Chlamydia In The Mouth

numbers and succession: metamathematical reflections, historical and educational activities on a song Leopardi (1)

GIORGIO TOMASO BATHROOMS


1. Medley of thoughts, November 28, 1820
wrote the twenty-two Giacomo Leopardi:
"The man without the knowledge of a speech, can not conceive the idea of \u200b\u200ba fixed number
. Imagine you have thirty or forty stones,
senz'avere a name to be given to each one, that is, one, two, three,
to the last name, ie thirty or forty, which contiene la
somma di tutte le pietre, e desta un'idea che può essere abbracciata tutta in uno
stesso tempo dall'intelletto e dalla memoria, essendo complessiva ma definita
ed intera. Voi nel detto caso, non mi saprete dire, né concepirete in nessun
modo fra voi stesso la quantità precisa delle dette pietre; perché quando siete
arrivato all'ultima, per sapere e concepire detta quantità, bisogna che l'intelletto
concepisca, e la memoria abbia presenti in uno stesso momento tutti
gl'individui di essa quantità, la qual cosa è impossibile all'uomo. Neanche
it should help the eye, wanting to know why the number of certain objects
present, and not knowing how to count, you need the same operation and simultaneous
individual memory. So if you do not know except one
numerical designation, and counting could not say more than one, one, one;
to how much attention you would put, akin to collect progressively
with the soul and memory The precise amount of these units until the last, you'd
in the same case. So if I did not know that two other names
etc.. Except a very small amount, like five or six, which
memory and intellect can not conceive of speech, because you get to
simultaneously present all it amounts to a few individuals ... Typically
the idea of \u200b\u200bthe precise number, or with the help of speech or not, has never
instantaneous, but composed of succession, more or less long, more or less
difficult, according to the measure the amount (by Zibaldone of thoughts, 28 November 1820
: Leopardi, 1969).
This track offers some reflections on the concept of natural number.

First, it is clear the central importance that the author attributes to the language
(1). Early onset ("The man without the knowledge of a speech,
can not conceive the idea of \u200b\u200ba fixed number), in fact, Leopardi
explicitly refers to the essential role of the name of the individual numbers
natural: it is thanks to 'name' that we can enumerate the elements of a finite
(that we can identify, gradually, his
subsets of increasing cardinality) until you hear the whole
(to fix "an idea that can all be embraced in the same time
intellect and memory, but defined as total and complete ").
This concept is therefore closely linked to the numerical count, when
to enumerate: the role of the 'speech' is to be decisive in its
as it allows the unfolding of the proper implementation of such a measure ("And so if you do not
I knew except a single numerical designation, and counting
could not say no more than one, one, one ...»). Leopardi, towards the end of the passage quoted,
clearly recognizes that the very concept of numbers through (and beyond)
the succession of 'Name', is linked inextricably
to count ("The idea of \u200b\u200bthe exact number, or with the help of speech or not, is not
never instantaneous, but composed of succession) (Borg & Pepe, 1998).
This consideration can be modern and thorough recovery
by examining some of the settings of arithmetic, as we shall see that based on the introduction of recursive
their roots.