Frege, Boolos, and Logical Objects

  title={Frege, Boolos, and Logical Objects},
  author={David J. Anderson and Edward N. Zalta},
  journal={Journal of Philosophical Logic},
In this paper, the authors discuss Frege's theory of “logical objects” (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the ‘eta’ relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the ‘eta’ relation to assert the existence of logical objects under certain highly… Expand
Relations Versus Functions at the Foundations of Logic: Type-Theoretic Considerations
There is an interesting system having a logic that can be properly characterized in relational type theory but not in functional type theory (FTT), which shows that RTT is more general than FTT. Expand
A Defense of Logicism∗
We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles,Expand
What is the Purpose of Neo-Logicism ?
objects are those, that are not possibly concrete; and ordinary objects are those that are possibly concrete. The notion of an ordinary object allows Zalta in other projects to propose a theory ofExpand
Avoiding Russell-Kaplan Paradoxes : Worlds and Propositions Set Free ∗ ( DRAFT )
The authors first address two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan and show that these paradoxes don’t affect the object-theoretic analysis ofExpand
What is Neologicism?
According to one well-received view, logicism was replaced by a very different account of the foundations of mathematics, in which mathematics was seen as the study of axioms and their consequences in models consisting of the sets described by Zermelo-Fraenkel set theory (ZF). Expand
Typed Object Theory
It is shown how typed object theory compares with other intensional type theories, and a number of natural language contexts without requiring the technique of ‘type-raising’ are analyzed. Expand
Reflections on Mathematics ∗
Though the philosophy of mathematics encompasses many kinds of questions, my response to the five questions primarily focuses on the prospects of developing a unified approach to the metaphysical andExpand
Mathematical Pluralism*
Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory,Expand
What did Frege take Russell to have proved?
  • J. Woods
  • Computer Science, Philosophy
  • Synthese
  • 2019
In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth ofExpand
Essence and Modality
The principal axiom for abstract objects, described in more detail below, is a comprehension principle that asserts the conditions under which abstract objects exist and encode properties: for any expressible condition 4 that is satisfiable by properties F, there exists an abstract object that encodes exactly the properties F satisfying. Expand


The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik
Reading ‘x(Fx)’ as ‘the value-range of the concept F ’, Basic Law V thus states that, for every F and G, the value-range of the concept F is the same as the value-range of the concept G just in caseExpand
Intensional Logic and the Metaphysics of Intentionality
In this book, Edward N. Zalta tackles the issues that arise in connection with intensional logic - a formal system for representing and explaining the apparent failures of certain importantExpand
Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects
It is shown that both Heck and TΔ prove the existence of infinitely many non-logical objects (TΔ deriving, moreover, the nonexistence of the value-range concept), and some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Expand
Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory
  • E. Zalta
  • Philosophy, Computer Science
  • J. Philos. Log.
  • 1999
The author derives the Dedekind–Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (philosophical) logicians implicitly accept. Expand
The Consistency of predicative fragments of frege’s grundgesetze der arithmetik
As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minorExpand
Mathematics1 begins with the question: how did the serpent of inconsistency enter Frege's paradise? In the section of that chapter called 'How the serpent entered Eden' Dummett says, 'The secondorderExpand
On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze
This paper shows that the more encompassing Δ11-comprehension schema would already be inconsistent, and proves the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. Expand
Twenty-five basic theorems in situation and world theory
  • E. Zalta
  • Philosophy, Computer Science
  • J. Philos. Log.
  • 1993
All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. Expand
The Development of Arithmetic in Frege's Grundgesetze der Arithmetik
Frege's use of the inconsistent Axiom V may invalidate certain of his claims regarding the philosophical significance of his work (viz., the establishment of Logicism), but it should not be allowed to obscure his mathematical accomplishments and his contribution to the authors' understanding of arithmetic. Expand
Frege's philosophy of mathematics
Volume I: Frege's Philosophy in Context Part 1. Frege's Life and Work Part 2. Frege and Other Philosophers Part 3. Frege's Epistemology and Metaphysics Volume II: Frege's Philosophy of Logic Part 4.Expand