Search results for "Foundations of mathematics"

What is Mathematics: Gödel's Theorem and Around (Edition 2013)

2013

Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2013. ATTENTION! New Edition 2015 available at https://dspace.lu.lv/dspace/handle/7/5306.

Some basic theorems on the foundations of mathematics and their philosophical implications

1995

Research in the foundations of mathematics during the past few decades has produced some results, which seem to me of interest, not only in themselves, but also with regard to their implications for the traditional philosophical problems about the nature of mathematics. The results themselves, I believe, are fairly widely known, but nevertheless, I think, it will be useful to present them in outline once again, especially in view of the fact that, due to the work of various mathematicians, they have taken on a much more satisfactory form, than they had had originally. The greatest improvement was made possible through the precise definition of the concept of finite procedure, which plays a …

Formālisms kā reālās matemātikas filozofija: 14 argumenti

2015

Referāts Latvijas Universitātes 73.zinātniskajā konferencē 2015.gada 13.februārī.

What is Mathematics: Gödel's Theorem and Around (Edition 2015)

2015

Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2015.

STEFANO DONATI. I Fondamenti della Matematica nel Logicismo di Bertrand Russell [The Foundations of Mathematics in the Logicism of Bertrand Russell]

2008

True V or not True V, That is the Question

2016

In this paper we intend to argue that: (1) the question `True V or not True V' is central to both the philosophical and mathematical investigations of the foundations of mathematics; (2) when posed within a framework in which set theory is seen as a science of objects, the question `True V or not True V' generates a dilemma each horn of which turns out to be unacceptable; (3) a plausible way out of the dilemma mentioned at (2) is provided by an approach to set theory according to which this is considered to be a science of structures.

Leon Henkin the Reviewer

2014

In this chapter, we intend to look at Henkin’s reviews, a total of forty-six. The books and papers reviewed deal with a large variety of subjects that range from the algebraic treatment of logical systems to issues concerning the philosophy of mathematics and, not surprisingly—given his active work in mathematical education—one on the teaching of this subject. Most of them were published in The Journal of Symbolic Logic and only one in the Bulletin of the American Mathematical Society. We will start by sorting these works into subjects and continue by providing a brief summary of each of them in order to point out those aspects that are originally from Henkin, and what we take to be mistake…