Why 1 + 1 does not equal 2

[Hans-Werner Hammen]

Neither will three wolves merge into one, nor will strain one wolf into three, this is correct. The wolves are very real, the number OF wolves is imaginary though, it, does not exist - is made up FROM/ABOUT the very real wolf and the wolves, respectively.
Oftentimes, when someone insists on taking and telling numbers and names "for real", it is merely (there exists BUT) the utteration of a misunderstanding:
You might be referring to the symbol "Symbol" (= object-ization of a thought) in the Semiotic Triangle, but i am referring to the symbol "Reference" (= abstract object = thought) in the Semiotic Triangle. Kind regards from GERMANY!

[Atla]

Indeed, the containers are veeery real. They are the outside-brain cause at the fabrication of abstract objects FROM/ABOUT them.
The number OF containers is no-thing made up, is imaginary, is an inside brain effect FROM/ABOUT them veeery real containers.
Abstract object = imaginary, can also be called observed-ness or observed-HOOD, one might be more familiar with the symbols "awareness" or "property"
--> I assert that not even the most precisely measurable property does exist.
I assert a standard for "to exist" as: is observable by us or by a device"

Containers are also practical made-up abstract objects, we project these containers onto the 'outside-brain' world. They can't cause anything.

[Hans-Werner Hammen]

I respectfully disagree. A real object is also called "Referent", and an abstract object is also called "Reference". The containers are real id est a causal agency at the fabrication of abstract objects such as numbers.
References are merely made up FROM/ABOUT Referents - sure is, FROM/ABOUT Symbols, assertions of References that is, too.

[Atla]

I respectfully disagree. A real object is also called "Referent", and an abstract object is also called "Reference". The containers are real id est a causal agency at the fabrication of abstract objects such as numbers.
References are merely made up FROM/ABOUT Referents - sure is, FROM/ABOUT Symbols, assertions of References that is, too.

And how do you know where one real object (referent) ends and another real object (referent) begins? You don't, you simply project references, for example containers onte the natural world, in order to divide it into separate objects.

[Hans-Werner Hammen]

I do not even move the containers. I move towards them, I observe them, I count them.

[Hans-Werner Hammen]

Containers are also practical made-up abstract objects, we project these containers onto the 'outside-brain' world. They can't cause anything.

I respectfully disagree: I presupposed that the symbols "wolves" and "containers" each symbolized visible objects.

[Papus79]

Neither will three wolves merge into one, nor will strain one wolf into three, this is correct. The wolves are very real, the number OF wolves is imaginary though, it, does not exist - is made up FROM/ABOUT the very real wolf and the wolves, respectively.
Oftentimes, when someone insists on taking and telling numbers and names "for real", it is merely (there exists BUT) the utteration of a misunderstanding:
You might be referring to the symbol "Symbol" (= object-ization of a thought) in the Semiotic Triangle, but i am referring to the symbol "Reference" (= abstract object = thought) in the Semiotic Triangle. Kind regards from GERMANY!

My question then would be - what do you do with circular geometries - when you have three 120°, four 90°, or five 72°angles. You can derive then an equilateral triangle, square, or pentagon. Whether there are three, four, or five equal angles seems to have meaningful consequences, in particular when you get to six you get hexagons - something that shows up in a structural context in all sorts of odd places ranging from insect nests and basalt columns to Saturn's poles. Getting even more grounded you have organic chemistry where quantity of oxygen, carbon, and hydrogen atoms in chains and functional groups yield very different chemical properties.

Can you maybe run with these examples and say a bit about how they're real but the numbers aren't?

[Hans-Werner Hammen]

You are talking about very real symbols OF References.
For an example, no where does an angle exist.
An angle is a Reference made up FROM/ABOUT a Referent (thing) or a symbol (drawing on a paper)

Let me ask you this: Is a law real or is it imaginary?
What is very real of a law?
My question is admittedly rhetorical: All that is real, it is
-- the Referent, the things we discover and are (as scientists or other so called law makers) making up laws FROM/ABOUT
-- and is the symbol ie the things we (as scientists or s.a.) create on this occasion, namely the utteration OF the law

The law as such is imaginary. Is NEITHER discovered NOR created (invented)
Did you ever read about the discussion about the issue, whether laws are discovered or invented - I assure you they are NOT EITHER.
Any law! Of a game, of legislature, of logic, of morality, of physics

Referents - THESE are discovered,
Symbols - are invented (created)
any utteration of the human thought is called a "symbol" in the Semiotic Triangle (also called world3 by Sire KR Popper)

Kind regards from GERMANY!

[Papus79]

To cut short what would otherwise be a long response - is quantity a referent or a symbol?

I don't have a problem with the suggestion that there are real things, commutable symbols or explanations that we extract, and that the two aren't the same. I'm just getting a bit confused as to what you're saying about quantity.

[Hans-Werner Hammen]

"Quantity" is a written or spoken symbol.
Now, what this symbol symbolizes, this is up to you and to me in the first place, or this is specified by a description (other symbols), which is yet to follow, and on which we are yet to agree or disagree on.

For me, "quantity" symbolizes, in that I always associate it in "quantity OF some-thing"
in other words: "no-thing from/about some-thing" = "Reference from/about Referent" or "Reference from/about symbols"

In other words, for me, quantity as such, it-self, in its own right, in its very essence, is a Reference = an information = no-thing = imaginary = world2, being made up from/about an orginial information source = Referent = world1, or from/about a secondary (manmade) information source = symbol = world3.
In any case, "information is in the eye of the beholder of the primary information source or of the secondary information source".

Sure is: The description above, with all these symbols in it, might have your brain make up the Reference uttered = symbolized as "useless, gibberish" so I suggest that you put the description to a test. Namely as regards the symbols "existence" and "property", "consciouness"
The description wil provide a response or, let us put it mildly, a suggestion, to the question whether existence, property, consciouness exist, as such, in their owen right that is.

IF! we agree to associate quantity, property, existence, consciousness with "OF something" THEN all them 4 symbols symbolize References, iow the imaginary, iow no-thing FROM/ABOUT some-thing. Iow neither of them does exist as such, on their own, in their own right.

Interestingly, my own listing of (symbols of) References has always been received with hostility by both cohorts, namely Theists and Scientists alike (regardless whether Theists or ATheists) which you might understand on the spot when you read the listing below:

First off forgive me for more symbols:
References = abstract objects = imaginary objects = no-thing = world2 (Popper) =

awarenesses, thoughts, feelings, sensations, informations, knowledge, opinion, truth, = the imaginary = properties
= no-thing- made up FROM/ABOUT some-thing

My own, synthesized (artificial) and favorized symbols of References are:
Detected-, realized-, observed-, not(ic)ed-, per-/conceived- -NESSES or -HOODS

Here is my own praeliminary listing of References = possible elements of the existence of some-thing and possible elements of the consciousness of some-body, respectively:

1) All proclaimed sensations, emotions, problems, values (such as beauty and usefulness), ought-, should-, and must-HOODS, relevance, importance and necessity that is; meanings, intentions, purposes, desires-/ wills - and the respective counteremotions. Such as: freedom and captivity, free will and determinedhood, love and hate, appreciation and disgust, bright-NESS and dark-NESS.

2) ALL proclaimed-, measurable parameters in the language of physics: (rest-) MASS, distance, area, space, density, time, velocity, acceleration (gravity is an example), force, impulse, pressure, power, ENERGY, temperature

3) ALL proclaimed numbers, measurable constants, all Axioms, Fields in the language of physics.
And all LAWS - of games, legislature, AND of logic, morality, physics!

4) ALL proclaimed gods - such as YHWH, Jesus (THE) Christ, Allah

References = observed-hoods = properties are not detectable let alone observable - they can only be
made up and be
expressed = proclaimed = asserted = determined = defined = symbolized = material-ized = object-IZED = FAKED
FROM/ABOUT some-thing iow all that is detectable if not even observable.

A so called measurement of a property is but an operation with some-thing:
At no point during a measurement is a property detected let alone being observed.
All that IS detected if not even being observed, it is some-thing. The smallest detectable elements of some-thing are subatomic particles.
The so called Higgs-field is merely proclaimed FROM/ABOUT the detectable = some-thing and elements of some-thing respectively. The Higgs field per se is imaginary, does NOT exist, it is, as such, a Reference, iow made up FROM/ABOUT all that DOES exist.

[Atla]

Containers are also practical made-up abstract objects, we project these containers onto the 'outside-brain' world. They can't cause anything.

I respectfully disagree: I presupposed that the symbols "wolves" and "containers" each symbolized visible objects.

That's factually wrong, your own mind automatically divided the visible world into objects. Okay maybe this process shouldn't be called abstraction, but neither is it a feature of concrete reality.

[Hans-Werner Hammen]

That's factually wrong, your own mind automatically divided the visible world into objects. Okay maybe this process shouldn't be called abstraction, but neither is it a feature of concrete reality.

Indeed, you are factually entitled to call whatever you want on the assertions of mine.
Which has no bearing on the following, namely that
I am factually founding my assertions on- = my assertions are factually caused by:
Some-thing, observable that is, namely my organs of detection, my brain, my organs of exertion, and the very symbol picture called Semiotic Triangle.

On the other hand, how do you account for an ominous thing that you call the mind? I mean, did you not just assert that my mind be doing something? I respectfully yet frankly disagree, on this occasion. I assert that you are factually referring to my brain. Nobody has ever factually shown me a mind, let alone factually measured a mass from/about the mind. Thus, I assert that the mind does not exist factually. The mind is rather, factually, no-thing (imaginary also called inside-brain effect) momentarily being made up (fabricated = faked) BY some-thing (also called the brain) and FROM/ABOUT some-thing (all that is around the brain, via a perceiving process, first and foremost my own body).
If you assert that the mind be per definition existing, in that it is being symbolized = asserted all days long, THEN, by the same assertion of standard, Winnie the Pooh, the tooth Fairy and the powerful QuadrUnity of the 4 Great Big Zampanos DO exist, just bcz I assert them, for the sake of argument.

If you assert that your mind ought, should, must be existing, in that you be feeling it, then I ask you: Can you
- factually -
see, hear, smell, taste, feel your mind?
And if you answer that yes, you do feel your mind, then I will remind you that
- factually -
any feeling is an awareness FROM/ABOUT some-thing that you (in other words somebody = some-thing) are touching and that is touching you, respectively.

[Hans-Werner Hammen]

Re-considering the original question, is the answer which we can deeem accurate and correct not just short and quite sobering:
1 plus 1 was proclaimed to be two...
iow 1 + 1 = 2 was declared FOR correct...
BCZ someone if not some people who had the saying said so -
and everybody (well not everybody lol) in the common people would agree on this assertion, THEN - and still does, NOW - bcz it turned out to be sooo useful?

Did you know, that more often than not, we can replace the word "true" by "useful" and "truth" by "usefulness" respectively?!

[Papus79]

Did you know, that more often than not, we can replace the word "true" by "useful" and "truth" by "usefulness" respectively?!

That's pragmatism, you see hard differences of opinion on display in the original Sam Harris / Jordan Peterson debate when they mired on the definition of truth.

I try to keep a foot in both worlds because on one hand, keeping inventory of what seem to be independent truths keep us from having social realities rip free and raining down shards of glass (and worse) when contact with the unforgiving is ignored. There's another kind of evil that can happen when we get so externally objective that we jackboot the subjective as well as the needs of the individual along that line - ie. a culture that can't cohere, and we're seeing a bit with our corporatist neoliberalism of the moment that's aiming it's futures toward neo-feudalism.

So far I haven't been able to really agree or disagree with your assessment that numbers aren't 'real' as 'referents' because I still don't know where your distinction lies between containers (most easily exemplified by units that may reduce to parts but not more of the same unit) and number of containers. I think you'll be making a much more powerful case when you can give that a good description.

[Hans-Werner Hammen]

No-where do we discover numbers. All that we discover on this occasion is some-thing, Referents, that we attribute numbers to and is symbols, some-thing.
I am yet to understand your containers. To me containers are some-thing, I see them and I attribute numbers to them. I can manifest my reference symbolized "number" in that i paint a "1" onto the first container I see, and a "2" onto the next and so forth. The number as such is always imaginary, is a Reference.