Logical Constants and Arithmetical Forms

On the Normality of Arithmetical Constants

Bailey and Crandall [4] recently formulated “Hypothesis A”, a general principle to explain the (conjectured) normality of the binary expansion of constants like π and other related numbers, or more generally the base b expansion of such constants for an integer b ≥ 2. This paper shows that a basic mechanism underlying their principle, which is a relation between single orbits of two discrete dy...

Logical Constants Across Varying Types

We investigate the notion of "logicality" for arbitrary categories of linguistic expression, viewed as a phenomenon which they can all possess to a greater or lesser degree. Various semantic aspects of logicality are analyzed in technical detail: in particular, invariance for permutations of individual objects, and respect for Boolean structure. Moreover, we show how such properties are systema...

Logical Constants as Punctuation Marks

This paper presents a proof-theoretical approach to the question "What is a logical constant?" This approach starts with the assumption that logic is the science of formal deductions, and that basic formal deductions are structural deductions, i.e. deductions independent of any constant of the language to which the premises and conclusions belong. Logical constants, on which the remaining forma...

The Arithmetical Invariants of Quadratic Forms

Logic , Reasoning and the Logical Constants