On 11/3/2012 5:39 AM, Bruno Marchal wrote:
[SPK] In the absence of a means to determine some property, it is incoherent and sometimes inconsistent to claim that the property has some particular value and the absence of all other possible values.


In math this is called (mathematical) solipsism.

Dear Bruno,

How is it solipsism? Solipsism is <http://en.wikipedia.org/wiki/Solipsism>: "Solipsism is the philosophical idea that only one's own mind is sure to exist. The term comes from the Latin solus (alone) and ipse (self). Solipsism as an epistemological position holds that knowledge of anything outside one's own mind is unsure. The external world and other minds cannot be known, and might not exist outside the mind. As a metaphysical position, solipsism goes further to the conclusion that the world and other minds do not exist."

My point is that numbers, by your notion of AR, are solipsistic as there is literally nothing other than the numbers. I reject AR because of this! Numbers alone cannot do what you propose.

This post argues similar to my point: http://mathforum.org/kb/message.jspa?messageID=5944965

"Conventional solipsism is a logical philosophy whose underlying views
apply equally to mathematical philosophies of neopythagoreanism and
neoplatonism as well as mathematical realism and empiricism generally.

The well established philosophical principle of solipsism is that only
the individual is or can be demonstrated to exist. But the problem is
that if this principle were actually demonstrably true it would also
make it false because the "truth" established would ipso facto make
the principle beyond control of any individual.

Nobody really thinks solipsism is true. But the difficulty is no one
can prove or disprove the concept because no one can prove the
foundations of truth in absolute, necessary, and universal terms."


This article http://digitalcommons.macalester.edu/cgi/viewcontent.cgi?article=1020&context=philo argues against the claim that Intuitionism is solipsistic. I reject Intuitionism as a singular coherent theory of mathematics, but I do accept it as a member of the pantheon of "interpretations" of mathematics.

--
Onward!

Stephen

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