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A non-ironic (like actually non-ironic -- I'm trying to be genuine here) discussion about Jreg's Frameworthless video, and potential language Jreg's ""Community"" could learn, borrow, or adopt.
I am going to introduce ideas that if one goes to look up, they will see that their formal versions are full of dense jargon. After seeing this, one may assume that I am some crazy internet person that is talking completely out of their ass, so let me tell you first why I am not some crazy internet person, and then let me tell you why you should not necessarily believe me.
Why believe that I am not some crazy internet person? The only credentials I can flash around are that I am a 5th year PhD student in math (but I'm leaving my program because I think that academia forgets that its students -- as well as some others inside of academia -- are actual humans; by this I mean that many people are -- what I think would be appropriate to call -- Freirean objects while they are in academia).
Why am I not an authority on what I am going to talk about? Well, first of all, one should (and, more importantly, one can) never be given knowledge, so I would go so far as to say that no one is an authority on almost anything, but, of course, this is not what I really am talking about when I mention I am not an authority. Lack of authority in this context means that I have not formally studied anything in foundational logic.
To reiterate, I may speak out of my ass, but I have shown you that my ass is toned in semi relevant areas, and I have reminded you that, as people used to say in my elementary school, farts have poop particles, and thus, you should be careful not to breath in too deeply. Now, with that preamble out of the way, let me say, guilt free, what I want to say.
In order for me to feel somewhat confident that I have given enough to detail for my readers to begin to understand what I mean to convey, I will need to meander a bit with exposition.
Let us start by trying to understanding what Jreg would probably call, a framework for mathematics. The reader at this point may be ready to get up and leave, so let me attempt to yank them back to their seats by telling them that I do not mean algebra, or geometry, or trigonometry, or calculus, or any other of the singularly boring versions of bullshit that are put forth in K-12 and early undergrad when I say mathematics. When I say mathematics, I mean the communication of ideas that we agree are true; let me be very clear here, I do not mean that math necessarily reflects real truth, I mean that we agree that the symbols, 1+1=2, are `good' or `true' in some way, but that the symbols, 1+1=3, are `bad' or `false.' In some way. I now urge the reader, without saying something like `if I have one thing, and I have another thing, then I have two things' or `that's just how it is' to explain to themselves, why 1+1=2 is a true statement. One can't (and don't be some fucking dumb shit who goes `ohhhh, but actually, Whitehead and Russell prove it in Principia Mathematica, so uhhh, you're actually wrong, and I'm right, and even though I am always right I still have this empty feeling I can't get rid of, why don't I feel validated, please help me, why doesn't society love me, I seriously need help, please help.' If you say that just fuck off because you know the point I'm trying to get at, and if you don't know the point I'm trying to get at, than you are just some weird fucking guy that googled why is 1+1=2 so you could say I'm wrong. Also, just in case you are one of my friends reading this and you think that this parenthetical is weird, let me just say that it is mainly here because I felt it was the kind of joke the Jreg community likes) prove it! It's just something that one, in some sense, agrees is formally true -- an axiom, one might call it. Now with this in mind let me make the following statement.
Mathematics is actually just a type of machine (whereby a machine, I mean, a sort of formalized version what Jreg calls frameworks) that may be described with the following four rules.
The Four Rules To Describe A Machine (Framework?):
Rule one: there is a universe of symbols (sometimes called an alphabet). Different machines may have different universes of symbols. There are many things one could use for a universe; two such examples are: the 24 letters of our alphabet and the set of all whole numbers (0,1,2,3, etc.).
Rule two: there are formal rules to be able to combine symbols. Different machines may have different symbol combining rules. Some rough examples: we can make a word by combining letters; we can make an equation by combining mathematical symbols with an equality in the middle; we can make a sentence with grammar and words, and we could use algebra to combine numbers.
Rule three: a combination of symbols that follows the formal rules is either coherent or incoherent (a sentence cannot be both coherent and incoherent), and a machine can read coherent combinations but cannot read incoherent combinations. We call such a combination -- whether it is coherent or incoherent -- a sentence. For example, the sentence `lidgijwlek and alkmq, lawoaq!' is incoherent in English. Another example, `5-=1=--+-=-.1.3' is an incoherent sentence in math.
Rule four: any coherent sentence can be read by a machine, and the machine knows if that sentence is true or false (a coherent sentence is never both true and false). For example, the coherent sentence 1+1=2 is true in the machine of math, but the coherent sentence 1+1=3 is false in the machine of math. Another example is that `my computer that I am typing on is black' is true in, what we might call, the machine of English (notice that this has a weird consequence that a command such as `go clean your room,' isn't a coherent sentence because it doesn't have a truth value. Let me be clear that this isn't to make any point about saying commands don't make any sense. It's just a peculiar consequence of the words I have chosen to use to describe what a `machine' is).
**\* this fourth rule is actually not correct, it needs to be slightly altered, but that's another long conversation... it would be better to say that a machine can read any coherent sentence and can say if that sentence is, what one sometimes calls, `derivable.' This takes a tiny bit longer to talk about, but if people are interested in this post, I can make another where explain what this means and why I think this also fits into a cool idea that Jreg touches on in his video. The reason we need to say derivable instead of true is that you can have a coherent sentence where that sentence isn't derivable and the negation of that sentence isn't derivable -- this is what Godel ends up showing with his incompleteness theorems -- but you can't have a coherent sentence where the sentence is false and the negation of the sentence is false **\*
Now, why have I brought all of this up, and why do I think that a machine is a formalized version of what Jreg call's a framework? Well, I think that that question would better be answered in the format of a dialogue, and, seeing as writing fails to be a dialogue, allow me instead to just jot down a few ideas, then, if you'd like, you can engage with me about those ideas in the comments.
How should we define an assumption in this language -
Sometimes coherent sentences being true can imply that another coherent sentence is true. For example, if my machine says `all unmarried men are bachelors' is true, and it says `Hatted_Ducks is an unmarried men' is true, then (let me preemptively cut off someone's possible objection to what I'm about to say. I'm assuming that all these machines follow some sort of propositional logic that allows for modus ponens. For those, like myself, that don't care for obfuscating jargon -- I'm just saying that let's assume that machines we are interested in can use if-then statements to get conclusions), we must conclude that the machine says the sentence `Hatted_Ducks is a bachelor' is true. Suppose that we somehow find a coherent sentence, let's call it X, that the machine can't prove by using other coherent sentences; let us call X an assumption relative to the system. For a lot of people the statement `God exists' is an assumption relative to the system they use. It may be that an atheist takes God's existence to be false as an assumption, or that a theist takes God's existence to be true by assumption. It is possible that to some machines, the existence of God is not an assumption. Let us think of such an example. We could imagine someone that has an assumption that the best version of things must exist (let's be clear that best here is vague), and then they could define God to be the best version of a living thing, thus, they could conclude -- without it being an assumption for their machine -- that God exists. Similarly, we could produce a machine for the atheist that allows them to conclude from other assumptions that God does not exist. Observe that our analysis reveals something rather cool.... at some unprecise level (that is to say, I think one could formalize what I'm about to say a bit more -- and I wouldn't be surprised if one already had -- but I don't think we need to do that right now) the information a machine can give us is equivalent to its assumptions and the rules that machine has for combining those assumptions.
Fun math fact I now have the language to tell you -
Now, if you really wanted to go learn about the foundations of the machine of mathematics, you might go learn that (most) mathematician's are secretly using the machine with the ZFC axioms. In fact, you might also end up learning that you can build different types of mathematics by adding in slightly different assumptions.
How we may define ideology with the language of machines -
Now, let us propose the following proposition:
People cannot interact with anything in the world without first using a machine.
It is not that the machines transforming of the world into coherent sentences and then into truths has to reflect reality (and, indeed, I don't personally think any machine can do anything more than give a rough approximation of whatever reality is). If I wanted, I could say that the sentence `my hands and my feet are the same thing right now,' but this is just really not correct in some very obvious way. I could also choose to say something that might be seemingly true --at least, if we go back over a few centuries -- `it is the divine right of the king to rule over his people,' and, though it may be the case that people used to often agree with this (I don't know enough about history to say if that's accurate), it is much more rare nowadays to find someone that would think that sentence was true. \For those that interested, Foucault points out some much more subtle ways that many of our current machines fail to reflect reality. Sometimes people think that their personal machine actually reflects reality, this is what I would like to call an *ideology.** That is to say, it is the belief that their machine is giving necessary truths in its interpretation of reality. Sometimes, when one realizes that there ideology isn't reflecting reality, they go and slightly alter their assumptions and thus slightly alter their machines -- for science, this is, I believe, what Thomas Kuhn would call a paradigm shift or scientific revolution.
How to try to get at true knowledge with machines -
Now, if we adopt this language of machines, we might get the worry that nothing is real... that knowledge can only be given in the context of a machine, but true knowledge can never exist. Thus, if we are to know anything, then we must first work within a machine (choose a framework, son). Now, let me use my bastard understanding of a platonic form to discuss what Jreg means when he says that the son should choose a framework and then find a better one. Pretend I am a baker, and that I want to become the ideal baker. I, as a baker, have no idea what the ideal baker is, but I can, in some meaningful way, strive to be better. Through my striving I will get closer to the ideal baker. To Plato, if I understand right, this is an example of the idea of a platonic form; the ideal baker in my scenario is the `platonic baker.' A platonic form is some perfect thing that can never be achieved, but it can be strived for by an approximation of the thing, and in the striving for it, the approximation becomes closer to its ideal version. The father's actual advice to the son (though he refuses to call it advice for some reason I don't understand) is to say, `son, I don't know what the platonic machine is, or where to find it, but I have strived towards it, and now it is your turn to strive towards it... we will never get to this machine, but maybe we can somehow get closer.'
Using the language that has been introduced, we can perhaps imagine that the ideology produced by the platonic machine is reality -- that true knowledge can never be achieved, but that it can be strived for.
The father points out that the son can't begin to move from machine to machine -- that he can't participate in journey of man kind towards true knowledge -- if he does not realize that he using a machine. This is how I like to frame (hahahaha, pun) Jreg's anticentrist idea. It is not that he is necessarily anticentrist, but it is that he wants people to understand that they are using a machine -- that ideology is not reality.
I wrote this post in an attempt to give additional or alternative language to this community. It seems that Jreg, and by extension those that watch his videos, are touching on some ideas that I have been thinking about for awhile. I think that he is touching on ideas that many people over many periods of time have touched on. It's rather fun to try to learn the different languages that people use to describe these ideas, and it's perhaps even more fun to produce the languages... but now I'm rambling.
Certainly, my post could be much more precise and much more accurate, but I hope it will be a good starting point for conversation.
All the best,
A duck with a hat.