Search results

Thanks a lot for caring, jambaugh. Further thinking and a look into Pedrottis' Introduction to Optics solved the problem. It turned out what I sought after was the usual refraction matrix: a11 = 1, a12 = a21 = 0, a22 = n1/n2. This constitudes the tensorial form of Snell's law. I even managed to...

Thanks a lot, jambaugh. Very nice explanation. Though, I am rather familiar with tensor analysis in coordinates. Perhaps I haven't stated clearly where my understanding fails. Assume you have a Riemannian metric g, e.g. the one induced by the existence of a transparent medium, you can simply...

Dear readers, In my recent study of dyadic products I found out that physical quantities expressend as 2nd rank tensors can also be expressed as a dyadic product of two vectors. Similarly 2nd rank tensor fields can be expressed as pointwise dyadic products of two vector fields. One such...

Greetz, As you possibly know, there's a book by Arthur C. Clarke with the same name. The movie and the book were made with cooperation of Clarke and Kubrick in a period from 1964 to 1968. The book later became part of a series, even though Clarke refused to do a sequel at first. The books...

Greetz, 1. For Mentat: You mean this situation is inevitable? Inbound Aristotelian logic, you're right but we could simply use another logical system capable of expressing Existence. This new logical system will have its own deficiency but this one may be located somewhere less controversial...

... continued from the previous post "Fairness," "precision and "clarity," all my criteria of preference, are part of my current paradigm, and the remnant of my previous ways. I know that I'll always be biased someway, why not determine part of my biases consciously. Most individuals are...

Greetz, 1. For Preator Fenix: I guess you're a bit late for this thread but anyway you're welcome. I got problems reading your post but I managed to get something out of it. For the part where you addressed me, I think, you're making a mistake in thinking that an AI entity can be "made...

Preamble: Some of these quotes aren't specifically by those who're usually called Philosophers. Some of the quotes belong to individuals who may seem naive to many. Yet I found all of them interesting and related enough to post after RageSk8's worthy quotes...

... continued from the previous post Some of these many questions: 00. If the paradigm is all that is available to a human observer, where does common experience of human observers come from? Is there anything independent of observers? 01. Could it be that common experience comes from one...

... continued from the previous post Deductive method gives "proofs." Inductive method gives "theories." That's indeed a characteristic of a free thinker. For "good" is still a reserved keyword for many. "Goodness" as an absolute quality still prevails in many human minds and one would better...

Greetz, 1. For Mentat: I see, but then don't you mean Descartes, and his mates, were somehow biased right from the start? :wink: I'm kidding. It's all right; you can have "further" there if you like it. No, there's no problem with "pre-assuming" Q = T. That's the process of postulation...

… continued from the previous post Stop right there, please :wink:. First, who is associating "goodness" with what I said? I, personally, would be happy if "absence of distinguishing" could be proven existent or non-existent but don't associate my "happiness" with "goodness," "truth,"...

Greetz, 1. For Mentat: All right but for the usage of the phrase "further validates" which is a reference to an illogical background. It sounds like Descartes' existence had been validated before and the Demon's challenge has only "further" validated it, while this isn't true for the Demon's...

Hey Mentat, where are you? Are you alright? I'm waiting...

... continued from the previous post A similar case is with a statement like: "through every two points passes one and only one line." This is an axiom of Euclidian geometry and perfectly logical. It doesn't matter that there's no definition for a "point" and a "line." And it doesn't matter...

Greetz, 1. For Mentat: Apologies for the delay. Let's sum it all up. We have the Demon claiming something and Descartes proving that claim problematic. That's all right. The Demon may not say that Descartes doesn't exist (inbound Aristotelian logic, of course). Descartes' proof...

... continued from the previous post Here's a diagnosis of your "usability" criterion: 00. Assume there's the idea A. 01. By you claim, this A is either "usable" or "unusable." 02. If it's "usable" there's no problem. 03. But you claim A's "unusable." 04. If you say A's "unusable"...

Greetz, 1. For Mentat: There is a logical flaw in that attempt and that's the making of a loop. A loop (in Descartes' statement) and a paradox (in Demon's statement) are equally illogical. I have proven that for sure. I showed and you accepted that Descartes' statement is a loop (eg, it's of...

... continued from the previous post I know, but it’s challenge that toughens the reason, am I right? Why aren't our ideas equally creditable? You see, I found two "uses" for Uncertainty. Even if I couldn't find those uses, what is there to distinguish usable ideas from unsusable ones? What...

... continued from the previous post Did I say the purpose of a number is intrinsic to that number? I said there's a value associated with every attribute. We have the attribute (for example, height) and its value (for example, 666.13). Does this mean that 666.13 is intrinsic to height...

Greetz, 1. For Mentat: To my understanding, the Demon was Descartes' sparring partner. Descartes made the Demon to challenge his suppositions and verify their truth. From this viewpoint Descartes and the Demon have equal places, they're the two sides of a philosophical debate. "Trying to...

... continued from the previous post Well, suppose so, what then? Please tell me if you have a non-paradoxical basic rule for fairness. Perhaps we're referring to the same thing under different names. If it's that way, I have to retreat some steps. Even though my discussion of Descartes'...

Greetz, 1. For Mentat: Thanks. I do feel better now. What I see as Evil Demon scenario is like this: 00. Rene Descartes is sitting by his fireplace. Satisfied by a French meal. Warmed by fire, daydreaming... 01. The Demon comes in, embodied in Aphrodite's most voluptuous figure. 02. The...

... continued from the previous post 1 and 2 are separate. The condition called for in 1 isn't the one talked about in 2. In case 1, the condition is that any system of thoughts one chooses after the realization of "fair" observer's paradox would better have a hint of that very basic...

... continued from the previous post By the way, suppose this "I was born 15 years ago therefore I am fifteen" is really an "I am 15 therefore I am 15." If you're right in that supposition then you have another loop at hand, nothing more. What's the point in finding another loop? Neither of...

Greetz, 1. For wimms: Thanks for your help. You said much more than, I think, I could've said. 2. For Mentat: I have a cold and I'm having a feverish time but I can take it, or make it, with Uncertainty . Q is "I am." To show the Evil Demon's attempt was in vain, Descartes must have...

... continued from the previous topic I have another definition of a "border," that's where one realm ends and another starts, a virtual line that inhabitants of one realm would pass in order to get to the other realm. Suppose I'm a rational thinker. I start sorting out things rationally. I...

= Greetz, 1. For Mentat: That P([beep]) was a generalization. I used it to prove that incompatibility case for all statements of the form "I [beep] therefore I am" ("I think therefore I am," "I eat therefore I am," "I want therefore I am," etc). Instead of using the specific verb, "think," I...

… continued from the previous post Nevertheless, if we were discussing it (which we never ever are) I would counter that knowing that symbolic things can be interpreted at will worsens the situation, but, more apparently than obviously we aren’t discussing it, so it more really than really...

Greetz, 1. For Mentat: Let's see. If I gave you a proof (just some proof not this one) that shows that Descartes' statement is incompatible with Boolean logic then would this exemplary proof be applicable to Descartes' statement? I think the answer is "yes." Now I claim that the proof...

... continued from the previous post Yes, "you" are doing that and "you" think it's "much too basic." Me . On a homogenous scale of credibility that starts from "most unreliable" and ends with "most creditable" those which are "equally unreliable" are "equally creditable." Scale of...

Greetz, 1. For Mentat: Questioning the applicability of this proof is senseless. "If" this proof is all right then it will show something about Descartes' statement (and that's clear), so it's applicable. It's "clear" that this proof is applicable for studying Descartes' statement because its...

... continued from the previous post You mean you've studied all "known" and "unknown" logical systems? How did you do this? And suppose, only suppose, it really exists in all logical systems. Doesn't it matter that its meaning changes from one system to the other? No. Monads are isolated. They...

Greetz, 1. For heusdens: Thank you. A logical system is a form of an axiomatic system, right? Truth values, structuring of statements and rules of deduction are the axioms of a logical system, I guess. 2. For Mentat: You "are" criticizing it by claiming it's inapplicable. Isn't that...

... continued from the previous post How do you know they're observing something? Isn't that you have a picture of an observing Physicist to compare them to? The alien Physicist may not comply with this picture so you'll never know it's been observing but you'll see the change. Moreover, this...

... continued from the previous post The balance you talk about is achieved after both extremes are experienced. That balance, I guess, is somehow like that "residual understanding" I wrote of. One experiences Certainty (in the form of scientific and/or religious and/or whatever belief) then...

Greetz, 1. For Mentat: I repeat, you said you didn't understand the proof (or you haven't put much in effort into that) then how could you criticize it? The storyline I used in describing the proof first goes through defining the state for P and then studies Q by asking what state you...

... continued from the previous post Let's see what "order" means. The books in the Library of Congress are "ordered." What does this mean? I guess it means there's a well-defined well-rounded rule set that assigns them to their respective places. This rule set has been chosen based on an...

Greetz, 1. For Mentat: Apologies for the delay. How could you say that if you still haven't understood what it's talking about? I explained many times the reason I think that proof applies, just look around the posts. Did you counter my reasons? It was/is relevant. Only because you...

Greetz, 1. For Mentat: No, unfortunately you don't seem to have a phantom of a shadow of having understood this proof. Your following sentences show this. And it's me who must be assured that you've understood the proof for you yourself are always sure you've understood the whole thing...

... continued from the previous post You have your choice but then I’m also interested in Certainty just as much as I’m interested in Uncertainty. In spite of this interest I don’t assess those situations, assessed by you as “must-be-avoided,” as “must-be-avoided” but as “must-be-thought-of.”...

Greetz, 1. For Mentat: I won’t discuss the proof anymore. You’re in harsh misunderstanding of it and I’ve done my best to clarify but have failed. I re-shape and re-explain the proof one more time, but I won’t discuss it until you show you’ve understood what I mean. I don’t mean for you to...

Greetz, 1. For Mentat: That's right. The P([beep]) statement is not the statement category ("I think therefore I am" and similar) proven absurd in that proof. You're just stating the reason I wrote that P([beep]) was "irrelevant to" and "independent from" Descartes' statement, that it was...

Greetz, 1. For Mentat: No, no, no! I'm not implying anything. Only if you got the catch of that proof! Suppose there are two independent statements, one is Descartes' statement and the other is my P([beep]). We want to see if Descartes' statement is true or not, but before we do this I ask...

... continued from the previous post That's another rule from Boolean logic. Another system of logic may even assign other states to a statement, no true or false. Sorry for the roughness of the analogy but your saying deserves some hard opposition. There was once a horse that loved her blinders...

Greetz, 1. For Mentat: First of all, there's one thing I'd like to draw your attention to: I put my words in the place I seem suitable for them so the way my words are is an expression of my opinion, I'm not humming dial tone I'm talking so please don't ignore the words. And I'm telling...

... continued from the previous post Don't use this word, "fact," this much. As long as we're debating uncertainty and existence, fact is out of context and using it is premature for if uncertainty is shown to prevail, no such thing as fact can be called for. You can't talk of some "fact" as a...

Greetz, 1. For Mentat: I didn't. You only repeated what you'd written many times before, so I wrote nothing in response. I asked you to show me the logical fault in my proof. If there isn't a logical fault in my proof and it leads to a dilemma while studying Descartes' statement then the...

... continued from the previous post Progressive knowledge can be seen more clearly in the light of uncertainty. It will become richer if it's accompanied by knowledge of its being temporal and its being uncertain. It's not you who determines if I can. I can think of "a Demon tricking"...

Greetz, 1. For Mentat: Don't ask me. Show where the logical fault is. I described a step-by-step procedure whose steps are logical. Nothing wrong happens during the transition from one step to the other. Consequently, this can be considered a logical proof. This reasoning is applicable...