Wolfgang Schwarz :: What is my telephone number?

What is my telephone number?

Posted on Tuesday, 25 Apr 2006.

I just realized that I don't know what my telephone number is. I used to think it is 44717384. But 44717384 is a number, and the same as 252452510 in octal, or 2aa5548 in hexadecimal. Yet it sounds wrong to say that my telephone number is 252452510 in octal, or that my telephone number begins with 4 only in decimal notation. What's more, telephone numbers are never pronounced "forty-four million, seven hundred and seventeen thousand three hundred eighty-four". (I know an old woman in a rural part of Germany whose number used to be 543; she, too, always said "five four three".)

So maybe my telephone number is not 44717384, but "44717384". It's a numeral, not a number, and hence it definitely begins with "4". This still doesn't explain why it's not pronounced like ordinary large numerals, though. Maybe it is rather a sequence of numerals: ("4","4","7","1","7","3","8","4"). But these suggestions both suffer from translation problems: my telephone number can be given in Braille, and I suppose it can also be given in Roman numerals: "IV IV VII I...". (Imagine a telephone where the buttons are labeled like that: it doesn't seem that you can't dial my number with it.)

So I think my telephone number is neither a number nor a numeral nor a sequence of numerals, but rather a sequence of numbers: the ~~quin~~octuple (4,4,7,1,7,3,8,4). This brings back the dependence on base notation: (4,4,7,1,7,3,8,4) in decimal is (4,4,7,1,7,3,10,4) in octal and (100, 100, 111, 1, 11, 1000, 100) in binary. But it's not as bad this time as it was above: at least my telephone number definitely begins with 4 (= 100 in binary, = IV in Roman), and the fact that we read it as a sequence of numerals in base-10 isn't really hard to explain. (In fact, I don't even know how the octal "10" is pronounced: "ten"? "eight"? "one zero"?)

Some might worry that the ~~quin~~octuple (4,4,7,1,7,3,8,4) is a complicated set-theoretic construction: an ordered pair of a number and an ordered pair of a number and an ordered pair... (and something much more baroque when the pairs and numbers are eliminated a la Kuratowski and von Neumann). Does everyone who knows my telephone number really know that set-theoretic entity? Doesn't that mean that you have to be a set theorist in order to know my telephone number?

I find this objection misguided, but a lot of philosophers have exactly parallel reservations about set theoretic constructions of propositions and meanings. If they are right, the conclusion seems inevitable: telephone numbers comprise a sui generis ontological category.

Comments

# lumpy buttocks cheese on 26 April 2006, 08:26

"So I think my telephone number is neither a number nor a numeral nor a sequence of numerals, but rather a sequence of numbers: the quintuple (4,4,7,1,7,3,8,4). This brings back the dependence on base notation: (4,4,7,1,7,3,8,4) in decimal is (4,4,7,1,7,3,10,4) in octal and (100, 100, 111, 1, 11, 1000, 100) in binary."

There is no dependence on base notation. All of those strings of numerals denote one and the same sequence of numbers given that their bases have been specified; otherwise it would not make sense to say that one is (equivalent to) the other modulo base.

What's wrong with saying that your telephone number is the number denoted by some numeral expression? Thus my telephone number, e.g., is the number denoted by the numeral 4985890. It just so happens that such numbers are read differently when they are associated with telephone lines in a particular way.

I don't think I see a problem, but perhaps that doesn't say much.

# Kenny Easwaran on 27 April 2006, 05:42

"So I think my telephone number is neither a number nor a numeral nor a sequence of numerals, but rather a sequence of numbers."

Actually, that's not quite true - people who watched much American TV a few years ago will be familiar with the numbers 1-800-FLOWERS and 1-800-MATTRES. Thus, I think it makes sense to also say that your phone number is 4471-SETH. (I used www.phonespell.org to come up with that.)

Given this data, I think it makes sense to say that a phone number is a sequence of keys on a phone - but those keys can be denoted however you want (with base 10 digits, base 8 numerals, letters of the alphabet, or whatever).

The worries about sequences don't seem too problematic, because people can certainly know all sorts of things about sequences without being committed to some set-theoretic reduction of them. So at worst this makes sequences into a sui generis ontological category - I don't think we quite reach the level of Jubien's worries about propositions. But it would be an entertaining reductio of such arguments!

# wo on 02 May 2006, 22:51

Hmm, it seems to me that your keys proposal requires some means of identifying keys, so that my number becomes something like (middle left key, middle left key, bottom left key, ...) or (fourth key, fourth key, seventh key, ...). But surely telephones could have different key orderings, and I suppose some don't have keys at all -- maybe there are phones where you just say the number.

You're right that I didn't think much about the American use of words for phone numbers. I'd say the words here are just codes for sequences of numbers.

Wolfgang Schwarz

What is my telephone number?

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