Ok, so, tonight, we're gonna discuss "reasoning". Actually, for you, nnp, who wanted a sum up, that'll do it. :) So, what's behind this "reasoning"? firstly, mathematical logic then, enigmas, deduction, formal logic, paradoxes, self-references, absurd, and.. AI Now, a quick explanation of the difference between an enigma and a paradox : An enigma has a solution or an hypothesis that avoids any contradiction. In a paradox, none of the hypotheses is valuable. Well, there are different kind of paradoxes. Mainly three types actually : 1) False reasoning : That is, when an error is "well hidden" in the reasoning. For example, I assume all of you know the "proof" that 1=2, right? yes actually that n = 2n for any n in Z but go on 1=2? yes So, I'll do it for those who don't know it yet ;) : hm.. never come across this before... explain I think C dissagrees with you here. So, explain please. :) Let's take : a=b. Now, let's multiply by a : aČ = ab. Then, let's add a : aČ+a = ab+a. you better use ^ to signal exponentiation it's appearing as weird symbols here ok, I'll do it again then : You fail SysSpider a=b a^2 = ab (let's add a^2 in fact) 2a^2 = ab + a^2. 2a^2 - 2ab = a^2 + ab - 2ab. 2(a^2 - ab) = 1(a^2 - ab) So : 2 = 1. ... Now, who can spot the mistake? :) the flaw is that a^2 - ab = 0 and you can't divide by 0 yep :O ahh, mmhmm did you get it? Yup. okee 2) The mental experience. This is a situation that we can easily imagine, but, that can hardly become true. This situation would show that conventional postulates can lead to a contradiction. This type of paradox shows that sometimes, our "intuition" is wrong. To illustrate this, you may want to see Galileo's paradox : http://en.wikipedia.org/wiki/Galileo's_paradox . 3) The authentic paradox : No false reasoning, no "intuition is wrong," these paradoxes remained unanswered... Now, another topic of "reasoning" is : Ontology. I'll briefly explain what it is. If you want a deeper explanation, see : http://en.wikipedia.org/wiki/Ontology (for the philosophical aspect) Or here : http://en.wikipedia.org/wiki/Ontology_%28computer_science%29 , for the.. well, you can guess it from the link ;) So, ontology is : the study of the most certain reality. Can we, just like Euclid did in geometry, deduce the theorems of knowledge from a limited number of axioms? Descartes got his hands on it. Unfortunately, almost all propositions, up to a certain point, are "doubtful". Example : Is Paris the capital city of France? What if we were manipulated and "someone" wanted to make us think that Paris is the capital of France? What's, up to you, closer to reality : the tyrannosaurus or the Loch Ness monster? Who assures you that there are not crazy people, who, manipulating your brain, make you believe that : 2+2 = 4, while it is in fact : 2+2 = 314? no one can do such thing i mean, assert it I think and therefore I am. unless you take a religious perspective and ask God the doubt-of-everything thinking is Descartes' in his Cogito Ergo Sum Indeed. :) nobody can assure you these things, you can only know something like "you" exists because of that you have the ability to "talk" in you rmind. *your but i think it's flawed, since at a point he takes the existance of certainty from the existance of uncertainty and in the real world there are multiple levels of uncertainty but sorry, i'm making a philosophical discussion here no, don't worry please continue qwerty. :) k :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture +m Now, let's study a kind of reasoning, namely : syllogisms. This is the following type of reasoning : Every time that : "all A are B", and that "C is A", then : "C is B". For example : Every programmer is addicted to his computer. Ch4r is a programmer. Therefore, Ch4r is addicted to his computer. There are four kinds of syllogisms : A : positive universal E : negative universal I : positive particular O : negative particular Classical syllogisms (like the one above) are on the model : AAA. An example of EIO : No lemon contains sugar. Some fruits contain sugar. Some fruits are not lemons. The object of the syllogism can be in the position of the subject, or in the position of the predicate. So, there are 4^4 possibilities of syllogisms. (=64) Only fifteen of those make a valid reasoning. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture -m i just wanted to make a remark, given that we're mostly programmers some declarative and functional languages work by syllogisms too like Prolog i find it amazing to see these concepts applied in so many varied areas indeed :) moreover, like I told my philosophy teacher, syllogisms, are, in a way, "flawed." indeed, when we say : All men are mortals. Socrates is man. Hence, Socrates is mortal. The conclusion that "Socrates is mortal" doesn't bring anything. What do you mean by that? Indeed, at the beginning, we have "all men are mortals," so, we already know that Socrates is mortal, otherwise, we wouldn't be able to say this proposition. ;) yes, it doesn't expand our sphere of knowledge it simply derives a particular case Ah, it's useless. Exactly. for sure :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture +m Now, there's a special class of syllogisms, it is in fact a chain of syllogisms where the predicate of the 1st one becomes the subject of the following one. :) Can you find one? :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture -m
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:/ recursive xD hmm poo is brown brown is a colour hence poo is a colour ? lol wtf i might've completely missed the point :P yes, you got the point :) whee can you find a longer chain Ch4r? hmm I think *i* missed the point :p so, I don't think so.. me neither oh back to you qwerty. ;) qwertydawom, why don't you give us an example? yup Varu, can you explain? :) erm i'll try :P C is a language languages use grammars grammars are structures C uses structures like that? now, we all know that poo is brown, correct? exactly :) we also know that brown is a colour. is it brown, or does it have the property, colour: brown. colour We say it is, we mean that it's colour is brownish. correct so, based on the syllogisms done so far, we could go "well, poo = brown and brown = colour... so poo = colour?" The thing where it goes wrong is the amount of detail in the predicate. of course, afaik, poo has not been deemed a colour correct if a . b and b . c then a . c? the transitive property? Yes, another example : All ravens are rooks, All rooks are birds, All birds are animals, All the animals need oxygen, Conclusion : All the ravens need oxygen. Got it now? ~yes mhmm Eh, what's special about it? well, that's just a chain of syllogisms Noted. you go through a chain of properties from the initial predicate and you arrive a conclusion it's like demonstrating a theorem So instead of.. Eh.. nvm me example. I get it, continue please. ok :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture +m Now, let's introduce the two main types of reasoning : Deduction and Induction. Deduction : a logic way to draw conclusions (or logic truths) from hypotheses. (e.g. : the syllogism) Induction : a familiar process thanks to which we make generalizations. e.g. : All the ravens I've seen were black. Hence, all the ravens are black. So, on one hand, we have : Hypotheses -> Logical truths, while, on the other hand, we have : Facts -> Intuitive generalization. Therefore, in deduction, the error can be in the hypothesis, but the logical structure is solid. And, in induction, the error can be in the reasoning. Usually, the induction principle always appear as "less legitimate" than the deduction one. Note that : we use inductive reasoning to justify inductive reasoning : "Induction resisted to time, so, induction is a reliable way of reasoning." Paradox?! :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture -m i assume inductive reasoning has nothing to do with mathematical induction? Indeed. :) ok Oh, well, it is in a way similar, by the base case I mean. yes, generalising yep Induction isn't to be taken as a truth, but a mere generialization. (<--- bad spelling) but mathematical induction has a logical structure so it's not ad hoc exact. and, in mathematical induction, the point is the base case in fact we check it's true for the base case, just as the "inductive reasoning." yes and then, we assume it's true for "n.", that's where the inductive reasoning stops but, in math, you need to prove that "n+1" holds so the property can be true Now, for those who want stuff to read : quickly : http://www.swif.uniba.it/lei/foldop/foldoc.cgi?deduction+-+induction briefly, but a bit more explanatory : http://www.socialresearchmethods.net/kb/dedind.htm and, rather long, but complete : http://falcon.jmu.edu/~omearawm/deduction.html Now, let us interest to Hume's fork. :) Hume showed that there were only two admitted truths : Logic truth (e.g. : 2+2 = 4) Facts (e.g. : The raven sitting on SysSpider's house is black - j/k, no offense meant) xD no offense taken k ;) All the things that are neither logic truths, nor facts, are : nonsense. Nonsense : e.g. : Does the exterior world exist? This dual conception of truth is called : Hume's fork. (David Hume, scottish philosopher and historian - 1711/1776) i've rad about him Sorry for interupting, but what's the point of it? Both state the obvious. a categorisation of truth Facts are.. facts.. d'oh. Oh aha :) What's true and what's not. Feeling like reading more about it? : http://en.wikipedia.org/wiki/Hume's_fork Now, that part of reasoning from a "logic" point of view.. is done! :) So, like you seem to like it we'll get back to the philosophical point of view. :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture +m Dreams and reality. Who are we? Are we in a dream? Pretty philosophical, eh? :p First of all, let's mention "Chuang Tzu's fable" : Chuang Tzu once dreamt that he was a butterfly, and, when he woke up, he wondered if he wasn't a butterfly dreaming that he was a man... (Chinese fable - 4th c. BC) :qwertydawom!qwertydawo@bu-61EE8C6D.fbx.proxad.net MODE #lecture -m i heard of it it's a spicy subject, the distinction of reality and dreams when you're dreaming that's your reality You can't know if you're dreaming or not. Or, does someone dissagree? i agree the subject can never know in which reality he's in assuming multiple ones that's what leads so many people to the idea of God an external observer that tells us what the "supreme" reality is like Indeed. obviously this merely based in faith and philosophically there can't be a reality more real than another one I'd also like to mention the "brain in a vat" paradox. Aaah yes! i like that one. You think you're reading this text. i don't think i heard of that one... go ahead In reality, nothing proves that you're not a brain "having a bath" in nutritive substances, somewhere in a laboratory. Some crazy researcher might be 'steering' our brain. :O so you're confined to a certain perspective
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and you can't access the others from your own however, nothing proves you are such a brain either Ch4r: fear not, for i am here Something is steering you. ;x For whatever you may be. There has to be something. Electrodes are connected to this brain to which a crazy guy sends a stream of electric impulsions who simulate exactly the action of reading this text. Ahem.. sorry qwerty. >_> got kinda excited here. he jerked off! sorry :x This name was given to the enigma by students in philosophy. yes it's always possible that our reality is fake No problem, it's the "open corner" ;) hehe but can it be fake if it's for us real? it's possible that it is, it's possible that it isn't. probably why it's declared an enigma? hehe, that leads us to an interesting point : it'll certainly be "fake" for external observers, but their reality will be "fake" for us so it depends on your perspective How to establish the distinction between dream and reality? you can't, as Nick stated before Which unbreakable test can we build? or i don't think we can I've thought of that for a long and hard time, I didn't come up with something. Let's make an array : Test - Cons Point is, you can't have any reach outside of your.. "you" To pinch - We can feel the pain even when we're dreaming. i think about it often, in a slightly modified version Color? - We can dream in color, even if it's rare. how can we know what other people experience uuh sys? explain? like, how can i know what you're seeing right know or how do you feel your body You can't. exactly Richness of the details? - Why not in a dream? qwerty: so a dream can have any aspect of what we call reality Well if this is all a dream it's damn realistic. ;) there's the problem Draw a reasoning, do computations and check them on a computer? - can you find a con to this? :) they're supposed to be realistic because they're your reality It becomes a circleredenatie. >_> A circle.. ah.. qwerty: why can't the computer be your mind Heck it could be. you still have it in your dream, or it's in your dream that's ut ;) it* aww sorry guys, i've got to leave :( i'll ask for the logs to someone heh.. ok! they'll get posted on the site SysSpider, they'll be up at http://binaryuniverse.net/lectures.php by tomorrow so cya guys tomorrow :) and thanks for the interesting lecture thanks Ch4r and varu so bye np cya whoops qwertydawom, go on If we're conscious to be woken up, it proves that we're woken up, doesn't it? - But then, we couldn't make dreams in which we realise we're dreaming? Saying: can we dream in our dreams? :) if you're interested into this kind of stuff, I suggest the following book : http://www.cscs.umich.edu/~crshalizi/reviews/labyrinths-of-reason/ Now, let's get back to your friend Descartes. In his "Essays," Descartes wonders if the exterior world, along with his own body, is not illusion created by an "evil genius", who's ready to abuse him. Descartes was also wondering if, only his mind and the evil genius existed. (Rene Descartes - 1596/1650 - French) COGITO ERGO SUM! w0rd Let's assume you are doubting about the existence of your own mind. Feeling dumb already. >_> Then, you are doubting that you're doubting - meaning that you're really doubting! Something must provoke this doubt. You might be abused in several ways, but, at least, this abused mind exists. Hence, the oh-so-famous Descartes' conclusion : I think, therefore I am. Define I. good question, that is actually a question we had to deal with in our first philosophical essay :) it was: "When I say 'I', who's this 'I'?" :) Now, just to end this lecture, a last point : the confirmation theory. If we speak about I we mean ourselves. But what part? Who are we? Flash and blood, brain in box or... merely something that we cannot define? hehe go ahead. xD I'll shut >_> The confirmation theory (or, in an even wider sense : "epistemology") consits in studying how we know what we know : an inquiry on the process of deduction of valuable conclusions from obvious things. It is based on the study of enigmas and logic paradoxes who have the same roles as the Physics experiments. This ends the lecture, I'll let you "meditate" on what's been said! ;)