On 11/1/2018 4:02 PM, Philip Thrift wrote:
On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote:
On 11/1/2018 11:59 AM, Philip Thrift wrote:
On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift
<[email protected]> wrote:
/> infinite time Turing machines are more powerful than
ordinary Turing machines/
That is true, it is also true that if dragons existed they
would be dangerous and if I had some cream I could have
strawberries and cream, if I had some strawberries.
/> How "real" you think this is depends on whether you
are a *Platonist *or a*fictionalist*./
No, it depends on if you think logical contradictions can
exist, if they can then there is no point in reading any
mathematical proof and logic is no longer a useful tool for
anything.
John K Clark
Of course logics are fiction too. (They're just languages after all.)
OK. Sentences written down are physical and not fictions. But can
they be contradictory? How does "This page is red." contradict
"This page is blue." unless they have some meaning as
propositions. But this must be a relation between a proposition
(an abstract thing) and a fact (the color of this page).
Brent
Sentences, like this one, are physical *only* in the sense that they
are (in this case) made up of electronic bits displayed on a screen
(as you are looking at right now, maybe on a laptop or smartphone) -
or they could be made up of ink strokes on paper, etc.
One can't read anything more into them physically that that. What one
reads out of them (a person looking at this sentence, or a computer
scanning one) is a difference matter.
There are no abstractions in an immaterial sense.
But there are abstractions in the sense that the same proposition is
instantiated in different substrates. So the contradiction can be
between different instances, e.g. a spoken sentence can contradict a
written one.
Brent
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