As is customary for me, I will put Marc's commentary in block quote format in green letters. The full text of Marc's comment is here (Link).
"...and nothing except the unfolding of the cards really happens." So.. nothing but EXPLORATION happens??I prefer not to use such charged language as "nothing but" here. In my experience, particularly in philosophy, "nothing but" statements are usually dubious and frequently wrong.
The problem here with "nothing but" is that eventually we meet the seams of what we can say within the axiomatic system we're exploring, e.g. when we follow the Peano Axioms out and realize that they predict the concept of infinity but do not account for it. At that point, we get to decide upon new axioms about the questions raised, which isn't really exploring anymore, at least not in the sense that it's all already there waiting to be found.
This takes us back to the cave example. We can still explore the unknown (in candyland the unknown is what color the next card is going to be), and can reveal truths about the universal system.The point here reveals why the cave example isn't any good. A video-game cave is actually a better example than a real physical one. Why? Because it's as if our axioms define a certain digital cave, but the programmer isn't actually able to close off all of the boundaries within that cave. Sure, the boundaries are relatively hidden in most cases, but like playing a glitchy game, there are places where you can kind of fall off the edge of the map. There is an outside to what the axiomatic system is able to describe in exactly the same way that the unprogrammed "void" is a "place" outside of the intended playable area in a glitched video game.
We try to set up the program to close off all the glitches, but we know because of the Incompleteness Theorems that we cannot actually do that. We'll always be able to find glitches that let us "leave the map." At that point, programmers can decide either not to bother with it or to flesh out areas for some of the more accessible, obvious glitches. Outside the metaphor, this is choosing new axioms that define more (or different) cave space to explore--knowing again because of the Incompleteness Theorems that these attempts will never close off all of the seams.
I'm most uncomfortable with your use of the term "universal system" for this reason. We have axiomatic systems that define truth values for a huge variety of statements, but they do not touch those statements that the axiomatic system cannot assess--which by the Incompleteness Theorems are always there (at least if we choose to avoid logical inconsistencies).
Similar to the child, all of humanity does not know what the cards in the deck of mathematics are, nor do we know how big the deck is.It's actually worse than that. The Candyland example really breaks down in a sense, it really just being a metaphor to give a sense of what's going on here, and that's hardly the point. We are actually in a situation where not only do we not know that, we also don't know what kinds of cards we'll decide we want to add to the deck until we face those questions, and we're in a situation in which we know that whatever cards we choose, literally no matter what, we aren't guaranteed to be able to "finish the game."
Don't get too caught up on the metaphor, though. It's just an intuition pump.
Nor do we know who 'shuffled' the cards.Whoa. Just whoa. I know where this is going, and whoa. Stop.
First, this is the wrong question to be asking, and second, yes we do. "The cards" in this case, really, are the truth values assigned by the axiomatic system, but those values are determined by the choices of axioms and logical framework, which are ultimately choices we have made and continue to make.
This points to a rules-maker who is outside of the boundaries of humanity who created these simple and universal(transcendental) truths(what you call axioms) such as 1=1.No it doesn't. First, I just said why it doesn't. Second, inventing a "rules-maker" is choosing an axiom (meaning you choosing an axiom, you being a person, just like all the other axiom-choosers).
I don't call these things axioms. "Axioms" is the word for these things. I use that word, but it's not the same as your connotative implication. Also, "axioms" aren't "universal(transcendental) truths," they are baldly asserted statements that we agree are sufficiently parsimonious and basic to be getting on with getting started, i.e. to be willing to baldly assert as sufficiently self-evident*. The asterisk here indicates a constant willingness to reassess them at a later date: Cf. the Peano Axioms predicting the axiom of infinity but being unable to handle it and so the Zermelo-Fraenkel axioms of set theory taking over the job.
This points to an ordered universe in which laws and rules are discoverable, because if 1=3 sometimes according to some axioms, and 1=red in other axioms, then the universe loses all meaning.Incredibly, you missed my entire point, then. It doesn't. It points to an ordered axiomatic system that humans have developed in order to attempt to make sense of the universe we live in. The point isn't that the universe "has meaning," it's that humans, as thinkers, can find meaning in it, which as often as not means defining for ourselves the constructs (languages, as it turns out) in which meaning resides. The central point is that we invent these logical systems and language to attempt to understand what we observe and to communicate those attempts with other people. The logical systems are not the universe itself.
Incidentally, under some definitions, 1 does equal 3 (e.g. in any algebraic system over the field with two elements). "1=red" is just silly--a category error, to let you know.
Again, thank you for your time and your comment.