On What Might Be The Case
On Numbers, Ontology, and Figuring Things Out
I noticed an intriguing tweet from my favorite podcast/podcaster and philosophic conversationalist as well as fellow UChicago lifeminder, Matt Teichman. [He didn’t know I thought this about him nor even really knew I existed beyond some recent tweet replies and podcasting analytics data point, so if he reads this he will now know and our acquaintance will now change.]
Several interesting things popped out to me:
- The subtle cultural commentary on social construction of mathematical facts aka alternative facts, fake news, science denialism and what not.
[while we have new words for our problems in society the debates seem to be the same. while we have a lot more facts about the world we seem to have an equal amount of strange non facts. history rhymes and what not.]
- A link to a philosopher new to me, Julian Cole
[the paper linked to is great. it’s short, covers a lot of ground, and gives me confidence that my devotion to taking abstract conversations and tying them together to really insane pop culture situations is acceptable to academic publishing. J. Cole manages to get odd history of Viagra as a case for the robustness of math via serendipity into the philosophic record.]
- A call to people who might be interested in all this
[I have long thought I might be the only listener of Elucidations that has consumed over 80 episodes and routinely to have done so at LA Fitness. I need to find the rest of my tribe.]
A couple of replies from Matt nudged me to remind myself of more of the ontological / epistemological arguments about what math, truth, and knowledge might be. I had to go back to a couple of episodes, some of my books, my old writings and brush back up. I also was flummoxed to come up with a way to summarize all the things swirling about that could fit into a tweet or three. This of course got me to put all my thoughts together on all this is all related and makes all the points. Yes, figuring out to provide all this context and make a cogent statement to enrich the debate all within the twitter medium has reinforced my own philosophic argument. I think. I hope? [A scrutiny process, convincing argument, a proof, a valid scientific process, a computation must include its subjects, objects, processes, conclusions and the explanations to make sense of all of it. A short sentence or two that references a larger process and operants doesn’t really stand on its own. Nothing at all exists without all of its references. Nothing is the only thing that exists without reference. Randomness and Uncountable Infinity are the only things that exist with every reference. Sentences, phrase fragments aka tweets, exist somewhere between nothing and randomness.]
On the main matter of what a fact might be, mathematical or otherwise, we have so much spilled ink on this it doesn’t seem useful to add a bunch more. I comment that common experience would indicate that assuming facts exist is useful and useful enough that we should take them as a reasonable thing to base discussions around. How we verify their factness (or truth) is a matter of many debates which to me all have something useful to say. In fact, we should use them all and continue to add to the ensemble of fact-verification processes we have at our disposal. If a fact is true it will hold up under scrutiny process and will only be strengthened by a better and better falsification processing. [a fact’s factness is measured by the size of falsification attempts and the degrees of freedom of those falsification attempts].
The old podcast episode Matt references usefully lays out mathematical facts/number objects as some facts of the world we can talk about and the scrutiny processes by which we talk about them. The episode makes clear that you could do this with other facts of the world — say colors or locations in spacetime or whatever - but numbers seem as a simple and reasonable thing we can jump off from. [a number is small enough as a fact that we can spend more of our scrutiny process, our observations, on the observation of the scrutiny process of the numbers. colors are larger facts and would require more scrutiny process on a description of the colors and would have less scrutiny process for the scrutiny processes of the colors, aka color perception, chemistry, physics of light]
The episode and the J. Cole philosophy essay on Social Construction in Mathematics discuss the dilemma of what numbers might or might not be and how their arbitrary non-arbitrariness has been confusing us for a very long time. In the episode Sutherland and the hosts lay out the many questions about whether you can know something about numbers without assuming something about their numberiness and whether a thing is known by its thingness or by what it does or what users/thinkers of the thing wish to do with it — just how abstract is an abstract thing. Does a tree falling in a forest with no one around make a sound and so on. J. Cole puts a bit more detail on it this problem. Specifically, it is not always clear that what one claims is socially constructed is actually socially constructed — our social constructions seem to be awfully reliable in emerging the same ideas over and over. [the boundaries of social awareness, meaning, observation, scrutiny processes are also scrutiny processes themselves — what can a scrutiny process say about another scrutiny process that isn’t tied to its own problems? what is a social construction vs a non social construction? what is constructed vs what just is? all of it considered is the total size of references required to comprehend any of it.]
This anchoring loop loops. If socially constructed ideas have some more universal, deterministic basis themselves then how can the constructions of the constructed be considered mere social constructions? If numbers are the thing we use to count then how do we count the things we number? The ends justify the means so long as the means define the end? We find this loop everywhere. [a description of the proof is not the proof. the proof is not the truth. the truth can be observed without the proof, but can’t be trusted, not completely. a truth that can’t be trusted completely without its evidence must not be the whole truth. the scrutiny process must include all that it scrutinizes and all that it doesn’t.]
Surrogate loops — these strange loops of subject-object confusion. [reasoning about numbers using words is not possible. reasoning about words using numbers is not possible. the truth of the matters lies in the truth of their matters using their matter. words are surrogates of the surrogates of the facets of reality. And when there is a number or word missing it is easy enough to invent one. So now a new problem arises. the scrutiny process of anything has been extended to anything we might invent in the process of the scrutiny.]
Algebras, algebras and algebras. When we are out of numbers or time to count them we divide and scrutinize. What is division? What is multiplication? Are they processes? or collections of objects? or objects unto themselves? or subsets of objects? sub-objects? A number divided is still a number but now it’s a different number, except if it’s 0 or infinity infinity or other strange numbers that can’t be divided, or divided in some scrutinizable way. What is division if it doesn’t really do the same thing to all the things it does things to? It what sense is it a singular process and not a collection of other processes? Division describes a general process of difference making, but it’s not the only way to make a difference. We’re back in a loop of insufferable surrogation and ambiguation. [There are many ways to get to the number 1. The full description of the number 1 is all of the scrutiny processes that lead to 1. There is a full theory of the number 1, and it includes all the theorems that give you 1. Unless all these theorems are isomorphic to 1 then you need only 1 of the theorems of 1, but not just 1, but which 1 should we chose as the right 1 description of 1. The shortest — both in description and that makes it clear to everyone. So all of the 1s.]
[Possibilities and Impossibilities co-define each other. But only the possibilities are finitely describable or have a possible scrutiny process. What is illogical still exists it just doesn’t have a particular scrutiny process other than any scrutiny process will do.] J. Cole gives a robust account of just how robust accidents are and how flaky our socially constructed narratives of the matters are. He provides several popular examples of what was a clear purpose or objective of the object ends up being the effect of something else. In what sense has the flake of a Kellogg brothers been caused? Was it the random event of being called forth from the work? was it the chemical process of being left alone? The cause was immaculately conceived and then reified into manu-fact-er history. Now the Corn Flake Scrutiny Process, its program, includes the history of the conception and the chemical cooking process and the wheat and the Kelloggs story and everything else that is a flake of wheat and corn (tm).
But the mathematics is still there, there are still facts. Just now a lot more of them. If you go up a bit, or inside, or around, you’ll find that’s it. The facts continue to pile up. the more you scrutinize the more facts show up. the more scrutiny needs to be applied. A number is just part of sequence — a sequence itself within a sequence. Surrogate sequences that all have just enough sequences to be sequenced. J. Cole and Searle and Benacerraf and Cohen and more want to force us to impose function onto reality. Perhaps it’s not their fault though. Perhaps reality imposes function onto us? Perhaps we’re imposing reality onto reality? The possible onto the impossible? [A scrutiny process is defined by what it scrutinizes and by what it cannot scrutinize. But it cannot know what it cannot scrutinize since it lacks the sense to scrutinize what it cannot. How can mathematics scrutinize completely about itself if it cannot scrutinize the non-mathematical? What if mathematics is never done and that it is an ever growing possible scrutiny process? what can be said about it before it has maximized its scrutiny processing? is a computer program just its program description or everything that can be computed by the program?]
By now, if we’ve made it this far, it should be clear there was no hope of bringing this essay back to how it started. Back to a tweet, a tweet constructed by a human, distributed through a series of computers connected to the network, bit-copied through disk after disk, rendered via electron diodes onto screens manufactured all over, seen through a set of faulty eyes, cognitated on by someone who reads perhaps too much and paints too much and ponders that which must come to an end, for god’s sake. The tweet said very little. It simply said read this little essay by this fellow, JC. But that tweet can’t be considered just by its character count — we must consider all the character it builds, all the characters it draws and draws in — that tweet must be considered by all that it has animated and the problems its resolved.
It might be hard to see what was really being challenged. “Benacerraf’s epistemological problem” was put forth as being a hard problem. No doubt it’s hard to see how the abstractions and truth conditions of mathematics are causally awake to the senses while at the same time trusting the truth conditions of mathematics to actually be truth. It’s wordy, it’s complex, it’s hard to deflate within formal theories and with logical inferences.
But… perhaps, just perhaps, like everything, the answer isn’t an answer, it is a question. [a scrutiny process is just a scrutiny process, its truth, the fullest extent of its truth, its fullest description, its everything, is everything it generates.]
The account of knowledge, whether using Bayes or causal or reliabilism or just old mother hubbard, says nothing about its own truth directly except by all that will be said about it. A positive account of something is a surrogate for its negative.
[A scrutiny process (aka a computation) is all that it can observe (reach) divided by all that it can’t observe (reach).]
[an account of knowledge is only knowledge so long as it can reach what it claims and not be reached by what it cannot.]
J. Cole leaves us a question inside a concluding statement. The boundary condition drawn by mathematics, mathematical reality and social or non-social constructivism or non-constructivism is generative. It sets loose other scrutiny processes to make sense of, make non-sense of and/or otherwise enrich — even by deflating what can be considered mathematical reality.
The contents of this essay probably do not resolve J Cole’s many questions nor Sutherlands from the podcast episode nor solve Benacerraf’s many problems, but its effects do. The effect of this essay is a response, one with many senses, making a claim that no claim need directly handle the initiating claim to handle other claims and be valid in the emergent claims it makes. In a sense, for the reader paying attention, perhaps too much attention, this essay could be considered the Viagra of philosophical rebuttals. It didn’t solve the problem it was designed to, is still arbitrarily non-arbitrarily useful but has gone on for four hours too long.
For a longer account of the author’s deeper theory of knowledge and existence that isn’t unclear enough here see this piece: Mapping Existence.