Results 51 to 60 of about 5,644 (162)

To infinity and beyond: A general framework for scaling economic theories

Theoretical Economics, Volume 20, Issue 2, Page 511-542, May 2025.
Many economic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness assumptions. Our sufficient conditions are on the theorem statement only, and not on its proof. This results in short proofs,
Yannai A. Gonczarowski, Scott Duke Kominers, Ran I. Shorrer   +2 more
wiley   +1 more source

Stationary sets and infinitary logic [PDF]

Journal of Symbolic Logic, 2000
AbstractLet be the class of structures 〈λ, <, A〉, where A ⊆ λ is disjoint from a club, and let be the class of structures 〈λ, <, A), where A ⊆ λ contains a club. We prove that if λ = λ<κ is regular, then no sentence of Lλ + κ separates and On the other hand, we prove that if λ = μ+ , μ = μ<μ, and a forcing axiom holds (and if μ = ℵ0 ...
Shelah, Saharon, Väänänen, Jouko
openaire   +2 more sources

Infinite inference and mathematical conventionalism

Philosophy and Phenomenological Research, Volume 109, Issue 3, Page 897-912, November 2024.
Abstract We argue that (1) a purported example of an infinite inference we humans can actually perform admits a faithful, finitary description, and (2) infinite inference contravenes any view which does not grant our minds uncomputable powers. These arguments block the strategy, dating back to Carnap's Logical Syntax of Language, of using infinitary ...
Douglas Blue
wiley   +1 more source

Intuitionistic fixed point theories over Heyting arithmetic [PDF]

, 2010
In this paper we show that an intuitionistic theory for fixed points is conservative over the Heyting arithmetic with respect to a certain class of formulas. This extends partly the result of mine.
Arai, Toshiyasu
core  

Wittgenstein on mathematics

Philosophical Investigations, Volume 47, Issue 4, Page 461-483, October 2024.
Abstract The mature Wittgenstein's groundbreaking analyses of sense and the logical must—and the powerful new method that made them possible—were the result of a multi‐year process of writing, re‐arranging, re‐writing and one large‐scale revision that eventually produced the Philosophical Investigations and RFM I.
Penelope Maddy
wiley   +1 more source

Carnap and the a priori

European Journal of Philosophy, Volume 32, Issue 3, Page 801-819, September 2024.
Abstract What are Carnap's views on the epistemology of mathematics? Did he believe in a priori justification, and if so, what is his account of it? One might think that such questions are misguided, since in the 1930s Carnap came to reject traditional epistemology as a confused mixture of logic and psychology. But things are not that simple.
Benjamin Marschall
wiley   +1 more source

On two arguments for fanaticism

Noûs, Volume 58, Issue 3, Page 565-595, September 2024.
Abstract Should we make significant sacrifices to ever‐so‐slightly lower the chance of extremely bad outcomes, or to ever‐so‐slightly raise the chance of extremely good outcomes? Fanaticism says yes: for every bad outcome, there is a tiny chance of extreme disaster that is even worse, and for every good outcome, there is a tiny chance of an enormous ...
Jeffrey Sanford Russell
wiley   +1 more source

Research on a General State Formalization Method from the Perspective of Logic

Mathematics
As information plays an ever more central role across disciplines, the lack of a precise and reusable definition of state impedes comparison, measurement, and verification. Building on Objective Information Theory (OIT), this paper proposes a logic-based
Siyuan Qiu, Jianfeng Xu
doaj   +1 more source

Center indifference and skepticism

Noûs, Volume 58, Issue 3, Page 778-798, September 2024.
Abstract Many philosophers have been attracted to a restricted version of the principle of indifference in the case of self‐locating belief. Roughly speaking, this principle states that, within any given possible world, one should be indifferent between different hypotheses concerning who one is within that possible world, so long as those hypotheses ...
David Builes
wiley   +1 more source

Towards a Church-Turing-Thesis for Infinitary Computations [PDF]

, 2013
We consider the question whether there is an infinitary analogue of the Church-Turing-thesis. To this end, we argue that there is an intuitive notion of transfinite computability and build a canonical model, called Idealized Agent Machines ($IAM$s) of ...
Carl, Merlin
core