The following is a conversation with a friend from undergrad, Christopher Carroll. Back in 2016, Christopher was my roommate, who studied History at Towson University before eventually becoming a Computer Science major. Our conversations have always traversed a range of topics from politics, science, mathematics, logic and biology. He is avid reader of history, philosophy, science and this blog. This conversation occurred in my FaceBook Messenger DMs and I thought it was an interesting conversation that I wanted to share here on my blog about the topic of mathematics, the philosophy of mathematics, certain positions and take he has versus the positions and takes I have. After dropping out from Towson University, Christopher began serving in the military and I am currently receiving my PhD from UCI in Comparative Literature. The conversation is only slightly edited for grammar and coherence. This is not a formal conversation nor is it an exhaustive one. Just a bridge for bigger questions to be asked and different dialogues to begin.
Christopher Carroll: Are you studying mathematics?
MumbleTheory: Philosophy of Math. Sometimes. But it’s like something I just do off the random. It’s not necessarily connected to my research.
CC: What maths do you know?
MT: I’m interested in set theory.
CC: Yes, I remember you saying that before. Have you taken calculus or a statistics? I ask because I am about to undertake a mathematics minor, and I was wondering how the introduction of mathematics to your philosophy has influenced or developed your perspective. I mean, I obviously see the implications in F A I T H, but I am asking on a more personal level like, did it change your view on everything?
MT: I’ve taken statistics. I want to learn calculus. Calculus is interesting in terms of philosophical history though.
CC: I agree. Calculus is when math really opened up for me. I haven’t taken statistics. I think math has been a redefining factor in my understanding of life itself.
MT: I think math is a special tool created by a particular kind of hominid species to apprehend its universe and the fact that this tool has been so historically accurate/precise is honestly metaphysically weird.
CC: I don’t think math is constructed.
MT: I do.
CC: I mean, the syntax is, but it’s just description… I have a book you may be interested in.
MT: We invent new maths all the time. Algebra was invented. Calculus was invented.
CC: They’re not really invented though. They’re just new ways of describing things.
MT: I think they are. There are mathematicians that agree with me too. But that’s with anything and everything honestly.
CC: Send me some references.
MT:
Henri Poincaré: https://en.m.wikipedia.org/wiki/Henri_Poincar%C3%A9?fbclid=IwAR10EBL_wqn1JW7qoaqG2rWVQxaQxPe82D-c_u68j15F-n6Mffj8YJ-eqcs
Conventionalism: https://en.m.wikipedia.org/wiki/Conventionalism?fbclid=IwAR04uMJcoV9BiFF9pF63MeFVIIs_QrSv-vjgyiFg2OMT35M2AEmjw9CzEFk
Intuitionism: https://en.m.wikipedia.org/wiki/Intuitionism?fbclid=IwAR09mtsVdQNAkjRdGPOvJEM7bL4k-Nk24mi-nXYTvmOyHBoe9ba1ZwXfOVk
L.E.J. Brouwer: https://en.m.wikipedia.org/wiki/L._E._J._Brouwer?fbclid=IwAR3-yCh5nZw2611Fx-dRVvvq7g2-AnyQxaN-cMjveD284zPOgW2aMfv3W7g
CC: Alright. I’m at a keyboard now. What do you mean by “math is constructed?”
MT: I mean that math is a system of symbols instrumentalized for the first time ever by a particular hominid species type in Ancient Egyptian and prior to the creation of the creation/discovery of this instrumental/model for understanding the function of the universe there was no such thing as math. Only the Earth, the Universe and all the other things that preexist human symbolic systems.
CC: I am not digging this intuitionism. I may be wrong, but it seems some of the first math instances come from Babylon but does the concept need to exist for the math to exist? I mean isn’t math just a descriptive language.
MT: Or Babylon. Sometime way back then. Math IS just a descriptive language. It is a language.
CC: But that doesn’t mean the principles of math are made up, just the symbolic language.
MT: People require language. But the universe does not.
CC: We use the language to describe what is, but we didn’t make up the principles. Also, I am finding myself very much NOT on the side of intuitionism.
MT: Yes, symbolic systems refer to and are themselves material contents/concepts. “Transformed meaning have led to transformed matter, to a transformed mode of experiencing the self.”[1]
CC: Perhaps philosophy of math is the best area for our conversations to converge. We will have the most overlap in formal education.
MT: Math is a meaning-making apparatus like all systems of symbolic representations that humans have used to get at the crux of what is. There is no notion of the quantum without a meaning-making apparatus. This “meaning-making” apparatus is what math is. But it is a meaning-making-apparatus-for-us as Humans. It is an highly effective meaning-making apparatus for Humans, in fact. And it developed, like other language systems and biological systems, from the simple to the more the complex as time developed. But the idea that math, as a meaning-making system, preexist humans and is always already there in the universe with or without humans is an anthropocentric fallacy that confuses what humans utilize to understand how the universe works with what the universe is as an entity that precedes and will exceed human signs, symbols and “understanding.” Which again goes back to the incompleteness theorem which sits at the heart of philosophy of mathematics, in my opinion, as an unresolved issue that if really sat with long enough it would have to halt the entire notion of “mathematical progress” or at least change it drastically. Because, every formal system cannot within itself prove that it is in fact logically consistency and every formal systems produces problems/equations that it fundamentally can’t solve. Even in the most powerful mathematical articulations like ZFT (Zermelo-Fraenkel Set Theory).
CC: I detest the idea, and for that reason I must necessarily study it.
MT: READ UP ON GÖDEL, CANTOR, BROWER, AND POINCARÉ. I would love to have this chat with you. My interest in philosophy of mathematics is a very esoteric interest. A leftover love for Pythagoras when I learned of him the first few days of “proper philosophy.” I’m interested in it for fun and pretty convinced that European history as a result of the Enlightenment and the fascination with Rationalism that came with it had to necessarily reduce and downplay the mystique of mathematics in order to constitute the intellectual project it was building as counter to the Feudal religious order and to further build the narrative of a mechanical, clock-work universe that would eventually be “discovered” by Isaac Newton’s classical mechanics. I find that if what I think to be true is right it has major implications for every single thing that ever happened ever, every single thing that has ever been thought to be understood. But, I don’t think it’s that absurd. It’s only absurd because we have a formal system that actually overdetermines the sociocultural (my favorite writer Sylvia Wynter would call it “sociogenic”) way that we view mathematics as well that says Man is the center of the universe such that Man’s most impressive tool for understanding the universe (Math) becomes synonymous with the universe itself. Just as Man and Man’s rationalism had becomes synonymous with the universe itself. The idea that people would object to is according to the following idea: if math is a part of Man’s imagination/symbolic system/language rather than a part of the universe than that means we have somehow missed something TRUE about the universe with our mathematics. And my point is: Yes, we do necessarily miss something true about the universe with our mathematics but that’s not math’s fault that just the inevitable result of TRULY sitting with and accepting the implications/consequences of the incompleteness theorem. But furthermore, that by not seeing math as a synthetic production instrumentalized by and for Humans to understand how the universe works we forget that the universe does not exist for our math but our math exist for the universe.
CC: I agree with the reverence for Pythagoras mathematical ideas, but have mixed feelings about the interjection of mysticism. I do definitely agree with the idea that math exists for our universe, not the inverse. I stand by Galileo when he said “Mathematics is the language in which God has written the universe.”
MT: Anytime you say that there are things that humans simply can’t know people will accuse you of being a mystic.
CC: This is true.
MT: And I would say that Galileo presumes to know too much about God and assumes that God is speaking in the same language as the one that he has available to him.
CC: I would think its more audacious to think that God wouldn’t if we assume God has any interest in humans.
MT: What I prefer to say is: in order to say one knows what one has to know is that there is something incomplete in their knowing. Always. And. Forever. Unless somehow the incompleteness theorem isn’t true. Or is overcome.
CC: I imagine if it is overcome, whatever overturns it will itself be overcome. Since the dawn of Philosophy, we’ve argued these exact ideas. Only in different terms, and different internalizations but many modern arguments can be reduced to the same as the ancient ones at least, so it seems to me, but I am not formally trained.
MT: Yes, but there’s always been people universally ascribed to mysticism whenever they state a rather simple claim which is: that humans cannot know everything and, that humans are not everything, and that what seems most special and significant to humans is not really all that special or significant at all and might as well be just as pointless to other species. Or, for example, what we consider the language of god as humans is meaningless verbiage to something else. And that this matters because humans don’t. And humans means of illumination and understanding are nothing more than that: human means of illumination and understanding some of which come to overdetermine their relevance in comparison to others for reasons that are ALSO products of social decisions on the basis of what constitutes the highest level of abstraction/intelligence. Math is that for us. Theology was that for the Feudal Order.
CC: What if that isn’t true though? What if humans do matter?
MT: What do you think that would change about what I’m saying? That we, and then when we say, “we” we would have to be remember that “we” has never included “all the humans” esp. in the case of math, since it is a preconception of the West to say that math began in Greece where the uniquely gifted lineage of all things rational is always thought to have began. So would you then say that being human did not have any relevance until the discovery of math in Babylon, Egypt, and Greece because we could not understand the language of God as the language of math and geometry (which was the primary math at the time.)
CC: I think it’s a mistake to say that math began in Greece. The book I am reading would even argue that the Greeks retarded math for thousands of years. If there was a presupposed purpose for humans, wouldn’t it be irrelevant what stage we were in, as every stage is equally as important let it be noted this is not my feelings on the matter. Just the argument.
MT: That would make sense if you think of the human species as some collective surge together towards a higher teleological ends. Which … would be absurd too considering slavery, genocide and the asymmetrical distribution of “human” suffering towards this human collective teleological end.
CC: I suppose this is true but there could be “afterlife” or alternate reality implication for these things. But that can have as many alternatives as there are numbers in infinity. Again, it’s not the grounds I take on my personal views. But are you supposing that it is impossible to have higher ends, or only if their are higher ends, then the architect is unjust? Both bare a heavy theological weight, and I almost feel that any assertion about anything (if Gödels incompleteness theorem is to apply to all systems) could be a fallacy since they’re asserted through the rules of the system we experience, unless we claim to be capable to understand a complete system (which is antithetical to the incompleteness theorem obviously). Likewise, does this suppose that reality is infinite? The deeper down this hole we want to go, the deeper it will get? Or does it just suppose that there are things that simply cannot be known, period, by any system and if so, would that be the essence of “God”. Or is it just how it is, it exists unto itself for no other reason than it exists? Far beyond my pay grade, to be sure.
MT: Yes, I believe we have to get rid of the desire for a complete system. Even God is often times invoked in order to complete the system. But we have to see that each complete system is necessarily incomplete and inconsistent. And then still navigate the world through an understanding of our understanding as rooted in that.
CC: Hmmm, I knew a person involved in chaos theory and anarchy that would agree with you but I do think the concept of complete, at least in this manner, is similar to the concept of perfect in that is is unattainable mostly due to the nature of change. Unknowable unknowns, as opposed to just unknown unknowns the very idea makes me uncomfortable though that’s not a firm foundation for anything. On a slightly unrelated note, there’s an old, old program that’s still quite in use today. The program, and it’s underlying language may be intriguing to you. There’s quite a mythos around the language to be sure. It has its own urban legends behind it. It was written in the late 1950s, and still one of the most powerful programming languages today. Based on the concept of symbolic processing and lambda calculus it also happens to have one of the most simple syntaxes of any programming languages around, consisting entirely of parenthesis () not that I think you’ll learn it, or have any real interest to. But I still stand by my stance that a philosopher’s toy can be computer programming. (I also think that it is a failure to not teach mathematics alongside of Philosophy, but that is my own personal bias.) The program that is still in use today is called emacs. It’s a text editor that can rewrite itself and be programmed to do basically anything. Getting use to it is a chore, but the combination of being infinitely customizable and written in lisp give it an amazing level of workflow improvement. If I could see one thing, I would wish every person out there grokked this program (or it’s flame war opponent vi, but thats another story).
[1] Sylvia Wynter, “Towards the Sociogenic Principle: Fanon, Identity, the Puzzle of Conscious Experience, and What It Is like to Be ‘Black,’” National Identities and Sociopolitical Changes in Latin America, 2001, 36.
Mumble Theory 