[FOM] First- Vs Second-Order Logic: Origins of the Distinction?

WILLIAM TAIT williamtait at mac.com
Fri May 20 20:38:22 EDT 2016

I would think that Hilbert's 1917-8 lectures (in the Ewald/ Sieg edition of his lectures on logic and foundations) is the first place in which our distinction between first and higher order logic is made. As opposed to Frege, Richard, Hilbert had the clear model-theoretic conception of logic.

Best, Bill

Sent from my iPad

> On May 19, 2016, at 9:59 PM, Alasdair Urquhart <urquhart at cs.toronto.edu> wrote:
> Greg Moore's article "The Emergence of First-Order Logic" is a good place to start.  It's in "History and Philosophy of Modern Mathematics" edited
> by Aspray and Kitcher.
> Moore emphasizes (and I agree with him) that the appearance of Gödel's incompleteness theorem was a key event in separating first- and second-order logic.
>> On Thu, 19 May 2016, Richard Heck wrote:
>> Does anyone have a good reference for historical work on the emergence of the distiction between first- and second-order logic? I'm
>> particularly interested in how first-order logic came to be seen as "really logic". Quine was of course famously hostile to
>> second-order 'logic', but I am guessing that there were earlier antecedents, probably emerging from work in mathematical logic
>> itself.
>> If anyone is able to sketch that story, I'd love to hear it.
>> Thanks,
>> Richard Heck
>> PS What I myself know about this concerns only the emergence of Frege's awareness of the distinction. That part of the story gets
>> told in my paper "Formal Arithmetic Before Grundgesetze", section 3, which can be found on my website.
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