[FOM] Which is clearer, "integer" or "symbol"?

[Timothy Y. Chow]

It is my impression that, at least among people without formal training in 
logic and foundations, there has been a gradual shift over time from the 
point of view that an "integer" is the clearest mathematical concept, to 
the point of view that a "symbol" is the clearest mathematical concept.  
I am wondering if other FOM readers have a similar impression, and if so, 
whether any solid historical evidence can be accumulated in support of 
my claim.

To give you an idea of what I'm talking about, in Kunen's book on set 
theory and independence proofs, he asks the rhetorical question, "But what 
is a symbol?"  The implication is that the concept of a symbol might not 
be totally clear.  Kunen then addresses the issue by *defining* a symbol 
to be an integer.  Again, the implication is that the concept of an 
integer is clearer than that of a symbol.

On the other hand, it has been my experience that nowadays many 
mathematicians, computer scientists, physicists, etc., who have some 
casual interest in logic and foundations have the opposite point of view.  
"Symbols," "strings," and rules for manipulating them are considered 
unproblematic.  Integers, on the other hand, are mysterious, and suspect.  
The suspicion may be fueled by a naive form of anti-Platonism, or by 
confusion about the status of statements such as "PA is consistent."  What 
prevents such people from seeing that analogous skepticism can be directed 
towards symbols and strings I'm not sure, but perhaps familiarity with 
computers has something to do with it.

So to recap my question...is it just me, or has there really been a 
sociological shift over the past several decades?

Tim