The idea that numbers really, actually exist as abstract objects is often a staple of things like Christian apologetics and more Platonic/Schopenhauerian philosophies. I think, however, that this is false.

The idea generally goes that mathematical objects exist; mathematical objects are abstract; and mathematical objects are independent of intelligent agents. Essentially, if humans were extinct then these abstract mathematical objects would still 'exist'. There is, in essence, a transdimensional holding pen of numbers which isn't spatiotemporal. Numbers, under this paradigm, are discovered and not invented.

However, I can quite easily define a mathematical set and label it. If I label a set as the "set of all Huragok". A property of this set is that there is an individual Huragok named Virgil, so whenever we speak of a set of Huragok then Virgil is necessarily included. For any existing Huragok, also, there is another Huragok which constructed it: the constructor.

The constructor of Virgil, however, must also be a Huragok to fit the definitions involved in the set. So for every constructor, there is another constructor. So:
- Virgil
- Virgil-constructor
- Virgil-constructor-constructor
- Virgil-constructor-constructor-constructor
- So on, so forth; we have essentially defined a never-ending train of Huragok.

Now, I'm just making this up (well, Bungie made it up). It was pulled out of somebody's ass. We could've defined two Huragok as necessary for the construction of a single, resulting Huragok, and we'd see a two-stemmed branch extending from Virgil. It's entirely up to me what defines a mathematical set.

Are the Huragok an invention, or a discovery? Do Huragok exist in their own abstract transdimensional way? If the answer is yes then any arbitrary set of elements I define also necessarily exists in their own abstract, transdimensional way. If the answer is no, then numbers too do not exist.

I have literally just demonstrated the process involving the creation of numbers, and all we need to do is alter just how we've defined the set and the elements within. Changing it from a set of Huragok to a set of integers, and changing Virgil to one and constructor to addition (denoted by +). So we get:
- 1
- 1+
- 1++
- 1+++
- 1++++ (ad infinitum)

Counting is just the process of streamlining the informational transaction of additions/increments to the original. So it just becomes:
- 1
- 2
- 3
- 4
- 5

This is arbitrary; I've defined this into existence. That is the entirety of mathematics, rules and definitions and axioms. If we're going to say that this exists, then all forms of rules and definitions exist too--such as the rules of blackjack. Following the rules of blackjack just means you're doing blackjack, and it's the same with mathematics.

Even assuming the existence of numbers in this Platonic way, how would you even demonstrate this? There is no metaphysical three which governs the threeness of a collection of oranges. In the same way the empirical togetherness of the properties of oranges define the substance of an orange, it is the same with numbers and a collection of oranges; three is an empirical property of an orange and another orange and another orange.

Math is literally just a conceptual framework for managing information.

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The idea that numbers really, actually exist as abstract objects is often a staple of things like Christian apologetics and more Platonic/Schopenhauerian philosophies.

Where in apologetics or Plato's metaphysical ramblings do either say that numbers are real objects?

William Lane Craig, specifically, for Christian apologetics.

Stanford Encyclopaedia of Philosophy:

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects' perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.

Oh, I misread your title. I'm not sure what relevance this has with apologetics. The very fact that you can make up this example shows that numbers do exist as abstract objects, at least to some degree. Formality of mathematics doesn't imply independence from an agent; the very fact that something is contingent on being defined by an agent makes it abstract. I can give you a proof of a theorem, completely brand new, and even though I just made it up it and gave it definition it will still be true when I am dead, and it was still true before I existed. Was your example correct before you existed, and will it be correct after you die?

P.S., you should read some Douglas Hofstadter. For this subject in particular, this book.

I'm arguing against the concepts of metaphysics and ontology and epistemology which seek to show the existence of literal objects which simply lack spatiotemporal extension.

Mm. I agree, I guess.

Here's a question: do we exist, as people? Is our personality anything more than the reaction of electrical signals on an incredibly complex grid of receptors, which themselves are just relatively complex configurations of carbon, water, and some other elements, which are themselves just moderately complex combinations of subatomic particles, which are themselves basically complex blocks of hadrons, which are actually just very basic groups of elementary particles?

Because I'm feeling pretty abstract right now.

Tennis, indeed, is an abstract object but only because its empirical properties make it so. I'm not arguing against abstract objects in this sense.

right, but that's all that i was saying, really

if i'm honest, i don't even know what that last sentence means--i think you're just saying that numbers (ones, twos, threes) don't exist in reality, which no one's gonna come out and say

i'm arguing for the existence of the adjectival nature of... numbers, which is their sole function, anyway--they describe quantity, nothing else

so... we have entities with demonstrable oneness, twoness, etc.
in the same way that knives have sharpness and rocks have roughness--objectively, realistically, regardless of our perception

in my opinion, only a solipsist or hard nihilist could deny the inherent qualities (and quantities, which--indeed, part of my argument posits that quantity is in itself a single type of quality) of ontological entities as well as conceptual or abstract entities--but, obviously, nothing beyond the healthy human's perception--you shouldn't be able to observe gamma rays, for example, but we still know they exist

and you have to use words like "entity" in discussions like this--"object" implies... singularity, but an "entity" can contain many objects and still be one holistic thing

also, no one's gonna argue that numbers are special, either--i think that was just a grabber

i'm arguing for the existence of the adjectival nature of... numbers

Well in that case I don't disagree. Prime's formulation of your position on the ontological nature of numbers wasn't exceptionally obvious, and I just felt like laying this out as a sort of "foundation" for thinking about numbers and then move from there. I wasn't explicitly criticising what I thought was your conception of the philosophy of mathematics.

just thought i'd set it straight then

i would say you'd be hard-pressed to find anyone who thinks numbers are anything more than adjectives, or properties, but apparently william lane craig does?

The problem is that anybody not well versed in philosophy (specifically epistemology and ontology) could easily be taken in by Craig because it seems reasonable enough on the face of it.

Not to mention, Platonists and other substance theorists tend to go batshit insane when you disagree with them >.> Better to keep their numbers thin.

Quote from: ⱭAS ᗺ00T x2 on February 05, 2015, 02:15:22 PM

I'll be honest, this is the kind of philosophical study that just makes me question when it will ever pertain to every day life and just walk away.

doesn't it matter whether shit exists or not?

Yes and no, depending on the subject. This is definitely a no.

That's funny Das, considering it's based on a discussion we had with Verb ages ago.

What was that discussion?

Quote from: Verbatim on February 05, 2015, 02:22:26 PM

Quote from: ⱭAS ᗺ00T x2 on February 05, 2015, 02:15:22 PM

I'll be honest, this is the kind of philosophical study that just makes me question when it will ever pertain to every day life and just walk away.

doesn't it matter whether shit exists or not?

Yes and no, depending on the subject. This is definitely a no.

It literally comes down to a question of what constitutes truth.

Disagreeing with my assertions necessarily leads to a non-empirical, non-naturalist form of epistemology.

one of the caveats of being a philosophy student--excessive jargon confounds the uninitiated

he's basically saying that anyone who disagrees cannot account for their assertions, because there's no empirical basis for their claims beyond what is posited to be axiomatic, or unquestionably true

you got it

it matters, in meta's case, because anyone who makes axiomatic truth statements like that can also make axiomatic truth statements about other, bigger things, as well--like the existence of god, for example

i think the idea of an unquestionable truth simply rubs meta the wrong way

All of our letters or written anythings are just bullshit. We look at funny shapes and lines and pixel arrangements that have meaning only because we've given them meaning.

Quote from: Kupo on February 05, 2015, 03:33:38 PM

All of our letters or written anythings are just bullshit. We look at funny shapes and lines and pixel arrangements that have meaning only because we've given them meaning.

this is just too rich, coming from one of the most pedantic users i've ever met
80% of all arguments (that you've levied against me, anyway) were based on semantics

unless i'm thinking of naoto
you're basically the same person to me

That's completely irrelevant and didn't even reject my central claim.