Add to ORKGIn reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis (SIA). I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so would involve making sense of mathematical quantities (infinitesimals) whose relationship to zero and to one another is inherently indeterminate
In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s matur...
I compare three sorts of case in which philosophers have argued that we cannot assert the Law of Exc...
ABSTRACT: I offer some brief remarks in reply to comments and criticisms of my earlier work on logic...
The idea that a circle is a regular polygon with infinitely many sides has a long tradition. This i...
The use of conventional logical connectives either in logic, in mathematics, or in both cannot deter...
Kant distinguished between sensible and intellectual representation. The intellect represents mathem...
We prove that many extensions of Intuitionistic Sentential Calculus ISC with new intuitionistic conn...
(Non)denumerability The focus of this article is the rise of modern set theory which, according to...
Newton and Gottfried Leibniz both used infinitesimals—numbers which are nonzero, yet smaller in magn...
Some philosophers have argued that the open-endedness of the set concept has revisionary consequence...
According to semantic antirealism, intuitionistic logic satisfies the requirement that truth should ...
A specification of a mathematical object is impredicative if it essentially involves quantification ...
A number of classical theories are interpreted in analogous theories that are based on intuitionisti...
Let us define the intuitionistic part of a classical theory T as the intuitionistic theory whose pro...
The infinitesimal has played an interesting role in the history of analysis. It was initially used t...
In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s matur...
I compare three sorts of case in which philosophers have argued that we cannot assert the Law of Exc...
ABSTRACT: I offer some brief remarks in reply to comments and criticisms of my earlier work on logic...
The idea that a circle is a regular polygon with infinitely many sides has a long tradition. This i...
The use of conventional logical connectives either in logic, in mathematics, or in both cannot deter...
Kant distinguished between sensible and intellectual representation. The intellect represents mathem...
We prove that many extensions of Intuitionistic Sentential Calculus ISC with new intuitionistic conn...
(Non)denumerability The focus of this article is the rise of modern set theory which, according to...
Newton and Gottfried Leibniz both used infinitesimals—numbers which are nonzero, yet smaller in magn...
Some philosophers have argued that the open-endedness of the set concept has revisionary consequence...
According to semantic antirealism, intuitionistic logic satisfies the requirement that truth should ...
A specification of a mathematical object is impredicative if it essentially involves quantification ...
A number of classical theories are interpreted in analogous theories that are based on intuitionisti...
Let us define the intuitionistic part of a classical theory T as the intuitionistic theory whose pro...
The infinitesimal has played an interesting role in the history of analysis. It was initially used t...
In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s matur...
I compare three sorts of case in which philosophers have argued that we cannot assert the Law of Exc...
ABSTRACT: I offer some brief remarks in reply to comments and criticisms of my earlier work on logic...