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Author Topic: Logic and Magic  (Read 7417 times)
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Alexandre Scriabin
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« on: 24 February 2011, 18:58:59 »

I've been thinking about this for a few days, and I've come up with a proposition:

1. Organize the semantic language of Ximaxian magic much in the way that Kripke and Leibniz organized "possible world" semantics.

2. Proceed to draw up basic equations for the variables in order for the content to be displayed as clearly as is humanly possible.

Organizing the vocabulary and thus making an orthodoxy for the semantics will make things much more clear. Imagine it like devising a map legend.

Drawing up an equation for each of the terms, Ounia, Car'all, Xeua, Ecua, and some other things, would make it possible for anyone familiar with reading a philosophical equation (or anyone interested), to comprehend magic rigorously.

If you don't quite understand what I am getting at, I can give the most accessible explanation possible. That is, this doesn't have to seem overly complex and we can speak in plain English with one another.
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« Reply #1 on: 25 February 2011, 04:35:45 »

Uhm... I'm not sure if everyone knows what exactly you suggest here, Alexandre - so why not try to do it yourself?  grin
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Alexandre Scriabin
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« Reply #2 on: 25 February 2011, 05:52:55 »

All right, Arti. Here is the explanation I promised (in which I will give an accessible explanation of one such system of logic in order to provide an example of what I am thinking of):

Getting the Language Down of "Possible Worlds"

Developed by Saul Kripke in the mid 20th century, "Possible World Semantics" is a way of introducing a formal way of evaluating a modal proposition as either "true" or else "false". What's a modal proposition, you ask?

    Def 1: A modal proposition is a true or false statement about could be the case (i.e. what is "possible") or what must be the case (i.e. what is necessary). (From now on, I'll use "necessarily true" as a synonym for "must be true" and the same for "could be true" and "possibly true."

Unlike a normal proposition, like "The sky is blue" --which is simply true or false because it's a fact of the matter -- modal propositions are a bit harder to formally evaluate. Say yesterday you said, "It could rain tomorrow", but when you looked out your window today, you found that there was no rain. Now, if you'd said "It will rain tomorrow", that statement would have been false. But since you only said "It could rain tomorrow", what you said was still technically true, even though content that the modal statement referred to actually ended up being false. And you'll think to yourself, "Yes, it happened to rain today, but it could very well have been otherwise." Kripke invented the following formalism, called "Possible World Semantics" (Yes, academics must give every intuitive idea a very impressive sounding name), in order to capture this very intuitive idea.

Firstly and most obvious, we're going to need to capture the idea of what is possible and what is not possible. Let's go ahead and hard code this into our language with the following:

    Def 2. A possible world is a model of a world with a collection of propositions about it.

Using the previous example: The model world would be your neighborhood, and the proposition would be "It is raining." The use of the word "world" is just to make these statements a little more intuitive, and does not imply that somewhere out in Reality, these "worlds" exist. They're simply conceptual tools for expressing these notions.

So explicitly taking the last example, we are considering between two possible worlds:

World A: "Tomorrow it rains" is true.
World B: "Tomorrow it rains" is false.

Now we have enough language to say whether or not the statement "tomorrow it will possibly rain" is true.

    Def 3. A proposition is possibly true, if and only if, in some world, the proposition is true.

This clearly encodes the information about what we think ought to be the case for the notion of possibility: we have some primitive notion of what could be the case (which we specify by selecting which possible worlds we accept), and then if the statement is true in at least one of these worlds, then the statement could be true, not knowing which world is "the real one." But note that all of this is with respect to which set of possible worlds that we're considering.

So this is a neat little way of talking about what could and could not be the case. But now we can just as easily talk about what must be the case:

    Def 4: A proposition is said to be necessarily true, if and only if, in every world, the statement is true.

So this is another cute, and obvious, statement. It has to be true because amongst the possible worlds you're considering, it is always true. And therefore, it must necessarily be true; if you're sitting in one of these worlds, you're always going to have to evaluate this statement as true, even if you don't know which of the worlds you're in.

Now, here are a couple of obvious corollaries that follow from these definitions:

    Prop 5: A statement is possibly true, if and only if, it is not necessarily false.

    Prop 6: A statement is necessarily true, if and only if, it is not possibly false.

(If they aren't obvious to you, you're probably over-thinking this. Just go back to the definition of what these things mean, and after a moment it'll click. If someone really wants to see a proof of these two, I'll give it.)

Now, to end the discussion on Possible World Semantics, I'm going to prove the following very non-trivial, counter-intuitive statement:

    Prop 7: If a statement is possibly necessarily true, then it is necessarily true.

Yeah, that's a bit of a hair-puller at first, but let's show that even though we used very intuitive definitions about what is possible, we're actually only encoding a very specific sense of the word "possible" (That is, the sense in which a word is "logically possible"). We would need different definitions to encode something like "For all we know, X could be true", which is a statement about knowledge and not logic, because such an idea is actually more general. (This distinction will be important later on)

    Proof of Prop 7:
    Assumption: "A statement is possibly necessarily true."

    1.) "In some possible world, the statement is necessarily true." (Def 3)

    2.) "In some possible world, the statement is true in every world." (Def 4)

    3.) "In every world, the statement is true." (Obvious reduction)

    4.) "The statement is necessarily true." (Def 4)

    5.) Therefore, "If a statement is possibly necessarily true, it is necessarily true."

And that is the same kind of numbered proof that I am saying we could use.
« Last Edit: 25 February 2011, 05:54:58 by Alexandre Scriabin » Logged

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« Reply #3 on: 25 February 2011, 06:42:16 »

And I am completely lost here ... even more lost than I was when I am when reading the magical entries, including the one on ounia.

I don't see how it helps with the entry on ounia, myself.
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Alexandre Scriabin
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« Reply #4 on: 25 February 2011, 06:56:09 »

Well Dek, if we can draw up an agreement as to what terms are essential to magic and standardize what they mean (either in one or more sense as Rayne pointed out), then we can come up with a semantic language to talk about magic, and can even use philosophical type mathematical proofs and notation to give the clearest picture as to the relationships between the different concepts of Ximaxian magic.

Think of it as a grand example of us finally drawing up a pie chart so that everyone can take a look and say "Oh I get that now!"
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« Reply #5 on: 25 February 2011, 07:23:13 »

Ok ... I actually understood what you said in that last post, Alexandre ... maybe that would have been a better post for you to have used to explain what you were meaning in the first place? You know, explain in basic language so that the broadest range of the readers can understand? Starting at a point were people understand and then going up to more precise language if need be.
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Alexandre Scriabin
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« Reply #6 on: 25 February 2011, 08:18:37 »

Ok ... I actually understood what you said in that last post, Alexandre ... maybe that would have been a better post for you to have used to explain what you were meaning in the first place? You know, explain in basic language so that the broadest range of the readers can understand? Starting at a point were people understand and then going up to more precise language if need be.

That's actually the plan I was proposing, and the description I gave of "possible world semantics" was a step by step of how to go from a simple explanation to a mathematical proof.
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« Reply #7 on: 25 February 2011, 08:42:51 »

Ah ... but the fact that I said I didn't understand it showed it wasn't simple :D
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« Reply #8 on: 25 February 2011, 08:47:20 »

What Deklitch is saying is that typically, one starts with terms a layperson can understand unless none of the other people involved are laypersons (a convention of professionals)

Let's examine your first post.

Quote
Organize the semantic language of Ximaxian magic

Quote
Proceed to draw up basic equations for the variables

Quote
Organizing the vocabulary and thus making an orthodoxy for the semantics

For those unfamiliar with what you are talking about, this sort language is just jargon. We recognize the words individually of course, but the way they're used makes them a form of technical jargon.

Quote
If you don't quite understand what I am getting at, I can give the most accessible explanation possible. That is, this doesn't have to seem overly complex and we can speak in plain English with one another.
If you had thought that people might not understand to begin with, then maybe you should have started with the "most accessible explanation possible" and written in plain English.
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Alexandre Scriabin
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« Reply #9 on: 25 February 2011, 09:21:57 »

Wait, we're having this conversation why? You now understand what I'm proposing, so do you or do you not think this site needs a formal system of logic for it's magic?

I've spent enough time clogging up someone else's thread so the next step from me will be a thread in the proposal section and an outline of ideas.
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« Reply #10 on: 25 February 2011, 10:00:33 »

I don't think it needs one myself, Alexandre. But I think I'd place more stock in the thoughts of Rayne on the matter than on my thoughts.
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« Reply #11 on: 25 February 2011, 10:19:58 »

I don't think it needs one myself, Alexandre. But I think I'd place more stock in the thoughts of Rayne on the matter than on my thoughts.

Well, the main reason I feel this way is because I have to go to different random places to get explanations of things. I'll look up Ounia for example, read the whole of the entry I find on it, and still find important details in other places.

So, if we lay down the definitions and relationships of everything in magic, and then lay down the same thing in bullet equations, then everyone can go to one resource on a subject and fully grasp it. As of right now, I'm still drawing up my first set of explanations and it's equation: How to perform a magic spell.

Not to mention that in all of these different equations it is necessary to cite information overlapping other subjects. After reading a few of these equations, and hearing a lot of the same definitions again and again, the different ideas in the magic system will seem less disparate and obtuse to a new learner. I still often find myself reading an entry like "Understanding Ximaxian magic through the Car'all Part II" and read a lot of material without one big picture to bring it together like an equation (and that entry even had a chart that was too vague).

Coren made a lot of these entries and he's probably pretty familiar with what I am bringing up in logic and in examples, so maybe he has something to say as well as Rayne?
« Last Edit: 25 February 2011, 10:24:50 by Alexandre Scriabin » Logged

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« Reply #12 on: 25 February 2011, 15:17:32 »

I never suggested Coren didn't or wouldn't, Alexandre. I suggested one person, the one who was writing the entry, as being a person who had a better understanding of magic than me. I didn't think it was necessary to list every single person on the development side who had a greater understanding of the magic here than myself, I can though if you'd like me to. :) I think it would be a waste of time, myself, but I'm happy to do so if you'd like me to.

That entry is about one part of magic, Ounía. It is not about the spells, the elements, how to cast magic, or anything else ... it is about Ounía. While those other things could and should and, from what I can tell, are referenced in this entry on Ounía, writing about them in any great detail in this entry in any great detail takes away from what the entry should be about ... Ounía. So, if someone wants to know about those other things, they should click on the links to the entries on the other things to find out the information on them.

This is the same process I follow if I want to know what animals and plants lived in the the lands of the Kanapans, I go to the entry on the Kanapan lands, and then follow the links to the specific entries I was after about the topic/s I was interested in.

Edit: As this discussion was split off from the entry it was originally attached to, I've edited this post slightly so that people know my comments were in relation to Rayne's entry and not this.
« Last Edit: 25 February 2011, 15:48:09 by Deklitch Hardin » Logged

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« Reply #13 on: 25 February 2011, 15:54:33 »

I've split the Ounía topic now and made a "Logic and Magic" topic out of Alexandre's comments, because the Ounía entry definitely isn't the right place for it to discuss this.

Quite frankly, though I've had to study logic as part of my philosophy studies, I'm not sure what exactly you intend to do with all those logical principles. I thought you'd try to organize the magic stuff yourself that way somehow, Alexandre, but as you can see people have difficulties grasping what you're aiming at by explaining it, so how would someone else be able to manage putting together what you try to suggest? Especially as I have no idea either what variables you want to equate for what reason to prove if a sentence is logically sound etc. - or what? It's all very abstract. How exactly would that look like? As I guess a concrete example that would get us somewhere is not really contained in your posts.

A sort of magical dictionary would make sense for example, to have the key words all together on one single page. Maybe show relations graphically etc. We've done that here and there with the Xeuágrams. But other than that I'm at a loss here where this is supposed to be heading, just like Dek.
« Last Edit: 25 February 2011, 16:12:11 by Artimidor Federkiel » Logged



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« Reply #14 on: 25 February 2011, 16:50:54 »

rolling

*switching on the mean old swamphag*

Dear Alexandre, what did you want to show with your first post? A means to organise Ximaxian magic or your own cleverness?

*switch of*

Frankly - did you expect from the majority of us to understand your terms?
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