"Absolutism" and whether 1+1 ALWAYS = 2

[AlanFromWichita]

I hope this is the right section to post this in. I come here with both and ax to grind and hopefully to seek instructions on how it should be ground. But I have no background in philosophy and in the past, discussions in this section have gone over my head so please bear with me; if you got this far then I thank and congratulate you for putting up with me.

Often when a person presumes to be making a statement that is absolutely true, or infallibly true, or objectively true, they tag it with an attempted snipe such as, “1 + 1 = 2 no matter what you say it is.” Normally I treat these on a case-by-case basis but I’ve seen two of them just today so I thought I’d come to get you Big Guns of philosophy to help me sort this out.

Actually the statement 1 + 1 = 2 has no meaning at all in binary arithmetic because there is no “2” in binary. A bit (Binary digIT, literally) can only hold values of 1 or 0. And yet binary is by entire dimensions the most common form of arithmetic “done” in the world, being at the basis of nearly all computer math. Scores of binary arithmetic computations are done for each and every character and emoticon I type to appear on the screen, and that’s just before I post it.

Now humans, of course, typically think base 10, but I’m a nerd, and a former math teacher so I don’t take it for granted we’re dealing with the same numbers. Just ask someone who has written a program and gotten octal and decimal mixed up and you’ll feel this pain.

I can give examples all over from physics and other disciplines, but here I’m talking grade school math. Or don’t they teach number bases in grade school like they used to – especially binary?

Now, if a person said, “in normal base 10 arithmetic, 2 + 2 = 4” I would have no problem. I’d even give them partial credit for “in normal arithmetic,” implying base 10, but to say, “2 + 2 = 4, PERIOD,” to me, just proves that the person writing it does not comprehend what absolute means, or at least what it means to me. It tells me they don’t know what there is beyond their own understanding, or even that there is something beyond their own understanding. To me, if you wish to tell me something is ALWAYS true, then we had better have agreed on the underlying axioms and assumptions or I might just get defensive feelings. And as we apply absolute statements to theology, we are often talking about marginal, atypical boundaries and extremes or the statements would even come up.

There are a couple reasons this bothers me enough to start this thread:

1.) When someone tells me 1 + 1 is ALWAYS 2, with no conditions, it automatically calls into question any other “absolute sounding” statement they make because I know they are not being careful about stating their assumptions.

2.) When I call someone on this, I end up looking like the schmuck. The one who doesn’t believe. The relativist who couldn’t get it right even if I cared enough to try. The one who picks and chooses what to believe of the Church Teachings. The one who will argue about anything just for the sake of being contrary and shutting down “real” discussion. These aren’t always stated, but that’s how it often comes across to me.

Who can help this wretched soul with my grief on this? To me these things are like Kryptonite. It would be like saying “two” and “to” are the same word. Well, they’re homonyms; I’ll give it that, at least in the language I know.

Yeah, I know 1 and 0 are symbols, too. In computers they could be voltage ranges. Pot calling kettle black? I just can’t seem to write anything without disclaimers.

Alan

 

[Gorgias]

1.) When someone tells me 1 + 1 is ALWAYS 2, with no conditions, it automatically calls into question any other “absolute sounding” statement they make because I know they are not being careful about stating their assumptions.

2.) When I call someone on this, I end up looking like the schmuck.

Alan,

You schmuck!


(I couldn’t resist…)

Anyway, I’m not sure that I buy your argument. Whether you write it:

1 + 1 = 2

or

1 + 1 = 102

or even

I + I = II

you’re still left with one basic truth, even though there are three (equivalent) expressions of that truth! C’mon … as a math teacher, you know that!!!

So, for the person who claims “1 + 1 = 2. Period.”, and is speaking about truth values, but you quibble about modes of expression, well… it is kind of pedantic and schmucky.

Just sayin’…

(Now, if the person were claiming that there was only one way of expressing the truth, and used the “1+1=2” line, then I think you’d have a point. But I don’t think that’s what’s going on here, right?)

 

[AlanFromWichita]

Alan,

You schmuck!

Thank you! You have given me some good ideas here.

you’re still left with one basic truth, even though there are three (equivalent) expressions of that truth! C’mon … as a math teacher, you know that!!!

OK, I think I can take that. So far I’m not sure where it gets me, though…

So, for the person who claims “1 + 1 = 2. Period.”, and is speaking about truth values, but you quibble about modes of expression, well… it is kind of pedantic and schmucky.

Just sayin’…

I think I see your point. There’s still something going on here though. Maybe part of it is the inferred emotional content, apart from the factual content, on my part or others, that tend to color my reaction. Typically I see such statements made as pejorative and that brings out the beast in me. But maybe it’s more than that; I’ll address after your last remark.

(Now, if the person were claiming that there was only one way of expressing the truth, and used the “1+1=2” line, then I think you’d have a point. But I don’t think that’s what’s going on here, right?)

Actually, you may have helped me target my comments better here; that may be exactly what I AM talking about. When we’re discussing Church Teachings, typically if we are in agreement with Church teachings we don’t claim to know the Higher Truth except as the Church has expressed herself to us through various means including written documents and even other posters. And it seems that even “theologians” disagree as to the underlying truth and even which of several possible ways of expressing it comes closest.

For one crude example and getting away from the math analogy a bit, “Thou shalt not kill.” Person A says, “it is a Commandment, not a Suggestion. What part of it do you not understand? You may not kill, period. End of story.” Person B says, “If I defend myself without intent to kill, but kill somebody in the process, then that is acceptable as taught by the Catechism.” A: “No it isn’t OK.” B: “Yes, it is.”

And so we have the battle lines drawn. We even may agree there is an Absolute Moral Truth involved, but how well versed we are in Church teachings and/or the specific way we express it in these cases make fundamental differences in how we would apply them in actual practice. And in this case, lives could be at stake depending on the interpretation and the means of expressing that truth.

I guess though at the moment I have conceded part of the major point of my initial rant, but this is fascinating to me and I appreciate your comments.

Alan

edit: I knew my math ego could rise to the challenge of defending the indefensible. If a really fast train left New York and one left Los Angeles at the same time, and each one was approaching Wichita on the same (straight) track with a speed of “1 unit” then at what speed do they approach each other? Depending on the units the answer could be quite different than “2 units.” For example, if the units were hundreds of thousands of miles per second, if memory serves the answer is much closer to 1.55 than 2.

 

[St_Francis]

Alan,
The thing is that math and language are different things. In normal conversational English, 1+1=2, but what they really mean is if you have * and then you get another * , you have **. They are just expressing that in conversational English and not math-nerd English (or French, Chinese, or anything else.

WRT your second problem, even if we kill in self-defense, we are not supposed to intend to kill. The death is to be a side effect. If my neighbor comes after me and I hate my neighbor and take advantage of this event to kill him, I will have committed a sin, even if the police say it was self-defense, because of my intention. But if I am walking down the street and my neighbor out of the blue starts attacking me and in defending myself, which I have a right to do, and in the course of that, the attacker dies, or if what I have to do in self-defense kills the attacker, then that was not intentional on my part: I did not intend to kill, which is against the commandment.

 

[kama3]

Actually the statement 1 + 1 = 2 has no meaning at all in binary arithmetic because there is no “2” in binary.

But that’s moot. Any technical text which uses numbers other than base 10 will say so explicitly, or put an appriopriate symbol on each number.

Plus, 2 is 2 regardless of representation. For a programmer, 2, 0x2 and 0b10 all mean the same thing.

 

[AlanFromWichita]

Alan,
The thing is that math and language are different things. In normal conversational English, 1+1=2, but what they really mean is if you have * and then you get another * , you have **. They are just expressing that in conversational English and not math-nerd English (or French, Chinese, or anything else.

I know what they mean in “normal conversational English,” but the problem is, it is used to make the point that absolute means absolute – and in “normal conversational theology,” we are not experts and are not privy to an underlying truth.

I did not intend to kill, which is against the commandment.

I totally agree with you here. I wasn’t so much talking about the commandment itself, but how two people with different amounts of Church background, can be at loggerheads where they contradict each other but both believe they are absolutely 100% correct. I might have picked a better example, but that’s the one that came to mind.

But that’s moot. Any technical text which uses numbers other than base 10 will say so explicitly, or put an appriopriate symbol on each number.

Note you said “any technical text.” I’m not talking about technical text. I’m talking about one Catholic to another, such as two posters, where one wants a statement to be so profoundly true that they grab a factoid from math and throw it in as if it meant anything. If all our opinions were limited to perfectly and precisely worded jargon and among people of equal and great expertise, then such disclaimers would be built in.

Plus, 2 is 2 regardless of representation. For a programmer, 2, 0x2 and 0b10 all mean the same thing.

You’re making my point. In binary, 0b10 looks and sounds nothing like “2” except by beings who transcend the limitation of 0 and 1 being the only symbols.

If I went around saying, 6 + 6 = C, PERIOD!! a programmer who uses hex all day knows exactly what I mean, but here in “normal conversational English” it is ludicrous while the more “refined” interpretation says it’s correct. So in that case the shoe is on the other foot.

Overall, I think I’ll try to calm down about when people use the “1+1=2, PERIOD” cliche but I’ll be noticing what sort of “absolute” statements are being defended by such cliche. That still doesn’t fix the problem of people believing that what they know is absolute and then telling others they are wrong because of it, which really underlies my problem. Maybe a more useful topic would be to come up with ways to address those sorts of situations.

Alan

 

[inocente]

1.) When someone tells me 1 + 1 is ALWAYS 2, with no conditions, it automatically calls into question any other “absolute sounding” statement they make because I know they are not being careful about stating their assumptions.

Another example is 1 + 1 = 1 in Boolean arithmetic.

The thing is, in normal counting 1 + 1 = 2 is an axiom, and is only true because it has been defined to be true in a particular system. Any resulting theorem such as 2 + 2 = 4 is only true by appealing to that axiom, and so is also only true by definition.

And you’re right, often when someone says something is absolutely true, they think it really is and never realized it’s only true by definition.

I blame math teachers for not making this plain in the first place.

 

[AlanFromWichita]

I blame math teachers for not making this plain in the first place.

NOW we’re talking. :dancing:

My dad always said we should teach kids how to think, not what to think. One of his favorite songs was Chapin’s “Flowers are Red.”

Alan

 

[MindOverMatter2]

NOW we’re talking. :dancing:

My dad always said we should teach kids how to think, not what to think. One of his favorite songs was Chapin’s “Flowers are Red.”

Alan

I think that there is such a thing as Objective Eternal Quantities, that are not defined by us, but are discovered. How could physics as a science work as a giver of truth if there were no mathematical absolutes?

Would you deny that if you put two human beings in the same room, you will always have 2 human beings in one room? Would you deny that to be an absolute truth?

Obviously context can change the relevance or the application of some quantitative fact. But if you can see a distinction as such that there is difference, you end up with true objective quantities.

 

[kama3]

If I went around saying, 6 + 6 = C, PERIOD!! a programmer who uses hex all day knows exactly what I mean,

The programmer does not use hex all day. The programmer uses a mixture of decimal, hex, and binary, whichever is most convenient at a given time. Statements like 0x0A + 12 are quite common.

but here in “normal conversational English” it is ludicrous

Nonsense. If I tell you that temperature in a tank is 70 degrees, this information is incomplete without specifying if we’re talking Celsius, Kelvin or Fahrenheit.

Such information can be provided by the context (i.e we both know that the tank holds liquid nitrogen, so only 70 Kelvin makes sense), nevertheless, it must be shared between parties.

 

[AlanFromWichita]

The programmer does not use hex all day. The programmer uses a mixture of decimal, hex, and binary, whichever is most convenient at a given time. Statements like 0x0A + 12 are quite common.

If you want to talk absolutes with me, I recommend you pay a little closer attention to detail. First, I never said any particular programmer does use hex all day, although I myself have done it. Second, to which programmer do you refer? You are telling me what “the” programmer does or doesn’t do. The fact that there may be some programmer who doesn’t use hex all day doesn’t even scratch my logic. More like tickles it.

Nonsense. If I tell you that temperature in a tank is 70 degrees, this information is incomplete without specifying if we’re talking Celsius, Kelvin or Fahrenheit.

Such information can be provided by the context (i.e we both know that the tank holds liquid nitrogen, so only 70 Kelvin makes sense), nevertheless, it must be shared between parties.

So in other words, you agree with my original premise that absolute-sounding statements are meaningless when the context, assumptions, axioms, whatever you call them, are not shared and agreed upon? I think you have made a good example for my side.

Alan

 

[kama3]

What is the difference between 70 Kelvin and -203 Celsius? None, they represent the same temperature.

But if you are communicating the temperature to someone, you better use the right units.

 

[ThinkingSapien]

What is the difference between 70 Kelvin and -203 Celsius? None, they represent the same temperature.

But if you are communicating the temperature to someone, you better use the right units.

Yeah, I think a lot of this thread has concentrated on differences in notation. The different representations of the natural numbers are isomorphic so I don’t think that matters much (I+I=II, 1+1=2, 001b+001b=010b, all evaluate the same). Likewise there is isomorphism between the temperature scales. As long as the mapping is understood it doesn’t matter.

Now if some one wanted to nail down “1+1=2” to a statement that invariably evaluates to true it would be necessary to reach agreement on the meaning of the + and = operators and for those to whom the numeric notation matters the number system used needs to be nailed down.

 

[AlanFromWichita]

As long as the mapping is understood it doesn’t matter.

Agreed.

Now if some one wanted to nail down “1+1=2” to a statement that invariably evaluates to true it would be necessary to reach agreement on the meaning of the + and = operators and for those to whom the numeric notation matters the number system used needs to be nailed down.

Exactly. If we’re going to bandy about absolutes, and then chide others for not being so absolute, then we really need to be careful. Like if we were using “+” and “=” as they frequently are for Boolean Algebra, then 1 + 1 = 1, and 2 makes absolutely no sense whatsoever. And I’d bet a great deal that more Boolean Algebra is done by machine in the process of handling this forum for a minute than “regular” math by all the humans in the world could do in a day.

Maybe the real question isn’t so much what a person means, but how big is their universe? People who think in small boxes make statements that are absolute as long as they are inside their boxes, but are vague when considered in any context out of that box.

Maybe a bit of self-disclosure would be helpful. When I was in kindergarten, my dad taught me arithmetic with negative numbers. I had a little blackboard and every night when he came from from work he’d write problems for me to do. Anyway, well over a year later, we were learning subtraction in school, and on a test I answered " 1 - 2 " as " -1 " and got it marked wrong. I asked why and the teacher fumed in front of the whole class about how you can’t take 2 from 1. I said, “can we at least say there is a way but we just haven’t learned it yet?” Then she went ballistic (Sister Charlene, I think) and her face turned purple – by now I was scared and defensive and I honestly was concerned about other class members being misled. She sputtered, “if I have only one apple I can’t give you 2.” I said, without the slightest intent at disrespect (I was a nerd – all I cared about was “truth”) and I reacted quickly, “you can owe me one.” Bam! Principal’s office, and nobody ever explained to me why I had gotten into trouble. As it turns out, she honestly didn’t know about negative numbers – but look who got into trouble for her ignorance.

Alan

 

[ThinkingSapien]

I answered " 1 - 2 " as " -1 " and got it marked wrong. I asked why and the teacher fumed in front of the whole class about how you can’t take 2 from 1. I said, “can we at least say there is a way but we just haven’t learned it yet?” Then she went ballistic (Sister Charlene, I think) and her face turned purple – by now I was scared and defensive and I honestly was concerned about other class members being misled. She sputtered, “if I have only one apple I can’t give you 2.” I said, without the slightest intent at disrespect (I was a nerd – all I cared about was “truth”) and I reacted quickly, “you can owe me one.” Bam! Principal’s office, and nobody ever explained to me why I had gotten into trouble. As it turns out, she honestly didn’t know about negative numbers – but look who got into trouble for her ignorance.

Ha! Too funny!

I almost failed a math class in high school, not because I was getting wrong answers, but because I wasn’t using approved methods. I had vision problems at the time and could not see how the teacher was teaching us to solve problems. So I had to figure it out myself. I remember getting back a test in which I had gotten no wrong answers. the teacher took off 30% because she didn’t feel like I had done enough work.

At the same time I’m struggling to conform enough to get a C in the class I was sent to a state math competition and I got 5th place. Not the best place, but not what you would expect for some one that was apparently failing math.

 

[AlanFromWichita]

the teacher took off 30% because she didn’t feel like I had done enough work.

Unapproved amount of toil. (beep!)
Bad student! (beep!)
Must punish… (beep!) Must punish … (beep!) …

At the same time I’m struggling to conform enough to get a C in the class I was sent to a state math competition and I got 5th place. Not the best place, but not what you would expect for some one that was apparently failing math.

I like the way you said “conform.” I used to love math contests, too. My biggest success was when I was in seventh grade I took second (because I didn’t know the vertical bars meant “absolute value” on one question ) in the Chicago Archdiocese … about 420 schools. That has been a blessing to me to refer back to when I am mobbed by fools who demand how I dare be the only one to say one thing when too many were saying another. I don’t tell them that because they are fools and, well, ya know …

Prov 27:22 (NIV)
Though you grind a fool in a mortar, grinding them like grain with a pestle, you will not remove their folly from them.

Have you ever heard of the Solomon Asch Conformity Experiment? You should watch it; it’s too funny.

Alan

 

[Gorgias]

If we’re going to bandy about absolutes, and then chide others for not being so absolute, then we really need to be careful. Like if we were using “+” and “=” as they frequently are for Boolean Algebra, then 1 + 1 = 1, and 2 makes absolutely no sense whatsoever.

On the other hand, why can’t we just recognize that, when someone says, “1+1=2. Period.” we recognize it for what it is: shorthand. It’s a lot more effective in discourse to say it that way, and use it as something recognizable as an axiomatic statement, then it is to have to say, “for standard arithmetic operations ‘+’ and ‘=’, and in the context of the natural numbers, 1+1=2.”. So, rather than debate the minutiae of how one grounds an axiomatic statement, and what presumptions (if any) are present, why not accept that this is simply a discursive placeholder for an assertion of axiomatic absolutes?

 

[AlanFromWichita]

On the other hand, why can’t we just recognize that, when someone says, “1+1=2. Period.” we recognize it for what it is: shorthand. It’s a lot more effective in discourse to say it that way, and use it as something recognizable as an axiomatic statement, then it is to have to say, “for standard arithmetic operations ‘+’ and ‘=’, and in the context of the natural numbers, 1+1=2.”. So, rather than debate the minutiae of how one grounds an axiomatic statement, and what presumptions (if any) are present, why not accept that this is simply a discursive placeholder for an assertion of axiomatic absolutes?

This is brilliant IMO, and is helpful to me. I think you have an excellent point. I’m not quite ready to agree with the conclusion but I like your logic and how you’ve written it.

From a sheer understanding point of view, I know what they are saying. But when it’s combined with an alleged “absolute” statement in another realm that clearly is not absolute, then it seems like both insult and injury. Insult because stating something that is so “completely obvious” is to belittle the complexity of the actual issue at hand and/or the opponent’s ability to recognize the “obvious” in that realm. Injury because it does not correctly characterize the actual point intended. I can back off the “insult” part based on a limited “universe” of the speaker, but not the injury. IMO a person speaking as absolutist had better know their stuff, especially when chiding others for not being in agreement. So from an emotional point of view, I find it troubling indeed.

Maybe a slight rephrasing would help me, personally, at least. For example,

a) “Come on! 1 + 1 = 2 whether you agree or not!”

– just like an “actual” I saw the other day –

b) “I don’t understand your difficulty. To me this is as clear as 1 + 1 = 2.”

– never seen anything like this before.

Shorthand, yes. Belittlement plus illogic, no. I guess that’s where I am at the moment.

Thanks again for the great post! And I thank all the posters and lurker who have taken time with me here; I’m glad I brought this to this section. :tiphat:

Alan

 

[thewanderer]

Am I right in saying that your problem boils down to frustration over people claiming that they are making an obvious absolute statement, not just an absolute? And using the example of 1+1=2 to make it so that they don’t need to provide any further evidence or attempt to address your issues with their position?

 

[AlanFromWichita]

Am I right in saying that your problem boils down to frustration over people claiming that they are making an obvious absolute statement, not just an absolute? And using the example of 1+1=2 to make it so that they don’t need to provide any further evidence or attempt to address your issues with their position?

Yes, and mostly.

They will see that it is all laid out so you should need no more evidence, but that won’t necessarily stop them from adding more evidence (possibly with additional pejorative statements). But either way, there is “I’m more absolute than you,” and often speculation as to why you either don’t care or are too blind to see. And I think “yeah, right … you wouldn’t know ‘absolute’ if the life of the President depended on it.” Turns out I’ve had to sign off on electronic designs that would do just that if there were a wrong detail or an unstated limitation.

As an engineer, I’ve worked very hard to talk to people like a “normal” person without disclaimers, limits, exceptions, etc. And then somebody comes up with some “absolute” statement clearly full of holes and wants to start a “you relativistic – bad you!” contest. (In a nutshell, it seems like “relativism” is a term or concept to label anybody who disagrees.) And I just want to mash them into the ground with logical superiority, but tempting as it may be, trying to do so doesn’t help. (Prov 26:4, Prov 27:22)

(Ever try to hang on to a drop of mercury by squeezing it between your fingers? )

It’s like the joke about the farmer and engineer. The farmer was going nuts trying to get the engineer to make an absolute statement. Finally the farmer points at a cow and says, “will you at least admit that’s a cow?” The engineer replies, “well, it does look like a cow … from this side.”

Alan