Re: Mathematical Logic, Podnieks'page ...
At 16:44 04/07/04 -0400, John M wrote:
I think we got into a semantic quagmire. I feel a different meaning in my
(5th language English) TRUTH from what I read as the (4th language French)
'verité'. I use 'truth' as the OPINION one accepts as being not false.
Yes but then you will misunderstand the Theaetetus definition of knowledge
(as true opinion). I think it is just a question of vocabulary. See below...
What
you imply sounds to me as 'constructing a reality. Truth has nothing to do
with decisionmaking. Decision comes into the picture only in the 1st
person thinking to decide whether the item is not false. If I agree, it is
(my) truth as well.
?
JM:
the fact
that anything we may know (believe or find), is interpreted by the ways
how our 'human' mind works -
BM: SURE! (but it is invalid to infer from that that truth itself
depends on
our beliefs and findings).
JM: Sorry, Bruno, you sound in the parethetized remark as a person who
believes
in some eternal 'truth' chisled in the (nonexistent) stone of (nonexistent)
supernatural 'law', - or rather: takes something like 'truth' as the
installations (facts??)of the world. There is no such thing as THE TRUTH -
ITSELF at least not among people who think... Maybe some religious fanatic
fundamentalists know the truth, the only ONE, worthwhile killing (-dying)
for.
Nobody in this list pretend to know the truth. A theory is always a
(hopefully consistent) set of beliefs, mainly.
But we can privately hope our beliefs are true. The point is: do you find
comp inconsistent? Do you find QM inconsistent? Do you find PA inconsistent?
(and then do you find that plausible, etc.)
Also, can you conceive that QM could be true, independently of us knowing
it, except in the thaetetus sense of just believing it, and that by chance
it *is* true.
Also, truth is an object of study by logicians. In classical
propositional logic
truth is just a function from the propositional variable {p, q, r, ...}
into {O, 1}, in
the company of rules to extend those truth values to compound propositions,
like saying that pq is true in case p is true and q is true, which for
the logician
means only the function above send p and q on 1. But logicians considers
many, many, many other sort of truth valuation (abstractly they are
sub-object
classifier, truth being the object itself, so in classical logic truth can
be represented
by a set, in intuitionistic logic truth can be represented by a
topological space,
in quantum logic truth can be represented by a Hilbert space, but that's
for much latter ...).
Even the facts are explanations for observations - and we saw lately
discussions on observers.
The flat Earth: a fact (Ptolemaios), hell: a fact (A. Dante), the atoms in
the molecules I synthesized: facts, then all these things turned into
fiction. Props of some belief system.
I doubt very much Ptolemaios maked flat earth a fact. For Dante I don't know
but I would have believe he wrote a fiction (?)
Anyway, we are interested in ALL belief systems. I should have give you a
better
answer last day when you asked:
With the ideas about 'quite' different universes why are we
closed to the idea of 'quite' different mathematical thinking?
I should have told you that this is exactly what the Universal Dovetailer
Argument (UDA) *forces* us to do: if comp is true we have to explain
the physical appearances by a sort of mean on all consistent belief
systems. And giving the fact that the tool exists to study the basic shape
of that means (the interview of the universal machine), we can do it, and
compare with the empirical physics.
Now let me take a deep breath and if I am still 'on' this list, later I will
come back to 'math'.
(I don't know Wilfried Hodge, will not read him for this purpose.)
You know John to tell you the truth I would like to confess you that I am
a believer indeed in the sense that I really feel bad (like lying to myself)
when I try to put into doubt the laws of the excluded middle concerning
arbitrary
arithmetical sentences. I believe the 667nth fortran program running on
the data
766 will either stop or ... not stop.
This does not prevent me to appreciate many other logics. (and classical logic
is the simplest to talk
It is Wilfrid Hodges, I put a e because it is a common Flemish name here,
I probably mess up with the s as I always do.
Apology to Wilfrid Hodges.
I recommend it much for the non mathematically minded people who
want a first rate introduction to (classical) logic. Hodges defines logic
as the study
of the consistent set of beliefs, and show quickly and simply the relation
with the more common definition of logic as science of the valid argumentation.
He wrote also good (but more technical) books in model theory.
Hodges' Logic book is a nice cheap companion to Smullyan's Forever
Undecided.
Shortcuts to G. (The key mathematical tool to transform the reversal
between the
physical universes/psychological universes forced in the UDA.
Re: Mathematical Logic, Podnieks'page ...
Bruno, I really cannot work this way. I still prepare to reply to your earlier post (to me) and here I have the repost on the 1st part with lots to be replied upon. G. I am in debt with ~30,000 books I did not read. Never will. How much time may I have left? 30-40 years? (I am pushing 83). Will my mind give up? My hip did already. (My fingers did not, I still perform classical piano-music for a local-public audience - next: October). So I gave up checking on past millennia wisdom and work on the present - absorbed and developed for myself since retirement. The oldies speculated in a cognitive inventory of the mind which was much poorer than the lately absorbed enrichments. I appreciate their wisdom, as 'function of mind', but the conclusions MAY be old. I am not a judge of that, but can stay out of such argumentations. Comp, QM, you ask? Aren't they within the mindset of the minds within THIS universe, which I deemed human ways of thinking? Same good old math-conceptualization. I am talking about something not-matching. Cohen and Stewart played such tunes in their enjoyable books (Collapse of Chaos and Figments of Reality) - their aliens, the Zarathustrans, with their octimalization (8?). Of course that was still sort of human switch, a bit of Tao etc. truth is an object of study by logicians. My best wishes for them. I went through many 'thruths' - different religious ones, reincarnational, pragmatic natural science, astrology, Indian, Marxist, Leninist, atheist (who require a god to deny), every one had something attractive, but... and settled with my scientific agnosticism: not even the contrary is true of what people believe. (That really came from politics). If you go into variables: my wholistic views allow no fixed conditions and unlimited variabilities upon which a mathematician friend remarked: well, this is a bit steep. Only models can have boundaries, quantities, fixed qualia etc. That goes also for QM (Comp I don't know, never let it clarify in my mind). Even topics are cut out from the extratopical wholeness. Limited Models. A map is a model, a territory a wider one. Most minds (on this and other lists) work within a certain modeling (we cannot do better, that's the way we can manage with the material tool we apply for thinking: the neuronal brain, restricting the mind into human logic (oops!). Is my wholistic thinking inept for achieveing practical conclusions? you bet it is. We just started to tackle with such ideas, have to find suitable concepts and (formulate?) words to express them. ...(UDA) *forces* us to do: if comp is true we have to explain the physical appearances by a sort of mean on all consistent belief systems. (if!) - now the 'physical appearances' are the mind's interpretations upon impact inknown, lately observed by instruments WITHIN this system of ours. And I did not ask for CONSISTENT belief systems, before I even know what kinds may exist at all. We know SOME, here and now, pertinent to our cultural basis (human mindset of the present local(?!) societal conditions). I am consistent in my agnosticism. All argumentative support from within is useless for without. Now I can return to thinking about math (for the 2nd part reply), although I don't know much about it. It was my elective in my Ph.D. work (1948), never used it later, beyond arithmetics, mostly by my slide ruler, while inventing and implementing a pioneering-worldlevel industrial branch, 38 patents, consulting (and solving technical production-problems) on 3 continents over 4 decades. All in the simplest reductionist technical common sense creativity. I am ready for a coffee, myself. John Mikes - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, July 05, 2004 10:52 AM Subject: Re: Mathematical Logic, Podnieks'page ... At 16:44 04/07/04 -0400, John M wrote: SNIP I copied out some sentences, the rest is in the archives.
