Wednesday, November 11, 2009

Discuss 14

'Florensky saw a relationship between the naming of 'God' and the naming of sets in set theory: both God and sets were made real by their naming. In fact, the 'set of all sets' might be God himself.'
Loren Graham and Jean-Michel Kantor


  1. There's nothing special about sets in this respect. To name anything corrals it, circumscribes it (eg Rumpelstiltskin, eg YHWH, eg any human being). It's like wave functions - everything is everywhere until it's observed / named. Then the wave function collapses and you've trapped whatever it is in your physical or categorical box.
    Does that make it more real, though?

  2. it's a bit like diseases, innit? :P

  3. Florensky sounds like some guy. As we think both of our war dead and the thorny relationship between politicians and scientists (and theologians) the manner in which this one met his end in according to Wikipedia rather hit me:

    Florensky was shot immediately after the NKVD troika session in December 1937. Most probably he was executed at the Rzhevsky artillery range ... about twenty kilometers north-east of Saint Petersburg and was buried in a secret grave in Koirangakangas near Toksovo together with 30,000 others who were executed by NKVD at the same time.

    Never being a great one for Anselm's Ontological efforts, my prefered statement in this area was the mathematician who said something like this:

    Arguably all disciplines require faith to arrive at understanding, but only in maths can we prove this to be the case.

    He was talking about Godel and all that. Please don't press me on the details, I'm a bit rusty.

  4. You would be disappointed, I'm sure, if I neglected the opportunity to point out that the 'set of all sets' is a contradiction, and instead mathematicians use category theory to speak (in a well-defined sense) of the 'category of all sets'.

    There are categories outside the category of sets, such as the category of topoi, hence if God were identified with the category of sets, there would be things which aren't part of God.

    You might then want to identify God with the collection of all categories, but the collection of all categories is something called a 2-category, and the collection of all 2-categories is something called a 3-category, and so on.

    I don't know what the infinite hierarchy of all n-categories is!

  5. Perhaps that's God, Gordon?

    "The infinite hierarchy of all n-categories" presumably doesn't fit on his business card.

  6. Well, Bryan Appleyard, after what I just went through in Discuss 13, you just might be the devil. Anyways . . .

    There's this really neat web page we might all enjoy called Logical Proof of Antinomy: A Trinitarian Interpretation of the Law of Identity. The author, Michael C. Rhodes from the Department of Theology at Loyola University, begins with this sentence: "This essay presents Pavel Florensky's paraconsistent logical proof of antinomy and delineates the relationship of his paraconsistent logic to the notion of the Holy Trinity."

    Slip down to here:

    2.1. P = (p · ~p) = V as 'God is Consubstantial' and 'God is Trihypostatic'

    One such proposition P, Florensky suggests, is 'God is Consubstantial' and 'God is Trihypostatic'. Taking 'Consubstantial' as the thesis and 'Trihypostatic' as the antithesis, the antinomy P in this case is a proposition with two contradictory predicates attributed to God.

    This is mystical thinking in action. A mystic will tell you that God is both consubstantial and trihypostatic.

    I am reminded of a quote that came up in Discuss 13:

    Gosh, what have I done?
    Bryan Appleyard


  7. It's dispiriting to see a real thinker give weight to this pseudo-scientific mashing up of the real with the armchair.

    This drivel could have been spewed by Deepak Chopra: quote some rigorously defined scientific term (set theory) and try to "find God" in it.