure mathematics have trivialExpand
Quantifiers Defined by Parametric Extensions
A metaphysically flexible theory of quantification broad enough to incorporate many distinct theories of objects and to yield notions of validity that are proper extensions of classical logic. Expand
Rescuing Implicit Definition from Abstractionism
  • 2020
Neo-Fregeans in the philosophy of mathematics hold that the key to a correct understanding of mathematics is the implicit definition of mathematical terms. In this paper, I discuss and advocate theExpand
NeoFregeanism and Quanti er Variance
ion of Direction, the effect is not to de ne directions into existence but to coordinate the question of the existence of directions with that of the existence of lines; and the latter can remain,Expand
Computational Abstraction
  • R. Turner
  • Medicine, Computer Science
  • Entropy
  • 2021
It is argued that representation and abstraction, while mathematical siblings, are philosophically quite different and should be interpreted, modified, extended and imported into type theory. Expand
Cardinality and Acceptable Abstraction
It is shown that a fix proposed by Richard Heck fails but an interesting idea on which it is based is analyzed, namely that an acceptable abstraction has to ‘generate’ the objects that it requires. Expand
Abstraction and Identity
and want to settle cross-sortal identity claims of the form: Both abstraction principles, however, are silent with regard to this identity - a special instance of the Caesar Problem . In whatExpand