At 06:57 03/07/04 -0400, John M wrote:
(Bruno: am I still in your corner?)
OK. Let us see.
Dear Kory, an appeal to your open mind: in the question whether ...."we discovered math or invented it"..., many state that the first version is 'true'. Beside the fact that anybody's 'truth' is a first person decision,
Then I would decide to have food when I am hungry, to have water
when I am thirsty. I would decide Riemann hypothesis true and even proved by me,
and I would decide to get those million dollars.
I would decide you to be a platonist, my friend, ...
I would decide peace everywhere,
...if truth was a matter of first person *decision*.
Seriously, I am afraid you confuse the luckily adequate first person feeling
the first person lives in front of truth and truth itself.
the fact that anything we may "know" (believe or find), is interpreted by the ways how our 'human' mind works -
SURE! (but it is invalid to infer from that that truth itself depends on our beliefs,
including comp and all kinds of computers, as we 'imagine' (interpret, even formulate) the thoughts. I find the above distinction illusorical. We may FIND math as existing 'before' we constructed it, or we may FIND math a most ingenious somersault of our thinking.
Then you will miss the discovery that a big part of math and actually the whole of physics is a most ingenuous somersault of the universal machine thinking. (and the discovery that comp imply that in a testable manner)
To 'believe' that 17 is prime? of course, within the ways as we know (and formulate) the concept 'prime'. Axioms, conventions.
Are you not confusing sentences/theories with proposition/truth? Read Wilfrid Hodge Penguin's Logic page 39. (I can quote it if you insist).
With the ideas about 'quite' different universes why are we closed to the idea of 'quite' different mathematical thinking?
Because for some reason we are (or we will be) studying different sort of
mathematical thinking, and so, to avoid confusion, it is better to agree
at the start on the elementary principle we share. Logic, is the science
of different thinking, actually. Boolean (classical) logic is the simplest to use
in math (but not the simplest to describe in boolean logic because
the similarity of the object and the subject ...)
We don't have to go to another universe: the Romans subtracted in their calendar (counting backwards from the 3 fixed dates in a month) like "minus 1 = today, minus 2 = yesterday and so on. I wonder how would've done that Plato (before the invention of 0)? Our list-collegues think about math(s) in quite different concepts from the classic 'constructivist(?)' arithmetical equational thinking.
Should I understand you are realist for intuitionistic arithmetic ? It is enough
for the reasoning I propose.
how far can go a quite differently composed mind - maybe in an organizational thinking/observing system of a universe NOT based on space - time?
You underestimate the hardness to understand ourselves despite our probable common space time background.
What can be called 'mathematics'? (Theory(s) of Everything?)
Here you jump to an infinitely difficult and controversial question. I have criticize Tegmark for relying on that problem. One of the power of comp is that it made possible to give information on fundamental matter without needing to define 'mathematics".
Vive le 'scientific agnosticism'!
Right! (At the condition that this principle does not discourage us to propose
(Bruno: am I still in your corner?)
If you really believe truth is just a matter of first person decision, you are not.
Neither if you belief the primality of 317 is a matter of convention.
Only the language is (partly) conventionnal, not the proposition, including their
We must agree on a minimal amount of reasoning if only to be able to talk
about others ways of reasoning. If not: it will be confusing from the start.
----- Original Message ----- From: "Kory Heath" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, July 02, 2004 4:10 PM Subject: Re: Mathematical Logic, Podnieks'page ...
> At 02:45 PM 7/2/2004, Jesse Mazer wrote: > >As for the non-constructivism definition, is it possible to be a > >non-constructivist but not a mathematical realist? If not then these > >aren't really separate definitions. > > It may be that all non-constructivists are mathematical realists, but some > constructivists are mathematical realists as well (by my definition of > "mathematical realism"). So "Platonism == mathematical realism" and > "Platonism == non-constructivism" are two different statements. I can > imagine a non-constructivist asking "Are you a Platonist?" (thinking "Do > you accept the law of excluded middle?"), and a constructivist answering > "Yes." (thinking, "yes, valid constructive proofs are valid whether or not > any human knows them or believes them.") This miscommunication will lead to > confusion later in their conversation. > > -- Kory > >