Trivial yes, pedantic no.
It is unclear what it is to conceptualize a number, consider a (celebrated
example) the Collatz number is the number of steps from any arbitrary positive
to 1 given the two rules here quoted
operation on an arbitrary positive
integer<https://en.wikipedia.org/wiki/Positive_integer>:
· If the number is even, divide it by two.
· If the number is odd, triple it and add one.
(nobody knows whether this is true of any number, it is true of what we know of
the numbers we know)
What would it be for the Collatz number of 2 to “cease” existing being 1?
(viz. take 2, the rule to be applied is the first the result is 1, collatz nu1
Viz take 3, appl 2nd rule = 10, appl 1st rule =5, appl 2nd rule =16 appl 1st
rule =8 appl 1st rule =4 appl 1st rule =2 appl 1st rule =1
I leave it to you to compute the Collatz number of 3)
Best regards
From: lit-ideas-bounce@xxxxxxxxxxxxx [mailto:lit-ideas-bounce@xxxxxxxxxxxxx] On ;
Behalf Of Omar Kusturica
Sent: Thursday, October 13, 2016 3:13 PM
To: lit-ideas@xxxxxxxxxxxxx
Subject: [lit-ideas] "You have dialed a non-existent number"
Okay, this is probably trivial and/or pedantic, but the above announcement is
surely false. If I have dialed a number, I must have imagined it first. If I
can imagine it, then it is NOT non-existent. A number which can be
conceptualized but does not 'really' exist seems to be an impossibility. In
other words, once a number is conceptualized, it exists necessarily.
Or no ?
Perhaps the resident Fregeans will have some comment on this.
O.K.
