Having recently re-read the Tractatus Logico-Philosophicus, I found that I understood it. My current direction is into Mathematics – specifically; Mathematical Logic – and have only just re-read the Tractatus with the comparatively new knowledge of logic imbued in me.
This book was written in 1918, and first translated into English in 1922 (in part by the late F. P. Ramsey, a mathematician who died tragically young – someone who learnt German in a week by sitting down with Nietzche and a dictionary for a week, so the story goes). This puts the work far in advance of the Great Discovery in Logic of the 20th century – Incompleteness.
This work was first put down as a polemic against Russell and Frege’s view of the Platonic nature of the foundations of mathematics and of the world. His irreducible part of ‘the Object’ – a figure of great intrigue and mystery in the work, as it is little defined, and its nature is allowed to approach the mystical – is still studied today.
However, when you read the Tractatus knowing about ‘Unprovability’, we can read a new direction for the work – one that essentially ends with the work being superseded by greater and more ‘actual’ results – that is, results on mathematics that lie withing mathematics – and the work requiring to be updated. This has not happened, and it is still lauded, studied. The Blurb on the back of the copy I read said it was a ‘cryptic’ work – yet it made perfect sense to a logician, as a historical text in the discussion of just what *is* the logical nature of the universe.
But what is the fascination in Philosophy with the old? So much of philosophy seems to rely on a legacy that involves old books. This is fine when you are studying Plato, and the Hellenistics. Then, right through to Decartes, Voltaire, Kant, and beyond Rousseau into Nietzsche, Kierkegaard and finally into Satre, maybe Foucault, and ‘Modern’ Philosophy. But when you have a ‘Philosophy of…’ subject, like the Philosophy of Mathematics in this case, why do philosophers dwell on texts that rely on objects that have long been abandoned by the subject they are thinking on?
Now, the Tractatus is not purely a work on the PoM. This is apparent from parts 6 & 7. It is a brilliant working of Ontology that shows how a ‘completeness’ (in the literal, not mathematical, sense) is required in any outlay of ontology, and finally resulting in how Language is deficient for talking *about* things, as opposed to just *expressing* them; amongst a myriad of other interesting results.
But considering the Philosophy of Mathematics – why are so few Philosophers in this field non-technically trained nor even interested? So much would be cleared up if Philosophers of Mathematics *truly* understood the objects upon which they were musing. It would be as considering a statue of Plato as representative of Plato’s thoughts. The true meaning of the mathematics lies beyond the simulacra of how it is written down.