Arithmetic is Determinate

Classical arithmetic is part of intuitionistic arithmetic

One of Michael Dummett’s most striking contributions to the philosophy of mathematics is an argument to show that the correct logic to apply in mathematical reasoning is not classical but intuitionistic. In this article I wish to cast doubt on Dummett’s conclusion by outlining an alternative, motivated by consideration of a well-known result of Kurt Gödel, to the standard view of the relationsh...

To Determinate Moment Problems

It has been proved that algebraic polynomials P are dense in the space Lp(R, dμ), p∈ (0,∞), iff the measure μ is representable as dμ = wp dν with a finite non-negative Borel measure ν and an upper semi-continuous function w : R → R+ : = [0,∞) such that P is a dense subset of the space C0 w : = {f ∈ C(R) : w(x)f(x) → 0 as |x| → ∞} equipped with the seminorm ‖f‖w := supx∈R w(x)|f(x)|. The similar...

Arithmetic Is Easy

Towards Determinate Exploratory Factor Analysis

It is well-known that the classic exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy pr...

Arithmetic Memory Is Modality Specific.

In regards to numerical cognition and working memory, it is an open question as to whether numbers are stored into and retrieved from a central abstract representation or from separate notation-specific representations. This study seeks to help answer this by utilizing the numeral modality effect (NME) in three experiments to explore how numbers are processed by the human brain. The participant...