Where do the topics covered in Lewis Carroll's 1896 book "Symbolic logic" fit in the modern mathematical curriculum? Where do the topics covered in Lewis Carroll's 1896 book "Symbolic logic" fit in the modern mathematical curriculum? And what is the modern substitute or notation?
It appears to me that all it covers is set logic, syllogisms, & fallacies(invalid syllogisms), I didn't read the whole thing; Does anyone else, remember it covering anything else? "No, it didn't cover anything else" is a legitimate answer here.
In case there is any discrepancy over what I am talking about; Here is the easy to read html version from project Gutenberg. And Here is the original text version from Google Books.
 A: Here's an Aristotelean syllogism in modern mathematics:

Major premise: All recursively enumerable sets are Diophantine. This is called Matiyasevich's theorem.  It was proved in 1970 by Yuri Matiyasevich, building on work done over several decades by Julia Robinson, Martin Davis, and Hilary Putnam.  The converse is trivial.
Minor premise: Some recursively enumerable sets are non-recursive. This was an important discovery made in the 1930s.  I think Alan Turing, Stephen Kleene, and others may have done it indepedently.  I am unsure of the details.
Conclusion: Some Diophantine sets are non-recursive. This laid Hilbert's tenth problem to rest.

A: In the Aristotelian syllogism, one premiss involves terms $x$ and $m$, the other premiss involves $y$ and $m$, and the conclusion involves $x$ and $y$. Each premiss, and also the conclusion, must have one of these four forms:


*

*A: All $S$ is $P$

*E: No $S$ is $P$

*I: Some $S$ is $P$

*O: Some $S$ is not $P$


where each of $S$ (the subject) and $P$ (the predicate) must be one of $x$, $y$ and $m$.
In the Appendix, $\S 2$, p.165, Carroll addresses the issue of the "existential import" of propositions, i.e.  which of the above four types "assert" (i.e. assert the existence of their subject), that is, from which of them may it be inferred that "Some $S$ exists".
In Aristotle's model, A does not assert, i.e. "All $S$ is $P$" is interpreted as "No $S$ is not $P$". Thus the four forms of statement boil down to E and I where $P$ may be either a term or its negation.
Carroll does not make that identification, and treats A and E as distinct forms. However, he treats I and O as the same form. He concludes (p.171) that there are two models "that can logically be held", and he picks the model where A (pace Aristotle) and I assert, and E does not.
Carroll extends Aristotle's model by allowing either $S$ or $P$ to be either a term or its negation. Thus the two occurrences of $m$ may have opposite signs: $m$ and $m'$ in Carroll's notation. This allows some sorts of syllogism that are not among Aristotle's forms. For example (Appendix, $\S$ 4, p.173)


*

*None of my boys are clever;

*None but a clever boy could solve this problem.

*[Therefore: None of my boys could solve this problem.]


With $x=$ my boys, $y=$ could solve this problem, $m=$ clever, this becomes


*

*No $x$ is $m$

*No $m'$ is $y$

*Therefore: No $x$ is $y$.


Carroll planned more than got published in Symbolic Logic. What got published is only Part I of a projected three parts. In this Appendix, $\S 10$, p.185, he gives "Some account of Parts II, III" with eight problems (though not their solutions or conclusions). One of them is in three-valued logic. The other seven are in Boolean logic, but with premisses of 3 (and sometimes 4) terms, so solving them is akin to extracting a suitable conclusion from the premisses of a 3-SAT problem.
Part I was published in 1896. When Carroll died in January 1898, his work on Part II was incomplete, but much of his MS survives (and some was even set in galley proofs). An account of what is extant is published in Bartley, William Warren, Lewis Carroll's Symbolic Logic, pub. Harvester Press, 1977, ISBN 0-85527-974-5.
