Meaning: The quote you provided is from Alonzo Church, a renowned mathematician and logician. In this quote, Church reflects on the nature of his work, suggesting that it was not a formal dissertation in logic, at least not in the manner of Whitehead and Russell's "Principia Mathematica." Instead, he implies that his work resembled mathematics and did not utilize a formalized language.

Alonzo Church is best known for his influential work in the field of mathematical logic, particularly for his development of the lambda calculus and the concept of computability. His work laid the foundation for the theoretical understanding of computation and is highly significant in the history of computer science. Church's contributions have had a lasting impact on various areas of mathematics, logic, and theoretical computer science.

When Church refers to his work not being a dissertation in logic "in the kind of logic you would find in Whitehead and Russell's Principia Mathematica," he is likely alluding to the rigorous, formalized approach to logic and mathematics that was characteristic of the Principia Mathematica. Written by Alfred North Whitehead and Bertrand Russell, this monumental work aimed to establish a foundation for mathematics based on logical principles. It is known for its complex formal system and detailed symbolic notation, as well as its ambitious goal of deriving all mathematical truths from a small set of logical axioms.

Church's remark about his work resembling mathematics and not using a formalized language can be interpreted in the context of his development of the lambda calculus. The lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application. It provides a framework for representing and manipulating functions, and it has been instrumental in the study of computability and the foundations of programming languages.

In essence, Church's comment suggests that his work may have differed in approach and style from the formal, axiomatic method employed in Principia Mathematica. Instead, his work may have been more akin to mathematics, possibly involving the exploration of mathematical structures and concepts through a different mode of reasoning and expression.

Church's perspective on the nature of his work offers insight into the diversity of approaches within the field of mathematical logic. While some scholars may have pursued formalized, axiomatic systems akin to Principia Mathematica, others, like Church, may have embraced alternative methods and modes of expression to investigate fundamental questions in logic and computation.

Overall, Alonzo Church's quote illuminates his unique perspective on the nature of his work in mathematical logic and hints at the rich diversity of approaches within this field. His contributions continue to inspire and influence research in mathematics, logic, and computer science, leaving a profound legacy in the development of foundational concepts and methods in these disciplines.