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From Greek Philosophy to Swedish Serfdom

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AJ replied on Mon, Mar 1 2010 11:20 PM

JAlanKatz:
Leary book is a great place to start to understand how mathematicians actually work with and view these concerns.  Another book you might consider is Frege's Foundations of Arithmetic.

All going on my reading list, thanks.

JAlanKatz:
That the map is not the territory, I think, is exactly what I've been saying, and I thought you were arguing opposite that point.

I should add that I think there is no way to know the territory, only to know the map (since I am apparently creating it). Hence when I call something "true" I mean to say that it seems to cohere with my map - that is, the set of assumption/beliefs I have about what presents itself to my senses. These effectively constitute my axioms at any given point in time.

(I'm using the first person here because at this level of analysis it would be sloppy to assume other people are like me. Cf. Edmund Husserl's bracketing methodology.)

JAlanKatz:
Rather than beginning with axioms and deriving conclusions, we ask people in other fields - either within math or in applied fields - what theorems they need to do their work, and then we attempt to discover minimal axiom sets that make this true.   Philosophically, we are asking just how far from ideal a structure/universe can be and still exhibit nice properties.  My interests are largely pure, in the sense that I do not look at how math is used in other fields.  On the other hand, my goal is application, but of a different sort.  Rather than looking for "how can this formula be used here?" I look at how other structures - biological, economic, political, etc. exhibit patterns that can be seen in mathematical structures, then look for isomorphisms so that math can be used to give some answers over there. 

Sounds interesting. You look for instances of mathematical structures in real-life situations and try to distill down a small set of axioms from which a mathematical model can be derived that exhibits analogous behavior? Is it very different from mathematical modeling?

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I don't remember anyone when I was 10 talking like that.

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AJ replied on Mon, Mar 1 2010 11:25 PM

PEZ:

Here's another thread where that same poster is in action.

http://www.reddit.com/r/reddit.com/comments/alggn/people_steal_left_shoes_in_sweden_then_goto/c0l2mv2

He seems to agree (with me) that anarchy is a more desirable state of affairs, but then says that the world is not yet "ready for it".

Interesting opinions. I linked him the post in my sig, because I think it answers the "not ready for it" objection, but I didn't want to continue with so few viewers. I'd rather debate where a ton of people are watching so that the ideas can get out to a much larger group. However, I certainly don't knock the idea of converting one intelligent person, for they will almost certainly influence many others.

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PEZ replied on Tue, Mar 2 2010 12:33 AM

Caley McKibbin:

I don't remember anyone when I was 10 talking like that.

Me neither, but then again, my parents were (maybe still are) communists so I heard a lot of the complete opposite.

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AJ:
I should add that I think there is no way to know the territory, only to know the map (since I am apparently creating it). Hence when I call something "true" I mean to say that it seems to cohere with my map - that is, the set of assumption/beliefs I have about what presents itself to my senses. These effectively constitute my axioms at any given point in time.

Is this not just a formal version of coherentism?  Once again, you have caught me being philosophically unsophisticated.  Of course, to say "we take the pattern in the real world, translate it into mathematical axioms, then prove theorems and send them back to the real world" only works if you assume the first step to be possible.  You don't, if you're a coherentist, but you can at least say that truth is what you've found to be coherent in the real world, rather than the set of theorems in the formalization.  I am an Aristotelian, and do believe that things can be known.  

AJ:
Sounds interesting. You look for instances of mathematical structures in real-life situations and try to distill down a small set of axioms from which a mathematical model can be derived that exhibits analogous behavior? Is it very different from mathematical modeling?

Actually, I should have had a paragraph break there.  When I talk of my interests, it is separate from my description of reverse mathematics.  The latter is my approach to math as a whole, whereas in reverse mathematics we work at a more formal level.  

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AJ replied on Thu, Mar 4 2010 10:47 PM

JAlanKatz:

AJ:
I should add that I think there is no way to know the territory, only to know the map (since I am apparently creating it). Hence when I call something "true" I mean to say that it seems to cohere with my map - that is, the set of assumption/beliefs I have about what presents itself to my senses. These effectively constitute my axioms at any given point in time.

Is this not just a formal version of coherentism?

It's close to coherentism. I'd have to review my notes to recall what the difference is.

I reached the position I'm at when I fully questioned everything, right down to determining what are my very basest of base assumptions, and then having a theory of mind and an understanding of words' relation to thought to tie it into. My theory of mind says that all thoughts and emotion - all experience - is sensations of the (five) senses. What's the very minimum I can take for granted, then? "I am experiencing sensations." Or maybe just "Sensations are being experienced." (Any statement that you can put "it seems that" in front of and have it not get any more certain is as certain as you can get.) I worked from there. I've found it's essential to have both a theory of cognition and a theory of how semantics tie in in order to understand such things (semantics is needed because all discourse is stated in words so there's a near-total emphasis on what can be stated and on words themselves).

Looking back, I guess I owe about 1/3 of the theory to the contemplation of Moore's Paradox, which I've been meaning to publish my solution to.

JAlanKatz:
I am an Aristotelian, and do believe that things can be known.  

What do you mean by "know"?

JAlanKatz:
The latter is my approach to math as a whole, whereas in reverse mathematics we work at a more formal level.  

Are you doing anything related to spontaneous order (have you read Hayek on that)?

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AJ:
I reached the position I'm at when I fully questioned everything, right down to determining what are my very basest of base assumptions, and then having a theory of mind and an understanding of words' relation to thought to tie it into. My theory of mind says that all thoughts and emotion - all experience - is sensations of the (five) senses. What's the very minimum I can take for granted, then? "I am experiencing sensations." Or maybe just "Sensations are being experienced." (Any statement that you can put "it seems that" in front of and have it not get any more certain is as certain as you can get.) I worked from there. I've found it's essential to have both a theory of cognition and a theory of how semantics tie in in order to understand such things (semantics is needed because all discourse is stated in words so there's a near-total emphasis on what can be stated and on words themselves).

Well, again, I can't say I'm as steeped in philosophy as you are, although I have spent time in philosophy departments.  I did go through a Cartesian stage at one point, but I chose to walk around the pit instead of falling into it.  You can claim that my belief that things exist, that knowledge is real, and so on, are illusions, but really, they are illusions that make my life possible.

AJ:
What do you mean by "know"?

A justified true belief.

AJ:
Are you doing anything related to spontaneous order (have you read Hayek on that)?

Not at present, but chaos and complexity are interests of mine.  After finishing my current program, I plan to work on that.  I also plan to work on it this summer at Mises.

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AJ replied on Fri, Mar 5 2010 8:18 PM

JAlanKatz:
You can claim that my belief that things exist, that knowledge is real, and so on, are illusions, but really, they are illusions that make my life possible.

Exactly. "Real" is what we call sensations that are more lasting (plus of few other typical features), as well as those that appear to actually influence subsequent sensory impressions. "Illusion" is what we call impressions that lack certain of those features. It's not Cartesion per se, it's just the recognition that "this could all be a dream," which I think must be acknowledged. Of course whether life is a dream or not is really pretty immaterial, because if it's this kind of dream, then it's just like what we know as "life," so it's no revelation of immediate importance. But it is, I think, a necessary thing to keep in mind. With this in mind, my explanation of "real" might make more sense. I don't think there's anything mystical about this, just the semantic confusion of the convention of language makes it sounds that way. I think it's just common sense once the language blinders come off.

JAlanKatz:

AJ:
What do you mean by "know"?

A justified true belief.

If then "true" means "corresponds with reality," what is reality? You sort of implied that reality is what makes your life possible, and by "life" I assume you just mean "all of this I'm experiencing/sensing." In essence, the pattern of pleasure, pain, and other sensations of the five senses. There is a set of sensations that is more permanent-seeming and which exhibits reliable consistency of apparent cause and effect with respect to my actions. These sensations I dub "reality."

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AJ:
Exactly. "Real" is what we call sensations that are more lasting (plus of few other typical features), as well as those that appear to actually influence subsequent sensory impressions. "Illusion" is what we call impressions that lack certain of those features. It's not Cartesion per se, it's just the recognition that "this could all be a dream," which I think must be acknowledged. Of course whether life is a dream or not is really pretty immaterial, because if it's this kind of dream, then it's just like what we know as "life," so it's no revelation of immediate importance. But it is, I think, a necessary thing to keep in mind. With this in mind, my explanation of "real" might make more sense. I don't think there's anything mystical about this, just the semantic confusion of the convention of language makes it sounds that way. I think it's just common sense once the language blinders come off.

You say twice here that this possibility, about which nothing can be done, which can never be verified or denied, and which is meaningless if it turns out to be true, must be kept in mind.  Why?  What do I possibly gain from at all times thinking that I may be a brain in a vat?  Is this really all that philosophy is capable of giving us - brains in vats?  It reminds me of a friend, a wonderful philosophy student, who when pressed to the wall justified murder (not self-defense, real live murder in some bad situations) because he is more convinced of his own existence than of that of others.  I don't think this is what philosophy exists to teach us.

AJ:

If then "true" means "corresponds with reality," what is reality? You sort of implied that reality is what makes your life possible, and by "life" I assume you just mean "all of this I'm experiencing/sensing." In essence, the pattern of pleasure, pain, and other sensations of the five senses. There is a set of sensations that is more permanent-seeming and which exhibits reliable consistency of apparent cause and effect with respect to my actions. These sensations I dub "reality."

Again, skepticism of this sort doesn't appeal to me.  You can feign ignorance about what reality is all you want, but it is clear from your actions, your interactions with others, and so on, that you know what reality is, and can reliably sort real from fake. 

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AJ replied on Sun, Mar 7 2010 10:53 AM

JAlanKatz:
What do I possibly gain from at all times thinking that I may be a brain in a vat?

"This could all be a dream" is indeed meaningless from the standpoint I am taking, so it wasn't a good way to state it. I suppose it's more that the spirit of that kind of thinking was important for me in initially realizing what I have.

The point isn't really that it might all be a dream or we could be in some crazy matrix, but rather to remind us that what we call reality just is that set of experiences that seems to have real consequences for us and our enjoyment of life. What we call illusion just is that set of sensations that doesn't seem to have such consequences. All I am really pointing out is a basic semantic trick going on. There are no immediate "whoah" type of philosophical implications to it; rather I consider it a matter of mental hygiene to recognize certain uses of language that can blind us.

Why this is important would take a while to explain, so at this point I'm just saying this sort of as an aside to what we were talking about. Of course, it has implications (very nice ones, to me) for various logical paradoxes and the philosophy of math, which I am still working out.

JAlanKatz:
You can feign ignorance about what reality is all you want, but it is clear from your actions, your interactions with others, and so on, that you know what reality is, and can reliably sort real from fake. 

Of course. That's not what I am saying, although I know I realize it sounds similar. It's basically all about 100% avoiding the fallacy of magical thinking. To realize that it's not "Reality is X" but rather that "We call certain things reality (and certain other things illusion)." In other words it's just the seemingly mundane observation that a word is a label for a thing, not the thing itself - but being very careful never to overlook that fact.

So when you say that I know what reality is, you're quite right: I know what I have labeled "reality." I don't deny the existence of reality, I just wish to point out that reality can only mean (to us) that thing that we have labeled "reality," not something else.

This gets confusing because here were are talking in words, but the words are the blinders that created the problem I'm trying to explain. Rest assured I'm not a skeptic, and I certainly don't like the idea that I'm just a brain floating in a vat somewhere. In fact, I'm saying that such skepticism in itself (as well as realism) is nothing more than a word game. At the "what is the meaning of life" level, what I am talking about says nothing special.

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JAlanKatz replied on Sun, Mar 7 2010 11:02 AM

AJ:
Of course. That's not what I am saying, although I know I realize it sounds similar. It's basically all about 100% avoiding the fallacy of magical thinking. To realize that it's not "Reality is X" but rather that "We call certain things reality (and certain other things illusion)." In other words it's just the seemingly mundane observation that a word is a label for a thing, not the thing itself - but being very careful never to overlook that fact.

Rather than keeping on the road we're on, I have a somewhat related question.  Do you have any thoughts about tracking an influence of Meinong on Menger?  He was a student of Meinong, I believe.

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AJ replied on Sun, Mar 7 2010 12:20 PM

JAlanKatz:
Do you have any thoughts about tracking an influence of Meinong on Menger?  He was a student of Meinong, I believe.

I don't know, but I looked up Meinong...

Certain objects can exist (mountains, birds, etc.); others cannot in principle ever exist, such as the objects of mathematics (numbers, theorems, etc.): such objects simply 'subsist.' Finally, a third class of objects cannot even subsist, such as impossible objects (e.g. square circle, wooden iron, etc.).

I think this is just a word game, but it's cool that he was thinking of things at this level.

In particular, take the square circle. He wants to call it an object (albeit an impossible one), but there is no "it" here. All he's done is take two words and put them side-by-side, as if "just because a set of words sounds like it's describing an object it must be." Really, it's impossible to think of a square circle.

Here's where I think this confusion comes from. Words are the names we give to objects of our perception. That I can put two words together and get a plausible name for new object I've never seen or thought of before but that can be clearly imagined (ex: "green dog") seems to have given many people the impression that this process will always produce an object that can also be imagined or could possibly exist somewhere. That it never results - so long as the words fit together grammatically - in something that is nothing more than two words placed side-by-side. But this is not the case.

In fact, the very nature of words is that they are symbols or tokens chosen to get a concept from one person's mind to another's. The process by which words do this is familiar: you hear words, and if you can comprehend them in any way they will form some kind of image in your mind, representing a state of affairs. If that state of affairs makes sense to you and there seem to be no other reasonable interpretations, you say you have "understood" what the words mean. In other words, the state of affairs you are imagining matches (sufficiently well) with the state of affairs the speaker is imagining.

But notice that this process is predicated on (the speaker, and later the listener) actually imagining some state of affairs. Of course, a speaker can forgo the imagining and simply utter some words and see what the listener makes of them. Perhaps the listener can imagine nothing corresponding to those words; or perhaps he can. Either way, from the perspective of the speaker, those words were nonsense - nothing more than sounds.

A "green dog" might be a proper name for a cocktail, or a dog that has a cold, or one that is envious, etc. It's the concept - the picture in your mind of a dog with green fur, say - that is the object of perception. "Green dog" is just a pair of words that lets you say, "Oh yeah, I can see how that picture in my mind would be called a 'green dog.' Yup, that must be what you're talking about." It's not the words but the concepts that are fundamental. Meinong has it the other way around.

Now Menger's theory of praxeology must have something to do with this kind of analysis, and indeed it was thinking about praxeology that really lit up this area of inquiry for me. Only, I cannot understand Menger's (actually the translator's) writing style, so I know what I know mainly from Mises and Adam Knott.

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JAlanKatz replied on Sun, Mar 7 2010 12:27 PM

AJ:
Here's where I think this confusion comes from. Words are the names we give to objects of our perception. That I can put two words together and get a plausible name for new object I've never seen or thought of before but that can be clearly imagined (ex: "green dog") seems to have given many people the impression that this process will always produce an object that can also be imagined or could possibly exist somewhere. That it never results - so long as the words fit together grammatically - in something that is nothing more than two words place side-by-side. But this is not the case.

I always took it that what motivated Meinong is the existence of real names, used as names, for things that don't exist.  For instance, Santa Claus.  The worst such case is something like "Santa Claus doesn't exist."  Certainly, we don't take this as meaningless, and to be meaningful, it would seem that it needs a sentence and a predicate.  But there can be no subject for this sentence, seemingly, without Meinong's move, referred to as the "population explosion."  So I don't think your examples really hit what he was going for.

Russell also has a way of dealing with such names without a population explosion.  But his (the descriptive theory) is generally seem as clumsy and not at all what we mean in using names.  Indeed, even he seems to, in his later work, limit it precisely to hard cases, and use proper names for usual cases - but then it seems entirely ad hoc. 

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AJ replied on Sun, Mar 7 2010 12:36 PM

JAlanKatz:
The worst such case is something like "Santa Claus doesn't exist."  Certainly, we don't take this as meaningless, and to be meaningful, it would seem that it needs a sentence and a predicate.  But there can be no subject for this sentence, seemingly, without Meinong's move, referred to as the "population explosion."

But a grammatical subject can be any word that we decide to use as a noun. I can say "*Z#^X7&@ doesn't exist," and you know automatically - by it's position in the sentence* and by the meaning of the word "exist" - that  Z#^X7&@ is a noun and the subject of the sentence. Once again the same problem: words are not the things they label. There is no need to populate anything.

In the case of Santa Claus, I can imagine him. To say he doesn't exist just means no matter where you look in this universe you won't find Santa Claus. That I can imagine as well - at least to my satisfaction in a way that has meaning for me.

*if you assume I am saying something coherent/grammatical, which I suggest that we always must do in order to talk about such utterances on this level

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AJ:
But a grammatical subject can be any word that we decide to use as a noun. I can say "*Z#^X7&@ doesn't exist," and you know automatically - by it's position in the sentence* and by the meaning of the word "exist" - that  Z#^X7&@ is a noun and the subject of the sentence. Once again the same problem: words are not the things they label. There is no need to populate anything.

So what is your sentence doing?  It is surely not attributing some trait to something, so what proposition does it express?  Does it express "nothing does not exist?"

AJ:
In the case of Santa Claus, I can imagine him. To say he doesn't exist just means no matter where you look in this universe you won't find Santa Claus. That I can imagine as well - at least to my satisfaction in a way that has meaning for me.

What are you imagining, and what are you looking for?  Does imagining Santa Claus and looking for Santa Claus differ from imagining and looking for a unicorn?

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AJ replied on Mon, Mar 8 2010 11:06 AM

JAlanKatz:

AJ:
But a grammatical subject can be any word that we decide to use as a noun. I can say "*Z#^X7&@ doesn't exist," and you know automatically - by it's position in the sentence* and by the meaning of the word "exist" - that  Z#^X7&@ is a noun and the subject of the sentence. Once again the same problem: words are not the things they label. There is no need to populate anything.

So what is your sentence doing?  It is surely not attributing some trait to something, so what proposition does it express?  Does it express "nothing does not exist?"

The short reply is that sentences don't express things; people do. So when we try to decipher the meaning of a sentence, we're really trying to decipher what a person means, or more generally trying to come up with a plausible interpretation for a set of symbols. The only reason it feels like we're doing anything else is that we have so much shared context to work with, and we spend our lives perfecting the art of utilizing words+context to get ideas across with a serviceable level of accuracy.

The tricky part is that sentences that look "reasonable" are strongly associated with being "meaningful" (from context) in our minds. Meaningfulness is a norm of assertion, as is truth - at least if you say it loud and like you mean it : - ) My point with the nonsense text is that there is no need to prove something is a subject, because that would be akin to trying to "prove" the meaning of a word you coined. (If you coin a new word, it of course means whatever you say it means. Likewise, the act of putting a word in a position where only a subject can go is essentially the act of marking that word as a subject.)

JAlanKatz:

AJ:
In the case of Santa Claus, I can imagine him. To say he doesn't exist just means no matter where you look in this universe you won't find Santa Claus. That I can imagine as well - at least to my satisfaction in a way that has meaning for me.

What are you imagining, and what are you looking for?

The actual imagery would be hard to describe, but the idea is that I think the thought that corresponds to (my interpretations of the sentence) "Santa Claus does not exist," hence I can understand the underlying concept. There are really quite a few (infinitely many?) ways to interpret this sentence in terms of imagination. I could, for example, simply interpret it as "[stereotypical example of a mythical entity] does not exist (and mythical=does not exist)." If I do that - and that is how I suppose it's intended to be interpreted - then it's just a tautology.

JAlanKatz:
Does imagining Santa Claus and looking for Santa Claus differ from imagining and looking for a unicorn?

Not in the way I interpret the sentence. I understand both in this context as typical examples of "mythical objects." [[On further consideration, what I mentioned above was actually one of many possible methods for determining if the statement is true (i.e., if someone asked me, "Are you sure he doesn't exist?" that might be similar to my thought process).]] However, as I mentioned, I don't think it's meant to be interpreted in that way. We recognize that Meinong and others choose entities like Santa Claus precisely because they are stereotypical examples of entities not considered to exist.

--

All this could be summarized by noting again that, at least at this level of extreme analysis, no plausible interpretation for a set of symbols can be called more "correct" than any other.

We can speak of what concept the speaker intends the words to correspond to, and we can speak of what concept the listener interprets the words to correspond to, but especially at this level it is meaningless to talk about what the words "mean" without regard to intention and/or interpretation.

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AJ:
The short reply is that sentences don't express things; people do. So when we try to decipher the meaning of a sentence, we're really trying to decipher what a person means, or more generally trying to come up with a plausible interpretation for a set of symbols. The only reason it feels like we're doing anything else is that we have so much shared context to work with, and we spend our lives perfecting the art of utilizing words+context to get ideas across with a serviceable level of accuracy.

And guns don't kill people, but it cannot be denied that people use guns to kill people.  Similarly, people express things, but sentences are the tools they use to do so. 

AJ:
The tricky part is that sentences that look "reasonable" are strongly associated with being "meaningful" (from context) in our minds. Meaningfulness is a norm of assertion, as is truth - at least if you say it loud and like you mean it : - ) My point with the nonsense text is that there is no need to prove something is a subject, because that would be akin to trying to "prove" the meaning of a word you coined. (If you coin a new word, it of course means whatever you say it means. Likewise, the act of putting a word in a position where only a subject can go is essentially the act of marking that word as a subject.)

No one is offering proofs here, we're trying to understand the proposition that a sentence is meant to represent.  To mark a word as subject just means that the speaker intends for it to refer.

AJ:
The actual imagery would be hard to describe, but the idea is that I think the thought that corresponds to (my interpretations of the sentence) "Santa Claus does not exist," hence I can understand the underlying concept. There are really quite a few (infinitely many?) ways to interpret this sentence in terms of imagination. I could, for example, simply interpret it as "[stereotypical example of a mythical entity] does not exist (and mythical=does not exist)." If I do that - and that is how I suppose it's intended to be interpreted - then it's just a tautology.

I'm afraid I don't understand what you're saying here.

 

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AJ replied on Tue, Mar 9 2010 9:44 AM

JAlanKatz:
And guns don't kill people, but it cannot be denied that people use guns to kill people.  Similarly, people express things, but sentences are the tools they use to do so. 

That's what I'm saying, yes. Words are tools to express concepts, not the concepts themselves.

JAlanKatz:
No one is offering proofs here, we're trying to understand the proposition that a sentence is meant to represent.

Something "is meant" by someone. If it wasn't clear, either (1) ask that person to clarify, or - if you just want to find a plausible interpretation for the words - (2) find a plausible interpretation. Is there a third option?

As to proof, perhaps not the clearest choice of words, I was referring to:

The worst such case is something like "Santa Claus doesn't exist."  Certainly, we don't take this as meaningless, and to be meaningful, it would seem that it needs a sentence and a predicate.  But there can be no subject for this sentence, seemingly, without Meinong's move, referred to as the "population explosion.

This seemed to imply to me that "Santa Claus" (being a nonexistent entity) wasn't a proper subject, due to Santa Claus's ontological status. It seemed that you or whoever's views you were talking about required proof that the subject was really admissible as a subject. If that's not at issue so much the better.

JAlanKatz:

AJ:
I could, for example, simply interpret it as "[stereotypical example of a mythical entity] does not exist (and mythical=does not exist)." If I do that - and that is how I suppose it's intended to be interpreted - then it's just a tautology.

I'm afraid I don't understand what you're saying here.

Short version: Keeping in mind interpretation options 1 and 2 above, I interpret "Santa Claus" as "stereotypical example of a mythical=nonexistent entity (for illustration purposes)." But then "Santa Claus does not exist" becomes "[Nonexistent entity] does not exist." (A tautology)

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Torsten replied on Tue, Jan 8 2013 11:16 AM

Rather than keeping on the road we're on, I have a somewhat related question.  Do you have any thoughts about tracking an influence of Meinong on Menger?  He was a student of Meinong, I believe.

I presume you mean Alexius Meinong. He wrote on Value Theory for example. 

 

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