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 - 16:43:01 PDT