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- "The Blind Spot: Lectures on Logic" by Jean-Yves Girard
- Jean-Yves Girard's The Blind Spot (2011) may be a better read for those who find this review a bit woo.
- The Blind Spot: Lectures On Logic by Jean Yves-Girard
For context, Girard is a mathematical logician, philosopher, and co-discoverer of the type system System F (Haskell, ML, etc.). The book is a monograph on proof theory, and I was interested in learning more about affine and linear logic to deepen my understanding of Rust and other language ecosystems focused around the ability to explicitly model resources. However, along the way, I learned some other great things: (1) continental philosophy is deep and cool; (2) mathematical writing can be simultaneously rigorous, clear, and hilarious; and it reinforced (alongside Alain Connes's Noncommutative Geometry, and various French philosophers) (3) French academic writing is both frustratingly and delightfully idiosyncratic. Girard writes polemically about other aspects of knowledge, mathematics, etc., and there's heaps of dry humor and anecdotes throughout the book. It's a hard book to read even by pure mathematics standards--a topic not exactly known for being a brisk read--but it was worth it just for the side discoveries alone.
- Jean-Yves Girard, a great logician, also has a lot of quarrels to pick with analytic philosophy. His prose is idiosyncratic, lyrical and definitely at odds with the dryness of "logic of the 20th century". If you like the idea of an energetic approach to reconceptualize philosophy, in particular the philosophy of logic, I recommend reading Girard's work. The Blind Spot: Lectures on Logic is an organized survey of logic starting with Hilbert's formalism and ending up in the operator algebras of Geometry of Interaction. Along the way, Girard's combative, highly opinionated and witty commentary ceaselessly entertains and engages.
Perhaps what is most striking about Girard in contrast to Nozick is how he manages to be very rigorous and artful simultaneously. Something as abstract of logic becomes a living creature when Girard talks about it. To see logic this way is to expect it to flourish in subordination to the rest of human experience, not languish in its own obscure enclave, ceaselessly chasing its own tail, reducing the alluring to the banal.
- See Girard, The Blind Spot: Lectures on Logic (2011) for some attempts at tackling this question. (in particular, his "proof nets" attempt to have a canonical form, such that we can identify differently drawn concrete proof nets as representing the same abstract proof)
- "Once in a while, I like to indulge in an informative anecdote concerning the genesis of the proof. The criterion was found by the end of 1985; then I remained more than six months making circles around the « splitting tensor ». One nice day of August 1986, I woke up in a camp in Siena and I had got the proof: I therefore sat down and wrote a manuscript of 10 pages. One month later, while recopying this with my typewriter, I discovered that one of my lemmas about imperialism was wrong: no importance, I made another one! This illustrates the fact, neglected by the formalist ideology, that a proof is not the mere putting side by side of logical rules, it is a global perception: since I had found the concept of empire, I had my theorem and the faulty lemma was hardly more than a misprint."
- Jean-Yves Girard, The Blind Spot
