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  1. Frege, Hankel, and Formalism in the Foundations.Richard Lawrence - 2021 - Journal for the History of Analytical Philosophy 9 (11).
    Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim that (...)
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  2. Nominalization, Specification, and Investigation.Richard Lawrence - 2017 - Dissertation, University of California, Berkeley
    Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...)
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  3. Frege, Thomae, and Formalism: Shifting Perspectives.Richard Lawrence - 2023 - Journal for the History of Analytical Philosophy 11 (2):1-23.
    Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...)
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  4. Giving the Value of a Variable.Richard Lawrence - 2021 - Kriterion - Journal of Philosophy 35 (2):135-150.
    What does it mean to ‘give’ the value of a variable in an algebraic context, and how does giving the value of a variable differ from merely describing it? I argue that to answer this question, we need to examine the role that giving the value of a variable plays in problem-solving practice. I argue that four different features are required for a statement to count as giving the value of a variable in the context of solving an elementary algebra (...)
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  5.  28
    Lectures on Complex Numbers and their Functions, Part I: Theory of Complex Number Systems.Hermann Hankel & Richard Lawrence - manuscript - Translated by Richard Lawrence.
    A transcription and translation of Hermann Hankel's 1867 Vorlesungen über die complexen Zahlen und ihre Functionen, I. Theil: Theorie der Complexen Zahlensysteme, a textbook on complex analysis that played an important role in the transition to modern mathematics in nineteenth century Germany.
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  6.  26
    Vorlesungen über die complexen Zahlen und ihre Functionen / Lectures on Complex Numbers and their Functions.Hermann Hankel & Richard Lawrence - unknown
    This is a bugfix release to correct some errors in.zenodo.json which prevented archiving of 1.0. -/- Version 1.0: This first release of the translation contains: -/- * a full transcription of the Preface and Chapter 1 * translations of select passages in these sections * a full transcription and translation of the title pages and the table of contents through chapter 3 -/- This release was focused on working out (most of) the issues with the markup of a parallel translation (...)
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  7. Knowledge and the Philosophy of Number. [REVIEW]Richard Lawrence - 2022 - History and Philosophy of Logic 43 (4):404-406.
    Hossack’s project in this book is to provide a new foundation for the philosophy of number inspired by the traditional idea that numbers are magnitudes.
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  8. Talking about Numbers: Easy Arguments for Mathematical Realism. [REVIEW]Richard Lawrence - 2017 - History and Philosophy of Logic 38 (4):390-394.
    In §57 of the Foundations of Arithmetic, Frege famously turns to natural language to support his claim that numbers are ‘self-subsistent objects’:I have already drawn attention above to the fact th...
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