I pick up a rock, I have one rock. Pick up another, have two. Drop them, have none. Only started counting rocks when I picked up the first one. So, numbers start at one. — Zolenskify

Before you picked up a rock, you had 0 rocks. So, numbers start at 0. :roll:

Well, this is... unexpected; appreciated, but unexpected. But nonetheless inconsequential; the rock is no longer if it's form is altered, and cannot fit the criteria of the assumption. At any rate, are we strictly talking about igneous rocks, or do you prefer another type? Because, this changes things completely depending on the classification. Thank you for the thoughtful response though; this leaves much to consider...

Here are some interesting sources on these classifications that I mentioned; even as someone who isn't totally versed in the field, I found these to be quite thought-provoking:

(1) Source 1
(2) Source 2

I always thought numbers started at -2/3.

I can't change your mind. I think it's too late. We'll never know if we could have started numbers some other way. We started counting, numbering, and in order to start, we already said "one" first. Starting is "one-ing".

First, there are no numbers. We don't just find numerical representations with our senses. We form them. Now that we've formed them, there are numbers. You pick up a rock, and you call it 1 (whether it is one or is not , maybe it's a rock with some moss on it and dirt, whatever, you pick it up and construct the basis of math by calling it "1"). You've made the first number.

You can't make two half rocks without the first rock. You don't name something a half, first. You have to have a whole before something can later be called half of that whole. By saying "half" you already referred to a whole. Halves come after wholes, not before they are made whole.

And you don't start with zero. We can't recognize zero until we recognize one. You learn and name zero by mentally removing the one rock or all of the rocks and things. Zero comes after 1 in experience, but is placed before one on the number line because of logic (mental functioning, just like naming something "one" or conceiving of "half-ones".)

There is no such thing as a negative rock. Negatives are mental constructs. Now that we have a new mental object we call "1" we can build off of it in all directions and build functions that yield zeros, twos, negative thirty-fives, the infinite.

The concept of "one" is the only that might have a referent in a world where you could make any start, such as the start of numbering things. Two rocks don't exist without a mind making a set called "two" having "rocks" as its members.

I can see where you are coming from, but this argument is unfounded. You are correct by saying I had 0 rocks before I picked up the first, but a 0th rock does not exist, and thus, does not fit the criteria of what it means to be "a rock." In a roundabout way of putting things (without going too far off from the topic of conversation), this is like saying "if I am a sea turtle, then I am Bill Gates (or [insert favorite billionaire])."

We certainly could make this argument, it's not wrong, but anyone who wishes to entertain this would be wasting time; as if there isn't enough of that happening already. We could go on all day about what the world would be like if I were a sea turtle (or any other member of the Cheloniidae family; some information can be found here: https://phys.org/news/2015-11-insights-family-tree-modern-turtles.html; really take some time and educate yourself on the various domains, genus', orders, etc, of the species before jumping to any sort of conclusions here; we could split hairs, but there are distinct differences), and have a hell of a time doing it. But I'm not a sea turtle, I'm a person. So, these arguments don't really matter.

At any rate, I think it agreeable to say that we should come prepared for any sort of discussion, as to not waste time on preliminary information. Just a thought, it may serve you in the future.

@Vaskane made a similar argument. But theirs's too was besides the point, as they failed to ground their definition of a rock in any sort of reality. At any rate, thank you for the response. This was a viewpoint I had not considered. Cheers!

Well, that is true. But if you stole from me, there would be hell to pay. So, don't do it.

Correction: Sorry, misread who you had responded to. But still, don't steal things, or at least avoid incriminating yourself in the process...

Well, that must just be the way you see things, because I think things are just fine starting at 1.

An issue here is with the arbitrariness of what a rock consists of. — Vaskane

That is a true issue for physics or metaphysis (identity of a rock), but no matter what the results of those inquiries, even if no results, it could have no impact on the definition of "1". That's the beauty of this math we've invented. Which seems to me, got it's start with some "one".

No worries, I know the feeling. But please get back to me as soon as you can.

but a 0th rock does not exist — Zolenskify

Saying someone has 0 rocks is not the same as "there is a 0th rock" — one is a nonsensical statement, the other is not. There is a difference between cardinal and ordinal numbers — I learned that in my first year of school.

"if I am a sea turtle, then I am Bill Gates (or [insert favorite billionaire])."

We certainly could make this argument, it's not wrong, but anyone who wishes to entertain this would be wasting time — Zolenskify

No we couldn't, it is wrong. Bill Gates and a sea turtle are mutually exclusive.

really take some time and educate yourself on the various domains, genus', orders, etc, of the species before jumping to any sort of conclusions here — Zolenskify

I don't think I need to educate myself on grade school biology, thanks.

At any rate, I think it agreeable to say that we should come prepared for any sort of discussion, as to not waste time on preliminary information. Just a thought, it may serve you in the future. — Zolenskify

There is no discussion, you started a thread with a claim that no mathematician will entertain — because first of all, what does the phrase "numbers start" even mean? You used an analogy which relies on the semantics of the English language to prove your claim and I showed another analogy using English that makes the contrary claim. Your OP does not even fulfill criterion B on how to make a new thread.

You are conflating counting (which assumes some existential statement) and mathematics, those two are not the same¹. Overall, another horrible thread by someone who did not research the topic they are starting. Here, have fun: https://web.math.ucsb.edu/~padraic/ucsb_2014_15/ccs_proofs_f2014/ccs_proofs_f2014_lecture4.pdf

1: Don't reply to this with a cut-off quotation that says "Mathematics is the study of counting", read the rest of the quote.

But if I steal your rock then we introduce a negative 1 to the equation... — Vaskane

Subtraction is derived from addition. So numbers would not "start" with a negative number.

I can't change your mind. I think it's too late. — Fire Ologist

I'm just gonna stop you right there: I really think you're wrong. You can change my mind, I just need a strong argument, and it's definitely not too late; I want to see things differently if they make more sense that way. Some people are close minded, but I am open to new ideas. Try to avoid putting yourself down too, especially in an online conversation like ours. I think we can really learn a lot from these sorts of discussions, and someone such as yourself (who I can already see is of an upper echelon of thinking to begin with; less you would not be on "The Philosophy Forum") has a lot to offer it seems. So please, restructure your argument without discrediting yourself; you can do anything you set your mind to.

I do see where you're coming from though. It seems that the world were in is so cut throat, that people take the slightest bit of criticism and form their entire identity around it. Well forget that jazz. As an artist, my ego is demolished on such a frequent basis that it is pretty much part of who I am at this point, and I feel all the better for it. This is not to say I do not have an ego, I certainly do, but I can cope with being wrong at times in a much better way than others it seems.

In other words: Ignore the haters, but still try to recognize the difference between blatant heckling and constructive criticism, because there is a difference.

At any rate, thanks for the response. This too has given me much to think about. And remember, take it easy and just take a minute to breathe; we're honestly all just here to help each other out and grow. But we can't do that if we are constantly holding ourselves to these impossibly high standards, and then blaming ourselves for not reaching them. Someone who I learn a lot from in Andrew Huberman, he has a pretty interesting podcast episode that relates to this that I think you would really benefit from:

https://www.youtube.com/watch?v=x4m_PdFbu-s

In this context counting physical objects like rocks can be a bit confusing to some because it's not always clear what exactly is being counted. On the other hand, counting time is more straightforward.

For example, when counting days, day 1 is considered at the end of the day, with the beginning of that day being counted as 0 and ending with count 1. The next day begins at 1 and ends at count 2. Therefore, 1 is the first complete count, but for this to be true, the count must begin at 0.

When counting rocks, what is actually being counted is the space the rock occupies. This can be seen as the space between 0 and 1 being counted as 1 (the counted entity is contained between 0 and 1). If a rock didn't occupy any space, there would be nothing to count, as there can't be a rock that takes up no space.

I think you read way more into my saying that I can't change your mind. It was not meant as a comment on the openness of you and your question, and it was not a comment my own abilities; it was a comment on the nature of numbers and the number 1. By saying "it's too, late" I meant that we've already started using numbers, and when we started, we were at "1".

I just meant it makes sense to me that 1 has to be the first number. I gave my arguments for that to demonstrate my first impression of the question you've raised. So far, I can't change my own mind, so I can't argue something that might change your mind. And I don't yet see there is any reason to think differently. Not yet, but I'm open to it.

The best summary of my thinking here is the notion of starting. If we are asking a question about a start, about starting something, like numbers, we are already in a position only to say "1", first. We can't start with anything else but the first, which numerically, is "1".

Because "1" is built into starting something, I don't see how to argue anything else but "1".

"Counting" may start at 1. Numbers, however, do not "start" (i.e. begin / end).

Every computer programmer knows that counting begins at 0.

programmatically in Python:


output = [1, 2] # correct output



output = [2] # incorrect output

"Counting" may start at 1. Numbers, however, do not "start" — 180 Proof

This clarifies the question for me.

I was talking about the fact that the first unit ever made in a mind, so the first number ever counted, was a "1", and all units since then (yes units), were multiples and divisions of when we first started counting units of one. So quantification started long ago with a 1. 'Numbers start at one' would be a weird way to say it, but it reflects this sense of "start" and "numbers" and "1" I meant.

Only started counting rocks when I picked up the first one. So, numbers start at one. — Zolenskify

But if the statement 'numbers start at one' means "of all numbers on the number line, numbers start at 1", then maybe it makes sense to say numbers don't start.

The act of counting itself moves in increments of 1. When physically counting, you have to say "1" in some fashion, first. If you count by fours, you first counted 4 ones, to make the first four, so you still started at "1".

However, we might also say we start counting from zero, and for the instant between zero and one, that is our start of counting. The first count, is a "1", but we start counting closer to zero, or at zero.

How about the genealogical-psychological first historical act of counting (way back when caves were still fashionable), the very first count was likely a physical word for "one". Just like our minds first made a unit, and one, to count at all, we made word "one" itself to follow, and then we had to make words for "two" and "three" probably quickly "none" or "zero". The word "one" may have been how numbers started. Maybe.

But now that numbers are here, however they started, we can start counting from any number. The number line gets laid out clearly the same every time; no matter what numbers you start at, it lines up the same. The only place we might find to "start" the number line, would be zero. There is a logic to it, a symmetry.

So it looks like four senses.
1. At the first moment quantification occurred to a mind, the number "1", the unit, had to be there first. Unitizing is the birth of all math. Numbers start at one.
2. When starting a count, you can be said to start "at 1" or "from zero" and so there is something unresolved there. Numbers may not start at one.
3. The first cave person who ever tried to count out loud, probably said and meant the word "one". Numbers start with one. (Who knows, throws in some actual skin in the game).
4. The most logical place to position the number line is from zero, but it can start from anywhere. So numbers don't start and if you had to choose, you would choose zero.

And what about lists? Has anyone ever started a list with anything, ever, besides 1? Put "Lists start with one" up there on my list, somewhere between 2 and 3.

Great, now I really don't know what I think anymore.

This is not to say I do not have an ego, I certainly do, but I can cope with being wrong at times in a much better way than others it seems. — Zolenskify

The only person here who ever said anything about "ego" was you. People replied to your poorly-made OP and you went on a rant like you were deeply hurt. Did you take LSD and suddenly made up your mind that you are enlightened? Because you are not.

There is nothing correct or incorrect about the output, it is just the way you programmed it and how Python works.

I was talking about the fact that the first unit ever made in a mind, so the first number ever counted, was a "1", and all units since then (yes units), were multiples and divisions of when we first started counting units of one. So quantification started long ago with a 1. 'Numbers start at one' would be a weird way to say it, but it reflects this sense of "start" and "numbers" and "1" I meant. — Fire Ologist

That is somewhat productively discussed in the Postmodernism and Mathematics thread.

There is nothing correct or incorrect about the output, it is just the way you programmed it and how Python works. — Lionino

What is your criteria for correct or incorrect? Are you saying it doesn't matter how i program it, that i can choose either one, and it'll be as good as anything else? If that is the case then it would appears that no one is correct or incorrect about anything, because it is just the way they said something. Really?

In the ancient Greek concept of number the first number is two. One is the unit of the count, what it is that is being counted. We see this here:

... are we strictly talking about igneous rocks, or do you prefer another type? — Zolenskify

The number of igneous rocks is not the same as the number of sedimentary rocks. To answer the question "how many" we need to know how many what.

I think that in the sense that practical logic is the foundation of more complex forms of reasoning, including mathematics, you could argue that numbers begin with self-identity, which is unity, or one.

The program simply outputs what you told it to output. There is no right or wrong. If you program print('The dog is a cat') and it says 'The dog is a cat', the output is not wrong, you told it to do that. And some programming languages start counting from 0 (Java), others from 1 (MATLAB).

I simply told the program to count 2 rocks, and yes, i told one to start from 0 and the other to start from 1. If you look closely, you will notice the two code examples are identical except for the starting or initial condition.

You are correct in that both code samples are logically correct in their execution, but as in logic, one began with a different 'premise' than the other. And we know that if you have an incorrect premise, then your conclusion would be incorrect no matter how flawless the execution of the logic.

The two code samples illustrate what happens when you start your count from 0 versus 1. Both cannot be correct for use in counting rocks.


Here is ChatGPT:
which one of these code examples is the correct one for counting rocks?

The first code example is the correct one for counting rocks. It initializes the variable "rocks" to 0 and then uses a while loop to increment the value of "rocks" until it reaches 2, printing the current value of "rocks" in each iteration. The output of this code is "1, 2." Here's the breakdown of the code:



This code will output:
1
2

The second code example initializes the variable "rocks" to 1 and then uses a while loop to increment the value of "rocks" until it reaches 2, printing the current value of "rocks" in each iteration. The output of this code is "2," which is not the correct one for counting rocks.

Also, notice that the output count did not include 0, although it's where it began counting. We forget 0 because it's usually invisible as our reference point before a count can begin. When you count, what you are doing is adding to 0, and you must start at 0, or your count will be off by the number that you started counting from.

The first code example is the correct one for counting rocks. It initializes the variable "rocks" to 0 and then uses a while loop to increment the value of "rocks" until it reaches 2, printing the current value of "rocks" in each iteration. The output of this code is "1, 2." — punos

Sure. But the programming language does not "know" that counting start at 1 — for some languages the first element of a list has index 0, in other languages index 1. And the fact that one piece of code counts "correctly" and the other "incorrectly" (like ChatGPT says) begs the question as to why one is right and the other wrong, which is the thread's topic.

The relevance lies in the logic, not the programming language. There is a right and a wrong way to count. When counting rocks, it is essential to establish whether there are already rocks present. If i have 2 rocks and then pick up and count another rock, i will have 3 rocks (the count begins at 2). Conversely, if i don't have any rocks and then pick up and count 1 rock, i will have just 1 rock (the count begins at 0).

I have never used MATLAB, so i can't comment on what it's doing. If you have a code snippet that i can look at, that would be helpful. MATLAB isn't a general-purpose programming language, but if MATLAB uses 1 as its base index, it must mean that it doesn't represent a count until the first count is made. In Python, the count begins at 0 before the first count is made. I'm sure that MATLAB uses a 0-based index under the hood and creates a 1-based index after the first count.

And the fact that one piece of code counts "correctly" and the other "incorrectly" (like ChatGPT says) begs the question as to why one is right and the other wrong, which is the thread's topic. — Lionino

The reason one is right and the other is wrong is that one starts from 0 and the other starts from 1. If i wanted to count rocks with an app that uses the example code that starts with one, then my app would count rocks incorrectly. It's just that simple to verify, like counting horse teeth.

This is a good point, I like the way you think; we shall exclude igneous. Although... I would refrain from calling rocks out on their lifestyles, it is not in their nature for them to be overly active. I always try to take the stance of acceptance and inclusion when it comes to workout routines.

For instance, my "workout" is pretty much comprised of cardio and legs only, that is, skateboarding. My upper body is quite thin (on this note, I would prefer to keep a lean build versus gaining any weight, I don't want to sink my surfboard, for when I do that instead of skating). I would compare my body type to a correctly-oriented pyramid; a stark contrast to what we typically see, the "upside down" pyramid, where you have these (albeit very kind and educated) fellows with massive upper bodies but are supported by two chop sticks. I am very much the opposite, and am okay with that. In fact, my legs are like works of art. In ancient Greece, I would hedge my bet that I would be worth sculpting in some capacity. Now, what type of rock the sculptor will choose for this endeavor, I don't know. But, if I had to guess, I would say perhaps igneous; although you seem to have something against this variety. Nonetheless, here is an article I found on various sculpting materials: https://www.britannica.com/art/sculpture/Materials and here they consider something I had not even thought about: stone. Which this completely changes the dynamic of the whole damn argument if you really wanted to go there.

But staying on topic, there is but one rock that is actually quite active. As we know, Dwayne "The Rock" Johnson is anything but sedentary, and he actually has more of a figure of what I was referring to. At least, that is just my opinion on things, and is not the end-all-be-all way of seeing the world. But thank you for your comment anyhow, I will think on this.

...my legs are like works of art. — Zolenskify

When making arguments it is good to have a leg to stand on, to take a stance, and have a proper and I assume in your case fetching attitude.

So, numbers start at one. — Zolenskify

You're half right.

The relevance lies in the logic, not the programming language. There is a right and a wrong way to count. When counting rocks, it is essential to establish whether there are already rocks present. If i have 2 rocks and then pick up and count another rock, i will have 3 rocks (the count begins at 2). Conversely, if i don't have any rocks and then pick up and count 1 rock, i will have just 1 rock (the count begins at 0). — punos

Well, when you wrote that program that's how you interpret "counting". You chose not include the initial value in the count; if you'd performed the print operation before the adding operation you'd get [0,1,2] and [1,2] (correct me if I'm wrong; I don't know python).

I really don't see a logical difference. Either one's fine. (In specific contexts one might be more efficient than the other, though.) Basically, you can have either initial value for the desired output; you just have to switch the operations around.