Right - in Gödel’s mind, he was trying to model how mathematics works - the same applies to the problem Hilbert and co were framing in the Entscheidungsproblem. They were wrestling with the foundational philosophy of how powerful mathematics could ever claim to be.
Turing I think resonates as a computer scientist more than a mathematician for the same reason that Ada Lovelace does: both of them shared, and made explicit in how they approached problems, the insight of the generalizability of computability beyond mathematics. Where Babbage saw a calculating machine spitting out numerical tables, Lovelace saw music and pictures. And not in the implicit reductive way most mathematicians assume that anything important can be modeled as mathematics: because if it can’t be modeled mathematically, it can’t be important. Turing and Lovelace both seemed to get that this is a mathematics that can act on anything, and that that’s what makes the mathematics interesting.
The extension beyond ‘and this lets you derive any provable true statement within a formal system in finite time’ to ‘and this lets you carry out any deterministic transformation on an arbitrary piece of text’ to something like ‘if machine translation is possible this machine can do it’ or ‘a sufficiently sophisticated machine like this could hold a convincingly human conversation’ is a through-line you can only make with Turing’s insights, not just Church or Gödel’s.
And sure, you need Shannon to give you a framework for information representation that extends it to any form of data and dozens of other contributions of course, and without the mathematical foundations of Church and Gödel et al there’s no foundation to build it on at all. But Turing’s bridge out of the mathematical philosophy world into the realm of stuff engineers like Zuse were building seems like as good a moment as any to draw a line and say ‘this is computer science’.
Encoding logical statement into numbers is foundational, but I do see your point. I don't know of any evidence that says that Gödel was interested in automating computation through his encoding.
That being said, I view Gödel's addition to be so mind-blowing that I can't help but privately think of him as the founder.
I makes sense to me. The "computer science" to "practical computer work" relationship has about the same distance as fundamental physics has to industrial chemistry.
yeah, but what he was doing was much more in the realm of logic and set theory, which is to say mathematics, not concerned with anything to do with computation.
Turing I think resonates as a computer scientist more than a mathematician for the same reason that Ada Lovelace does: both of them shared, and made explicit in how they approached problems, the insight of the generalizability of computability beyond mathematics. Where Babbage saw a calculating machine spitting out numerical tables, Lovelace saw music and pictures. And not in the implicit reductive way most mathematicians assume that anything important can be modeled as mathematics: because if it can’t be modeled mathematically, it can’t be important. Turing and Lovelace both seemed to get that this is a mathematics that can act on anything, and that that’s what makes the mathematics interesting.
The extension beyond ‘and this lets you derive any provable true statement within a formal system in finite time’ to ‘and this lets you carry out any deterministic transformation on an arbitrary piece of text’ to something like ‘if machine translation is possible this machine can do it’ or ‘a sufficiently sophisticated machine like this could hold a convincingly human conversation’ is a through-line you can only make with Turing’s insights, not just Church or Gödel’s.
And sure, you need Shannon to give you a framework for information representation that extends it to any form of data and dozens of other contributions of course, and without the mathematical foundations of Church and Gödel et al there’s no foundation to build it on at all. But Turing’s bridge out of the mathematical philosophy world into the realm of stuff engineers like Zuse were building seems like as good a moment as any to draw a line and say ‘this is computer science’.