Math doesnt allow you to use raw concrete reality(reality/physical matter/observation of physical matter) to rebut or justify an axiom. This applies to definitions as well.

This arbitrary rule where you canot use raw concrete reality to rebut or justify an axiom in math effectively kills any kind of alternate math where its referents is grounded.

any attempt to create a "grounded math" that relies on physical objects/raw concrete reality for its truth gets completely locked out.

Math is used to model reality. if they kill off grounded math with arbitrary rules they effectively control perception of physics and censor anyone who attempts to ground it out.

You attempt to make a grounded math and youre locked out. You basically have to make a break away math civilization which is near impossible from how the system is set up and how people are indoctrinated into it.

They reversed cause and effect. Theyre mapping maps onto maps instead of mapping reality

You would never calculate your rate of speed and how long it will take you to travel 3 miles at that speed in the same math sentence. That isn't how our brains work, and that isn't how math works. So why, then, do we say that stupid viral math problem is ambiguous?

It's not. The only way to get anything besides 1 is to allow a computer, who can't read fractions, to calculate for you. Yet, we are treating 9 like it's an acceptable answer. It doesn't exist in reality as a scenario, and it's not how we do math.

And when you plug the problem into a calculator, it uses obscure notation to combine the sentence into two individual questions, (the equivalent of calculating rate of speed and distance at that speed in the same math sentence), which encourages and exploits bad math habits, disconnecting people from the intuitive notation of basic algebra and how it relates to the real world.

What is going on here? Are we just letting the computers think for us? How is this acceptable to the science/math/physics community? Do equations not have their own context anymore?

Seeing the difference between these two things and knowing that one is nonsense is how we interpret ambiguity in a very real sense in the real world. If we insist upon 9 being an answer, we are giving up an ability we have to decipher ambiguity IRL.

Separating these two is massive deception.

Separating metaphysics from math allows self referential delusion. If you don't separate them, it exposes a massive fallacy: mathematical groups, zero, and infinity have no concrete referents. Logic calls your starting foundational multiplication operation a fallacy because mathematical groups are untethered from raw concrete reality.

This is not just deceptive but a logical fallacy. Consistency and utility can still work and be found inside of a false axiom. And it doesn’t matter whether math claims to model reality or not because we treat math as if it models reality (physics,engineering)

TLDR: When the field of mathematics claims that formal proofs don't need metaphysical grounding, they can hide the fact that groups, zero, and infinity have no concrete referents. That's deceptive.

So the idea that a "set" is a thing in and of itself such that it can even be empty means that a "set" is more than the things in the "set" collectively considered. Without this concept of an "empty set", if we just considered a set a collection of things, what would math be missing and would calculus and other such things still hold?

Is there an area of math from which all other areas can be considered special cases? It seems like math has so many branches of specialization, but is there an area from which all other areas can be deduced or that is most encompassing that has the most prerequisites? For instance, if one studies topology or differential geometry, does that entail understanding virtually all other areas of math as special cases?

Thanks,

I’ve just started learning logic, and I understand that valid inferences come from rules of inference, one of them being modus ponens. But what I don’t understand is why we accept these rules as valid in the first place (the same question applies to the others). I know it would be circular or pointless to try to prove them using logic itself, I started this 1 week ago, so experts of Reddit, bear with me.

I'm no mathematician so maybe I misunderstand but it seems to me like something in zfc might be arbitrary. I think I understand the concept of a set, where the quantity of 5 is a set of 5 thus numbers are sets. However, let's take the idea of an empty set.

Now my understanding of what an empty set is, is a box of chocolates w/o any chocolate. It's purely a mental overlay of reality when we say the box is an empty set. But the question is does nature deal in empty sets outside of the one's invented by our minds?

It seems to me that if mathematics may be said to exist in some capacity, such as if math is merely the laws or rules of existence, that it would not be meaningful to have an "empty set". As that's saying there is something ontologically more to a set than it being the collection of things in a set. In one instance your saying a set is a thing in and of itself, in the other "set" just refers to the things collectively considered such that an absence of the things leaves you with no set rather than something that's empty.

This "something" that is called a "set" such that it can even be empty seems like something that has no ontological reality and things that have no ontological reality can't be said to exist.

I guess the question is if mathematics exists mind independently can an empty set actually exist also or is it merely invention and if so how can the concept be said to be a "foundation" of math? Thoughts?

Here “observer” means a role inside a formal model: the place where distinction becomes part of the system itself.

The conditions below are proposed as a minimal formalizable scheme. Each of them should allow a stricter expression, and removing any one of them should change the content of the model. The observer appears as the wholeness of the process: the conditions of distinction are held together as a single act.

Below are three minimal structural conditions.

1. A positional condition.
The distinguisher and the distinguished should not coincide. If they collapse into the same point, the act of distinction loses its content: there is no way to draw a distinction, or a boundary, between two coincident positions.

2. A trace.
After the act of distinction, there has to be some recognizable difference: in a state, a record, a correlation, or some other trace. If there is no such difference, the observation is indistinguishable from no observation at all.

3. Self-closure.
The criterion of distinction should be internal to the structure. If the distinction depends only on an external arbiter or external observer, a regress appears: that external observer now needs another basis of validation.

If any one of these conditions is removed, a different kind of failure appears.

Without the positional condition, there is collapse into identity.
Without a trace, there is an act with no distinguishable result.
Without self-closure, there is an infinite regress of grounds.

These three failures seem different to me. None of the three conditions appears to follow from the other two: each blocks its own way in which observation can break down.

In that sense, the structure is similar to a Borromean link: three elements work only together, and removing any one of them breaks the whole. This is not meant as a proof, but as an image of minimality: the observer is not a separate entity added on top, but a bundle of conditions under which distinction becomes stable and checkable inside the structure itself.

Then an “observer” can be understood not as an original subject, but as a formal role: a structure with positional separation, trace, and an internal criterion of distinction.

I’d be grateful for any criticism of the idea.

I am self-learning Mathematics. Here is one question that arised when I was learning about Axioms.

Are there infinite possible theories in Mathematics as there can be an infinite combination of Axioms as long as the Axioms and the whole System is consistent and don't contradict each other?

So this means that Mathematics knowledge is infinite?