Formal Logic and Change

[Rosa Lichtenstein]

Here is another non-dialectical nail driven into the Hermetic coffin holding the DM-corpse:

[AFL = Aristotelian Formal Logic. MFL = Modern Formal Logic. DL = Dialectical Logic. DM = Dialectical Materialism.]

"Dialecticians often claim that Formal Logic [FL] cannot cope with change. Rarely do such comrades substantiate these allegations with quotations from or citations to a single ancient or modern textbook. That, however, does not stop them pontificating about logic -- a subject few seem to know much about.

Despite this, does the charge that FL cannot cope with change itself hold water? In order to answer this question, consider a valid argument form taken from AFL:

L1: Premiss 1: No A's are B.
L2: Premiss 2: All C's are B.
L3: Therefore: No A's are C.

With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation, the premisses are true then the conclusion is true. This claim is not affected by the fact that schematic premisses themselves cannot be true or false, since such schema express rules, and the above depiction is hypothetical.

One interpretation of L1 that might illustrate its capacity to reflect change is the following:

Premiss 1: No moving object is stationary.
Premiss 2: All objects with zero velocity are stationary.
Therefore: No moving object is one with zero velocity.

This syllogism is valid, and would remain valid even if all motion ceased. But it also 'copes' with movement, and hence with change, which fact is abundantly clear from what it says.

And we do not have to use what seem to be necessarily true premisses to make the point:

Premiss 1: All human beings are aging.
Premiss 2: All New Yorkers are human beings.
Therefore: All New Yorkers are aging.

Here once again we have change, easily expressed (and in ancient logic). This means that our logically-challenged, dialectical friends have yet to catch up with a subject that is already 2400 years old.

[There is an excellent account of Aristotelian Logic at:

http://plato.stanford.edu/archives/fall200...ristotle-logic/ (http://plato.stanford.edu/archives/fall2004/entries/aristotle-logic/)

And a useful account of MFL (i.e., now called "Classical Logic") at:

http://plato.stanford.edu/entries/logic-classical/#3

Comrades should also consult Robin Hirsch's article at:

http://eserver.org/clogic/2004/hirsch.html.

Hirsch’s essay, while deeply flawed itself, represents a major step in the right direction, by a comrade well-versed in MFL.]

Now in the above rather uninspiring valid argument schema the conclusion follows from the premisses no matter what legitimate substitution instances are found for the variable letters.

So, L3 follows no matter what. But the argument pattern this schema expresses is transparent to change: while it can cope with change, it takes no stance on it. Some might regard this as a serious drawback, but this is no more a failing here than it would be for, say, Electronics to take no stance on the evolution of Angiosperms (even though it can be used to help study them). Otherwise, one might just as well complain that FL cannot predict the weather or kill MRSA, and DL cannot saw wood.

To illustrate the absurdity of the idea that just because FL uses certain words or letters it cannot handle change (because it allegedly uses nothing but ‘rigid’ terms), consider this parallel 'argument':

(1) If x = 2 and y = 2x + 1, then y = 5.

(2) Therefore x and y can never change or become other numbers.

No one would be foolish enough to argue this way in mathematics, for that would be to confuse variables with constants. But, if this is so in mathematics, then DM-inspired claims about the alleged limitations of FL seem all the more bizarre -- to say the least.

So much for ancient logic; in modern logic we have this simple argument:

(1) If atoms of Copper undergo beta decay then Nickel atoms, positrons and neutrinos will be formed.

(2) Atoms of Copper do undergo beta decay.

(3) Therefore, Nickel atoms, positrons and neutrinos will be formed.

This schema was in fact known to the ancient Stoics 2000 or more years ago (!), but this stale old news will be a breaking story to most dialecticians. Their reliance on the ‘logic’ they have found in Hegel, which was already out of date as it was being written, failed to inform them of this. So much for the ‘scientific’ credentials of DL.

This argument pattern is called ‘Modus Ponendo Ponens’, or MPP for short.



This simple version of MPP (and one involving reasonably rapid change) is perhaps as good a counterexample as one could wish to find that refutes the claim that FL cannot handle transformations in nature and society.

Not only that, there are [i]countless other inferences that MPP itself can instantiate, and many inferential forms other than MPP in MFL, all depicting change equally well, when suitably interpreted.

This indicates that DM-theorists' accusations aimed at MFL are even less accurate than the ones they direct at AFL.

Of course, the example above will hardly satisfy dialecticians, since no "new content" has been added in the conclusion. This is relatively easy to fix. Consider the following argument (which has only one premiss):

Premiss 1: All dialecticians are human beings.

Therefore: The refutation of a dialectician is the refutation of a human being.

Here, the conclusion contains more information than the premiss, so new content has emerged – but, with no dialectics anywhere in sight.

And, even better, it depicts change to our dialectical friends, perhaps just to annoy them.

This argument form is used in Mathematics and Science all the time to derive truths not available to those super-glued to the old logic.

Of even greater significance is the fact that over the last hundred years or so theorists have developed several post-classical systems of logic, which include (among others), modal, tense, deontic, imperative, epistemic, multiple-conclusion and second order logic.

Several of these sanction even more sophisticated depictions of change than is allowed by AFL.”

[This has been taken from Essay Four, at my site.]

More details at:

http://www.anti-dialectics.org

[Faceless]

Premiss 1: No moving object is stationary.
Premiss 2: All objects with zero velocity are stationary.
Therefore: No moving object is one with zero velocity.

Where on earth is there an object with "zero velocity". And isn't it possible that I might move alongside this object and thus this moving object has zero velocity relative to me?


Premiss 1: All human beings are aging.
Premiss 2: All New Yorkers are human beings.
Therefore: All New Yorkers are aging.

Now the more pressing criticism. What scientific use does this have? New Yorkers are defined with reference to the fact that they are human. Suddenly what you have stated becomes much less profound. All humans are aging already contains the conclusion that all new yorkers are aging as "humanity" is a set which includes by definition all new yorkers, englishmen, scots and irishmen. This is the same "science" that allowed men of the middle ages to talk about agels dancing on pinheads and with amazing powers of logic proceed to discover absolutely nothing.

No dialectician disputes the truth of Aristotlean logic, nor that it is often used as an approximation of circumstances on a daily basis. However, all Aristotlean logic can really be reduced to is that A = A at any one time, for any one object. That I am myself here and now is no surprise to me. That humans are humans and have the characteristics of humans is true, but it is not a feat of scientific discovery nor is it an explanation of interactions between such obvious syllogisms.

That your first syllogism is partially wrong as explained (although, as a dialectician I accept that it is parially true), and that New Yorkers are only humans to the extent that they have not "quantitatively" developed away from the rest of humanity enough to count as a seperate species, although there are of course elements of evolution within the New Yorker which may make them non-human one day. You have made a number of huge generalisations which I myself will accept as good approximations but they are nontheless flawed logic.

[Rosa Lichtenstein]

Faceless:

It is easy to arrange for any object to have zero velocity, all you do is define a suitable inertial frame. Perhaps you do not know enough applied maths?

And you are doing what most novices do, confusing the truth or falsehood of a premiss with the validity of an argument. Perhaps you do not know any logic, either?

"Now the more pressing criticism. What scientific use does this have?"

Well, I specifically chose boring and trite examples so that you and everyone else would not get flummoxed by technicalities. It would be very easy to alter this, and make it eminently scientific.

You need to recall that I am using ancient logic here to refute the claim that FL cannot cope with change, and only that. One thing at a time. The usefulness of FL is an entirely different matter. However, I tackle that problem in the essay from which this was taken.

So, since AFL (which was the logic Hegel appropriated) is out-of-date it is more difficult to reveal its practicalities. But it is not impossible.

If you want to see how modern logicians do this, check out any book on modal or tense logic -- I list several at my site, in Essay Four.

It is also worth pointing out that the computer you are using employs formal logic; all standard processors use the Propositional Calculus. So, MFL is eminently useful. DL has no known use in science or technology.

And, as I also show in Essays Seven and Eight, DL cannot account for change itself.

As to whether arguments drawn from FL contain their conclusions in their premisses, I gave an example where this was not the case. There are countless more like this.

I suggest that the difficulty you are having over this is down to the fact that, like many other comrades who think Hegel is the last word in logic, you know very little logic. Hegel knew very little too.

"all Aristotelian logic can really be reduced to is that A = A"

This is another myth you DM-fans put about, and with no proof; you probably read it somewhere in a DM-article and just swallowed it. I bet you have never checked it against anything Aristotle himself says.

So, I challenge you to:

1) Find the law of identity in anything Aristotle wrote -- or anything like it.

2) Prove that all of AFL can be reduced to this 'law' -- including Aristotle's modal logic, his practical logic, etc. heard[/b] of [i]those!]

3) Find just one (genuine) use of Dialectical Logic in science and/or technology.


Faceless, you need to stop believing everything you read in the outmoded and largely fabricated comments on 'logic' one finds in DM-tracts* (comments that are never supported by quotations from Aristotle's work, or from modern logic textbooks) and start thinking for yourself.

And check out Essays Four and Six at my site where I demolish the demonstrably false things DM-fans say about FL.


[* It is quite remarkable that comrades are usually quite careful with the things they say about politics, economics, history or current affairs (quoting sources and data, etc.); when it comes to FL and dialectics in general, this scrupulous attention to detail goes out of the window. All we see are baseless assertions, fabrications, the construction of straw men, invention, non sequiturs, lack of evidence, anecdotal evidence -- and comrades like Faceless who just do not check what they read in DM-books/articles. Why is that? Who are you DM-fans tying to kid?]

[Faceless]

Rosa Licktenstein:

Firstly, I approached this thread, which is something of a cliche by revleft standards even, with respect for you and whatever content of your arguement there may be.

Your response is surly and smacks of bitterness. For what I don't know since I have never spoken to you.


It is easy to arrange for any object to have zero velocity, all you do is define a suitable inertial frame. Perhaps you do not know enough applied maths?

In practice you can only approximate to this. You, if you are as educated as you think you are, should know that that is just an idea and that your chosen object is going to be moving with an uncertainty which you will be insufficiently able to eliminate. Now perhaps you see my point. I am taking logic from a practical point of view, the only sense in which it can have any meaning.


And you are doing what most novices do, confusing the truth or falsehood of a premiss with the validity of an argument. Perhaps you do not know any logic, either?

I expanded to make clear the fact that the "validity of the arguement" infact is irrelevant as "newyorkers" are what helps define "humans", and if you are unable to make a single premise along the lines of A = B or A has qualities B, then what is the use of the logic? a "true" premise which does not have within it an element of untruth or uncertainty is but an idealisatio. You then believe that the logic is true. Which it would be if the inherent uncertainty and element of untruth in the premises was eliminated. However, that would presuppose a world in which humans DID NOT EVOLVE or in which something remains ABSOLUTELY STATIC (your first example) relative to some perceived "ideal" frame of reference. You see now why your examples, which contain an idealised "motion" or rather a time dependence, still fail to satisfy an accurate understanding of reality, of evolution.

I have not denied mathematics, or for that matter the "validity" of your arguement. But valid to what end when you can not make premises which are totally true?

you said:


Well, I specifically chose boring and trite examples so that you and everyone else would not get flummoxed by technicalities. It would be very easy to alter this, and make it eminently scientific.

but I said:


All humans are aging already contains the conclusion that all new yorkers are aging as "humanity" is a set which includes by definition all new yorkers, englishmen, scots and irishmen.

The point was not the compexity, but that your trite example contains the conclusion within the first premise.
Take:
Premise 1: All stars emit light
Premise 2: All red giants are stars
Conclusion: All red giants emit light

See, I can make a syllogism as easily as you. The same flaw remains in this example. When profiling, "what is a star?" and making observations, we observe red giants (along with blue dwarfs and MS stars) as being stars. That is to say that red giants form part of the first premise. We can not know the premise without knowing the conclusion. The premise "stars" is but an abstraction which deals with the conclusion "red giants".

Give me a less trite example, and I'm sure it will prove equally useful, as well as vague, since my above example is also quite dubious. e.g. at a certain point a red giant expands and becomes a light emitting "planetary nebula" and not a star at all. One would be hard pushed to write one syllogism which takes into account of the complex death of the red giant into a white dwarf and the expanding shell of the giant into a nebula, involving the accumulation of quantitative changes in breadth and transparancy of the outer shell until the star can be considered to have qualitatively changed (oops, dialectical words). There are also neutron stars which one may ask, "are they really stars?"


2) Prove that all of AFL can be reduced to this 'law' -- including Aristotle's modal logic, his practical logic, etc. [I bet you haven't even heard of those!]

you arrogant little piece of shit, why don't you suck my dick. I hadn't read that far down the article until now, and I lament that you had to be such a fuckface. I'm not going to read your "article 4" or "article 7". It's a real shame you think you're actually worth your own webpage. and stop using them fucking abbreviations. If you have "better" examples then write them here, otherwise shut up.

the syllogism is a simple thing. Yet you have not written one which does not contain contradictions and flaws or doesnt contain conclusions which are inferred by the premises. You assume that just because the logic is ok, it doenst matter what contradictions the premises and conclusion contain. You can't say a dog is a dog without my pointing to ambiguous examples. Go for your bestest most complicatedest syllogism that i can't understand or go for a wank for all i care.

your stupidity amazes me. when can "anecdotal evidence" be used to discuss aristotle or dialectics or anything philosophical? wtf? I once heard there were these two interpenetrating opposites!

[Rosa Lichtenstein]

You are right I am bitter, and at the failures induced in our movement by this crazy 'theory'. I have been 'debating' this topic on and off now for over 20 years with DM-fans, and you all say the same things, no matter how many times they are refuted.

As to this:


"In practice you can only approximate to this."

Not so; since it's a definition relative to an inertial frame, it can be specified precisely.

You are clearly confusing a measurement with a definition.

"Now perhaps you see my point. I am taking logic from a practical point of view, the only sense in which it can have any meaning."

Well, this just shows you have confused logic with science.

"I expanded to make clear the fact that the "validity of the argument" infact is irrelevant as "newyorkers" are what helps define "humans", and if you are unable to make a single premise along the lines of A = B or A has qualities B, then what is the use of the logic?"

I was unable to make head or tail of this. I think you need to learn some logic before you try to pontificate about it.

The rest of the same paragraph seemed no less confused. What has evolution got to do with what I was saying?

I am surprised you did not mention Tibetan pottery.

More irrelevance:

"I have not denied mathematics, or for that matter the "validity" of your arguement. But valid to what end when you can not make premises which are totally true?"

I am sorry, I did not know you had not sobered up.

The material you posted on stars is highly interesting, but how it shows that AFL is reducible to "A = A" you forgot to say.

Containment, or indeed implication, is not equality, nor is it identity.

Like Hegel, you have confused the "is" of predication with the "is" of identity (this was in fact a medieval mistake).

"you arrogant little piece of shit, why don't you suck my dick."

Ah, now we get to the dialectical abuse.

No change there for you Apostles of change.

Well as far as the request to suck your teeny weeny goes, I would if you had one. Come back to me when you get one.

"and I lament that you had to be such a fuckface"

I note that you still know more abusive words than you do Aristotle. No matter - it proves my point.

"and stop using them fucking abbreviations"

OK. Wilko. And asap.

"the syllogism is a simple thing."

But it clearly beats you, for now we have this LuLu:

"Yet you have not written one which does not contain contradictions..."

Such a big word; well done.

But I bet you do not know what one is -- as is clear from your inventing a few where they do not exist.

Watch out, there's a tooth fairy in your last post.

"You can't say a dog is a dog without my pointing to ambiguous examples"

And how do you know this, oh divine one? Please tell, [i]only don't use Moses this time....

"Go for your bestest most complicatedest syllogism that i can't understand or go for a wank for all i care."

I prefer to have a go at wankers like you.

"I once heard there were these two interpenetrating opposites!"

In rehab, were you?

"your stupidity amazes me."

Maybe so, but simple-minded folk like you were always easily impressed.

That is why you like DM, but not MFL, AFL, and know nothing about the LOI, LOC, LEM or HEX.

Brainless: please come back for another drubbing; I enjoyed that....

[Faceless]

Firstly, I have been told that to tell you to "suck my dick" is sexist abuse, so instead just have a wank. I would like to point out that i thought you were a man.


Not so; since it's a definition relative to an inertial frame, it can be specified precisely.

You are clearly confusing a measurement with a definition.

Well, a definition which requires "measurements" to even give it any meaning. How for instance can I define my frame as being the rest frame without constantly reestablishing my relative motion to other objects in "my" frame? I will always be making small accelerations, there will always be small forces acting upon me. For a start, I am always accelerating towards the centre of the Earth due to the rotation of the planet. Therefore this frame that you measure everything else relative to is either an idealisation; a figment of your imagination (or your so-called "definition"; or it is merely an approximation. Either way, its weaknesses have to be accepted.


Well, this just shows you have confused logic with science.
Or that you have confused logic with something which is "real", independent of science. You think your "frame of reference" is real beyond its actual use to people, beyond being able to measure it. Logic is nothing unless you apply it to science, in which formal logic becomes a crass approximation which requires building upon.


I was unable to make head or tail of this. I think you need to learn some logic before you try to pontificate about it.

Let me make it easier and speak down to you for a bit instead;
we do not know what is human before we have had a direct experience of humans. When we have had an experience of humans we then abstract the qualities of "humanity". New Yorkers are a concrete element of humanity which must be assessed before we can define what the boundaries of "human" is.


I am sorry, I did not know you had not sobered up.
You have created syllogisms where the boundaries of your objects are blurred and which contain abstractions which you have confused with real things. As I have also pointed out, in the case of the new yorker who ages, he is already an element within "all humans age" which supposes that you have already taken a profile of all humanity./


The material you posted on stars is highly interesting, but how it shows that AFL is reducible to "A = A" you forgot to say.

It is reducible to A=A because a red giant only equals a red giant at one instant. Otherwise there are numerous differences in this evolving concept. At a certain point I was showing that these small differences are what lead to a qualitative leap and the emergence of the white dwarf/planetary nebula. This was a positive example of quantity transforming into quality shown against the insufficiency of formal logic which desires to make the star either a red giant or a planetary nebula.

Even if you manage to show how amazing formal logic is, this example shows that regardless of this, dialectics has some applications.


You are right I am bitter, and at the failures induced in our movement by this crazy 'theory'. I have been 'debating' this topic on and off now for over 20 years with DM-fans, and you all say the same things, no matter how many times they are refuted.

Check that against what you have written in the other thread. Here you have no intention of winning me round. You went into this arguement with the intention of defeating me, you couldnt care a less if I become a convert to your new "marxism" (interestingly you have not made a positive contribution to my understanding of society or the sciences, nor have you pointed out what mistakes this dialectics caused marx, engels, lenin and luxemburg to make. The question arises, if I overlook the fact that your arguement has no substance, "so what?") If you intended to win me over, you would have approached the discussion more respectfully. In the other thread you are happy to stoop down to those less inteligent workers and vulgarise your "ideas".


And how do you know this, oh divine one? Please tell, only don't use Moses this time....

You have yet to create one so far.


I prefer to have a go at wankers like you.
Hey! No fair! you promised in your second post that you could


Well, I specifically chose boring and trite examples so that you and everyone else would not get flummoxed by technicalities. It would be very easy to alter this, and make it eminently scientific.


So, since AFL (which was the logic Hegel appropriated) is out-of-date it is more difficult to reveal its practicalities. But it is not impossible.

Your examples are boring, trite and asstoundingly obvious since the statement "all humans age" assumes a knowledge of all humans, including new yorkers. The same can be said for stationary objects which is just another word for having no velocity. The first example is even more mundane because the premise is just another statement for the conclusion. One is not even a set which contains the other (eg humans and new yorker). They are the same set!

If it is difficult to reveal the practicalities then again I have to ask, why bother?

[Rosa Lichtenstein]

Brainless:

"Well, a definition which requires "measurements" to even give it any meaning."

You really are a lost cause.

In order to define an inertial frame we need make no measurements.

"How for instance can I define my frame as being the rest frame without constantly reestablishing my relative motion to other objects in "my" frame?"

You are again confusing a definition with measurement.

There is nothing I can do to help you if you cannot grasp this point.

Try taking up busking, instead. Or maybe not; I think you might confuse that with trout fishing.

More gobbledygook:

"Let me make it easier and speak down to you for a bit instead;
we do not know what is human before we have had a direct experience of humans. When we have had an experience of humans we then abstract the qualities of "humanity". New Yorkers are a concrete element of humanity which must be assessed before we can define what the boundaries of "human" is."

I defy you to do any abstracting.

I'd explain why I say this, but I have just re-written two long essays on this topic(totalling over 60,000 words), which your tender eyes will not look upon, so I will leave you in outer darkness.

"You have created syllogisms where the boundaries of your objects are blurred and which contain abstractions which you have confused with real things."

I do not deal in abstractions. I do not believe in them. You do, but then I expect you believe in the tooth fairy, too.

"It is reducible to A=A because a red giant only equals a red giant at one instant."

Eh?

What has this got to do with Aristotelian Formal Logic (sorry AFL)?

"Otherwise there are numerous differences in this evolving concept."

What evolving concept?

Are you still inebriated?

"At a certain point I was showing that these small differences are what lead to a qualitative leap and the emergence of the white dwarf/planetary nebula."

What leap? Is it an athlete?

Anyway, I thought we were dealing with 'evolving concepts', not nebulae?

As I suspected, you are an Idealist -- like other DM-fans, you confuse 'mental constructs' with objects in the real world.

"Here you have no intention of winning me round."

Well, I did say on page one of my site that I have no interest in debating with clowns -- so make of this what you will.

You pontificate about logic, a subject you clearly know nothing about (just like the majority of DM fans) -- that is why I will not take you seriously.

Stop acting like the pope in this area, and I might be less horrible to you.

I do not want to 'win you over'; the class struggle with get rid of you lot on its own. As the working class gets larger, the less impact you dialectical muddle-heads have on it. You are all wallowing about in tiny sects, with no impact, ones that are getting smaller as your inflated opinion of yourselves gets bigger (now there we do have interpenetrating opposites!); you will be down to zero soon, all without my help.

I blame all this partly on the mystical, divisive, anti-democratic theory you lot have imported into the workers' movement.

Fine by me if you stick to it. In fact, please do.

It will leave the field free for us genuine materialists to try to repair Marxism's reputation among workers.

"nor have you pointed out what mistakes this dialectics caused marx, engels, lenin and luxemburg to make."

More fabrication. You are good at this. Have you thought of getting a job writing WMD dossiers for Tony Bliar? You are a natural.

And, I have pointed this out (I rule Marx out here -- he made few mistakes), but I hope you do not read what I have to say on this at my site since I do not want your very sensitive eyes to get hurt.

"If it is difficult to reveal the practicalities then again I have to ask, why bother?"

Ah, but I have, at my site -- but since you find my ideas too intimidating (or perhaps too difficult), you have declared it out of bounds, so you will never know, will you?

Just like the traditionalists in Galileo's day, you refuse even to look own the telescope.

Only this time, I do not want you to.

Your present state of ignorance is the best punishment I can think of to inflict on you.

And, even better, in this area you appear to be a self-made 'man'.

[ComradeRed]

Rosa, I hope you don't mind if I play the "devil's advocate" for a second, but what about "nonlinear change"?

You know, nonlinear in the sense that under such conditions this variable will range between a and b, but if the conditions become this then the variable ranges from x to y, etc. Not nonlinear in the sense of curves.

I am particularly curious because dialecticians frequently assert "chaos theory = dialectics"...but the logicists assert just as much "math = logic"; deductively, since chaos theory extends math (it is a subject of math), and since math is "reducible" to logic, wouldn't logic incorporates extends farther than dialectics?

Which puzzles me even further that a dialectician wouldn't accept logic :huh:

But I digress, "classical" logic (to me) seems to be synonymous with "linear" logic (this bias I have picked up from programmers). How can one reconcile nonlinear change from the linear aspect?

On the one hand I suppose the argument could be presented that there hasn't been any proof as to why nonlinear change is important...on the other hand isn't that why there are booleans (again, a prejudice I picked up from programming, a sort of object that returns true (1) or false (0) or is null (ie. nothing))?

Just a thought on my mind...

[mikelepore]

>>> "Dialecticians often claim that Formal Logic [FL] cannot cope with change"

But why are these two things even being compared? Dialectics isn't a kind of logic at all. A system of logic is a method to distinguish between a true proposition and a false proposition. Dialectics can't do that. Dialectics is problem-solving heuristic, alongside such other well-known problem-solving heuristics as "Try drawing a diagram", "Try working the problem backwards", "Try brainstorming." Dialectics is a heuristic that often highlights aspects by contrasting properties with their opposites.

[Faceless]

More pontification for thee:


I do not deal in abstractions. I do not believe in them. You do, but then I expect you believe in the tooth fairy, too.

That is quite possibly the stupidest thing I have ever heard. Mathematics abstracts a quantity from some object, to describe anything in words is to use abstraction. You can't do without abstraction. But that is entirely different to recognising what is abstract and that it has a place below the concrete subject from which you have made that abstraction. Terms such as "human" are abstractions taken from the concrete reality of living humanity. "New Yorker" abstracts the quality of actually living in New York from the complete person. "Frame of reference" is an even greater abstraction since it is a purely mathematical concept, involving all the abstractions of number and dimension from the concrete world.

That's over and out for the pope today

[Comrade-Z]

Originally posted by [email protected] 12 2006, 08:29 AM
>>> "Dialecticians often claim that Formal Logic [FL] cannot cope with change"

But why are these two things even being compared? Dialectics isn't a kind of logic at all. A system of logic is a method to distinguish between a true proposition and a false proposition. Dialectics can't do that. Dialectics is problem-solving heuristic, alongside such other well-known problem-solving heuristics as "Try drawing a diagram", "Try working the problem backwards", "Try brainstorming." Dialectics is a heuristic that often highlights aspects by contrasting properties with their opposites.
Exactly. And this seems to be the exact way in which Marx used dialectics in practice. Dialectics might have given him hints as to how to set out on the right track. It was a sort of "scaffolding" that gave Marx ideas for pursuing certain lines of thought with his reasoning (such as focusing on contradictions, etc.). But the final product (historical materialism) still needed formal logic, ordinary reasoning, and empirical evidence to explain and "prove" itself, insofar as historical materialism could be "proven." At that point dialectics could contribute nothing.

I think it is reasonable to say that some problems happen to fit the "dialectical framework." That means one might try thinking of the problems in those terms and see if one "gets lucky." However, many problems don't fit the dialectical framework, and trying to approach those problems from that angle will get you nowhere. Then, if thinking in terms of contradictions doesn't jumpstart any insights, one might draw a diagram, or try thinking the problem backwards, or draw an "idea web," or draw a venn diagram highlighting the similarities and differences, or use some other heuristic, like mikelepore noted.

That means dialectics cannot be consistently used to arrive at conclusions, and in no circumstances can it prove conclusions. Ordinary reasoning must be used for that.

[Rosa Lichtenstein]

Brainless:

"That is quite possibly the stupidest thing I have ever heard."

That is probably because you have never listened to yourself.

Mathematics does not use abstractions.

I'd explain why, but you seem to be happy in your state of ignorance.

"That's over and out for the pope today."

Head back in the sand for you, then, is it?

[Rosa Lichtenstein]

Comrade Red, I am not sure what question you were asking me in particular.

I also do not know what a 'linear' logic is, as opposed to a 'non-linear' logic, so unlike the various 'popes' at this site (not you obviously!) who comment on stuff of which they are ignorant, I will not comment.

However, I am not a logicist; more a natural deductivist.

You also need to note that the only point I was making in the original post (something Brainless finds a little too challenging) was that the hackneyed criticism DM-fans make of FL (that it cannot cope with change, etc.) is false.

And I gave examplers where it does this. In addition I kept them simple so that comrades could see the point.

The separate issue of how FL copes with change I did not comment on (but I do in the essays at my site -- and I will be adding to what I say over the coming months).

Of course, the point is that it is scientists who study change in material reality (logicians merely formalise sound arguments), and they can, and do, use various forms of modern logic to do this -- and they have done this for centuries. That is why they were interested in, and helped devolop, logic.

But I am not going to give Brainless the details -- he is happy enough to be ignorant on this issue.

And so he should remain.

[Rosa Lichtenstein]

Mikelepore, the only reason I was doing this above is because dialecticians constantly make this claim. So I have now refuted it. But, you watch; that won't stop them saying it.

They do this almost invariably from a position of total ignorance (of logic, both ancient and modern) -- exhibit A for the prosceution being Brainless.

However:

"A system of logic is a method to distinguish between a true proposition and a false proposition."

If you do not mind me saying so, this is not correct. Logic is the systematic study of valid argument, and as such it is only indirectly realted to truth.

Follow the links I gave above to find out more.

And I think that dialectics has only one confirmed practical application: confusing comrades.

Hence my aim to eradicate it from Marxism.

As I explain at my site, I do not think I can do this; this crazy doctrine/method has sunk too deep into the minds of comrades.


In which case the unsuccesful career of Marxim will continue.

Dialectics -- disproved in practice.

[Rosa Lichtenstein]

Comrade Z, I agree, but you can say this till the cadres come home; dilecticians have word blindnee in this area.

[mikelepore]

Originally posted by Rosa [email protected] 12 2006, 08:58 PM

"A system of logic is a method to distinguish between a true proposition and a false proposition."

If you do not mind me saying so, this is not correct. Logic is the systematic study of valid argument, and as such it is only indirectly realted to truth.

You're right -- I think now that I should have said: A system of logic is a method to distinguish whether the truth of a proposition does or does not follow from the premises.

What I had in mind was the inability of dialectics to render practical advice. For example, some people cite dialectics as a reason why they think socialism can be established through the incremental reform of capitalism, while others cite dialectics as the reason why they think the incremental reform of capitalism cannot lead to socialism. If the "method" is so nebulous that people come to different conclusions, then, whatever it is, it's not a system of logic. I think it's just a problem-solving heuristic, useful to generate numerous ideas, but incapable of checking the validity of them.

[Rosa Lichtenstein]

Mike;

Fair enough; I think we see eye-to-eye on this.

[encephalon]

do {
$x++;
if (($x/2) == int(($x/2)) {
print "integer $x is divisible by two";
} else {
print "integer $x is not divisible by two";
}
} until ($x == 987);



There you go, pure logic that incorporates and is entirely adaptable to change. You can apply the same principle to any degree of change and any number of variables. If you wish, you can even build an if-then/do/until loop that incorporates quantative change into a qualitive change.

Dialectics is entirely unnecessary to incorporate variables. Variables themselves are objects of change.

When dialectics creates observable results, then perhaps I'll start using it. Until then, I'll stick with logic. It provides useful results that are tangible in the real world.

[Rosa Lichtenstein]

Thank you for that Encephalon, but you might like to translate your example into more ordianry terms so that non-experts can appreciate your point.

[vox_populi]

Sorry...computer trouble...

*erased because of involuntary post*

[encephalon]

Thank you for that Encephalon, but you might like to translate your example into more ordianry terms so that non-experts can appreciate your point.

Sorry.. it's programming pseudocode, which is a mere extension of formal logic. It's really easier than it looks. My main point was that programming works, and exceedingly well; and until a computer that runs on dialectics pops up, there's nothing showing that dialectics works, or can even possibly work. It's a mere faith without material bases.

This program snippet works in one way and one way alone, as opposed to any "dialectical" contraption. You will always get a definite result no matter who interprets it or how many times you try it. I'll try to go through it line by line..



1. do {
2. $x++;
3. if (($x/2) == int(($x/2)) {
4. print "integer $x is divisible by two";
5. } else {
6. print "integer $x is not divisible by two";
7. }
8. } until ($x == 987);

The first line simply says that this is the beginning of a loop; when line eight is encountered, it will return back to line one unless the value of $x (a variable--can be any value) is equal to 987.

The second line simply increases the $x variable by 1. So (assuming that $x is initially zero), on the first pass $x is equal to 1, on the second pass 2, on the third 3 and so on until 987.

Line three simply tests whether or not $x divided by two is equal to the integer part of $x divided by two; that is, if $x is one then $x divided by two is 0.5, which is not equal to the integer part of 0.5, which is 0. If $x is 2, however, then 2/2 = 1.0 and the integer is 1.0.. they are the same. Basically, it's saying "if $x divided by two is a whole number, then do line 4. If it isn't, do line six instead.

So, if it is a whole number, it simply tells you "integer x is divisible by two." This would happen with the number 2,4,6,8.. any even number. If it isn't, then it says "integer x is not divisible by two." This will happen with odd numbers.

After that, it goes to line 8.. which, as stated before, loops back to line one unless $x is equal 987. Otherwise, the program ends (or continues to whatever else might follow it).

Here's the thing: without even thinking about dialectics, you can calculate quantative and qualitive change in this manner with pure logic. Even if dialectics could provide actual results, it is entirely unnecessary--puyre logic can and does fulfill its function quite well. You could, in essence, write an algorithm that handles economic concepts just as well if not better than marx does in das kapital.

Even better, that entire program is actually based on boolean logic, but simply made easier for humans to understand.. if one were so inclined, he or she could write the entire program in a series of ones and zeros. This makes it entirely mathematically calculable and requires it to produce consistent and correct results.

The basic fact is that logic works, whereas dialectics has never yielded indisputable results. The fact that all of these "dialecticians" are accessing the revleft forum is absolute material proof that logic works. Everything in a computer is based on boolean logic.

[Rosa Lichtenstein]

Encephalon, thanks for that, but DM-fans re-interpret variables along 'dialectical' lines, so they would recognise this as an example of 'dialectical mathematics'.

In Essay Seven at my site, I tackle this 'response' head on.

Anyway, DM-fans ignore the fact that logic uses variables (and has done since Aristotle's day); no wonder, it scuppers their objections to it.

[encephalon]

Encephalon, thanks for that, but DM-fans re-interpret variables along 'dialectical' lines, so they would recognise this as an example of 'dialectical mathematics'.

In Essay Seven at my site, I tackle this 'response' head on.

Anyway, DM-fans ignore the fact that logic uses variables (and has done since Aristotle's day); no wonder, it scuppers their objections to it.


That's fine; except even if dialectics could work, logical algorithms such as that render dialectical approaches entirely arbitrary. If it can be handled by logic in its purest form and yield consistent results (whereas dialectics has not), then anything else is entirely unecessary. One should go with what works, not with what one would like to work.

[Rosa Lichtenstein]

Right, but as far as they are concerned you know you are speaking Martian, while my writing is in fluent Venusian.

Their simple faith is all they need.

Fortunatley their influenc on the working-class is small, and getting smaller.

They can't see this, so are not inclined to do anything about it. Which is all to the good, too.

[LoneRed]

Rosa and redstar always say dialecticians resort to the same thing, but the anti-dialecticians always resort to, it doesnt work in practice which if one even looked at society, would know that thats wrong. The failures in the USSR,China, show just how dialectics works, and how it goes and isinterconnected to historical materialism. You claim to refute DM but uphold HM, which cant be done, as with refuting DM you are refuting HM, because DM is used in marxist theory to justify the HM. Nothing in Russian or Chinese societies, have disproved DM, if anything it reaffirmed it. Historical Materialism shows us that the peasantry is a reactionary class, DM shows us the antagonism between this class, and its relation to society,if indeed it tried to overthrow this "feudalism".

Take this

Premise One: A cat has four legs
Premise Two: A cat is an animal
Conclusion: All animals have four legs

formal logics, cant take change into consideration, A isnt always A, A=B=C
Nothing is the same, things are changing continually, the failure of formal logics

[ComradeRed]

Lone Red, you are confusing properties of things (A is in the set of B) with equivalence of things' properties (A is a set that is identical to B). Logic doesn't do this.

Math actually does best to avoid this trap; could it therefore be better than dialectics by your own argument?

(Besides you committed a fallacy even by classical logic, A is B, A is C, therefore some B may be C but not necessarily!)

Hell, just analysis alone can do this. So "therefore" analysis is better than dialectics.

*gasp* Reject dialectics for math? What blasphemy is this?! As though one wanted something useful! :o

Leninists use dialectics like a kid with ADD uses anything shiny: as a mere distraction!

And if you really are serious, math (calculus alone even!) incorporates (and extends much further beyond) dialectics. The "negation of the negation": the integral of a derivative (or vice versa). "Quantitative changes become qualitative" the tipping point, or inflection point. The "interpenetration of opposites" again derivative and antiderivative.

So what?! Why bother to go for math then?

Simple: math is precise, dialectics is sloppy. Oddly this is one of the big selling points for dialectics! I don't know whether to laugh or cry.

I have previously made requests for proof that dialectics is "irrefutably superior" to formal logic through the means of a geometric proof; the dialecticians laughed this off, but try to solve a proof dialectically. Or as encephalon points out, programming dialectically (the two are really one in the same).

Until you, Lone Red, or any other dialectician provides proof that dialectics is "superior", dialecticians are simply blowin' smoke. Math has done it, Logic has done it; dialectics has not. Just that makes the score Math 1, Dialectics 0.

[Rosa Lichtenstein]

Comrade Red: at last a voice of sanity.

On the basis of your expert knowledge of science, you might like to put Axel 1917 (yeah, right!) straight -- now, don't laugh, he actually thinks Woods and Grant contains genuine science!

And he was sober when he gave that impression....

[bezdomni]

Dialectics are used frequently in mathematics, as a way to find the solution to a problem.

Let's consider a simple algebra problem. Let's say...
5x+10=20
Obviously, the answer is going to be 2, but if the problem was more complicated, we would use "contradictions" to find the answer.

5x=20-10 (the antithesis is brought in)
5x=10 (synthesis, but still not finished)
5x/5=10/5 (synthesis creates another antithesis)
x=2 (final synthesis).

Dialectics were not necessary for this simple of a problem, but in a more complicated problem, where guessing and checking wouldn't suffice, we would need to use a more complicated means to find the solution. The problem with applying dialectics to history (and getting nebulous results) is not necessarily that dialectics is nebulous, it's that history is nebulous, as it's open to interpretations.

However, dialectic thought is used more frequently than one would realize. It would be impossible to balance an equation without "contradictions".

[ComradeRed]

Dialectics were not necessary for this simple of a problem, but in a more complicated problem, where guessing and checking wouldn't suffice, we would need to use a more complicated means to find the solution. The problem with applying dialectics to history (and getting nebulous results) is not necessarily that dialectics is nebulous, it's that history is nebulous, as it's open to interpretations. And what of the negation of the negation, or quantitative changes becoming qualitative, or how the use of formal logic causes an angel to lose its wings?

The "synthesis" is nothing new, it's simply an exchange. But this violates the negation of the negation and concedes to the thought that A is A.

Nothing that is the same but different is brought in, only the same thing in different clothing; if that is the negation of the negation you wish to associate with, then dialectics is even worse than I thought it initially.

Not to mention that it would prove inconsistent on the matter of "form v. content" :lol:

Could you program something dialectically in pseudocode or write a geometric opus (think Euclid's Elements) with dialectics? I would be very fascinated if that could occur, yet little has come from the thought other than dialecticians changing the subject.

P.S. There were no grounds for identifying "contradictions" or when an "antithesis" or "synthesis" will occur; this is going to be a serious problem if one tries to seriously present a formulation of dialectics that is coherent.

[bezdomni]

To be honest, I had an ulterior motive.

I've been trying to use dialectics and math, I knew that you (comradered) would be the first to jump on anything about math and criticize it, constructively.

Now I know where to go with it.

What I proposed in my last post is that the dialectic is used as a process to solve a complex problem, in which conventional logic would be very difficult or impossible to use.

The idea is obviously still in it's infancy, but I haven't brougt it up to people who understand dialectics (from either side). I would like to demonstrate the process in more complex math.

By the way CR, didn't you just say that calculus incorporates (and goes beyond) dialectics?

[Rosa Lichtenstein]

CPA, in what way is your example drawn from dialectical logic?

You need to recall that the simplistic 'Thesis/anti-thesis/synthesis' formula is from Fichte, not Hegel.

So, it is not even an example of dialectical 'logic'.

"However, dialectic thought is used more frequently than one would realize. It would be impossible to balance an equation without "contradictions"."

Well, if you are referring to reductio ad absurdam [RAA], that could not work given dialectcial 'logic'.

RAA only works because classical logic and mathematics rejects true contradictions.

As soon as they are allowed in, this gums up the machinery, and RAA fails.

So, using RAA, you assume the truth of something, validly derive a contradiction, which because it is false (and logic disallows the valid derivation of falsehoods from truths), permits the inference that the original assumption must be false, too.

But, if contradictions are true, then the original assumption cannot be discharged.

However, if you are not referring to RAA, you might need to explain more clearly how a system of 'logic' that allows for true contradictions can be used to help balance anything.

[Rosa Lichtenstein]

As far as your next comment is concerned, in what way is classical logic incapable of handling complex mathematical inferences?

Modern classical mathematical logic developed hand in hand with modern mathematics.

Sure there were problems in Foundational Studies (but only if you were a logicist -- and those difficulties look like they are about to be cleared up anyway), but apart from that, what do you mean (if you mean that)?

[bezdomni]

I definitely want to put it out that I, unlike many Leninists, am not a dogmatist. I am open to argument without creating ad hominem or strawman attacks. I also think my concept of the dialectic might deviate from precdent, as in I have actually put thought into it.

That said, I wanted to show that complex mathematical equations are not solved immediately, and they are solved by using contradictions. If we add on one side of the equation, we will subtract on the other to create a synthesis between the two. I wanted to show the process of solving a math problem with the dialectic (as people typically solve problems in math). Like I said, the idea still needs development, but the two principles that I've found (in algebra, at least...I've just started with calculus) are:
1) Equations are solved in steps, not immediately.
2) Equations are solved by using opposites.

This is essentially what Marx did with history. The dialectic is not used to create some sort of abstraction. It is used to show that class society is inherently antagonistic, and that these antagonisms will eventually cease...just as a math problem eventually ceases when you come to a definitive conclusion. The answer to the problem in math is a number, the answer to the problem in history is communism. Without dialectics, how can we prove that history will end up with communism? I've yet to see a viable alternative.

I also want to say that I don't put dialectics above or on a different page as mathematics. The goal is not to prove math wrong (which is impossible), but to combine math with dialectics. Much like the fusion of quantum mechanics and relativity. ;)

I hope I've explained it correctly.

[bezdomni]

Originally posted by Rosa [email protected] 8 2006, 11:24 PM
As far as your next comment is concerned, in what way is classical logic incapable of handling complex mathematical inferences?

Modern classical mathematical logic developed hand in hand with modern mathematics.

Sure there were problems in Foundational Studies (but only if you were a logicist -- and those difficulties look like they are about to be cleared up anyway), but apart from that, what do you mean (if you mean that)?
I think I might have cleared this up in the comment above, but just in casee.

I mean that mathematics incorporates dialectical logic as the process to find the solution.

Math and dialectics are not as "contradictory" as it might seem. I intend to end the idea that dialectics is contrary to logic...that it's "something else" (like god).

I'm sorry if I didn't answer the question properly. If I'm missing something, you could perhaps rephrase and I could try to give a better answer.

[Rosa Lichtenstein]

CPA, the way you express yourself tells me immediately you are not a dogmatist, hence I try to treat what you say with due respect, so I hope you do not think I was attacking you.

However, you said that classical logic could not do certain things, and I merely asked for examples, or for an explanation (since it seems to me that modern logic and mathematics go together quite well).

Since the word 'opposite' is not much use in mathematics, or logic, your 2) is misconceived, I think.

That it appears in dialectcial 'logic' is therefore no surprise.

As I point out too, you are using Fichtean notions, not dialectical ones.

Sure, crude dialecticians use these terms (and they copy them off one another, thinking they are 'dialectical'), but they are almost totally absent from Hegel (and as much as I despise the man) his work is all the better for this (since the schema you gave was too formulaic even for him), so he never uses it.

Your point 1) does not seem to be unique to dialectics.

So, I am still not too clear what you are proposing, or even why.

[Rosa Lichtenstein]

CPA:

"I mean that mathematics incorporates dialectical logic as the process to find the solution."

Where does it do this?

In fact, mathematics would fall apart if it did.


Your schema is not dialectical.

And even if it were, it is not logical.

[bezdomni]

I'm going to try fuse this so we don't have to constantly double post.


CPA, the way you express yourself tells me immediately you are not a dogmatist, hence I try to treat what you say with due respect, so I hope you do not think I was attacking you.
I don't think you were attacking me. One doesn't get themself taken seriously when they come off as a dogmatist. I want to seriously develop my ideas, therefore I remain open to the ideas of others.


However, you said that classical logic could not do certain things, and I merely asked for examples, or for an explanation (since it seems to me that modern logic and mathematics go together quite well).
As much as I know you hate it when people quote others, a comrade of mine explained where classical logic can "fail". It isn't a quote from Marx, Lenin, or Mao...so hopefully it isn't too pointless.

"For example, "A = A" is a basic formula of logic, extracted from the basic acknowledgement that there are many apples, many trees, many cows, etc. We can equate one with the other: apple = apple. "A does not equal B" is also a very basic logical formula. It reflects that a cow is not an apple; a tree is not a cow, etc. That's all very basic stuff, and it is very useful to a certain point, but only within certain limits. For complex phenomenon, basic logic doesn't get you very far. For example, on the surface, you might think that a dolphin is a fish: it looks like a fish, swims like a fish, eats the same food as a fish, lives in the water like fish do, etc. But on closer examination, we see that they are mammals: you can't take the superficial appearance as the whole story!

Dialectical logic is far more complex - and therefore, far more able to explain complex phenomenon. Dialectical materialism is the logic of change, development, motion - and revolution. Also, dialectics is not an invention of Marxism: it was first developed by the ancient Greeks, and then developed more fully by Hegel. But Hegel gave it an idealistic interpretation, which Marx and Engels gave a materialist content.
So it is not an invented thing, an abstract thing, a strictly Marxist thing: even without Marx or even humans, nature would still behave dialectically: pressure would still build up under ground and erupt in earth quakes and volcanoes; water would still boil at 100 degrees Celsius; wood would still burn up when heated too far and break down into carbon, oxygen, hydrogen, etc. In short, no matter what we all it, modern science give tremendous proof that nature behaves dialectically: chaos theory, ubiquity theory, atomic theory, etc.

Human society grows out of the natural world, and therefore the same general laws apply - made much more complex of course by the fact that we an think and influence nature so much!

So having Dialectical Materialism at our disposal gives us a powerful tool to analyze society. It is the theoretical compass that allows us to penetrate beneath the superficial appearance of things and understand the processes below the surface. For example, just as a volcanologist can analyze the data to get a better idea of when and where a volcano will likely erupt, so must we as Marxists take the "pulse" of society to prepare for social explosions. We don't know EXACTLY when or where, but we can get a pretty good idea!"

He basically admits the "shortcomings" of dialectics...that we can't know anything exactly, but that it is a tool with which we can conduct a more indepth deduction. Also, I think he might have an erroneous concept of chaos theory...but that is another debate for another time.

Dialecticians are NOT anti-logic (although you'd hardly know it by some of the morons on this forum). Classical logic does work, and it is logical (hence the name), but it makes shortcomings with certain instances in which dialectical logic would be more conducive to understanding.


Since the word 'opposite' is not much use in mathematics, or logic, your 2) is misconceived, I think.

That it appears in dialectcial 'logic' is therefore no surprise.


Opposites are used quite often in mathematics. Like I said earlier, when you add on one side of the equation, you will subtract on the other (the only exception that comes to mind is when you complete the square to solve a polynomial..but you are still adding the value to both sides and then factoring).

When you solve an algebraic equation you are using the process of dialectics. You are taking the statement of 2x=4. You are then taking the opposite statement of x=4/2 and you are arriving at the conclusion that x=2.


As I point out too, you are using Fichtean notions, not dialectical ones.

Sure, crude dialecticians use these terms (and they copy them off one another, thinking they are 'dialectical'), but they are almost totally absent from Hegel (and as much as I despise the man) his work is all the better for this (since the schema you gave was too formulaic even for him), so he never uses it.

I'm aware of this. I use Fichtean notations for simplicity's sake. I arrive at pretty much the same conclusions, and I think Fichtean notation seems to be more applicable to Marxism and class struggle. I also dislike Hegel. He used the dialectical process in a nebulous and backwards manner. Marx "set it straight", but it still remained somewhat nebulous. Dialectics must be made more concrete, and I agree that there are some problems with it. We disagree at the point that I believe dialectics just need a tune up, whereas you want to get a whole new car. ^^

I couldn't care less about Hegel. He did nothing for the class struggle.


...In fact, mathematics would fall apart if it did

Your schema is not dialectical.

And even if it were, it is not logical.

My contention is that mathematics assume dialectics.

Are you saying that the manner in which equations are solved are illogical or not dialectical? It seems to be both, to me. Where does it deviate from dialectics and/or logic?

[encephalon]

Premise One: A cat has four legs
Premise Two: A cat is an animal
Conclusion: All animals have four legs

formal logics, cant take change into consideration, A isnt always A, A=B=C
Nothing is the same, things are changing continually, the failure of formal logics


Nice try, but that's an unsound logical argument and if you know anything about logic, which I assume you do, then you know just how unsound that argument is. It is a categorical fallacy of composition, and is unacceptable in logic.

It's reaching a conclusion that because part of the whole has certain properties (the part being the cat, the whole being animals and the property being the possession of four legs), that must mean the whole must also have the same property. If you think this is acceptable in logic, then it's no wonder that you've attached yourself to the mumbo jumbo of dialectics. Either you were aware of this and decided to ignore it, intentionally creating an entirely false argument to dupe others, or you are ignorant of logic itself. I'm hoping it's the latter.

Perhaps you should read up on it?

Edit: Sorry, didn't notice that this was already addressed.

[LoneRed]

yes i realized after i posted it, that it was a fallacy of composition, and didnt fit in. But to ComradeRed we all know about your love affair with math, we dont gotta hear about that. When you say that math uses dialectics, then go and say dialetics is useless, or sloppy, you are committing an error. If there were no dialectics you wouldnt have that math you speak of.

All these anti-dialecticians seem to have grudges with Hegels dialectic and fail to distinguish between his and Marxs. Without Dialectics there is no movement, so you might as well go join those hippies on the lawn, as they have conherent theories either

[ComradeRed]

Originally posted by LoneRed+--> (LoneRed)But to ComradeRed we all know about your love affair with math, we dont gotta hear about that. When you say that math uses dialectics, then go and say dialetics is useless, or sloppy, you are committing an error. If there were no dialectics you wouldnt have that math you speak of.[/b] Well, look, all I am saying is two things, two very simple things:

Dialectics haven't proven itself useful, Math has proven itself useful, this alone gives math an upper hand.

If dialectics is composed of the "three laws" (negation of the negation, interpenetration of opposites, and quantitative changes becoming qualitative), then there is a superior tool that extends beyond these things with precision. Why keep dialectics?

There is no error here (:o), but I would so love to see a geometric proof done dialectically.


CPA
What I proposed in my last post is that the dialectic is used as a process to solve a complex problem, in which conventional logic would be very difficult or impossible to use. Well, that would be damn near impossible to do. The beauty of math is that each step can be done logically, so an equation like Schrodigner's wave equation, the geodesic deviation, or any other complex equation, becomes a cake walk.

From what I can tell of dialectics is that it is contextual; you would want to look at relational math like category theory (viz. topoi), graph theory, etc.

Perhaps writing an algorithm would work?


The idea is obviously still in it's infancy, but I haven't brougt it up to people who understand dialectics (from either side). I would like to demonstrate the process in more complex math. Lemme get this straight, you are trying to present how dialectics work mathematically? Is this correct?


By the way CR, didn't you just say that calculus incorporates (and goes beyond) dialectics? The negation of the negation is where something is the same but different than something else, right? Like if I have a function f(x)=x^n, then take its integral (a funky form of multiplication really) I get (x^{n+1})/(n+1) + C. Where C is some constant of integration (depending on where I start ;)).

The derivative is the opposite of this, so f(x)=x^n becomes n*x^(n-1) + C' where C' is some different constant of differentiation.

The derivative of an integral (or the integral of a derivative, whichever) is thus x^n + C' + C. It's "equal" to f(x) but it's "different", is this not the negation of the negation?

If it is, it has no use :(

Or the tipping point, the inflection point (or point of inflection, whichever): where the curvature changes sign. That is to say when "quantitative changes become qualitative".

Again, not too much of a use. It's remarkable, I can put dialectics in a mathematical form (if I understand dialectics correctly, and since it was Hegel who dealt with them, I doubt anyone understands them correctly), yet the cost would be that it would expose their uselessness ;)

Calculus (as a branch of analysis) does contain "dialectics" but it also exposes their uselessness. I don't think you'd want to work with this ;)

[LoneRed]

Another thing that is interesting is that you constantly resort to mathematics to prove your point, when it is one of the most boring and dry things out there to have a debate on. As well that just because for some reason or other you know bit more about math than most of the board, doesnt necessarily make you right. when someone argues in a way that excludes the majority of the would be debaters, its basically easy for you to say, oh im right cause of this, because not all people, nor even most work in such a static way.

[Axel1917]

Originally posted by [email protected] 9 2006, 07:05 AM
Another thing that is interesting is that you constantly resort to mathematics to prove your point, when it is one of the most boring and dry things out there to have a debate on. As well that just because for some reason or other you know bit more about math than most of the board, doesnt necessarily make you right. when someone argues in a way that excludes the majority of the would be debaters, its basically easy for you to say, oh im right cause of this, because not all people, nor even most work in such a static way.
I wonder just how old and outdated his beloved "Number is the essence of everything" way of thinking really is.

[Rosa Lichtenstein]

"For example, "A = A" is a basic formula of logic, extracted from the basic acknowledgement that there are many apples, many trees, many cows, etc. We can equate one with the other: apple = apple. "A does not equal B" is also a very basic logical formula. It reflects that a cow is not an apple; a tree is not a cow, etc. That's all very basic stuff, and it is very useful to a certain point, but only within certain limits. For complex phenomenon, basic logic doesn't get you very far. For example, on the surface, you might think that a dolphin is a fish: it looks like a fish, swims like a fish, eats the same food as a fish, lives in the water like fish do, etc. But on closer examination, we see that they are mammals: you can't take the superficial appearance as the whole story!"

First, as I explain at my site, this is not a basic law of logic, or of mathematics. DM-fans always quote this, but not from any modern source. And they all say the same thing, which means they merely copy ot off one another.

Second, this is not the law of identity, but the principle of equality, which is an entirely different matter.

Third, even if it were a basic law, it is not inimical to change since if anything changes, anything identical with it will change equally quickly.

"Opposites are used quite often in mathematics."

Well they are used in mathematical prose, not proofs, since the word is ambiguous.

What is the oppposite of a-bi in complex number theory: a-bi, -a-bi or -a+bi? And that is a simple example.


"You are then taking the opposite statement of x=4/2"

Why is that the opposite?

2x = 4 has many opposites.

Much esle of what you say has been tackled in this thread already and at my site so i am reluctant mertely to repeat myself.

Classical and dialectical logic are opposed to one another, they do not complememt each other. This is not because one is right and the other wrong, it is because DL is not even a logic -- it is mystical HJermeticism dressed up as profound rubbish. So DL doea not even make it onto the list.

That why mathematicians and scientists ignore it.

I will respond to other things you say later.

[Rosa Lichtenstein]

CPA:

"Dialectical logic is far more complex - and therefore, far more able to explain complex phenomenon."

Well, as I show at my site (in Essays 4 to 8) DL cannot explain anything at all -- not even a bag of sugar.

"Also, dialectics is not an invention of Marxism: it was first developed by the ancient Greeks..."

Correct, but thast just proves it has excellent ruling-class credentials, so no wonder it has been a disaster when applied to Marxism.

"Human society grows out of the natural world, and therefore the same general laws apply - made much more complex of course by the fact that we an think and influence nature so much!"

Well, even if this were so, dialectics is not even in the running -- it is far too confused even to be called a theory, let alone put into practice (so, once again, no wonder practically every scientist that has ever existed has not used it, even if they ever heard of it, and those that have have yet to tell us how it was of any use to them in comprehensible terms).

Now, I am just asserting these things here; I actually prove them to be correct at my site.

So, to save you saying things that are demonstrably wrong, you should check out what I have to say.

http://www.anti-dialectics.org

[Rosa Lichtenstein]

Lone Red:

"Without Dialectics there is no movement..."

But this is plainly not true, since things cannot move themselves, as Lenin said they could.

And, internal contradictions cannot account for change; if anything change accounts for them (even if they existed).

And unless you believe that nature is capable of arguing with itself, contradictions cannot exist in nature anyway.

Hence, even though they make a crazy sort of sense in Hegel's ideal system, they do not in material reality -- unless you are an idealist and think nature is mind.

Perhaps you do.

[ComradeRed]

Originally posted by LoneRed+--> (LoneRed)Another thing that is interesting is that you constantly resort to mathematics to prove your point, when it is one of the most boring and dry things out there to have a debate on. As well that just because for some reason or other you know bit more about math than most of the board, doesnt necessarily make you right. when someone argues in a way that excludes the majority of the would be debaters, its basically easy for you to say, oh im right cause of this, because not all people, nor even most work in such a static way.[/b]I'm surprised you didn't jump on the attack "Metaphysical nonsense! Metaphysical nonsense!"

Math is quite simply a tool, like "dialectics". You have asserted, as others have, that dialectics is "better". You have also, like others have, failed to demonstrate why or how.

Does that make me "work in a static way"? Well, if using tools that work is "statical", so be it.

My point remains that dialectics have yet to prove itself of any use in any manner; math has proven itself useful. Yet this is a "boring point". Maybe if I wrote it incoherently with bombastic jargon, it would get more press.

As the antidifferentiation of the dialectical point approaches one, dialectics vanish at a maximal rate via the Euler-Lagrange equation. :lol:


Axel1917
I wonder just how old and outdated his beloved "Number is the essence of everything" way of thinking really is. Really? I wonder just how many times dialecticians make stuff up and source it to me, then attack it.

Or how the duration of time numbers existed affects the usefulness of math.

It's one of those things, like why metal is shiny, that dialecticians will never understand :lol:

[Axel1917]

Originally posted by Rosa [email protected] 9 2006, 01:20 PM
Lone Red:

"Without Dialectics there is no movement..."

But this is plainly not true, since things cannot move themselves, as Lenin said they could.

And, internal contradictions cannot account for change; if anything change accounts for them (even if they existed).

And unless you believe that nature is capable of arguing with itself, contradictions cannot exist in nature anyway.

Hence, even though they make a crazy sort of sense in Hegel's ideal system, they do not in material reality -- unless you are an idealist and think nature is mind.

Perhaps you do.
Again, it seems that Rosa cannot even understand basic logic. No one has ever asserted that things, like a light bulb, moves itself. Why don't you bother understanding the context of such words and phrases before attacking them? You wonder why no one looks at your site. With such faulty logic displayed at this site, who wants to read hundreds of thousands more words of it?

[Rosa Lichtenstein]

Excuse 1931:

"No one has ever asserted that things, like a light bulb, moves itself..."

Well, it seems you can add to your ignorance of logic, your lack of knowledge of Lenin, since he foolishly said that everything in the entire universe is self-moving.

So, either light bulbs aren't in the universe, or Lenin was wrong -- or light bulbs can change themselves.

I suspect light bulbs are a little bit brighter than you, Excuse 1932.

"You wonder why no one looks at your site..."

Are you going for a new world record in getting things wrong, Excuse?

As of today, and since November 2005, just over 2000 comrades have looked at my site, read what I have to say, and from the e-mails I recieve, they are mightily impressed.

But, please stay away; I'd hate for your logic to improve by visiting my site.

I prefer you to remain a push-over.

In fact, a changeless push-over....

[Axel1917]

Originally posted by Rosa [email protected] 10 2006, 08:31 PM
Excuse 1931:

"No one has ever asserted that things, like a light bulb, moves itself..."

Well, it seems you can add to your ignorance of logic, your lack of knowledge of Lenin, since he foolishly said that everything in the entire universe is self-moving.

So, either light bulbs aren't in the universe, or Lenin was wrong -- or light bulbs can change themselves.

I suspect light bulbs are a little bit brighter than you, Excuse 1932.

"You wonder why no one looks at your site..."

Are you going for a new world record in getting things wrong, Excuse?

As of today, and since November 2005, just over 2000 comrades have looked at my site, read what I have to say, and from the e-mails I recieve, they are mightily impressed.

But, please stay away; I'd hate for your logic to improve by visiting my site.

I prefer you to remain a push-over.

In fact, a changeless push-over....
And of course, she does not know what Lenin meant, yet again. Ugh. Talk about dogmatism. Lenin knew, and everyone knows, that light bulbs do not change themselves. She has not even analyzed this, and the phrase is not applied in the literal sense Rosa is thinking of, hence Lenin's use of quotation marks around it.

Wow. 2000 people. Big deal. The site of the organization I am in was averaging something like 2.2 MILLION hits per month in the last months of 2005. Your "logic" also breaks at a very weak link, given that you deny the existence of the class struggle by denying the existence of contradictions. So, you are some kind of reformist, Bourgeois pacifist, what? Perhaps some Bourgeois agent trying to destabilize Marxism?

That cocky attitude of yours will also do nothing but to repel people from you as well.

[Rosa Lichtenstein]

Excuse 1932:

"she does not know what Lenin meant..."

So, you now admit I quoted him right.

Progress at last, since that proves you still have a few brain cells not totally damaged by that Hermetic virus.

Only, now you claim that he did not mean what he said.

Interesting tactic.

Lenin says all thing change themselves, but you change him externally so he does not say that.

I think that refutes Lenin quicker than if you had agreed with me.

Thanks!

"Talk about dogmatism."

Go on then... seeing as you are my superior in this respect.

Can you give me a few tips?

"everyone knows, that light bulbs do not change themselves..."

Well that means that both Lenin and dialectics are wrong.

Thanks again!

I suspect you are beginning to see what a crazy theory this is.

More progress.

And it took external contradictions (courtesy of moi) to move you.

Another refutation -- even you are not self-moving....

"and the phrase is not applied in the literal sense Rosa is thinking of, hence Lenin's use of quotation marks around it."

So, the ghost of Lenin is in personal contact with you is it?

Here it is again, for all those who think Excuse 1933 is right (emphases added):

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing….

"The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Lenin (1961), pp.357-58.]

One of these "self-movements" is in a single quote, the other is not. So, Lenin himself uses it literally.

Since light bulbs exist, then their internal contradictions (resulting from their union of oppopsites) moves them, and thus light bulbs, according to Lenin, can change themselves.

Twist his words all you like, he said it.

Get used to it.

"2000 people. Big deal."

Thanks!! I thought you'd be impressed.

500 alone since Feb 2006.

Since you said no one reads my Essays, you are wrong again.

I accept your apologies in advance.

"2.2 MILLION hits per month in the last months of 2005."

Well that just shows how important it is to expose the crazy logic that this site promotes.

Thanks again for making my task all the more important.

supporter....? You feed me so mant unintentional refutations of your own words, so much helful data, and makes so many mistekes, I can't believe you oppose me, deep down. I mean, no one so foolish as to auto-destroy intentionally 'his' own arguments, like you do.]

"given that you deny the existence of the class struggle ..."

Wrong.

You are going for the world record (as the comrade to commit the most mistakes in 2006)!

Anything I can do to help you, just ask.

You are helping me so much, I feel I should return the compliment.

"That cocky attitude of yours will also do nothing but [to] repel people from you as well. "

So long as it puts you off, that is all I can ask.

---------


Find out what Excuse 1934 is so scared of at:

http://www.anti-dialectics.org

[Axel1917]

Originally posted by Rosa [email protected] 11 2006, 09:56 AM
Excuse 1932:

"she does not know what Lenin meant..."

So, you now admit I quoted him right.

Progress at last, since that proves you still have a few brain cells not totally damaged by that Hermetic virus.

Only, now you claim that he did not mean what he said.

Interesting tactic.

Lenin says all thing change themselves, but you change him externally so he does not say that.

I think that refutes Lenin quicker than if you had agreed with me.

Thanks!

"Talk about dogmatism."

Go on then... seeing as you are my superior in this respect.

Can you give me a few tips?

"everyone knows, that light bulbs do not change themselves..."

Well that means that both Lenin and dialectics are wrong.

Thanks again!

I suspect you are beginning to see what a crazy theory this is.

More progress.

And it took external contradictions (courtesy of moi) to move you.

Another refutation -- even you are not self-moving....

"and the phrase is not applied in the literal sense Rosa is thinking of, hence Lenin's use of quotation marks around it."

So, the ghost of Lenin is in personal contact with you is it?

Here it is again, for all those who think Excuse 1933 is right (emphases added):

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing….

"The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Lenin (1961), pp.357-58.]

One of these "self-movements" is in a single quote, the other is not. So, Lenin himself uses it literally.

Since light bulbs exist, then their internal contradictions (resulting from their union of oppopsites) moves them, and thus light bulbs, according to Lenin, can change themselves.

Twist his words all you like, he said it.

Get used to it.

"2000 people. Big deal."

Thanks!! I thought you'd be impressed.

500 alone since Feb 2006.

Since you said no one reads my Essays, you are wrong again.

I accept your apologies in advance.

"2.2 MILLION hits per month in the last months of 2005."

Well that just shows how important it is to expose the crazy logic that this site promotes.

Thanks again for making my task all the more important.

supporter....? You feed me so mant unintentional refutations of your own words, so much helful data, and makes so many mistekes, I can't believe you oppose me, deep down. I mean, no one so foolish as to auto-destroy intentionally 'his' own arguments, like you do.]

"given that you deny the existence of the class struggle ..."

Wrong.

You are going for the world record (as the comrade to commit the most mistakes in 2006)!

Anything I can do to help you, just ask.

You are helping me so much, I feel I should return the compliment.

"That cocky attitude of yours will also do nothing but [to] repel people from you as well. "

So long as it puts you off, that is all I can ask.

---------


Find out what Excuse 1934 is so scared of at:

http://www.anti-dialectics.org
And again, you have no idea what Lenin was saying there, now do you? Why don't you digest and understand something before you attack it? You wonder why no one bothers going into an in-depth refutation of your points. It would be a waste of time, and you show repeated weakeness with abusive ad hominems. Anyone can quote something and give a distorted depiction of it. Capialists do it all the time. So do you.

[Rosa Lichtenstein]

Excuse 1935:

"And again, you have no idea what Lenin was saying there..."

Well, unlike you, I can read.

"Why don't you digest and understand something before you attack it?"

Excuse, I am following your lead, since that is exactly what you do with my ideas.

"You wonder why no one bothers going into an in-depth refutation of your points."

No, that is excatly what I do not do -- since there is nothing to wonder about. Neither you nor your dialectical clones are capable of mounting so much as a superficial refutation of my ideas, let alone an in depth one.

And that, my logically-challenged friend, is because diabolical logic has destroyed too many of your brain cells.

The dialectic has taken revenge on your cognitive capacities; in your case a defineit reduction in quality, and non-nodally.

"and you show repeated weakeness with abusive ad hominems..."

I am sorry if my attacks show up all your "repeated weaknesses".

Stop trying to debate with me if you can't take it, or you do not want them advertised any more.

"Anyone can quote something and give a distorted depiction of it."

Well, since you at first refused to believe it was a quotation from Lenin, this is a new turn of events. Now you retreat to the implausible claim that his words do not mean what they say.

Since you do not even so much as try to bale Lenin out here, I take it you can't.

And light bulbs can go on changing themselves, a la Lenin, I trust?

"Capialists do it all the time." [Emphasis added.]

Do you mean that the Capitalist class en masse now spends all its time misquoting Lenin, and have given up trying to make a profit?

Is this the rubbish they teach in the scag-end of the Militant Tendency these days?

Well, it makes more sense than dialectics; so I mustn't complain.

[Axel1917]

Originally posted by Rosa [email protected] 11 2006, 11:02 PM
Excuse 1935:

"And again, you have no idea what Lenin was saying there..."

Well, unlike you, I can read.

"Why don't you digest and understand something before you attack it?"

Excuse, I am following your lead, since that is exactly what you do with my ideas.

"You wonder why no one bothers going into an in-depth refutation of your points."

No, that is excatly what I do not do -- since there is nothing to wonder about. Neither you nor your dialectical clones are capable of mounting so much as a superficial refutation of my ideas, let alone an in depth one.

And that, my logically-challenged friend, is because diabolical logic has destroyed too many of your brain cells.

The dialectic has taken revenge on your cognitive capacities; in your case a defineit reduction in quality, and non-nodally.

"and you show repeated weakeness with abusive ad hominems..."

I am sorry if my attacks show up all your "repeated weaknesses".

Stop trying to debate with me if you can't take it, or you do not want them advertised any more.

"Anyone can quote something and give a distorted depiction of it."

Well, since you at first refused to believe it was a quotation from Lenin, this is a new turn of events. Now you retreat to the implausible claim that his words do not mean what they say.

Since you do not even so much as try to bale Lenin out here, I take it you can't.

And light bulbs can go on changing themselves, a la Lenin, I trust?

"Capialists do it all the time." [Emphasis added.]

Do you mean that the Capitalist class en masse now spends all its time misquoting Lenin, and have given up trying to make a profit?

Is this the rubbish they teach in the scag-end of the Militant Tendency these days?

Well, it makes more sense than dialectics; so I mustn't complain.
Rosa, no one bothers with an in-depth refuation because first of all, your arguments break at very weak links, and you don't even understand the ABC of Marxism. Secondly, your site poses absolutely no threat to dialectical materialism or the socialist movement.

Also, I never denied that quote being from Lenin. I think that Marxism-Leninism did that. I have noted that you have not understood that quote, and CYM elaborated one of your basic flaws in your nodal thread.

Also, by capitalist, I was referring to their ideologues and such. Your "almighty, superior intelligence" should have been able to recognize the context I put that term in.

[Rosa Lichtenstein]

Excuse 1936:

"Rosa, no one bothers with an in-depth refuation..."

Yeah right.

"and you don't even understand the ABC of Marxism..."

No, but I do understand the XYZ.

"your site poses absolutely no threat to dialectical materialism or the socialist movement."

Well, once again, you wouldn't know, would you?

"Also, I never denied that quote being from Lenin."

Correct, it was another benighted soul. Apologies.

"I have noted that you have not understood that quote, and CYM elaborated one of your basic flaws in your nodal thread."

What is there not to understand? According to Lenin (and a whole range of other DM-worthies I could quote), light bulbs should be able to change themselves.

And I note you are yet again allowing others to fight you battles for you.

At least you are a consistent wimp.

[Cym actually managed to tie himself in knots, so at least he is self-moving.]

"Also, by capitalist, I was referring to their ideologues and such."

So, I should stop taking your words literally now. Is that it?

[Axel1917]

From Rosa:


Yeah right.

Well, it is actually quite true. I wonder how your influence will be in ten years from now. It won't get anywhere.


No, but I do understand the XYZ.

Thanks for admitting that you do not understand the basics.


Well, once again, you wouldn't know, would you?

Actually, I do know. If it were really a threat, would not major organizations be writing many articles in defence of Marxism against Rosa's outlook?


Correct, it was another benighted soul. Apologies.

One mistake corrected. Many more to go! :P


What is there not to understand? According to Lenin (and a whole range of other DM-worthies I could quote), light bulbs should be able to change themselves.

Now why would one of the four most important Marxist theoreticians in history overlook such a basic fact that light bulbs don't screw themselves in and make such rubbish up? Surely he would not be so well known, and his Bolshevik party would not have led the workers and peasants to victory if that were really the case. An organization is worthless without the right ideas.


And I note you are yet again allowing others to fight you battles for you.

I could spend more time on refuting you, but I will reserve such time for more important things.


At least you are a consistent wimp.

You continue to be a consistent ad hominem monger.


[Cym actually managed to tie himself in knots, so at least he is self-moving.]

This arguement cannot posess merit, for it is made from a point of misunderstanding of the original claim of your opponent.


So, I should stop taking your words literally now. Is that it?

You should have been able to understand the context of that. Do you actually think that socialism was achieved in Russia just because Lenin sometimes used the word in a noticeable context that differed from normal interpretations?

I will give you something though, you have an equal chance at winning the masses over as the sectarians that try to use dialectics here and there! :P :lol: :lol:

[Rosa Lichtenstein]

Excuse 1940:

"Thanks for admitting that you do not understand the basics."

Well, I already acknowledged that days ago, but I noted that since none of you DM-fans seem to understand your own theory, that put me in bad company.

You need to wake up.

"I do know."

Well, you are doing a good impression of someone who doesn't.

"One mistake corrected."

Notice, when I make a mistake I own up; you have made dozens, and still you cling to your errors.

"Now why would one of the four most important Marxist theoreticians in history overlook such a basic fact that light bulbs..."

People have swallowed stranger ideas.

Newton believed in God; you believe nature argues with itself. Whacky, eh?

You figure it out. [Hint: diabolical logic seems to have destroyed their critical faculties in this area.]

"Bolshevik party would not have led the workers and peasants to victory...."

Er..., failure. There is no workers' state now in the USSR.

I am not surprised you haven't noticed, though. Head still in the sand.

"I could spend more time on refuting you..."

Right....

"You continue to be a consistent ad hominem monger."

So long as you remain a wimp....

"This arguement cannot posess merit, for it is made from a point of misunderstanding of the original claim of your opponent."

Wha????

"you have an equal chance..."

So you do accept the Law of Identity, then?

[bezdomni]

Sorry I haven't made a response in the defense of what I was saying earlier. I was pretty swamped with work at the end of last week, went out of town saturday night and pretty much literally just got home. I have to go get my brother from the airport in about 20 minutes, so I'll just make a quick response (I can see this thread has already debased itself, I wonder if it would be better to just let it die).

Every argument that somehow incorprates the phrase "my site" I will respond to later, when I have more time to read your site. I've glanced over it a bit, but haven't gotten enough time to really immerse myself in it. I'm going to discuss unique arguments to this particular topic (math and dialectics).


Well they are used in mathematical prose, not proofs, since the word is ambiguous.

What is the oppposite of a-bi in complex number theory: a-bi, -a-bi or -a+bi? And that is a simple example.

The opposite of an imaginary number is a rational number. So the opposite of i is sr1.

The way I would define an "opposite" in mathematics is a quantity or operation that cancels another quantity or operation. For example division is the opposite of multiplication. 2 is the opposite of -2. i is the opposite of sr1...etc


Why is that the opposite?

2x = 4 has many opposites.

In order to find the value of x, you have to use the opposite operation to isolate x on the other side of the equation. To find the answer of an equation, you have to constantly use the opposite numbers or operations.

Everything else somehow revolves around me reading your essays, which I haven't had time to do yet (to the appropriate extent). I'll get around to it later this week.

[Rosa Lichtenstein]

CPA:

Well, the point of setting my site up was to provide as comprehensive a case against DM as I could, and to save myself having to keep answering the same questions over and over.

"The opposite of an imaginary number is a rational number"

Why isn't the opposite of a complex number (what you call 'imaginary', but no one calls them this these days) a quaternion? Or a Real number?

http://en.wikipedia.org/wiki/Quaternion

And why isn't the opposite of a rational number and irrational?

And why are they opposites anyway? Are they in 'struggle' with one another?

Furthermore, your later 'definition' of an opposite:

"The way I would define an "opposite" in mathematics is a quantity or operation that cancels another quantity or operation."

Does not apply to complex numbers and rationals (which you also say are 'opposites'); they do not cancel. So, your own 'definition' rules your example out.

And 'opposites' do not cancel, they merely produce an out-put when the operation is performed.

So -2 x 2 does not cancel either -2 or 2; there they are still on the page, totally unscathed.

You are confusing mathematical operations with bus services, or orders at a restaurant. They can be cancelled, but numbers cannot.

In Group Theory, as I am sure you know, such things are called inverses, which notion is pretty clear.

But there is not sense of opposite here at all, they merely produce the multiplicative or additive identity elements of the group concerned.

E.g., a x 1/a = 1. Nothing cancelled; merely an output produced.

"In order to find the value of x, you have to use the opposite operation to isolate x on the other side of the equation."

Well, you keep saying this, but it does not make it so.

Sure, in mathematical pedagogy this is called an 'opposite', but it is an inverse in group theory.

But, there is no opposition here; they do nothing to each other; they are not in struggle.

So, even in DM terms the use of this word makes no sense.

"you have to constantly use the opposite numbers or operations."

No, there are other ways of solving equations. Trial and improvement is one (fixed point iteration, interval bisection, etc.)

Newton Raphson is another. Linear interpolation, too. And so on.

[bezdomni]

No, there are other ways of solving equations. Trial and improvement is one (fixed point iteration, interval bisection, etc.)
It is the most efficent way of solving an equation. I would hate to do differential calculus using only guess and check methods. It's possible to drive with your eyes closed, but it's harder to get to where you're going. (although in factoring polynomials, it is almost inevitable).




Why isn't the opposite of a complex number (what you call 'imaginary', but no one calls them this these days) a quaternion? Or a Real number?

http://en.wikipedia.org/wiki/Quaternion

And why isn't the opposite of a rational number and irrational?
Got me there. I mixed up my terminology. Haha, I use imaginary numbers because it is what my math teacher uses for some reason.

What I recall, is that a complex number is a real number +\- an "imaginary".

The bulk of your argument relies on my mistake of calling a real number a rational number, which I admittedly did fuck up. Sorry about that.

I might be wrong on the whole thing, of course. I probably should have developed my idea a little more before I posted it. The premise of my theory is that dialectical theought is used frequently in mathematics. I thought of it when I was doing math one day and realized that I kept putting the opposite of an equation on the other side to find a solution.

I think I'll give this a little more thought, because there seem to be exceptions.

I probably won't reply to this thread until I think some more, read your site, and do more math.

[Rosa Lichtenstein]

As far as equations go, I was merely challenging your use of a 'must'; there is no must about it; we do what works.

Sometimes we have to use inverse operations (which are not opposites; see below); sometimes we have to use other methods since there is no analytic solution.

So we can solve 2x=8 in several ways;

2x x 1/2 = 8 x 1/2, or:

2x/2 = 8/2; or:

x + x = 4 + 4.

With more complex equations, the options merely widen.

But, if everything had a unique opposite (but countless things do not; again, see below), there would only be one such method, one would think.

Anyway, you assume everything has an opposite (or even a unique opposite); I have yet to see your proof.

"The bulk of your argument relies on my mistake of calling a real number a rational number..."

But, when you multiply Reals by Complex numbers, they do not cancel (so, according to your 'definition', they cannot be opposites).

So my argument did not depend on your mistake since I said this in that earlier post.

And, since we have so many different sorts of numbers, it is only a Hegelian prejudice (or something akin to it) that decides some things are the opposites of others. He was an idealist who saw the world as mind – so no wonder these things come in the pairs, and they are just the sorts of pairs we see in Hermetic Philosophy, a mystical theory based on the idea of warring gods/principles in nature.

In that case, are integers the opposites of rationals, or of Reals, or transcendentals, or transfinite cardinals, or ordinals, or complex numbers, or even quaternions?

Or, are negative integers the opposites of positives? You seem to think that Reals are the opposites of complex numbers, but isn't each Real the 'opposite' each negative real? Or is each Real the opposite of 1/(that Real), or what? [E.g., is 2 the opposite of -2 or of 1/2? Or of 2+i, etc?]]

And what is the opposite of 2+i? Is it -2-i, 2-i, -2+1, or -2, or 2, or i, or -i, or 1/2, or 1/(-2-i), or 1/(2-i), or 1/(2+i), or 1/(-2+i), or a whole host of other candidates I could suggest?

And what is the opposite of a triangle? Or of a torus? Or an Abelian Group? Or a Hermite Polynomial? Or Sturm Louiville Theory? Or a Laplace Transformation? Or a Fourier Series? Or a Lebesgue Integral?

http://www.maths.mq.edu.au/~wchen/lnilifolder/lnili.html

There are countless objects in mathematics that have no opposites, or that have numerous (see above; which just means that this word loses its sense, and you might as well use any word at all).

And anyway, what is the point of all this?

These 'objects' are not struggling against one another. They do not change; and even if they did, it would not be as a result of contradictions internal to each 'object'. Do you really think that -2 has 'internal contradictions'? Or, that if we set up a homeomorphism to transform a cube into a sphere, say, that 'internal contradictions' would have done this, and not us?

"The premise of my theory is that dialectical thought is used frequently in mathematics."

In that case, you need to ditch that premise, then.

Functions, operations and processes in maths are certainly used (but these are based on extensions to mathematical logic, a modern branch of formal logic), but you have yet to show that a single dialectical concept has any use in mathematics, except creating confusion.