Why 1 + 1 does not equal 2

Discuss any topics related to metaphysics (the philosophical study of the principles of reality) or epistemology (the philosophical study of knowledge) in this forum.
User avatar
Sculptor1
Posts: 7087
Joined: May 16th, 2019, 5:35 am

Re: Why 1 + 1 does not equal 2

Post by Sculptor1 »

baker wrote: December 8th, 2020, 11:34 am
Sculptor1 wrote: December 8th, 2020, 10:52 amOrange A and Orange B. Make Orange A and Orange B. Since Orange A = Orange B is FALSE.
If you do this, you're not counting to begin with.
We're talking about counting. Counting requires deciding what your unit for counting will be.
WIth you I feel like I am banging my head against a wall.
I shall cease
User avatar
katarsis
New Trial Member
Posts: 1
Joined: December 12th, 2020, 5:23 am

Re: Why 1 + 1 does not equal 2

Post by katarsis »

Addition is defined in Peano's Arithmetic as following: ( in Wikipedia : Peano_axioms#Addition )

a + 0 = a
a + S(b) = S(a+b)

If you apply these rules to the symbols "1+1", you get:

1 + 1=1 + S(0) = S(1+0) = S(1) = SS0.

The symbols "SS0" can be represented as "2". In fact, in the core axiomatization for arithmetic (PA), we don't even use the digits 1,2,3,4, ... We just repeat the symbol S. So, "3" is represented as SSS0, meaning the third successor to zero. The logic sentence "S0+S0=SS0" is true in the model of the natural numbers and every other nonstandard model of PA arithmetic. The physical universe is indeed not a model of PA.
Fellowmater
Posts: 77
Joined: November 23rd, 2017, 11:12 pm

Re: Why 1 + 1 does not equal 2

Post by Fellowmater »

Thomyum2 wrote: December 8th, 2020, 1:31 pm Everyone's making this way to complicated. 1 + 1 equals 2 because it is defined that way, not for any other reason. "1 + 1" means exactly the same thing as "2". These are just two ways of writing the same thing.
TS probably just making it an example to make sense of his point.
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

baker wrote: December 8th, 2020, 9:59 am This is a matter of mathematical notation. If something is measured in the same units, then, for the purposes of calculation, we can drop the units. If, in a mathematical text, no units are given, it is assumed that the units are the same for all the numbers.

We mean
1a + 1a = 2a

and for the sake of brevity, write
1 + 1 = 2
This is pretty much what I was going to chime in with - ie that they're sets, and if you do 1a + 1b = 1a + 1b then it's really not 1 + 1 != 2, rather it's inferred when someone says 1 + 1 = 2 that they mean 1a + 1a = 2a, otherwise if they mean 1a + 1b != 2a and they say it as 1 + 1 != 2 then they're leaving out critical information.

I can't help but think of James Lindsay's 2 + 2 never equals 5 a bit here. At that level he's correct.
Humbly watching Youtube in Universe 25. - Me
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

I get the conflict though - ie. no two things are identical down to an atom, the most common places where things are exactly the same are man-made measurements as well as currency.

Maybe worth probing however - what fixed intuitions are we trying to break?
Humbly watching Youtube in Universe 25. - Me
evolution
Posts: 957
Joined: April 19th, 2020, 6:20 am

Re: Why 1 + 1 does not equal 2

Post by evolution »

impermanence wrote: December 7th, 2020, 12:15 pm Reality is a slippery slope indeed. And assumptions are just that. It seems unlikely that the first math equation we are taught, 1 + 1 = 2, is only correct under a specific set of assumptions that are easily proven false.

I believe everyone reading this can agree that all points in the Universe are unique, that is, each occupies a space that is subject to unique forces. Therefore, each object, no matter how similar it may appear to another, is not similar.

Therefore, how can "2" of anything exist?
Very simply and very easily, by just saying that they can. For example, we can say one of 'this' and one of 'that' equals two of 'them'. See, how SIMPLE and EASY we can say two of ANY 'thing' exists, and/or envision two of ANY 'thing' existing?
baker
Posts: 608
Joined: November 28th, 2020, 6:55 am

Re: Why 1 + 1 does not equal 2

Post by baker »

Papus79 wrote: December 18th, 2020, 9:10 pmMaybe worth probing however - what fixed intuitions are we trying to break?
For one, people not having internalized the basic rules of mathematical notation.

For two, the idea that it is up to us to decide on the unit of counting, ie. that the unit is not a given. If there are beans, apples, oranges, keys, and pens on the table, it's up to you and your purposes how you're going to count them.
If your chosen unit is "things on the table", you'll count all the beans, all the apples, etc. and add up the number.
If your chosen unit is "apples", you'll count just the apples.
If your chosen unit is "red apples", you'll count just the red apples.
If your chosen unit is "unique red apples", you'll count just one red apple.
I get the conflict though - ie. no two things are identical down to an atom, the most common places where things are exactly the same are man-made measurements as well as currency.
Exactly. Which is why if one wishes to count things, one has to decide on the unit of counting. Many people seem to be rather averse to seeing this as a matter of choice.
User avatar
UniversalAlien
Posts: 1577
Joined: March 20th, 2012, 9:37 pm
Contact:

Re: Why 1 + 1 does not equal 2

Post by UniversalAlien »

It's all matter of the "observer effect" - If you observe 1 + 1 in this universe
it usually is defined as equaling 2.

But again even in the same universe this is not necessarily constant.

As has been shown in the just passed Presidential Election in the United States.

Here the adding of all the votes in the United States showed that Joe Biden won the election.

However Donald Trump and his followers do not see simple math as a legitimate way of totaling election votes and therefor concluded that unless the votes added up to Trump winning there must be fraud involved.

So, yes, in the universe of Donald Trump and his followers 1 + 1 do not equal 2.
And Donald Trump actually won the election !!!

So therefor in philosophy as in other things, be careful of what you ask for
- As you may get it !

As for me, and probably most of the rest of us: 1 + 1 = 2
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

baker wrote: December 19th, 2020, 6:00 am Exactly. Which is why if one wishes to count things, one has to decide on the unit of counting. Many people seem to be rather averse to seeing this as a matter of choice.
I'm probably bringing up a bit of a political bugbear but our own anti-intellectual movements of the day pretty much show that what one might call 'epistemic sufficiency' is seen as an enemy by those who want power and the right to exercise it, especially if they feel like they need to take that power from someone else. It seems like it's the nature of Darwinian evolution to beat facts with violence, whether that violence is physical, social, or intellectual. Our own subconscious minds always seem to be wriggling out from under those constraints (Gad Saad was talking about this with Tom Bilyeu a while back).

I also learned that if I followed society's rules to me or took them as the rules of polite civilization or good morals that the very purpose of those rules was to run me into the ground, make sure other people had kids while I didn't, etc.. The trouble we're dealing with then is that people tend to be maximalist piglets, especially under conditions of zero-sum competition. Rene Girard's memetic theories touch well on scarcity, how much that deforms our behavior (say a bunch of guys or girls chasing after a 10), it's the differential success in Darwinian evolution that causes people to constantly feel the need to overthrow logic, truth, and reason to replace it with whatever would server them better personally.

I at least am starting to feel a bit more optimistic now, ie. it seems like fewer people really seem to blindly think that humans are these natural little Greek philosophers by birth who want to want to learn as much as they can about the world, all want to get along, and that any violence or 'evil' is just misunderstanding or ignorance. For as much as I can't be bothered to watch them I'm at least glad there have been as many professional sports leagues to siphon some of this competitive orientation off.

To clarify what any of the above meant if it seemed circular or confusing - the person who wants to assert that 1 + 1 = 2, or suggest that any phrase that could have opposite meanings is incomplete as a tool and just hasn't been aligned with what it should measure (like saying 'is this level accurate?' when its in someone's hand), people don't like people who try to assert logical consistency and integrity on the world for precisely the above reasons. It's a big part of why nerds get beat up in school.
Humbly watching Youtube in Universe 25. - Me
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

^^
That third paragraph kinda landed strangely - I'm optimistic that as more people see this clearly we'll start having social rules that actually make sense and account for it rather than having this strange idea that malevolence is caused by ignorance. At the same time I do worry that so much of what the current anti-intellectual movements are doing, like turning people away from watching sports who really can't do much else, is a worrying indicator - I'd have to hope that they find other productive things to do but, humans being human, I'm not sold that they won't just drift farther right and left politically as a result.
Humbly watching Youtube in Universe 25. - Me
User avatar
Hans-Werner Hammen
Posts: 145
Joined: December 25th, 2020, 4:17 pm

Re: Why 1 + 1 does not equal 2

Post by Hans-Werner Hammen »

The assertion THAT 1 plus 1 be 2,
it founds on the assertion of a societal agreement FROM/ABOUT the assertion of a thought, an idea, a presupposition,
that the order of number be 1, 2, 3, 4 and so forth.

From/about a different assertion of an order, namely it be 2, 1, 4, 3 (and so forth)
it would follow an assertion that 1 plus 1 be 3.

Any number is - as such, it-self, on its own, in its own right, in its very essence -
elicited, made up, fabricated, is no-thing (inside-brain-effect = imaginary + non causal = epiphenomenal) FROM/ABOUT some-thing (real, outside brain cause

Any number and any order of numbers does not exist - not as such, not it-self, not on its own, not in its own right, not in its very essence -
it is merely made up and is proclaimed = asserted = object-IZED = faked.
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

Hans-Werner Hammen wrote: December 25th, 2020, 4:41 pm The assertion THAT 1 plus 1 be 2,
it founds on the assertion of a societal agreement FROM/ABOUT the assertion of a thought, an idea, a presupposition,
that the order of number be 1, 2, 3, 4 and so forth.

From/about a different assertion of an order, namely it be 2, 1, 4, 3 (and so forth)
it would follow an assertion that 1 plus 1 be 3.

Any number is - as such, it-self, on its own, in its own right, in its very essence -
elicited, made up, fabricated, is no-thing (inside-brain-effect = imaginary + non causal = epiphenomenal) FROM/ABOUT some-thing (real, outside brain cause

Any number and any order of numbers does not exist - not as such, not it-self, not on its own, not in its own right, not in its very essence -
it is merely made up and is proclaimed = asserted = object-IZED = faked.
There's a trope, among psychologists of the 1990's at least, about people with Asperger's not being able to suss out the human condition. I remember one of those researchers giving an example of a kid with all kinds of astronomy books and star charts asking the question 'How did we discover the names of the stars?'. What scares me - I might have been the source of that, as a seven year old that resembles me a little too well for comfort, and my parents did have me to see enough specialists that it's not unreasonable to assume that could have escaped my lips and stuck.

Where am I going with that? 1, 2, 3, one, two, three, these are names for containers. The question of whether numbers actually can be real in and of themselves is a question of whether containers are real. If we dive far enough down a rabbit hole and refuse scope we can possibly obliterate the value of the term 'real'. As far as I can tell 'sets' are 'real' or 'fictitious' based on what a person is willing to call real or fictitious. I find being able to pick up an orange, look at it, and say 'this is one orange' too persuasive to say it's unreal, particularly in the radial symmetry of an orange from it's center and it's likely lack of perfect match, if cut in half, to another orange hemisphere. That might give preference to biological and self-organizing systems being unique 'things' but even there - one can look at a skyscraper, hemmed in by four streets and sidewalks as 'that's a building'. There doesn't really seem to be any practical purpose in saying 'It looks like one buildings but it's really two or three'.

If we were going to dispense with quantity we'd have to ask the question why? What does dispensing with quantity give us? I think this is where practical implications have to win out to some extent against deconstruction and the possibility of nearly infinite criticism.
Humbly watching Youtube in Universe 25. - Me
User avatar
Hans-Werner Hammen
Posts: 145
Joined: December 25th, 2020, 4:17 pm

Re: Why 1 + 1 does not equal 2

Post by Hans-Werner Hammen »

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"
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

Being in the wild by yourself and dealing with one wolf, two wolves, or three wolves are very different situations. One wolf can't divide itself and do a multi-angled strategy of attack much like one human hunting a mastodon couldn't circle it and hit it from multiple sides with spears.

I'd say number OF containers is also real (the names and symbols are linguistic), there might be disagreements in situations less existential than the ones I mentioned above where people can debate whether two apples and an orange is best thought of as that or three pieces of fruit - a situation where 2x + y = 3 is as valid as 3f = 3 where f can be x or y. Numbers seem to imply either like containers or 'like enough' (such as three pieces of fruit). One can make distinctions between apples and oranges but there aren't many ways to, in that situation, validly say that there are three apples and one orange or four pieces of fruit when there are clearly two apples and one orange.
Humbly watching Youtube in Universe 25. - Me
User avatar
Papus79
Posts: 1798
Joined: February 19th, 2017, 6:59 pm

Re: Why 1 + 1 does not equal 2

Post by Papus79 »

On a side note, I have not unfortunately been able to dig into The Road To Reality nearly as much as I've wanted, work got insanely busy for me from this past summer until the last few weeks and even now it might be a few months before I can dig back into it and really make much progress past chapter 8 and even at that I'd like to go back and review chapter 4 onward.

One of the places where Sir Roger Penrose was commenting on the real series being applicable was quantum particles. What gets really interesting, and would probably be off-putting for a lot of people, is that nature also seems to have a place for negative square roots and complex numbers. I remember he got into that in some fascinating ways in which the Euler formula and the complex number (xi plane) tidied up a lot of problems in mathematics.
Humbly watching Youtube in Universe 25. - Me
Post Reply

Return to “Epistemology and Metaphysics”

2023/2024 Philosophy Books of the Month

Entanglement - Quantum and Otherwise

Entanglement - Quantum and Otherwise
by John K Danenbarger
January 2023

Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul

Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul
by Mitzi Perdue
February 2023

Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness

Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness
by Chet Shupe
March 2023

The Unfakeable Code®

The Unfakeable Code®
by Tony Jeton Selimi
April 2023

The Book: On the Taboo Against Knowing Who You Are

The Book: On the Taboo Against Knowing Who You Are
by Alan Watts
May 2023

Killing Abel

Killing Abel
by Michael Tieman
June 2023

Reconfigurement: Reconfiguring Your Life at Any Stage and Planning Ahead

Reconfigurement: Reconfiguring Your Life at Any Stage and Planning Ahead
by E. Alan Fleischauer
July 2023

First Survivor: The Impossible Childhood Cancer Breakthrough

First Survivor: The Impossible Childhood Cancer Breakthrough
by Mark Unger
August 2023

Predictably Irrational

Predictably Irrational
by Dan Ariely
September 2023

Artwords

Artwords
by Beatriz M. Robles
November 2023

Fireproof Happiness: Extinguishing Anxiety & Igniting Hope

Fireproof Happiness: Extinguishing Anxiety & Igniting Hope
by Dr. Randy Ross
December 2023

Beyond the Golden Door: Seeing the American Dream Through an Immigrant's Eyes

Beyond the Golden Door: Seeing the American Dream Through an Immigrant's Eyes
by Ali Master
February 2024

2022 Philosophy Books of the Month

Emotional Intelligence At Work

Emotional Intelligence At Work
by Richard M Contino & Penelope J Holt
January 2022

Free Will, Do You Have It?

Free Will, Do You Have It?
by Albertus Kral
February 2022

My Enemy in Vietnam

My Enemy in Vietnam
by Billy Springer
March 2022

2X2 on the Ark

2X2 on the Ark
by Mary J Giuffra, PhD
April 2022

The Maestro Monologue

The Maestro Monologue
by Rob White
May 2022

What Makes America Great

What Makes America Great
by Bob Dowell
June 2022

The Truth Is Beyond Belief!

The Truth Is Beyond Belief!
by Jerry Durr
July 2022

Living in Color

Living in Color
by Mike Murphy
August 2022 (tentative)

The Not So Great American Novel

The Not So Great American Novel
by James E Doucette
September 2022

Mary Jane Whiteley Coggeshall, Hicksite Quaker, Iowa/National Suffragette And Her Speeches

Mary Jane Whiteley Coggeshall, Hicksite Quaker, Iowa/National Suffragette And Her Speeches
by John N. (Jake) Ferris
October 2022

In It Together: The Beautiful Struggle Uniting Us All

In It Together: The Beautiful Struggle Uniting Us All
by Eckhart Aurelius Hughes
November 2022

The Smartest Person in the Room: The Root Cause and New Solution for Cybersecurity

The Smartest Person in the Room
by Christian Espinosa
December 2022

2021 Philosophy Books of the Month

The Biblical Clock: The Untold Secrets Linking the Universe and Humanity with God's Plan

The Biblical Clock
by Daniel Friedmann
March 2021

Wilderness Cry: A Scientific and Philosophical Approach to Understanding God and the Universe

Wilderness Cry
by Dr. Hilary L Hunt M.D.
April 2021

Fear Not, Dream Big, & Execute: Tools To Spark Your Dream And Ignite Your Follow-Through

Fear Not, Dream Big, & Execute
by Jeff Meyer
May 2021

Surviving the Business of Healthcare: Knowledge is Power

Surviving the Business of Healthcare
by Barbara Galutia Regis M.S. PA-C
June 2021

Winning the War on Cancer: The Epic Journey Towards a Natural Cure

Winning the War on Cancer
by Sylvie Beljanski
July 2021

Defining Moments of a Free Man from a Black Stream

Defining Moments of a Free Man from a Black Stream
by Dr Frank L Douglas
August 2021

If Life Stinks, Get Your Head Outta Your Buts

If Life Stinks, Get Your Head Outta Your Buts
by Mark L. Wdowiak
September 2021

The Preppers Medical Handbook

The Preppers Medical Handbook
by Dr. William W Forgey M.D.
October 2021

Natural Relief for Anxiety and Stress: A Practical Guide

Natural Relief for Anxiety and Stress
by Dr. Gustavo Kinrys, MD
November 2021

Dream For Peace: An Ambassador Memoir

Dream For Peace
by Dr. Ghoulem Berrah
December 2021