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Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician
In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Expand
Introducing Philosophy of Mathematics
Acknowledgements Introduction 1. Infinity 2. Platonism and realism 3. Logicism 4. Structuralism 5. Constructivism 6. A pot-pourri of philosophies of mathematics Conclusion Appendix Notes FurtherExpand
We provide a means to measure distances (and explore connections) between formal theories. Expand
On the epistemological significance of the hungarian project
There are three elements in this paper. One is what we shall call ‘the Hungarian project’. This is the collected work of Andréka, Madarász, Németi, Székely and others. The second is Molinini’sExpand
Boole: From Calculating Numbers to Calculating Thoughts
We are often taught in a first course in the history of logic or in the philosophy of mathematics that Frege singlehandedly invented second-order logic, and that there was no one close to his achievements before him. Expand
Introduction to the Philosophy and Mathematics of Algorithmic Learning Theory
Algorithmic learning theory is a mathematically precise, general framework for studying the existence of computational strategies for converging to the truth in empirical questions. Expand
Embracing the Crisis in the Foundations of Mathematics
The crisis in the foundations of mathematics is a conceptual crisis. I suggest that we embrace the crisis and adopt a pluralist position towards foundations. There are many foundations inExpand
Using a Formal Theory of Logic Metaphorically
I look at three ways in which the pluralist makes use of a formal logical system. Expand
Keeping Globally Inconsistent Scientific Theories Locally Consistent
Most scientific theories are globally inconsistent. Chunk and Permeate is a method of rational reconstruction that can be used to separate, and identify, locally consistent chunks of reasoning orExpand