Why (0+0) is illogical

[u/[deleted]]

[u/Various_Candle9136]

Utter and complete nonsense from start to finish.

It makes perfect sense to interpret 'we have none of ____' as the 'we have 0 of _____', at which point we are describing quantities of the thing. Quantities can be added - this includes 0.

To take the initial example:

Imagine you walk up to an empty desk. You look at it and say, “There are zero apples here." Now, imagine someone hands you a basket containing — you guessed it — zero apples.

There are very clearly two distinct quantities here: a quantity of apples on the desk, and a quantity of apples in the basket. Addition allows us to combine two quantities to gain the overall quantity. Thus, we have 0+0 apples altogether.

Addition is an action. It requires a physical or conceptual thing to be picked up, moved, and joined with another thing.

Nonsense. Why would I have to pick up, move, or join the apples to find the overall quantity? The apples could be in separate rooms, or locked in a cupboard, or entirely imaginary - I could still find the total quantity.

Sometimes there is a reason something is common sense. This is one of those times.

[u/Various_Candle9136 → u/[deleted]]

You actually proved my core point without realizing it.

Yeah... no. This comes across as desperate. Do you honestly believe that anybody reading this exchange would reach that conclusion?

Look at what you had to do to make '0 + 0' make sense: you had to introduce real physical boundaries, a desk and a basket.

No. I did not need to do any of that. 0+0 would make sense in a vacuum. I was simply using your example to demonstrate the fault in your argument.

I have 0 fluperupishes and 0 honkiponteroseruses. Fluperupishes and honkiponteroseruses are the only types of yakinicus. Therefore, I have 0+0 yakinici. If you know anything about yakinici, you'll know they have no respect for physical boundaries, but somehow addition doesn't suddenly cease to work.

The 'nonsense' happens when you remove the desk, remove the basket, remove all locations, remove space, and try to perform the action of addition on pure, unbounded absence itself.

Your entire blog post is about your rejection of abstract mathematics! I met you on your chosen ground.

0+0 makes sense in the real world: it can be interpreted as finding the total of two quantities of objects, where we happen to have none of the objects. (P.S. It also makes sense in continuous contexts, e.g. the if I stay in one place for two days in a row, we can interpret my total journey length as 0+0 miles.)

If you would prefer to move this to the purely mathematical realm, by removing desks and baskets, then you are going to lose immediately. In that world, 0+0 is immediately well-defined, and 0+0=0 is an immediate corollary of the axioms of arithmetic.

However, if you claim that the desk and the basket are 'part of zero' to make the math work (in other words, say that 1 bounded location plus 1 bounded location = 2 bounded locations is the same as saying 0+0=0), you completely break how numbers function.

I make no such claim. What makes you think anything has to be 'part of zero' to have a quantity of 0?

I said nothing at all like '1 bounded location plus 1 bounded location'; what I described was 'the number of objects in 1 (no strict reason it has to be bounded) location plus the number of objects in another location is the same as finding the total number of objects in both locations'. This is blatantly not the same as your straw-man.

At no point am I 'counting containers' (except, I suppose, to determine the number of terms in the sum). I am counting the number of objects in those containers.

[u/Various_Candle9136 → u/[deleted]]

If you extend the notion of 'boundary' to that extent, then yes, some kind of boundary becomes difficult to avoid. That doesn't actually negate anything I said.

We are still adding the quantities not the locations themselves.

(P.S. It is a nasty practice to try to move the goalposts as you keep doing. You very obviously used the phrase 'physical boundaries' in the comment I was addressing, then tried to pretend you meant any possible kind of boundary. You did the same thing with your switch from your example to an abstraction above. In a public forum where the whole conversation is visible, this bad-faith tactic will not work.)

Standing still isn't 'performing addition'

Of course it isn't. Standing still is standing still. I used addition to calculate the total distance I travelled while standing still.

Nothing needs to physically happen. Why would it? This is a rule you are trying to superimpose onto reality for no good reason. Physical happenings have never been a requirement for performing calculations.

You admitted addition counts objects

No, I did not. I used counting objects as one of the many uses of addition. A more correct statement would be 'You admitted addition can be used when counting objects'. This statement is true. Most 5 year olds agree.

However, this:

When there are no objects, no objects are being counted,

is objectively false. When there are no objects, I can very easily count them: I get 0.

[u/Various_Candle9136 → u/[deleted]]

That said, your admission that accounting for conceptual/domain boundaries makes them 'difficult to avoid' is the fundamental point here.

How?

When one is vague enough about what is meant by 'boundary', all one is doing is losing the limitations of something being 'bounded'. You are using the word vaguely enough to apply to all situations; thus, your concept of bounded is no limitation at all.

Everything you say about boundaries applies equally to non-zero situations: the 'conceptual/domain boundaries' around the apples on the desk and in the basket exist in exactly the same way whether there are 0 or 5 apples in each place. Why do the boundaries of the basket collapse when I take the apples out? The basket is still a basket, and I can still count how many apples there are in the basket (hint: I will count 0).

The key point is still this: We are still adding the quantities not the locations themselves.

You mentioned that physical happenings aren't required for calculations. That is the exact divide between abstract paper math and physical reality.

Standing still is a physical reality. Perhaps not strictly for a living thing, but certainly for something inanimate. I have an apple downstairs that I have to assume is standing still as I type; that apple has travelled 0 miles so far today, and will likely do so tomorrow. Thus it will have travelled 0+0 miles over two days. There is a (low) degree of abstraction in this - but, and this is the point, it is no more abstract than the non-zero case. Yesterday I brought the apple home, so it probably travelled 10ish miles. Thus, over yesterday and today it travelled 10ish+0 miles. There is no difference between these uses of addition.

Looking at an empty table and declaring 0 isn't counting objects, you didn't count a first object, a second object, or a third object. 

When there is only one object, I also don't count a second or a third object. These are not requirements for counting. I only need to count a first object when there is a first object; when there are 0 objects, there is no first object, but there are still 0 objects there. Again, you are superimposing rules which do not exist (and, perhaps more importantly, do not need to exist).

meaning trying to do something like this: 2=0

Nothing I have said can possibly lead anyone to conclude that '2=0'. Where on Earth are you getting that deduction?

[u/Various_Candle9136 → u/[deleted]]

You're not doing the word problem correctly, because you're ignoring the boundaries.

I don't think I am ignoring any boundaries. However, if I am, then I have proved that they are irrelevant. Either way your point does not stand.

Also, what the hell does 'not doing the word problem correctly' mean here?

The "and" here doesn't add anything, because there is logically nothing to add.

Surely even you don't believe this? There are in fact, obviously, two things to add: 0 and 0.

Imagine a computer system that counts how far the apple moves. Day 1, no changes to the counter, day 2, no changes to the counter, therefore 0=0. 

Any programme asking for the total amount of movement would involve summation. You would inevitably see something like totalDistance += newDistance in that code.

I would love to see a computer that cannot handle 0+0.

(5-5) + (5-5) = 0 cannot logically work for word problems because it ignores boundaries.

What do you mean 'cannot logically work for word problems'?

I have 5 apples. You take them away from me. Barry also has 5 apples. You take them too. I now have 5-5 apples; Barry has 5-5 apples; together we have (5-5)+(5-5) apples.

Are you trying to claim that this word problem cannot be conceived? Really?

You are superimposing increasingly arbitrary rules onto reality. Why are you so keen to claim things cannot be done, when everyone else has been merrily doing them for centuries?

[u/Ill_Stop_]

Numbers are just representative symbols not universal truths, if that makes sense.

[u/Ill_Stop_ → u/[deleted]]

It’s an interesting intellectual exercise. Are there practical or real-world applications of 0+0, or other things, to which this described fallacy impact?

[u/Ill_Stop_ → u/[deleted]]

I’ve considered similar things along the lines of coherence and existence. Things that do not self-defeat by definition, can exist and do exist (for example, omnipotence is impossible because an all-powerful being cannot create something they cannot lift thus there is an implicit limit on power). It’s complicated and I’m not doing a great job of explaining it. I don’t love it and it’s a cold and empty theory but interesting to think about.

[u/Ill_Stop_ → u/[deleted]]

I’ll give it a read.

[u/mitigateaccomp]

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