Vx. Princess "size_t queen" Grace 
No nuance. Choose.
Math is discovered.
Math is invented.
Poll ended at .
twilight
☁️your local angel☁️@BestGirlGrace finally proper discourse
Sherclod Holmes@BestGirlGrace incredible results so far
@wallhackio i think this is the most even split i've seen on here
🇹 Ti@BestGirlGrace I found math under a rock once
@The_T what if someone put it there
@BestGirlGrace who cares, I discovered it
Datenegassie@BestGirlGrace @The_T finders keepers
Kaito@The_T @BestGirlGrace was it delicious
marabilles, smala libre@BestGirlGrace
Too complicated for a monday morning 😑
Too complicated for a monday morning 😑
Blippy the Wonder Slug 🇩🇪
usmu 🍋🏳️🌈🤟@BlippyTheWonderSlug @BestGirlGrace
Indeed, math is discovered based on founding principles we invented.
DMTom@BlippyTheWonderSlug @BestGirlGrace agree, this, or c) I, honestly, don’t know;)
and there’s the unreasonable effectiveness of it, that is mystifying either way one answers the poll;)
and there’s the unreasonable effectiveness of it, that is mystifying either way one answers the poll;)
Andrea (Drea) Tamar PinskiNeither, math is described.
Sewer Pirouette
bencourtice@BestGirlGrace maths consists of abstract logical concepts dreamed up by humans. As such it is definitely invented, a very important invention in human culture.
Travis BriggsMath exists only in the Realm of Thought, where we reduce experience to abstractions. In some sense, mathetmatics is the root/ultimate abstraction.
Mathematics cannot be "discovered" because it does not "exist" in any meaningful way outside of human thought, which itself does not have any tangible form.
@audiodude @BestGirlGrace yeah that's what I said ;) but you said it better
peterF@BestGirlGrace
Math is based on integers. Integers are a human construction.
Math is based on integers. Integers are a human construction.
Patch You Up@PeterF @BestGirlGrace *Our understanding of math is based on integers. We can describe the natural logarithm as approximately 2.718, but in reality that is just a way to represent it in our minds in a base-10 system. The parts of math that most people encounter on a daily basis are integer-based, but much of the more complex areas used to explain reality are conceptual or make use of non-integer descriptors.
(Apologies for the wall of text in reply to your short comment)
(Apologies for the wall of text in reply to your short comment)
@Jumpmed @BestGirlGrace
No problem.
Pi and e among others cannot be expressed as a ratio of integers, but are used extensively in maths ( I use the UK maths as opposed to the US math)
In quantum mechanics 'reality' is hidden behind 'imaginary numbers'.
Physics is best by 'singularities' e.g. black holes.
It seems integers are just a simplification humans need for understanding.
(These are my wild imagination, I have no proof!)
Marcus Adams@BestGirlGrace Math is just what we call it, but what it actually is, is how the universe works. The universe doesn't obey our rules, we didn't impose the mathematical formulas that describe how things work, we just discovered and wrote them down.
Lethe@BestGirlGrace The premises are invented, the conclusions discovered.
Louise 🏳️⚧️@BestGirlGrace I would say that mathematics is a language so it is invented, but what the language describes is mostly discovered
Mark Whybird@xorlou @BestGirlGrace Yes - I see it as a language and a series of techniques that we *invented* for rigorously *discovering* and describing certain fundamental truths about the universe. But the question said we can’t do nuance, so I went with “discovered” to refer to the more fundamental of the things covered by the term “mathematics”.
Jane Doe@BestGirlGrace Mathematics is a conceptual framework that exists within a human mind. To me, all concepts are inherently distinct from the physical phenomena they describe. Ergo, mathematics is invented.
fool@BestGirlGrace Quantity, together with all the emergent properties thereof, is a natural phenomenon and is therefore discovered. Tools operating on those properties, such as notation and terminology, are arbitrary attempts to describe those phenomena and are therefore invented.
Is mathematics the study of quantity, or is it the study of tools for characterizing quantity? A student of anything learns both the tools themselves and that which the tools manipulate.
@BestGirlGrace Some of those sentences ended up a bit redundant due to how many times I rewrote them, but I hope the point came across.
@BestGirlGrace Even the finest and most perfectly justified taxonomy is a model. The inner and outer boundaries of that model were chosen based on simplification, approximation, abstraction, and other creative acts on the part of observers, for the sake of those observers' goals.
Nonetheless, the model describes some thing whose existence arose independently of the observer. Even though the concepts of "thing," "existence," "independence," "observer," and "concept" are all components of models!
@BestGirlGrace Ontology gets really weird and hard to talk about when you push it to its limits like this!
@BestGirlGrace I am pretty sure that I don't know nearly enough Sanskrit to engage with the most developed thoughts on this topic.
AndrocatQuantity is most decidedly not a natural phenomenon.
This is because quantity is a product of Type.
Type, e.g. "a horse" is a human invention along the lines of metaphor.
In reality, every four-legged hoof-haver is a unique being, and certainly not some "exemplar" of some "type".
Without Types, there is nothing to count. Everything is unique. 1 is the only number, and that too is superfluous.
@androcat Quantity is evident elsewhere than in what our models abstractly deem countable. Distance, for instance. To the extent that this one and that other one are not the same one (and if we can meaningflly speak of uniqueness, then we can on that same basis also speak of distinction), then some distance separates them, and that distance has quantity.
(@BestGirlGrace if this continues should we refrain from tagging you?)
Again, the same applies. These things are made countable through mental metaphors.
Ultimately every point of our worldly topology is unique. They only turn into "distances" by metaphorically asserting that "distance" even makes sense.
You'll see in ancient texts that the focus was on the way, the path, the road.
And similarly for time. In ancient speech we were using ordinals for time, because each moment was unique, and made sense only in context.
And even that ordinality was an abstraction performed solely to make the unique into something ennumerable.
When I say the uncountability is fundamental, this is historical fact. We didn't always have the technology required for enumerating these things == arithmetic was invented, and its invention required deep changes in how we speak of and conceptualize things.
@androcat @BestGirlGrace I didn't know Zeno of Elea was on this web site
You can literally track how we invented this stuff by how language changed.
Starting from Types will end up in absurdity, because all of a sudden the specific fish you caught is interchangeable with the one that got away.
That isn't how the world works.
But it is how the game we invented works.
(All logics are essentially games. Logicians understand that, and do not take them overly seriously. After all, almost every logic will contradict almost every other logic)
To put it in a different and more obvious way:
Types are subtractive categories. Actual entities have location, identity and all manner of uniquely identifying traits.
These are subtracted to make them fit the Type.
This loss of information is unrecoverable.
In other words, the Type is most decidedly Not Real.
Even if it means you have to accept that "Horses do not exist".
Countables do not exist.
But we can make games that have countables, and we can sometimes make use of such games for organizing how we think about reality, because sometimes the individuality of entities, while undeniable, isn't relevant to what we are doing at the time.
But only a fool would assert that the abstraction is real because it has utility.
Utility is perpendicular to truth.
@androcat @BestGirlGrace If you're saying that entities are real and that they are identifiable, then makes them cardinal. You haven't asserted the nonexistence of types at all - rather, you're asserting that there is exactly one type, "entity." And because there's still a type, that brings with it countability.
Go back and re-read everything until you understand it. It's in there.
I have absolutely asserted the irreality of types.
And I have explained why "but types have immense utility" doesn't mean "types are real".
We literally have this entire development as historical fact.
Invention of math == historical fact.
Your viewpoint only makes sense in an ahistorical context, where you assume math as fundamental.
It smacks of mathematical platonism, a much better candidate for Zeno-like folly.
@androcat Leave my argument out of this. I'm talking about your argument. You're the one who showed up suddenly.
You assert that countability is an attribute of types, and types are an element of a model rather than of reality.
However, you also assert the reality of entities; that entities are not a model, but the true reality which models attempt to describe. (Seems to me like it's also a model, but I'll play along.)
You have not shown why countability is not an attribute of entities.
@fool
I haven't explained that because it is rather obvious.
If what you're counting is not "stones" but unique objects, with location and identity, the only number you need is 1.
As for "entities", it's a regular translation of the sort of Object that includes the animate. It's a philosophical term that refers (as much as it is possible to refer to such) to parts of objective reality.
If it is animate, it tends to be called a Being and if it is inanimate it tends to be called an Object. With entity I attempt to cover both.
You seem to be in danger of conflating two completely different things:
The sort of things that may exist.
and
The system of language we are forced to rely on when talking about things that may exist.
The latter isn't capable of working without Types, so I have to rely on your ability to construct the correct meaning, even though I am constantly forced to use Types in the language.
You have to imagine a world where it would be possible to uniquely label every single object.
Again: Utility is not truth, and in this case utility is the enemy of truth.
It wouldn't be possible to maintain much of an economy in such a world, for instance.
Type is an illusion without which we could not build economies.
Chris@androcat
you are Bertrand Russell and I claim my note which is deemed equivalent to (but not the same as) 5 units of currency
I'll get your unique currencies to you as soon as I discover which ones were intended.
This may take a while.
@androcat @fool @BestGirlGrace herein lies the problem: can you find five separate pieces of the same currency that are all the same in every respect? and then, if you can't, how do you expect me to believe a certain note is somehow equivalent to those five non-identical things? if indeed you can meaningfully classify each of those things as a thing?
You're confusing convention and ontology.
I am specifically pointing out that over the course of history we have invented types and countability and other such conventions.
And now, we have things that really only make sense on the basis of those types.
They are dependent on those inventions.
But they aren't real things as such.
@androcat @fool @BestGirlGrace possibly. i thought russell's argument was that counting real things was nigh on impossible because you don't have two the same?
Well that's correct in the prehistoric sense.
Countability relies on abstraction.
But we have all learned our numbers and arithmetic, right? And we live in a world that could not exist without the utility derived from all that abstraction.
I don't deny the utility, I am just pointing out that "ubiquitous" doesn't mean "foundational".
George B@androcat @fool @BestGirlGrace
When you get into particle physics though, you get particles that are not distinguishable which meant that "Type" is effectively a name for a collection of fundamental properties that they have
However, Physics is a model of the world, not the world itself.
And in the process of "finding things that successfully reproduce observations", physics makes a whole host of claims which are not actually true, such as abstracting away friction, modelling things as inelastic and point-shaped, etc. etc.
Physics doesn't need identity, and indeed is based on iteratively discarding identity again and again.
And then physicists are surprised when all of a sudden they come up against limits to knowability, such as in Quantum mechanics, with its various Uncertainties and "Spooky action".
Or, put more succintly: The map is not the territory, and if you have made your map out of countability itself, you should not be surprised if the map shows no uncountables.
@BestGirlGrace
Math is two things:
- A set of notations for describing relationships;
- A set of techniques for reasoning about those relationships.
Many of the relationships we describe and reason about are discovered, as are relationships-between-relationships, but the notations and techniques are necessarily invented.
@ShadSterling @BestGirlGrace I think Math is three things: the two you mentioned, and the relationships themselves. The relationships themselves, in my view, are discovered, and the language invented, and the techniques in between are a mostly invented but heavily intertwined with the discovered relationships (to the point where a few of the techniques are merely expressions of the relationships, and therefore those few might count as “discovered”.)
@ShadSterling @BestGirlGrace A simple example: the Pythagorean theorem itself is a fundamental fact (i.e. discovered); the way we express it and prove it (or not), and the way we use it to calculate things, is entirely up to us (i.e. invented). The underlying logic of those calculations, however, are intrinsic parts of the fundamental fact (i.e. discovered).
All three things mentioned (the relationship itself, the language of expression, and the surrounding techniques) can definitely all be called parts of math. The either/or of the question has been useful because it has been very successful in achieving some really good discussion, but as a logical argument it is a false dichotomy. The actual answer is “both”.