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 <[email protected]> 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/ > > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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