On Learned Ignorance

This book [available from that link as a .pdf online for free] is a text by 15th-century German Catholic cardinal & polymath Nicholas of Cusa, although to read it (apart from its obvious grounding in Christian orthodoxy) you could be pardoned for assuming it's a work of ancient Greek philosophy, so inchoate & fundamental does it seem in its scope & gist.

   Whereas other medieval mystical Christian texts concern themselves with the nature & practice of contemplation or the spiritual rigours of a life as a disciple, in this extremely concise & precise work Nicholas presents us with a solid axiomatic procedural argument for the fundamental incomprehensibility of God in his infinitude, yet given the nature of that infinitude he remains knowable, relatable to, enjoyable even, in his personal triune essence. The logic undergirding this position draws on mathematical geometric truth [similarly to Spinoza's method but superior, as it employs geometry as essential fact rather than merely the axiomatic method of logical procedure*], pure as it is, to fabricate images of infinity & possibility, thereby to provide handholds for the imagination in its fruitless attempts to imagine anything more transcendently perfectly plausibly than the Trinity itself in its divine community & personality.

   This is easily the most compelling argument for Christianity that I have ever read - an apologetic for our admittedly weird & paradoxical notions of God in his truest fullest being that proceeds not from eclectic esoterica or theological winds but from extremely basic self-evident truths about consciousness, cognizance, structured thought & imaginings & possibility, walking you straight up to the doors of perception of God then ringing the doorbell & running away, leaving you to stand empty-handed & dry-mouthed to explain yourself to the triune God whose ineffable presence has just been more or less proven yet about whom you realise you can say or know nothing suitable. God is bigger, God is more beautiful, God is far beyond - as much as right here. This text achieves what in my view is one of the most outlandish victories in the history of philosophy, and I am alarmed that old Nick isn't better-known (see - he doesn't even get a single mention in Russell's History); it's also extremely readable, far more so than the majority of philosophy or theology books that pop up on this blog. I would implore anyone to read it & take a serious hammer of intentionality to see whether there are any cracks in the edifice of this text's idea, because I can't discern any.

   I'll leave you with a copy-paste of the book's contents page, as the chapter titles alone give a clear idea of how the argument proceeds:

1. How it is that knowing is not-knowing.

2. Preliminary clarification of what will follow.

3. The precise truth is incomprehensible.

4. The Absolute Maximum (coinciding with the Minimum) is understood incomprehensibly.

5. The Maximum is one.

6. The Maximum is Absolute Necessity.

7. The trine and one Eternity.

8. Eternal generation.

9. The eternal procession of union.

10. An understanding of trinity in oneness transcends all things.

11. Mathematics assists us very greatly in apprehending various divine [truths].

12. The way in which mathematical signs ought to be used in our undertaking.

13. The characteristics of a maximum, infinite line.

14. An infinite line is a triangle.

15. The maximum triangle is a circle and a sphere.

16. In a symbolic way the Maximum is to all things as a maximum line is to [all] lines.

17. Very deep doctrines from the same [symbolism of an infinite line].

18. From the same [symbolism] we are led to an understanding of the participation in being.

19. The likening of an infinite triangle to maximum trinity.

20. Still more regarding the Trinity. There cannot be fourness, [fiveness], etc., in God.

21. The likening of an infinite circle to oneness.

22. How God's foresight unites contradictories.

23. The likening of an infinite sphere to the actual existence of God.

24. The name of God; affirmative theology.

25. The pagans named God in various ways in relation to created things.

26. Negative theology.

Ignorance of the learned type described herein is a powerful humbling tool in the quest to know God; here, with brute-force mathematical logical brushstrokes, Nicholas of Cusa makes it easy - we are able to shake the hand, in a tiny, silent, virtually meaningless yet utterly unignorable manner, of the triune God who defies knowledge.

* An infinite line is an infinite triangle. An infinite triangle is an infinite sphere. An infinite sphere is [though perfectly lacking] God.

Logic

This book by Wilfrid Hodges is an introduction to the field of elementary logic. I bought a copy of this way back in 2012 after my interview at Oxford university, having found out that this was the standard textbook for first year logic in the philosophy strand of PPE that I had applied for - then I didn't get in, so I never got round to reading it.* Until now. Formal logic straddles that bizarre border between philosophical and mathematical kinds of thinking, but despite maths being far from my best subject I found Hodges's distillation of the core principles, methods, and tools at play to be well-paced, accessible, and engaging.

   We start off with the very basics - sentences as expressions of beliefs, how we determine whether one of these is true or not, ambiguities and borderline cases entailed herein, how these simple constituents of thought can be built up into more complex forms, and how one can test these for logical consistency and validity. Moving onto the next level up, we are introduced to logical analysis and its truth-functors, the process of converting sentences into tableaux, and the formal language of propositional calculus. Then we work through designators, identity, relations, and quantifiers, all the while relating all of this back to everything we've learnt so far. The penultimate section puts it all together in predicate logic, before finally ending on a section that considers the problems that logicians are still wrestling with (as despite having been an established field of philosophy/mathematics since at least Aristotle, most of the major advancements have been made only in the last three or four centuries and there are still areas displaying niggling room for improvements to be made) and where these may, or may not logically be able to, go in the future.

   Aside from being an extremely user-friendly introductory text, never assuming you to be familiar with a term or concept or technique not already covered by Hodges himself, this book really cements itself as of academic value by its inclusion in every section of several exercises relating to what you've just read. I tried to do most** of these throughout my reading, and was pleasantly surprised to note that I got on the whole (unsurprisingly with the margins slipping the closer to the end of the book I got) about 60-65% of my answers (all the correct answers are included in a very lengthy appendix) correct - which in university terms is a 2:1 so I'm pretty chuffed about that.

   Formal logic is not a field that being good at means you're going to be right all the time. That's not what logic is or does. Formal logic is a field that being good at does, however, mean that you're going to be secure in the validity and consistency of your own truth claims in the context of their premises as your beliefs. Logic is not an answer - not does it supply these; it is a tool for working out whether any given answer is commensurate with the questions being asked. Halfway through a complex debate it's hardly reasonable to hold up a finger to request a pause in the discourse while you break down every sentence uttered thus far in the established context into a predicate tableaux to make sure that both sides are debating logically. But the more familiar you get with the linguistic and Obvious elements at play in logical analysis the easier it will be for you to spot and avoid invalid or inconsistent sets of claims. Truth is Obvious when it is so, but why then does argumentation exist? Let beliefs be what they subjectively will be, and let logic never supersede itself to determine those but only govern its own realm - that is, of thinking well. And this book will help you get better at that.

* I went on to study philosophy and economics for my undergraduate in Sheffield, then a Masters in politics - so I got to do PPE after all, screw you Oxford... that said, I still wish I'd read this sooner after acquiring this, as it may well have helped me boost my grades anyway.

** Anything that could be answered by pencil scribbling in the margins of the book itself I devoted my full effort to - but a fair few of the exercises demanded a reader to construct truth tables or sentence tableaux or what have you, which are not the kind of things you can fit in the margins of an A5 textbook, and though I did attempt some of these properly, I didn't always have both scrap paper to hand AND the mental wherewithal to bother, so in these cases I simply read the correct answer in the appendix and then re-read the exercise and worked through it in my head until I was confident I understood why the answer was what it was.