We describe how to specify object-oriented systems using the bunch notation [5] of predicative programming [6]. We specify class interfaces and definitions, static and dynamic collections of objects, methods, inheritance, and polymorphism, and use the approach in two examples. In the process, we consider limitations with the technique, and contrast it with using the Z style of [4].

The predicative programming design calculus is integrated with an object-oriented method that uses a subset of the Unified Modelling Language. The integration is carried out so as to make the calculus and refinement techniques more applicable to the development of large-scale objectoriented software. The two methods are integrated using a meta-method for formal method integration based on heter...

Frege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected). We also prove the finitistic consistency of the extensio...

In theorizing about perception, philosophers have often multiplied qualities. To perceptible qualities of external objects, like colors and shapes (‘sensible’ qualities), have been added qualities of experiences (‘sensory’ qualities) or of sense-data (‘sensational’ qualities). Start with sensory qualities. The phrase ‘sensory quality’ is not much in use these days, having lost out to ‘phenomena...

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of ref...

This paper will be a short examination of the notions of support verbs (e.g. ‘make’) and predicative nouns (e.g. ‘estimation’ ). A support verb and a predicative noun form a support verb construction (e.g. ‘Peter made an estimation of the damage’). The governing element in a support verb construction is the predicative noun whereas in a phrase like ‘Peter wanted an estimation of the damage’ , t...

The Tychonoff Theorem is discussed with respect to point-free topology, from the point of view of both topos-valid and predicative mathematics. A new proof is given of the infinitary Tychonoff Theorem using predicative, choice-free methods for possibly undecidable index set. It yields a complete description of the finite basic covers of the product.