FYI. This post recaps my reply to a twitter post by Gwern on Transhumanism. It begins with Gwern remarking: “Platonism may be a useful trick for giving yourself the motivation to push on in math & exploit intuitions, but is not true in any pragmatic sense…” I reply.
Neil Stephenson wrote a scifi novel “Anathem” predicated on Platonism being “real”. Eric Raymond wrote “Homesteading the Noosphere” in the early days of open source, basically saying “Software is the realization of Platonic ideals; go out there and grab your 40 acres!”
A thread on Platonic ideals. Most physicists believe in the Many-Worlds Interpretation of QM, in that those worlds “really exist”. Stephenson in Anathem, does something clever: he identifies those “Quantum Worlds” with Kripke Frames (or General Frames; see Wikipedia.)
In Stephenson’s novel, they are called “Hylean Theoric Worlds” and in the climax, they are popping in and out of quantum-mechanical reality, like Schroedinger’s Cat. Ahh, you say, ‘but this has nothing to do with Platonic ideals, such as “chairs” or “rivers”; its just scifi.’
What is a “chair” in StableDiffusion? It’s a specific vector in a very high-dimensional vector space. Perhaps a collection of such vectors, to which is attached a name, an ASCII string “chair”. Something the nominalists would do.
Does the ASCII string “chair” exist? Or is it “just a name, a label, a signifier” (for some region of vectors in StableDiffusion?) Does that region of vectors “exist”? It would seem to; we can do stuff with it, much like we can do stuff with a jackhammer (which “exist”?)
Does the ASCII string “chair” exist on some Twitter cloud, or is it just a “bunch of electrons in some NAND gate“? Individual instances of NAND gates are just chairs for electrons; it does not imply the existence of a Platonic Form “NAND gate”. Right?
Every time I write the word “chair”, is it just a different instance of writing (and thus nominal) or is there an abstract form for this five-byte sequence? Data deduplication is predicated on all ASCII strings “chair” being exactly alike, and thus universally unique.
Do “universally unique” things “exist”? Current incarnations of Quantum Field Theory claim that all electrons are alike, are indistinguishable, unmarkable (cannot be marked), cannot be tagged. But they can tunnel and swap with one-another, for they are all but one and the same thing.
But isn’t this a paradox? If they are all alike, how do we tell them apart? Well, by their surroundings: Those in my coffee cup are near my coffee; those in my electrical wiring are near copper atoms.
Imagine the atoms in my coffee cup as a vertex+edge graph: nearby atoms form an edge; distant ones do not. The specific electron I talk about is localized with respect to this graph. This is how I distinguish it from others.
Well, what’s a deep-learning artificial neural net? Well, a very large vertex+edge graph of weighted edges. Does any collection of such vertexes exist as a Platonic Form? If not, then what about the electrons floating in NAND gates, holding those floating point numbers?
Are all those electrons just nominal “specific instances”? Well, we know from QM that there are no “specific instances” of electrons; they can only be identified by their millieu, and not some tag (signifier, name, symbol) attached to them.
And so we appear to be in a Nominalist nightmare: the only “names” we can attach to “specific instances of things” are just “large graphical networks” which just point to regions of other “large graphical networks”.
To conclude: personally, I’m not a Platonist, but, for me, Nominalism is just silly hare-brained magical thinking, wishing for something to be true simply due to a lack of understanding of physical reality. The End.
That was the tweet thread. Despite being pinned to my twitter profile for two months, got exactly nine views and zero likes. So much for using twitter to spread neat ideas.
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