This post lists the titles of and links to the posts I publish in the series, the “After Aristotle Introduction to Philosophy Initiative,” devoted to Thomas Nagel’s What Does It All Mean? A Very Short Introduction to Philosophy (New York and Oxford: Oxford University Press, 1987).
The list is in the posts’ order of appearance and will be updated with every subsequent post.
I will include a link to this “table of contents” in each post.
0. Announcing the After Aristotle Introduction to Philosophy Initiative. Posted on April 10, 2016
1. Nagel’s Comparison and Contrasting of Philosophy and Science. April 12, 2016
2. Nagel’s Comparison and Contrasting of Philosophy and Mathematics. Posted on April 19, 2016
3. Nagel’s Omission of Theology as a Mode of Theoretical Knowledge, Posted on May 5, 2016.
After Aristotle 
Dear Richard,
Let me commend you once again for your weighty website.
I’m posting a reply, hoping you will give us your opinion on Jacques Lacan’s efforts to undercut Aristotle’s square of opposition from within. Here’s a synopsis I found recently:
http://www.swingtradesystems.com/lacan/lacan-and-aristotle.html
If Lacan does manage to undermine the universals of both qualities by the ‘existence without essence’ of his own reworked particular negative proposition as he claims, the psychoanalyst’s logic is no longer in anyway Aristotelian.
What do you think?
BC, Umass
Thank you for your comment and for the link to the synopsis on the, well, intriguing website.
Let me begin my reply by confessing that I know next to nothing about Lacan. So, I’ll confine what I have to say to that which bears on the traditional square of opposition, and more specifically to the statement appearing on the website you directed me to, that:
The site is quite correct in its recognition that there is an ambiguity in the typical statement of a particular affirmative proposition, e.g.:
That is, taken in one way, and given a more explicit formulation than is often done, the statement as Aristotle and the “classical tradition” would have, or should have, understood it asserts:
So formulated, this proposition neither implies nor contradicts the corresponding universal affirmative proposition:
Lacan, on the other hand, is quite right in holding that a particular affirmative proposition can, however, be taken in another way, as, keeping with my example, asserting:
And this is where the website misconstrues the logical situation, when it tells us:
For this in no way “undermines the logical relations of the classical logical square.” That is, the statement, as understood to have resolved the ambiguity of “some” by reading it as “some, not all,” simply expresses a compound proposition, a conjunction, which classical logic would or should express as:
Because, then, the second of the two conjuncts, contradicting the universal affirmative proposition that:
is equivalent to:
that conjunction and the Lacan formulation are equivalent to the conjunction:
There is, then, with respect to the specific point here explored, nothing that undermines the traditional square of opposition of classical logic. Otherwise put, “Jacques Lacan’s efforts to undercut Aristotle’s square of opposition from within,” at least, again, with respect to the specific point here explored, do not succeed.
I can’t comment on the specific logical propositions you are using because I am just not there yet. But from what I am reading, ‘Lacan’s efforts to undercut Aristotle’s square of opposition from within’ seem to be linked to his particular negative proposition. That is, his impenetrable ‘Not-all X’ statement.
I found the ‘continuation’ of the page you are referencing on that same site:
http://www.swingtradesystems.com/lacan/lacanian-textual-analysis-20.html
It goes on and on and like I said, I can’t follow it at the logical level just yet. But it’s clear to me that the Not-all X is key for Lacan. So if he did manage to ‘undercut Aristotle,’ it was with his Not-all X.
This is a great site, Professor Hennessey. It is giving me a great grounding in logic. Better than my own professors at my college! By the way, I’ve heard that Ayn Rand’s books have been selling like hotcakes since November 8. But are those reading her Trump supporters or never Trumpers? I suspect it is the latter. That was a good post, too. Please keep this site going. There is so much irrationality on campuses today, that we need a strong dose of clear thinking!
Amir