Why Existence is NOT a predicate


BaalChatzaf

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Baal:

~ Re your post #14...

~ Do you know how to actually straightforwardly answer a simple question without changing the subject in the most moronically insulting ways? You've responded this way with several others I've noticed, MSK included. It does not become you. You sound like Fred Weiss. Not a good role model, trust me.

~ The 'scare quotes' are not such but distinction I stressed as I see 'sets' and concepts and am pointing such out as such , and, they are there because I've never read any references to 'sets' as being 'concepts' (a simple book quote would have sufficed, you know)...to answer only one of your least insulting (rhetorical?) questions. The rest of your 'questions' (note THOSE 'scare quotes'!) are ignorable.

~ Now, how about a 'relevent' response, pretty please? You know: an actual 'answer' rather than a snobbishly intellectual-elitist evasion? Give it the 'old college try', this time, ok?

~ Otherwise, unplug your keyboard (I'm trying to be diplomatic here.)

LLAP

J:D

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Bob,

Does the law of identity operate with math?

Michael

Yes. It is equivalent to the law of non-contradiction.

However there are some weird type logics call para-consistent logics where contradictions are permitted but implication is sufficiently weakened so that there are formulas that are not inferred from the remaining corpus of formulas. This maintains a restricted type of consistency.

In mathematical system by and large (meaning virtually all except para-consistent systems) contradiction is not permitted.

Ba'al Chatzaf

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Baal:

~ Re your post #14...

~ Do you know how to actually straightforwardly answer a simple question without changing the subject in the most moronically insulting ways? You've responded this way with several others I've noticed, MSK included. It does not become you. You sound like Fred Weiss. Not a good role model, trust me.

~ The 'scare quotes' are not such but distinction I stressed as I see 'sets' and concepts and am pointing such out as such , and, they are there because I've never read any references to 'sets' as being 'concepts' (a simple book quote would have sufficed, you know)...to answer only one of your least insulting (rhetorical?) questions. The rest of your 'questions' (note THOSE 'scare quotes'!) are ignorable.

~ Now, how about a 'relevent' response, pretty please? You know: an actual 'answer' rather than a snobbishly intellectual-elitist evasion? Give it the 'old college try', this time, ok?

~ Otherwise, unplug your keyboard (I'm trying to be diplomatic here.)

LLAP

J:D

O.K. The notion of set (or class or collection) IS a concept and the empty set exists. For example the set of four sided triangles. The empty set exists so that set difference can be made perfectly generally. Equivalently that means the set product of a set and its complement is well defined. That was my references to complemented lattices.

Are we happy now?

Ba'al Chatzaf

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Bob,

Does the law of identity operate with math?

Michael

Yes. It is equivalent to the law of non-contradiction.

Bob,

Close but not precise. The law of non-contradiction rests on the law of identity. It is not equivalent to it, but inferior to it. Without the law of identity (an axiom), there is no law of non-contradiction.

However there are some weird type logics call para-consistent logics where contradictions are permitted but implication is sufficiently weakened so that there are formulas that are not inferred from the remaining corpus of formulas. This maintains a restricted type of consistency.

You mentioned modal logic elsewhere. This seems fascinating and I will look into it. Gimme some time on this one, though. (But I will do it.) I am not producing my own stuff these days. Gotta get back to work.

Michael

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Reading Rand's comments regarding imaginary numbers, I had to make a comment here.

First of all, I have perhaps what one might call a 'reasonable' background in mathematics, and specifically applied math. I would hardly call myself an expert - far from it - but I have formally studied complex numbers (applied them to circuits), numerical methods, differential equations, Fourier transformations and many other at least somewhat 'advanced' topics.

If you have a background in math, I think it would be hard to draw any other conclusion other than Rand just doesn't get it and simply shouldn't have made those comments. I don't want to degrade into Rand bashing and defense against such. Saying or admitting you don't understand something is not a big deal. Making prophetic pronouncements on topics that you know little or nothing about IS a problem.

Dragonfly wrote in a post on this topic on another board

"You still don't get it: in mathematical number theory numbers do not "refer to somethings", they are an abstract construction that may have once originated from the kindergarten arithmetic you mention, but no they longer depend on such primitive notions for their definition"

Why would she make statements like she did with an obvious 'kindergarten' background? It's not right. I'm sorry - this gets under my skin. Her comments oversimplify and indicate a profound ignorance of the subject matter. The fact that she asked about the utility of imaginary numbers simply means she doesn't have a clue, and should therefore reserve judgment.

Maybe though I don't understand enough advanced math to see how her comments were deep, meaningful and accurate - or not.

Bob

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Bob M,

Do you think Rand should have said that imaginary numbers are valid if they can be used for not computing? That is the real opposite of what she actually said.

As I keep saying, there is plenty of legitimate stuff to criticize in Rand's writing. There is no need to make stuff up or replace her meanings with wrong ones so the bashing will fit.

Michael.

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She was NOT referring to what the math was to be used for in that example, but to the method—to the math itself. Prof. C's example was a random example. It could have been "math problem" instead of "problems involving electrical circuits." That is why the imaginary number can be called a "concept of method." I am repeating myself, so let's just leave it for another time.

No, you're wrong. Rand said: "If you tell me that the concept, let's say, of an imaginary number doesn't do anything in reality, but somebody builds a theory on it, then I would say it is an invalid concept". "Building a theory" are her words for pure mathematics. So she said that concepts in mathematics are only valid if they can be applied to physical systems.

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Why would she make statements like she did with an obvious 'kindergarten' background? It's not right. I'm sorry - this gets under my skin. Her comments oversimplify and indicate a profound ignorance of the subject matter. The fact that she asked about the utility of imaginary numbers simply means she doesn't have a clue, and should therefore reserve judgment.

That's a good point: how can anyone claim that she had any knowledge about mathematics if she even didn't have a clue what you can do with imaginary numbers? And why should pointing out this obvious fact always be called "bashing"? No one can be an expert in everything. It's only when someone starts to make grandiose claims in a field that's obviously outside his or her expertise that we will protest. Why defending the indefensible?

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No, you're wrong. Rand said: "If you tell me that the concept, let's say, of an imaginary number doesn't do anything in reality, but somebody builds a theory on it, then I would say it is an invalid concept". "Building a theory" are her words for pure mathematics. So she said that concepts in mathematics are only valid if they can be applied to physical systems.

Dragonfly,

I am commenting here just to register that you still did not understand. And "building a theory on it" does not mean her term for pure mathematics.

I see nothing at all in her writing that excludes solving math problems, for instance. She was even studying algebra at the end of her life, and these studies are full of math problems that are not related to physical systems.

I won't correct you again, so feel free to persist in the error. This is good for those who want to defend Rand at all costs (not my case). They can point to it as a perfect example of what extremes Rand-bashers go to.

Michael

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I am commenting here just to register that you still did not understand. And "building a theory on it" does not mean her term for pure mathematics.

No, you don't understand it. Of course a mathematical theory that doesn't have applications in physical reality is pure mathematics.

I see nothing at all in her writing that excludes solving math problems, for instance. She was even studying algebra at the end of her life, and these studies are full of math problems that are not related to physical systems.

Of course she wouldn't exclude solving math problems if she thought these could be used in physics or technology. Her questions about imaginary numbers are quite revealing in that regard. You just don't get it.

I won't correct you again, so feel free to persist in the error. This is good for those who want to defend Rand at all costs (not my case). They can point to it as a perfect example of what extremes Rand-bashers go to.

Now you sound like Valliant, with your continuous unfounded accusations of Rand-bashing.

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Of course she wouldn't exclude solving math problems if she thought these could be used in physics or technology.

Not at all. She would be (as was) very happy to use pure math as a form of learning it.

If you are so concerned about the way she thought math should be applied, note that she also used the cardinal and ordinal forms and included solely mental operations. There are not only concepts of method, there are other concepts of consciousness where math is used. These have nothing to do with physics or technology. Sorry, Dragonfly. Your allegation just doesn't hold up.

Now you sound like Valliant, with your continuous unfounded accusations of Rand-bashing.

I apologize for this being badly worded. I did not mean that you are a mindless Rand-basher. I believe your criticisms are always well thought-out and sincere, even when mistaken like in the present case (and even when tinged with a bit of rhetoric). My intent was the opposite. It was to say that mindless Rand worshipers could use an error of this nature for their mindless purpose of rewriting reality by pretending that it proves that Rand's real shortcomings do not exist.

Michael

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x

Close but not precise. The law of non-contradiction rests on the law of identity. It is not equivalent to it, but inferior to it. Without the law of identity (an axiom), there is no law of non-contradiction.

In classical (non-Intuitionist) logic one can demonstrate that -(P&-P) is equivalent to (P <->P) which is equivalent to (P v -P). Here v means inclusive or.

The most important characteristic of a formal system is that at least one well formed formula of the system is not derivable from the postulates (this is equivalent to consistency).

In Intuitionistic Logic (this is a technical term) the law of the excluded middle does not hold.

You might not be aware of it, but there are a lot of different logics out there. There are logics in which there are truth values other than True and False (for example). Such are called multi-valued logics. These logics are designed to handle situations where the truth or non-truth of a proposition is not definitely known.

Ba'al Chatzaf

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To be is to be related. Numbers are used to represent unique, specific, symmetric and asymmetric relations. Zero and one are used to represent the symmetric relation of equality in addition, ie. x+(-x)=0 and in multiplication, x*(1/x)=1 . Other numbers are used to represent unique, specific asymmetric relations, ie. 1+1=2, 2+1=3, etc.

In the context of this discussion it could be said that numbers are "concepts of relations" and this includes ALL numbers, including complex numbers.

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Baal:

~ Re your question in post #28, after your personal assertion that concepts and 'sets' are identical...(like, I needed that confirmation!)

Are we happy now?

~ No.

~ Give me an 'authoritative' professional philosopher's or logician's book quote re the synonymity (synonymosity? synonymy?). THEN, and only then, I'll be :)

~ You apparently missed my point: they never were identified as such anywhere (what logic text on 'sets' mentioned 'concepts'?); instead, a 'bait-and-switch' mental con-game was used there to seduce one into thinking such. Think of all arguments about 'sets' with the term 'concept' instead; like, what does an 'empty concept' mean?

LLAP

J:D

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Baal:

~ Re your question in post #28, after your personal assertion that concepts and 'sets' are identical...(like, I needed that confirmation!)

Are we happy now?

~ No.

I will quote myself from #28

"""""O.K. The notion of set (or class or collection) IS a concept and the empty set exists. """""

That is what I said. That are many concepts, some of which have nothing whatever to do with set (meaning collections).

If we disagree we disagree but puhleeeeeze do not misquote me or misrepresent what I said.

Ba'al Chatzaf

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Baal:

~ 1) Please 'quote' me where *I* 'mis-quoted' you, as you accuse me of doing.

~ 2) Please answer my questions.

LLAP

J:D

In #42 you wrote

Baal:

~ Re your question in post #28, after your personal assertion that concepts and 'sets' are identical...(like, I needed that confirmation!)

I never asserted any such thing. I did not set concepts and sets are the same thing. Ever. You misunderstood what I -did- say.

And I have answered your question. The concept of the empty set exists, it is a proper concept and a necessary concept, since the empty set is required for set intersection to always be defined.

Ba'al Chatzaf

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RTTYUZYUWVZCZC

211730Z Y 20SEP07

Fm: Someone or Other, not an approved "authority" on anything

Baal:

~ Re your question in post #28, after your personal assertion that concepts and 'sets' are identical...(like, I needed that confirmation!)

Are we happy now?

~ No.

~ Give me an 'authoritative' professional philosopher's or logician's book quote re the synonymity (synonymosity? synonymy?). THEN, and only then, I'll be :)

~ You apparently missed my point: they never were identified as such anywhere (what logic text on 'sets' mentioned 'concepts'?); instead, a 'bait-and-switch' mental con-game was used there to seduce one into thinking such. Think of all arguments about 'sets' with the term 'concept' instead; like, what does an 'empty concept' mean?

LLAP

J:D

John

Though I usually agree with what you say, I have to say I have to go beyond Bob on this one.

Before explaining myself, I will make some personal references :

When I was a child, I had an "educational toy", a "game" called "WFF'n'PROOF". It was something like a dice game, but instead of having numbers on the dice, it had "p". "q", "r", "s", etc., representing various hypothetical propositions, axioms, etc. The point of the game was to learn to form a "WFF" (pronounced "WOOF"), which stands for a "Well-Formed Formula." Advanced levels even played against a timer, as in chess. Once you had formed your formula, you were required to present a logical "proof" as to why it was a "WFF." This was one of my earlier exposures to symbolic logic.

A few years went by, and while I learned set theory in school, my father developed the first college-level courses in Fluidics, the study of fluid-powered machine logic. (He's the one who built the motor I told you about, Bob -- first, a prototype at home, then a fully functional one in the lab at work,) This course was developed at the time of the first Earth Day and all, was being hailed as a potential replacement for the inherently self-destructive technologies based in magnetoelectricity and fossil fuels. I was the "alpha tester" for the fluidics course, and learned boolean logic in the process.

As well as being the "guinea pig" in that learning experiment, I also got to study learning as a a psycholgy subject in college. At the time, the psych department was pure skinnerian, which helps eliminate a lot of the mystical crap. It also pegged its hopes on the Stimulus-Integration-Response behavioural paradigm, which, when expanded with the Feedback Loop concept, becomes a viable model for both describing and directing human learning (though a little heavy on the reductionism).

I then became aware of AR's books, and found that this learning paradigm was essentially the same as her descriptions of human concept formation. And also compatible with any workable definition of empirical induction.

Between tinkering with the computer club timeshare dialups over the years, and finally buying one of the early TRS-80's, I stayed involved with computers. Later on I taught myself to become a software engineer: programming (with soldering iron in hand) in Assembler and 'C', creating my own logical constructs, and in general, playing God.

Now a number of years ago, there was a movie of a Tom Clancy "semi-true" cold war thriller starring Denzel Washington and Gene Hackman. The premise was a callup to US Navy nuclear submarine duty at the time of the soviet empire collapse. Gene Hackman as nuke sub commander gets orders to counter a rogue soviet general, and to start WW III. Meanwhile his comm system goes down, and he gets a partial message, one that is not properly "formatted,", ordering him to stand down. Because the message is incomplete he is forbidden by Navy security policy to act on the message. His subordinate Denzel Washington cannot follow these orders (to start a nuclear war) in good conscience, and starts a mutiny. Blah blah blah. Action tension death noise. Blah blah blah.

Many moons before this movie was made, I had developed secure comm systems for the US Navy (and NATO) that included the capability of determining whether incoming messages were properly "formatted". The systems I developed ($8K for a system that did all their $1/4-million NAVMACS systems did!) worked off of "fuzzy logic" natural language pattern-recognition algorithms (since "incorporated" into ECHELON), with a user-selected "acceptable" error rate of anywhere from 0% - 80%. Yes, I could accurately pick out a message with an inherent 80% error rate. (These systems were used at land installations and shipboard, but were prohibited from submarines due to their use of **noisy** dot-matrix graphics printers.) If they'd used my system, they never would have had that problem on the submarine...

So here I got this threaded multitasking dynamic timeslice realtime event-driven system (not to mention "butterfly" interrupts and a system timer circuit configured as 12-bar blues written in 3/4 time -- yes I had to reinvent the wheel, and IT WAS NOT APPRECIATED), working off a "tri-state" logic -- "YES"/"NO"/MAYBE" (or "SORTOF" or "DUNNO" or "WAKEMEUPWHENYOUMAKEUPYOURMIND"). Try explaining THAT to a military man, or putting it into DOD documentation format. Had to turn off over 12,000 internal grammar-checking rules (boiled down to a set of 4 logical constructs) just because they couldn't understand the explanation of automatic data stream pattern editing. Oh well. Their loss.

The point of this is that I understand concept = set. And I think that Ayn Rand said the same thing, without using the teminology. It's certainly how I utilize the "concept" -- a "concept" is the hierarchical set that subsumes percepts of all concretes identified with having a particular (set of) shared characteristic(s), as well as other concepts. (With one proviso: that every set is a member of itself, thus avoiding self-referential paradoxes.) The law of identity and the law of non-contradiction are thereby upheld: a concrete cannot both be and not be the member of its set(s) at the same time. You asked, in reference to an "empty set", what would an "empty concept" be: it is a label without referent in reality. I don't see the problem here.

You would understand the term "stolen banana", but find the term "stolen concept" meaningless? I don't think so.

vty

Steve

NNNNN

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Baal:

~ You are correct. *I* mis-interpreted what you said. You did not say that the concept of 'sets' is identical to the concept of 'concepts'. But, it was sure easy to think you meant that re your responses to my points and question; ok: my bad.

~ However, nothing that you did say seems relevent to what I originally asked...in post #14 (re 'empty sets' [like, there's more than one?])...

...but, if there's no contents (so to speak), there's no way of telling one empty [set] from any other...Yet it seems there ought to be a way to distinguish the two, apart from the labelling, no?

...nor in anything else I argued re the superficial relationship between 'sets' and 'concepts.'

LLAP

J:D

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Baal, ADDENDUM:

~ Further: I apparently wasn't clear (though I argued the distinction as existing, but, that this distinction is 'bait-and-switch'edly glossed over in prof texts in terms of 'collections'), but my 2nd question was: WHAT is the supposed 'distinction' between (get ready here...) 'sets' and 'concepts'? -- Please don't talk about 'sets' as 'collections', since I don't know what a 'collection' of concepts is...unless you can explain this latter idea.

LLAP

J:D

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Baal, ADDENDUM:

~ Further: I apparently wasn't clear (though I argued the distinction as existing, but, that this distinction is 'bait-and-switch'edly glossed over in prof texts in terms of 'collections'), but my 2nd question was: WHAT is the supposed 'distinction' between (get ready here...) 'sets' and 'concepts'? -- Please don't talk about 'sets' as 'collections', since I don't know what a 'collection' of concepts is...unless you can explain this latter idea.

LLAP

J:D

See http://en.wikipedia.org/wiki/Set_Theory

for an introduction. Read, learn, think. Set theory is the grounding of just about every part of mathematics and it is an important part of mathematical logic. This is basic stuff. If you can't follow this, then I can not help you.

Ba'al Chatzaf

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