Spurred by a footnote in Peter Sullivan’s Frege’s Logic, I wanted to find out a bit more about Ernst Schröder. His wikipedia page included a long excerpt from a Putnam paper, exhibiting a very different perspective on the history of logic than the usual. Putnam’s paper was published in Historia Mathematica, then reprinted in Realism With A Human Face, which is available on Gigapedia. Since I’m poorly informed about the Boolean tradition, I’ll just present a selection of quotations in lieu of commentary:

“[

Begriffschrift] is astonishing because it has no predecessors: it appears to have been born from Frege’s brain unfertilized by external influences.” Michael Dummett, Frege: Philosophy of Language.

A partial, and, perhaps, a somewhat dishonorable exception is Schröder. Clearly offended by Frege’s neglect of existing work in logic, not least his own, the general drift of Schröder’s review is that Frege, working in naïve isolation, has achieved no more than to reinvent in cumbrous and eccentric form the Boolean wheel. But Schröder was too good a logician for his irritation to have altogether hidden from him the inadequacy of that verdict…” Sullivan, Frege’s Logic, fn 24.

“I assumed that everyone realized that with the appearance of a complete “algebra of classes” the dam was broken, and (given the mathematical sophistication of the age) the subsequent development was inevitable. It seemed inconceivable to me that anyone could date the continuous effective development of modern mathematical logic from any point other than the appearance of Boole’s two major logical works, the Mathematical Analysis and the Laws of Thought.” Putnam, Peirce the Logician

For what it’s worth (probably not much), I completely agree with Putnam. I don’t know to what extent Dummett’s claim is true. Frege discusses Schroder in the Grundlagen, but had he noticed Schroder before the review of his Begriffschrift? (My memory is hazy here, but the Grundlagen was a few years later, right?)

It’s apparently unknown whether Frege read Boole before writing Begriffschrift, or only after reading Schröder’s review. Schröder’s logical work seems to start being published around 1877, so it’s unlikely Frege would’ve been acquainted with it before BS.

Just to be clear, then, do you think exactly one of the Putnam and Dummett quotations is correct or that both are correct (or neither are)? Given the dates that you note, I would lean toward both being correct.

I doubt that Putnam would dispute the claim that Frege’s work was brilliant. But doing interesting, brilliant, even correct work does not necessarily make one influential. Nor does it make one the beginning of “continuous effective development” of the subject of the work — in this case mathematical logic.

I guess I’m just not sure how you were thinking about the quotations when you wrote them down instead of a commentary.

Well, mostly I think I just don’t know. But my impression is that they’re both correct, or could both be correct. It does seem like Frege worked in relative isolation from previous authors’ work. As I said, I’m not familiar enough to say whether Putnam’s evaluation of the Boolean program is accurate. But it certainly seems plausible, since an author in the Boolean tradition apparently independently introduced the essentials of quantification theory a few years after Frege (and in ignorance of Frege’s work).

I was just thinking of the quotations as establishing an interesting divergence in perspective. The only story I was previously familiar with had Frege at its center.