Abstract
19 September 2012
I’m looking to turn my thesis from last semester into a publishable article. Here’s an abstract I’ve knocked together. Comments encouraged.
Nietzsche, in Beyond Good and Evil, exhorts us to recognise humanity’s place within nature and to stand “deaf to the siren songs of old metaphysical bird catchers,” (BGE 230) who have sought to separate the two. The foulest of such temptations, according to Nietzsche, are traditional notions of freedom which serve to underpin moral responsibility. In this paper I argue that Nietzsche’s engagement with freedom goes beyond the dismissal of these traditional notions and that, on the contrary, freedom remains a central concern of his ethical program. To this end, I explicate Nietzsche’s conception of freedom through two contemporary accounts, representative of two distinct traditions in the interpretation of Nietzsche: Rutherford’s (2011) Freedom as a philosophical ideal: Nietzsche and his antecedents and Pippin’s (2010) How to overcome oneself: Nietzsche on freedom. Rutherford places Nietzsche within a neglected philosophical tradition which finds freedom in the creation of, and commitment to, self-given laws. In contrast, Pippin engages Nietzsche’s notion of self-overcoming, whereby to achieve freedom is to overcome not just the impositions of the external world, but those parts of ourselves, including past commitments, which prevent us from developing and exercising the full extent of our capacities. These two readings diverge in the attitude they advocate towards one’s past self and commitments. I argue that Pippin’s account, in highlighting the tension Nietzsche diagnoses within a free spirit, more faithfully represents Nietzsche’s views on freedom and thus informs how we come to grips with Nietzsche’s ethical program.
Foundations
20 June 2011
Russell and Whitehead, famously, tried to secure a foundation in logic for formal mathematics. The common1 view is that they failed for reasons expounded by Gödel (his incompleteness theorems). Not all mathematical truths can be captured as theorems of a formal system (like that in Principia Mathematica. This is incompleteness), because if they were an inconsistent pair of statements could be constructed (this is the hard part). Since classical logic is explosive, we resort to incompleteness to avoid triviality.
In my reading for a piece on Russell’s theory of descriptions, however, I came across a much simpler and quite disarming problem with the Fregean project which Russell and Whitehead were furthering. In short, the argument goes like this. Complex numbers are essential parts of mathematics, not just in explicitly “complex” theorems, but in real analysis and probably every subfield of maths2. The basis of complex numbers, the imaginary unit, is defined as the square root of negative one. But this is a definite description which, according to Russell, should denote uniquely. But it doesn’t, and the indistinguishability of the two roots of x2 + 1 sinks the theory. The paper, was targeted at Frege, and maybe I am mistaken for considering it an objection to Russell and Whitehead, but the idea seems valid.
Of course, as soon as I open up Complex Variables and Applications to check on the arguments validity against modern complex analysis, I find it has problems. Primarily because the imaginary unit is not defined by a definite description. Instead, statement 1.1.1 on page one describes a complex number as an ordered pair of real numbers. While solving x2 + 1 = 0 is a property of (0,1), it’s not its defining characteristic. (0,1) and (0,-1) are unambiguously different (complex) numbers. While Brandom’s paper causes problems for our pre-theoretical ideas of what i and -i are, that’s not a particularly strong case to make against modern mathematics as it is practiced.
1 I am always as nervous when claiming that a view is common as I am skeptical when reading. If you disagree, entertain the proposition for a moment and/or tell me why I’m mistaken.
2 For example the distribution of the primes depends on the Riemann hypothesis. Who knew that maths was a tangle? Everyone.
Public Space
24 April 2011
I spent my morning today at the cultural centre, first at the State Library and then at GoMA. Someone on twitter remarked surprise that Librarians and gallery staff, as public workers, would be working on a public holiday. This reminded me of a comment made by UQ Senior Deputy VC Prof Michael Keniger’s at a previous GoMATalks event. Prof Keniger’s point was the cities require public spaces to act as ‘points of certainty’ against the constant upheaval of privately held city land. I asked, through twitter, whether a place like the cultural centre would fit his conception of a public space. He suggested locations of a more geographical and, dare I say, natural bent: the river, fig trees. It sounded a lot like New Farm Park.
This might expose my ideological background, but I see the intellectual exchange embodied in the cultural centre to be crucial to a place’s publicity. On this measure, parks require a particular contingent social infrastructure which seems to come immediately alongside a library.
Reading Radical Brisbane today, I came across a nice passage which has a tangential relevance.
Libraries, however, are crucial. It has long seemed to me that the Left collects books as surrogate for the wealth accumulated by the Right, which puts more of its trust in the police than in the power of ideas.
(Humphry McQueen)