Distinguished Professor
Brooklyn College and CUNY Graduate Center, NY, USA

1. Why were you initially drawn to formal methods?

When a graduate student at Harvard, I took a logic course with Quine. I was not turned on by that course, although I foundQuine quite helpful in personal interactions. I then took a second course with Burton Dreben. Dreben was quite disorganized, and the course was rather chaotic, but Dreben brought to the course the enthusiasm of a young man, and that caught. Indeed, Dreben remained a ‘young man’ until his death in 1999 at the age of 71. Moreover, after an unsuccessful attempt to introduce us to Herbrand’s thesis (it was discovered later than there were mistakes in that thesis) Dreben abruptly switched to Martin Davis’s book Computability and Unsolvability (McGraw Hill, 1958). I had spent the previous summer as a programmer for Minneapolis Honeywell, and Davis’ Turing machine based treatment went down as easy as pie. I decided to do my dissertation in Logic.

But Dreben suddenly took a leave of absence, and many of the
students at Harvard decided to study with Hartley Rogers at MIT. Rogers was an absolutely first class teacher in Recursion theory, and after studying with him, problems in that area started to seem quite easy. I did my dissertation in transfinite progressions, influenced by and extending some work of Kreisel.

A different acquaintance with formal methods came about as a
result of my work with Noam Chomsky as a research assistant. I introduced the notion of semi-linearity for studying context free
languages, and proved that inherently ambiguous context free languages existed (this last result has been attributed by Hopcroft and Ullman — Introduction to Autmata Theory, Languages, and Computation, to Gross, but since Gross himself attributes the result to me, Hopcroft and Ullman must be mistaken!). This work became much better known than my dissertation but had little influence in the purely logical work which was my main concern.

But there had also been an earlier ‘logical’ influence on me. As
a first year graduate student I had come across a copy of Wittgenstein’s Remarks on the Foundations of Mathematics. I did not really follow what he was saying, but I realized that he was a genius and that some day I must understand him. This event happened only many years later, with the help of my then colleague, Arthur Collins, and Mr. Saul Kripkenstein. Kripke did not correctly represent Wittgenstein, in my view, but he was extremely clear, and after reading Kripke on Wittgenstein, it became much easier to understand the master himself. Wittgenstein’s treatment has always remained with me and kept me away from falling into a groove which, while well traveled, is an impediment to understanding.

Read the remaining part of Rohit Parikh's interview in the book Formal Philosophy

ISBN-10    87-991013-1-9    hardcopy
ISBN-10    87-991013-0-0    paperback
Published by Automatic Press ● VIP, 2005

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