While reading this morning’s post by a number theorist known to the world as Persiflage, the author of this blog decided to entertain the possibility that Mathematics without Apologies is a real book written by a fictional author. It’s the sort of thought that comes naturally to the author (of this blog) during his first extended visit to Yale since the years immediately following his PhD, when he used to come to New Haven to pursue his interest in comparative literature. (Naturally that was not his primary object of pursuit; but it was an interest he could always be sure would be gratified.) As of this morning, Persiflage has only got as far as the beginning of Chapter 5; had the author of this blog been consulted, he would have advised Persiflage to start with Chapter 7, which provides hints as to how the author became convinced of his own fictionality, even before his earliest visits to Yale.
Persiflage wants to convince his readers that the fictional author of Mathematics without Apologies, whom he describes as “a chimera,” holds real opinions. Out of respect for the genuine cultural critics with whom the author (of MWA) interacted, at Yale and elsewhere, the author (of MWA) cultivated the habit of assuring the reader that, whatever kind of fictional character he might be, he does not mistake himself for a scholar (as Persiflage was careful to note, though he seems to have found the disclaimer disingenuous). To illustrate how this works, the author (of this blog) turned straight to the article Fiction on the Stanford Encyclopedia of Philosophy in search of an answer to the question: do fictional characters have real opinions? If that’s what you want to know, don’t bother looking: you will not find the answer there. (You will find out how philosophers have addressed the tricky question of whether Casaubon in Middlemarch was a scholar, or more precisely the slightly less tricky question of whether “[Sherlock] Holmes is cleverer than any actual detective.”)
Maybe the answer is in one or more of the references listed in the bibliography. A true scholar would have refrained from comment until he or she had read all of these references, and continued reading until the relevant literature was exhausted; the author of MWA, in contrast, would have checked a few of the references that looked most promising; but the author of this blog has to finish quickly in order to get to this morning’s lectures at Yale, and therefore will offer a fictional opinion after having looked at nothing beyond what is written in the Stanford Encyclopedia article, which incidentally needs to be cited as follows:
Kroon, Fred and Voltolini, Alberto, “Fiction”, The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2011/entries/fiction/>.
This morning the safest opinion seems to be that the author of MWA is a Meinongian object; to quote the Stanford Encyclopedia:
Meinong (1904) thought that over and above the concrete entities that exist spatiotemporally and the ideal or abstract entities that exist non-spatiotemporally, there are entities that neither exist spatiotemporally nor exist non-spatiotemporally: these are the paradigmatic Meinongian objects that lack any kind of being.
Some readers may find it helpful to think about mathematical objects in that way; and Persiflage may find it helpful to think about MWA’s author as Meinongian, in order to find an ontological slot in which to file his opinions. I (the author of this blog) advise Persiflage to assume that both participants in the number theory dialogues reflect the author’s opinions and maybe then to check the Stanford Encyclopedia article’s bibliography to determine whether or not Meinongian objects are capable of ambivalence.
I (the author of this blog) do want to make one thing clear: under no circumstances, even Meinongian, would the author of Mathematics without Apologies ever want to leave the impression that Vladimir Voevodsky is any kind of “villain,” as Persiflage clearly thinks the author of MWA “definitely” thinks. Both authors (of this blog and of MWA) are sympathetic to Voevodsky’s motivations although neither one shares them. If Chapter 3 needs a villain, it’s the Powerful Beings, or at least those among them that exist spatiotemporally.