Bruno, I cheerfuly accept both of your notations about a genius. Everybody
is one, just some boast about it, others are ashamed. I just accept. I feel
what you call classical logic is my 'common sense' (restricted of the ways
how the average person thinks). Linear logic (Sorry, Jean-Yves Girard, never
heard your name) is not my beef: in my expanded totality vue nothing can be
linear. We 'think' in a reductionist way - in models, i.e. in limited
topical cuts from the totality, becuse our mental capabilities disallow more
- I think pretty linearly.
I just try to attempt a wider way of consideration (I did not say:
successfully). In such the real 'everything' is present, in unlimited
relations into/with all we think of - without us noticing or even knowing
about it. (Some we don't even know about).
We just follow the given axioms (see below) of the in-model content and stay
limitedly.
When Gerolamo Cardano screwed up the term* 'probability* - as the first one
applying a scientific calculability in his De Ludo Aleae he poisined the
minds by the concept of a - mathematically applicable - homogenous
distribution-based probability (later: *random,*
the reason why the contemporaries of Boltzman could not understand him
- before Einstein.) Alas, distributions are not homogenous and random does
not exist in our deterministic (ordered) world (only ignorance about the
'how'-s)
*Statistical* as well are the 'given' distributional counts within the
chosen model- domain.
*Math (applied)* was seeking the calculable, so it was restricted to the
ordered disorder.
If something is fundamentally impredicative (like the final value of pi) I
am thinking of a 'fundamental' ignorance about the conditions of the
description.(cf: 2-slit phenomenon).
*AXIOMS, however, are products of a reversed logic:*
they are devised in order to make our theories applicable and not vice
versa.
My point:
with a different logic, different axioms may be devised and our explanations
of the world may be quite different. E.g." 2+2 is NOT 4". You may call it
'bad' logic, Allowed. What I won't allow is *"illogical" *unless you checked
ALL (possible and impossible) logical systems.
Reading your enlightening remarks (thank you) I see that I don't need those
'signs' to NOT understand, you did not apply them and I did not understand
your explanatory - lettered and numbered - par. (Why are 'idem per idem' *
not* identical, (as A = A & A) when naming 1+1=2 as A, - from 1+1=2, the
format 1+1=2 & 1+1=2 is deducible? (Of course I don't know the meaning of
'deducible'.) You also sneaked in the word 'modal' operator, for which I am
too much of a beginner.
That much said: I ask your patience concerning my ignorance in my
questions/remarks on what I think I sort of understood. I may be 'on the
other side'.
Best regards
John
On Wed, May 20, 2009 at 10:43 AM, Bruno Marchal <marchal.domain.name.hidden> wrote:
>
>
> On 20 May 2009, at 00:01, John Mikes wrote:
>
> > As always, thanks, Bruno for taking the time to educate this bum.
> > Starting at the bottom:
> > "To ask a logician the meaning of the signs, (...) is like asking
> > the logician what is logic, and no two logicians can agree on the
> > possible answer to that question."
> > This is why I asked -- YOUR -- version.
> > *
> > "Logic is also hard to explain to the layman,..."
> > I had a didactically gifted boss (1951) who said 'if you understand
> > something to a sufficient depth, you can explain it to any avarage
> > educated person'.
> > And here comes my
> > "counter-example" to your A&B parable: condition: I have $100 in my
> > purse.
> > 'A' means "I take out $55 from my purse" and it is true.
> > 'B' means: I take out $65 from my purse - and this is also true.
> > A&B is untrue (unless we forget about the meaning of & or and . In
> > any language.
>
>
> As I said you are a beginner. And you confirm my theory that beginner
> can be great genius! You have just discovered here the field of
> linear logic. Unfortunately the discovery has already been done by
> Jean-Yves Girard, a french logician. Your money example is often used
> by Jean-Yves Girard himself to motivate Linear logic. Actually my
> other motivation for explaining the combinators, besides to exploit
> the Curry Howard isomorphism, was to have a very finely grained notion
> of deduction so as to provide a simple introduction to linear logic.
> In linear logic the rule of deduction are such that the proposition
> "A" and the proposition "A & A" are not equivalent. Intuitionistic
> logic can be regain by adding a "modal" operator, noted "!" and read
> "of course A", and !A means A & A & A & ...
>
> Now, a presentation of a logic can be long and boring, and I will not
> do it now because it is a bit out of topic. After all I was trying to
> explain to Abram why we try to avoid logic as much as possible in this
> list. But yes, in classical logic you can use the rule which says that
> if you have prove A then you can deduce A & A. For example you can
> deduce, from 1+1 = 2, the proposition 1+1=2 & 1+1=2. And indeed such
> rules are not among the rule of linear logic. Linear logic is a
> wonderful quickly expanding field with many applications in computer
> science (for quasi obvious reason), but also in knot theory, category
> theory etc.
>
> The fact that you invoke a "counterexample" shows that you have an
> idea of what (classical) logic is.
>
> But it is not a counter example, you are just pointing to the fact
> that there are many different logics, and indeed there are many
> different logics. Now, just to reason about those logics, it is nice
> to choose "one" logic, and the most common one is classical logic.
>
> Logician are just scientist and they give always the precise axiom and
> rule of the logic they are using or talking about. A difficulty comes
> from the fact that we can study a logic with that same logic, and this
> can easily introduce confusion of levels.
>
>
>
>
>
>
>
>
>
> > *
> > "I think you are pointing the finger on the real difficulty of logic
> > for beginners...."
> > How else do I begin than a beginner? to learn signs without meaning,
> > then later on develop the rules to make a meaning? My innate common
> > sense refuses to learn anything without meaning. Rules, or not
> > rules. I am just that kind of a revolutionist.
>
>
> I think everybody agree, but in logic the notion of meaning is also
> studied, and so you have to abstract from the intuitive meaning to
> study the mathematical meaning. Again this needs training.
>
>
>
>
> > Finally, (to begin with)
> > ..."study of the laws of thought, although I would add probability
> > theory to it ...???"
> > I discard probability as a count - consideration inside a limited
> > (cut) model, 'count'
> > - also callable: statistics, strictly limited to the given model-
> > content of the counting -
> > with a notion (developed in same model) "what, or how many the next
> > simialr items MAY be" - for which there is no anticipation in the
> > stated circumstances. To anticipate a probability one needs a lot of
> > additional knowledge (and its critique) and it is still applicable
> > only within the said limited model-content.
> > Change the boundaries of the model, the content, the statistics and
> > probability will change as well. Even the causality circumstances
> > (so elusive in my views).
>
>
> I am afraid you are confirming my other theory according to which
> great genius can tell great stupidities (with all my respect of
> course <grin>).
> Come on John, there are enough real difficulties in what I try to
> convey that coming back on a critic of the notion of probability is a
> bit far stretched. Einstein discovered the atoms with the Brownian
> motion by using Boltzmann classical physical statistics. I have heard
> that Boltzman killed himself due to the incomprehension of his
> contemporaries in front of that fundamental idea (judged obvious
> today). But today there is no more conceptual problem with most use of
> statistics 'except when used by politicians!).
> Of course you are right, statistics depends on the "boundaries", but
> that is exactly the reason why we need a theory of probability, to
> avoid dishonest applications, and this has been done by Kolmogorov in
> a convincing way.
> here, I was just following George Boole in defining, in a very general
> way, the laws of thought by LOGIC + PROBABILITY. This is still
> defensible if we accept those words in a large open minded sense.
>
> I will have opportunities to say more when I will explain a bit more
> of the math, for UDA-step7, and a bit of AUDA, to Kim.
>
> Best,
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
> >
>
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Received on Wed May 20 2009 - 15:41:33 PDT