On 10/30/2012 2:31 PM, Stephen P. King wrote:
On 10/30/2012 5:21 PM, meekerdb wrote:
On 10/30/2012 2:03 PM, Stephen P. King wrote:
On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of symbols "17 is prime"
is an indicator of some particular mathematical object and one of its particular
properties, then how does "17 is prime" come to mean anything at all?
I agree with that. But you're talking about the tokens "17 is prime" not the concept
that 17 is prime. Could not a person who grew up alone on an island realize that 17
has no divisors, and he could even invent a private language in which he could write
down Peano's axioms.
Why are you using such trivial and parochial framing for abstract questions? Why
the reference to single individuals? Did you not understand that I am claiming that
meaningfulness requires at least the possibility of interaction between many entities
such that each can evaluate the truth value of a proposition and thus can truthfully
claim to have knowledge of true statements?
A person that grew and died on a desert island may have discovered for itself that
17 objects cannot be divided into equal subsets,
So no additional entities are needed for a person know that 17 is prime and to express
it symbollically. You seem to contradict what you just wrote in the prior paragraph.
Rubbish. You are projecting your concept of "17 is prime" onto an imaginary entity
and discussing the idea of that entity with me, that makes 3 people - not one; even if
one - the person on the island - of them is just in your and my mind.
And another dozen people may be reading this. What different does that make to the
question of whether one person alone can know a mathematical truth? You seem to agree
that he can and yet deny it is meaningful at the same time.
Brent
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