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Thread: Abstraction - is it valid method of thinking

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    Default Abstraction - is it valid method of thinking

    What i understand of abstraction is very basic. It's like finding something about a thing, and then making the key idea of that thing independent of the original thing.

    like, hammering a fence together, in the abstract is labour power.

    Or for example, value is an abstraction of many things inside of a commodity.

    or Classes are an abstraction of individuals relationship to certain modes of production.

    and historical epochs are abstracted into societies being ruled by one class or another.

    What im trying to say is, for marxism, abstraction seems to be really really important.

    Is, however abstraction scientific and is it the best method of thinking out important ideas?

    Can anyone explain to me, or give me a link to a simple reader or book which explains why i should except abstraction, because i seem to say it alot these days, but cant even begin to actually argue WHY i should use this way of thinking.

    Thanks!
    Last edited by bloody_capitalist_sham; 2nd June 2008 at 22:16.

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    Philosophically, abstraction is the thought process wherein ideas are distanced from objects or processes. Generalizations are abstractions. Whenever you're thinking conceptually, you're usually abstracting.

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

    Induction and deduction are important different ways of abstracting.

    http://en.wikipedia.org/wiki/Inductive_reasoning
    Eppur si muove -- Galileo Galilei


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    Marx writes about this aspect of his method in the introduction to Grundrisse - in the section called The Method of Political Economy.

    You can locate it here: http://www.marxists.org/archive/marx...sse/ch01.htm#3
    "Events have their own logic, even when human beings do not." - Rosa Luxemburg

    "There are decades when nothing happens; and there are weeks when decades happen." - Lenin


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    Abstraction has yet to be explained philosophically or scientifically by anyone -- and the process remains a complete mystery to this day.

    And no wonder; it was invented by ancient Greek ruling-class theorists, who, unfortunately, did not notice that this process turned general words into the names of abstract particulars, thus destroying the capacity language has for expressing generality.

    Marx gestures at using this process, but he never showed how he could, or even how he actually did, use it. His remarks are thus no more substantive than are the hand movements of stage magicians.

    No wonder he chose not to publish Grundrisse. He did not need this mythical process, anyway; ordinary language already contains enough resources for expressing generality as it is.

    I have traced the source of this idea, and explained how and why this mythical process cannot work, here:

    http://homepage.ntlworld.com/rosa.l/page%2003_01.htm

    http://homepage.ntlworld.com/rosa.l/page%2003_02.htm
    Last edited by Rosa Lichtenstein; 3rd June 2008 at 20:15.

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    BCS, the things you tell us are abstractions are not. They are general words. No mystery there.

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    Incidentally, for those of you who like shorter essays, I have summarised my arguments here:

    http://homepage.ntlworld.com/rosa.l/...e_Part_One.htm

    http://homepage.ntlworld.com/rosa.l/...e_Part_Two.htm

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    Quote Originally Posted by bloody_capitalist_sham View Post
    What i understand of abstraction is very basic. It's like finding something about a thing, and then making the key idea of that thing independent of the original thing.

    like, hammering a fence together, in the abstract is labour power.

    Or for example, value is an abstraction of many things inside of a commodity.

    or Classes are an abstraction of individuals relationship to certain modes of production.

    and historical epochs are abstracted into societies being ruled by one class or another.

    What im trying to say is, for marxism, abstraction seems to be really really important.

    Is, however abstraction scientific and is it the best method of thinking out important ideas?
    Of course. Abstraction is part of a system of inquiry into nature and its laws and tendancies. Evolution is an abstraction of genetic perpetuation and comparison, but it is a very useful approach to understanding a vast array of processes.

    Is it the best method? I couldn't tell you. Class may be a great concept when it comes to deciding whether or not revolution ought to occur. But when we look specifically at a victim of the revolution, perhaps a capitalist who is being killed, it may not be very meaningful. It doesn't prove that he deserves to die, but in a general sense it indicates that he shouldn't have power over others.

    I think there are places and discussions where abstraction is necessary. And it could be argued that all of our linguistic and symbolic concepts are abstractions, since we could always break things down into smaller, more atomized and specific processes. So I guess the argument about abstraction is ultimately defeatist.

    Can anyone explain to me, or give me a link to a simple reader or book which explains why i should except abstraction, because i seem to say it alot these days, but cant even begin to actually argue WHY i should use this way of thinking.

    Thanks!
    Sorry, I don't have any links

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    Quote Originally Posted by Rosa Lichtenstein View Post
    BCS, the things you tell us are abstractions are not. They are general words. No mystery there.
    Okay, but i was under the impression "value" and "labour power" were abstractions of real material things.

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    Well, the ancient Greeks invented 'abstract ideas' because they thought that there was a world behind 'appearances' that was more real than the material world around us, one that was inaccessible to the senses, but was accessible to thought alone (i.e., their thought).

    They did this to provide 'philosophical' justification for the status quo, for these 'abstract ideas' represented either 'God's' thoughts, or the 'rational core' of the world (thus implying nature was the product of mind). This then allowed ruling-class thinkers in every subsequent mode of production to argue that the class structure of the day was 'god'-ordained, 'rational' or 'natural' (using different arguments as each mode of production came and went).

    Now, to answer Dean; scientists do not use 'abstractions', they use general terms, which they introduce by stipulation, or by extending the meaning of terms already in use (by metaphor, or analogy, etc.).

    Moreover, they could not use abstractions.

    Admittedly, this way of putting things might differ from the way that scientists themselves theorise about what they do. But once more: their practical activity belies whatever post hoc rationalisations they might advance concerning the nature of their own work.

    In seeking to advance scientific knowledge scientists report neither on the results of their processing of mental entities, nor on the contents of their heads -- and they certainly do not require the same with respect to the heads of others in their field, nor anywhere else for that matter. On the contrary, as far as their work goes, researchers develop new theories at the very least by extending the use and application of publicly accessible scientific language, theory and technique. And they do the former by means of analogy, metaphor and the novel employment of familiar general terms already in the public domain -- allied to the construction of specific models and 'thought experiments', alongside various other rhetorical devices.

    [Naturally, this does not mean that these features are unrelated to advances in technique motivated by the development of the forces of production, etc.]

    Despite this, it could be objected that the above comments thoroughly misrepresent the way that knowledge advances. In fact (but edited down) the objection could run as follows: scientists attempt to discover the underlying nature of objects and processes in the world in order to reveal the laws and regularities (etc.) that govern objective reality. To take one example: an animal's essential nature -- arrived at by increased use of abstract terms -- turns out to be its DNA (or whatever). Another example could be the way that Physicists extend knowledge by developing more general and abstract theories expressed in increasingly complex mathematical formulae.

    But, this cannot be correct; scientists manifestly did not discover DNA by the use of greater or more refined abstractions. They used the theoretical and practical advances of others (which themselves were not arrived at by abstraction), and augmented them with their own ideas (often they were those of a team, or research tradition) and the results of other innovative experiments -- all of which were based on cooperative work and observation -- assisted by the use of models and yet more 'thought experiments', all expressed in a public language in this material world.

    None of these (save the penultimate one) remotely looks like a mental process, still less an abstractive one. And as far as 'thought experiments' are concerned, these are typically carried out in the public domain, too, and in an open fashion, in a common language. Any alleged mental processes that accompany them are likewise connected with the innovative use of language -- but with the volume turned down.

    Of course, it could be argued that no one supposes that abstraction is "done in the head", just as it could be acknowledged that scientists do indeed employ a theoretical/public language in their work. It might therefore be maintained that scientists still endeavour to form abstract ideas based on their use of resources such as these, and in this way.

    Again, this is not what scientists actually do. The above is a myth put about by professional Philosophers and amateur metaphysicians.

    And this brings us to the heart of the problem, for this approach to language in fact fragments knowledge. This is because it is surely impossible for Abstractor A to decide whether or not he or she possesses the same general idea (of anything) as Abstractor B. This is not just because no one has access to the thoughts of another, but because it has yet to be established that one and all share the same understanding of the word "same". And how might that be determined, for goodness sake?

    The problem, of course, began much earlier. Traditional theorists saw language as fundamentally representational (that is, its primary role was to re-present the thoughts of the 'gods', or the 'rational order', to humanity), which helped create a series of 'problems' that could not be solved (and have remained unsolved to this day). In ancient and feudal society, only the elite could abstract the 'correct' divine representations, and commonality was imposed by divine fiat, or state/church authority.

    Later, in nominally 'equal', bourgeois society, theorists could not rely on such crudities, hence it was impossible for theorists to guarantee that the thoughts represented in each bourgeois skull would agree with those contained in any other. This abstract Humpty Dumpty, fragmented by representationalism, could not, it seems, be put back together again. Not even the 'objective' or 'inter-subjective' concepts of Kant and Hegel could repair the damage, since it is plainly impossible to tell if one Kantian/Hegelian means the same by the words they use to depict the contents of their privatised skulls as any another Hegelian/Kantian. Just calling such fragmented concepts "objective" would have no more effect on the problem than a "keep off" sign would have on a swarm of locusts.

    Abstractionism thus could provide knowledge with no objective foundation. But worse, it threatened subjectivity too, for Abstractor A would not now be able to tell if the fresh deliverances of today's abstractions were the same as, or were different from, the increasingly stale ones arrived at only yesterday, in his/her 'consciousness'. Memory would be little help here, for it too is subject to the same constraints.

    Naturally, the adoption of traditional thought-forms like these (representationalism and abstractionism) has had a disastrous effect on dialecticians, too, for it is now impossible to decide if dialectician A means the same as dialectician B about anything whatsoever, let alone with regard to their respective 'abstractions'.

    On the other hand, dialecticians at least say they accept Marx's emphasis on the social nature of language, but in fact one and all have adopted a bourgeois-individualist theory of the origin of meaning. According to this approach, we all represent the world to ourselves first (by means of "images" and/or abstractions), and then try to share our ideas with others second. Unfortunately, this would destroy communication; except by sheer coincidence, no two dialecticians would share the same ideas about anything, making communication impossible.

    Of course, had dialecticians not bought into traditional thought, and had they adopted instead the communicational model of language proposed by Marx and Engels (wherein each of is socialised into the use of language and we are all taught what our words mean, so that when we try to represent the world to ourselves, we have something common to share with others), none of this would have happened.

    Naturally, if this mysterious abstractive skill had ever been important in the history of science then we would find evidence of it in the work of great scientists. Alas there is none.

    However, even the attempt to investigate the truth of that particular assertion would automatically bring into question the role of abstraction in science. This is because such an inquiry would have to examine the documents and writings (etc.) of scientists -- not their brains. Indeed, any recognition of the relevance of the linguistic production of such scientists, their equipment and techniques (etc.), their social surroundings -- as opposed to the contents of their heads -- would show that in their practical activity no historian (whatever theoretical and/or philosophical views he or she might otherwise protest) actually believes that abstract ideas underpin scientific knowledge.

    Here, as elsewhere, actions speak louder than abstractions.

    Now, if we base an account of science on language employed in the public domain, on the general terms actually used (and ignore the philosophical hype built around what is done), a materialist understanding of science becomes possible, for now we would have an investigation carried out in a public arena, not one obsessed with an uncheckable and mysterious process that supposedly goes on in the head (which still defies description to this day).

    So, for example, the theory of evolution was built on evidence and on language already in the public domain -- when writing his book, Darwin did not think once to report on the secret activity of his brain. And, those who either agreed with him, or who took exception to his theory, did not think once to criticise the contents of his head.

    Same with Marx; he used general terms already in the public domain, extended their meaning in the way that scientists have always done, in order to develop his theory.

    To understand his work, not one of us needs to try to access his alleged mental 'abstractions'. And even if we tried, none of us would be able to say that we had arrived at the same 'abstractions' as he had, or even as one another. How could we? None of us has access to his brain, or to that of anyone else!

    So, in Marx there are abstractions anywhere in sight (despite the tradition built up around him, and despite some of the things he says) -- so this whole way of viewing reality needs to be ditched, and we need to stop looking at science and at Marx through the eyes of ruling-class hacks.

    To be sure, this is a controversial view, but only because this ancient mode-of-thought has dominated 'western' philosophy, and has similarly dominated the thought of the majority of Marxists, even those who post here. And, we now know why:

    The ruling ideas are always those of the ruling-class...
    Last edited by Rosa Lichtenstein; 3rd June 2008 at 20:31.

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    Okay rosa, thank you. What about when Marxist's use the terms "abstract" and "concrete" to talk about things. again like, discussing concepts of "value contained in a commodity" and a the "concrete substance the commodity is made of".

    Within other scientific fields, like the process of evolution, is that the same of the process of commodity production (material, concrete stuff) and the creation of new values into the society (abstract?).

    What i am very confused on, is when we say a term like "value", is that materialist to do so, or is it idealist.

    I know it must be painfully obvious to some of you, but im really struggling to understand why there is a difference between "abstract and concrete" and how we differentiate them given that we are materialists.

    I find because i know nothing of philosophy, even though i try to think about complex issues, i am at a disadvantage because of terms which Marx used came from an education in a time where philosophy was key.

    Can we say things like "value" in concrete terms, or is it okay and scientific to talk in abstract terms?

    is Evolution an abstraction too?

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    BCS:

    What about when Marxist's use the terms "abstract" and "concrete" to talk about things. again like, discussing concepts of "value contained in a commodity" and a the "concrete substance the commodity is made of".
    Well, Marx was trained in traditional ruling-class thought, and never fully shook it off.

    His use of terms like 'abstract' and 'concrete' need to be viewed in that light -- we need to translate the terms you mention into less prejudicial forms. Hence, to help you out, I would need to see the entire passage from which you have quoted these phrases.

    What I am very confused on, is when we say a term like "value", is that materialist to do so, or is it idealist.
    Well, no, because Marx expalined these notions in materialist terms; so just as scientists today talk about, say 'forces', when pressed to explain what they mean, they have to resort to materialist language -- to the interaction between bodies in nature, or 'particles' in fields.

    I know it must be painfully obvious to some of you, but im really struggling to understand why there is a difference between "abstract and concrete" and how we differentiate them given that we are materialists.
    You are not alone; I have yet to meet anyone who understands these terms (or who can explain them without the use of even more impenetrable jargon).

    I suggest you interpet 'concrete' to mean 'real and material', and 'abstract' to mean 'general term we use to make sense of capitalism'.

    Can we say things like "value" in concrete terms, or is it okay and scientific to talk in abstract terms?
    We can say what we like, but if we want to be clear we have to be careful of what we say. I personally do not like to use the word 'concrete'. If I speak of 'value' I just leave it at that, and explain it in theoretical terms, without the use of 'concrete'.

    Is Evolution an abstraction too?
    It's the name of a process in nature; why do you even need to so much as consider the use of the word 'abstraction' in reference to it?
    Last edited by Rosa Lichtenstein; 3rd June 2008 at 20:48.

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    Quote Originally Posted by Rosa Lichtenstein View Post
    Well, the ancient Greeks invented 'abstract ideas' because they thought that there was a world behind 'appearances' that was more real than the material world around us, one that was inaccessible to the senses, but was accessible to thought alone (i.e., their thought).
    There is a world behind appearances. It's exposition and explication is the object of science. Appearances don't explain themselves.
    Last edited by trivas7; 3rd June 2008 at 23:31.
    Eppur si muove -- Galileo Galilei


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    Trivas, as if to prove me right, that the ruling ideas are always those of the ruling class, says this:

    There is a world behind appearances. It's exposition and explication is the object of science. Appearances don't explain themselves.
    Appearances are indeed explained by yet more appearances. What do you think scientists see down their microscopes, telescopes, or in their bubble-chambers, except more appearances?

    'What about theory?', I hear you say.

    Well, every single theory has to be written down somewhere, and as such it becomes an appearance. This is true even of mathematics.

    So, not even theory can get 'behind' the material world -- despite what you might have read in the works of ruling-class hacks.

    And, since you are such a smarty-pants, you might like to tell us where this 'hidden' world is, and how you know?

    In your sock drawer? Out past Alpha Centauri?

    Sounds a bit too much like 'heaven' to me.

    [No wonder I call dialectics the opiate of petty-bourgeois elements in Marxism.]

    Anyway, it's nice to know you too have surrendered your thought to those nasty ruling ideas Marx warned us about.

    In your case, that warning was clearly a waste of time.
    Last edited by Rosa Lichtenstein; 4th June 2008 at 00:25.

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    Quote Originally Posted by Rosa Lichtenstein View Post
    Well, every single theory has to be written down somewhere, and as such it becomes an appearance. This is true even of mathematics.
    You seem to have a limited knowledge of physics if you insist on using the word "appearances" and scientists "seeing" things... This is but one of our senses. Further, I would not call mathematics a theory, as from your post you seem to do. Additionally, mathematics can not just be "seen", it is also heard in rhythm and the frequencies of the tones, for example. One of the interesting things about mathematics is that it does indeed transcend any one sensory information source. In this context I'd think of mathematics as the language we use to talk about the organization of the universe.

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    Quote Originally Posted by Rosa Lichtenstein View Post
    Well, every single theory has to be written down somewhere, and as such it becomes an appearance.
    Now that's a positively dialectical move!
    Last edited by trivas7; 4th June 2008 at 01:29.
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    from Alan Woods's "Reason in Revolt":

    Abstraction is absolutely necessary. Without it, thought in general would be impossible. The question is: what sort of abstraction? When I abstract from reality, I concentrate on some aspects of a given phenomenon, and leave the others out of account. A good mapmaker, for instance, is not someone who reproduces every detail of every house and paving-stone, and every parked car. Such an amount of detail would destroy the very purpose of the map, which is to make available a convenient scheme of a town or other geographical area. Similarly, the brain early on learns to ignore certain sounds and concentrate on others. If we were not able to do this, the amount of information reaching our ears from all sides would overwhelm the mind completely. Language itself presupposes a high level of abstraction.

    The ability to make correct abstractions, which adequately reflect the reality we wish to understand and describe, is the essential prerequisite for scientific thought. The abstractions of formal logic are adequate to express the real world only within quite narrow limits. But they are one-sided and static, and are hopelessly inadequate to deal with complex processes, particularly movement, change and contradictions. The concreteness of an object consists of the sum-total of its aspects and interrelationships, determined by its underlying laws. It is the task of science to uncover these laws, and to get as close as possible to this concrete reality. The whole purpose of cognition is to reflect the objective world and its underlying lawfulness and necessary relationships as faithfully as possible. As Hegel point out, "the truth is always concrete."

    But here we have a contradiction. It is not possible to arrive at an understanding of the concrete world of nature without first resorting to abstraction. The word abstract comes from the Latin "to take from." By a process of abstraction, we take from the object under consideration certain aspects which we consider important, leaving others to one side. Abstract knowledge is necessarily one-sided because it expresses only one particular side of the phenomenon under consideration, isolated from that which determines the specific nature of the whole. Thus, mathematics deals exclusively with quantitative relations. Since quantity is an extremely important aspect of nature, the abstractions of mathematics have provided us with a powerful instrument for probing her secrets. For this reason, it is tempting to forget their real nature and limitations. Yet they remain one-sided, like all abstractions. We forget this at our peril.
    Eppur si muove -- Galileo Galilei


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    Trivas, getting desperate, quoting Woods (another comrade who has bought into ruling class ideas):

    from Alan Wood's "Reason in Revolt":
    An appalling book, taken apart at my site:

    http://homepage.ntlworld.com/rosa.l/page%2004.htm

    http://homepage.ntlworld.com/rosa.l/page%2007.htm

    But, even so, Woods gestures at answering the serious difficulties I raised above, and neither has you, my desperate friend.

    Here are several more for you to just ignore (taken from Essay Three Part One, at my site):

    (1) How is it possible, in the privacy of the mind, for each lone abstractor to know if he or she has arrived at the correct abstract notion of anything at all (by whatever method they claim to have used)? With what, or with whom, can any of their results be checked? No one has access to a single 'abstraction' that anyone else has produced, nor has anyone ever been trained to perform this feat correctly. Does a single human being posses so much as a diploma in this mythical skill?

    An appeal to the existence of a public language would be to no avail, for on this basis no one would be able to tell whether Abstractor A meant the same as Abstractor B by his or her use of words or concepts like "Substance", "Being", or "Nothing".

    And it is even less use appealing to the 'logic of concepts', that drive 'thought' along, as, say, Hegel might have done. Not only is it unclear what his jargon actually means, even if all he said were crystal clear, since he was the first to dream much of it up, 'thought' cannot inevitably be driven along these lines (otherwise we would not now have to read Hegel to help it along). Finally, of course, 'thought' can only take this route if it too accepts without question the logical classical/Hegelian blunders outlined in this Essay, in which case 'thought' deserves all the confusion it receives as a result.

    Moreover, if abstractions are arrived at in a more law-like way, as the 'mind' tries to grapple with scientific knowledge, a là Hegel, how would it still be possible for one mind to check the results of any other to see if either or both had arrived at the same ideal result?

    (2) If abstractions are produced by a 'subtractive' process (as more and more particular features are disregarded) to produce increasingly general terms, who decides which parts should be subtracted first, second or third? For example, do we abstract a cat's whiskers first, its curiosity or its purr? Do we ignore its position or its number? And if this is all done 'in the mind', who is to say that everyone does exactly the same things to exactly the same subtracted parts in the same order and in the same manner?

    Naturally, if 'abstractions' are cobbled-together by a process of generalisation, or law-like development, then the same questions would still apply.

    (3) The actual process of mental subtraction is somewhat difficult to conceive too. When we ignore the various parts of the objects we are supposedly performing this trick upon, is it like a sort of mental striptease? But, if we take away too much, how might we know whether the rest of this ceremony is being performed on the same object with which we began? We might all start with a chaffinch, say, but after the feathers, beak, claws, colour, song, wings, size and number have been stripped away, how might we distinguish the amorphous mass left behind from an similarly processed Axolotl? Or indeed, from the Crab Nebula?

    Of course, abstractionists are never this crude (at least, not in public); they restrict themselves to rather more well-behaved "concepts", "categories" and refined "ideas", ones they trust to reason, or better still, to 'dialectical/speculative' thought. But these shadowy beings are even more obscure. Does, therefore, the concept of Robin Redbreast have wings, a head and a stomach full of worms? If not, then we might wonder if this concept genuinely applies to him. If it does, we might wonder (even more) what the difference between him and his concept is.

    Worse still, any conclusions drawn about the 'concept' of Robin Redbreast, or indeed birds in general, would apply to that concept, and not to its supposed feathered external correlate. That is, unless we are to suppose that, just like a Black Magic doll, whatever we do to the concept, we do to the real object(s) it is said to mirror. Now, Idealists might not be able to distinguish reality from illusion in this regard, but materialists would be unwise to follow them into the same dense fog -- or, indeed, adopt a philosophical technique that cannot tell fact from fancy, or a frog from fog.

    And how exactly does one dissect a concept? Do they each have an 'objective' anatomy, ones that any rank amateur can poke or prod?

    Nevertheless, this traditional tale is deeply engrained in our culture -- you will even find psychologists who will say that all of us can form "abstractions", even if they go rather quiet when asked to fill in the details -- so much so that experience has taught me, in polite company, not try to deny that such 'phantoms' exist, or risk being treated as one who has just confessed to murder.

    Truth be told, this Emperor has no clothes, abstract or concrete; indeed there isn't even so much as a single drop of blue blood in 'his' veins -- as both halves of this Essay seek to demonstrate. Worse, there isn't even an Emperor, clothed or otherwise.

    This ruling idea has been on the epistemological throne long enough; it is time to wheel out a very material guillotine.

    --------------------------

    Now, care to deal with my objections, or are you going to withdraw into your dogmatic sulk once more?

    Now that's a positively dialectical move!
    Exactly why, and how?

    Do tell...
    Last edited by Rosa Lichtenstein; 4th June 2008 at 02:00.

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    Dystisis:

    You seem to have a limited knowledge of physics if you insist on using the word "appearances" and scientists "seeing" things... This is but one of our senses. Further, I would not call mathematics a theory, as from your post you seem to do. Additionally, mathematics can not just be "seen", it is also heard in rhythm and the frequencies of the tones, for example. One of the interesting things about mathematics is that it does indeed transcend any one sensory information source. In this context I'd think of mathematics as the language we use to talk about the organization of the universe.
    Look, I not only have degrees in Philosophy, I have one in mathematics, so I am not ignorant of Physics.

    Of course, scientists use other senses: they listen, smell, taste and feel things -- but, what they record with their senses is how things appear to them.

    And, where did I say mathematics is a theory? I did say it had to be written down like a theory, but that does not mean it is a theory, any more than your signature is a theory.

    But, the way you talk, you seem to think mathematics is a theory of the universe.

    I deny that. It's a method we use to help us understand nature.

    To be sure it is a language, as you say, but, since it has to be put into physical form for us to be able to read it and to follow it, it is part of the world of appearances.

    That is the only point I wished to make in this context.

    But, you surely do not think that there are mathematical objects out there in the universe -- perfect lines, planes, and manifolds; actual scalar or vector fields (with real or complex numbers floating about in Banach space) --, partial differential equations drifting past the Crab Nebula, perhaps?

    And, these mathematical objects cannot be abstracted into existence, since they share nothing with anything in the material world. Real circles are not at all like mathematical cycles; mathematical lines are not made of anything, unlike real lines.

    And how on earth would you 'abstract' into existence a Hermite Polynomial, or an Abelian Group, for goodness sake?
    Last edited by Rosa Lichtenstein; 4th June 2008 at 02:28.

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    Keep it up comrades; the more you try to argue in favour of abstract ideas, the more you confirm Marx's claim that ruling-class ideas always rule.

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    my take is that abstraction is important because the universe is not just the sum of its parts, little enlightened self-interested cogs working away rationally, which can be understood by simply looking at them in themselves. fromw hat I've read this approach si pretty discredited even in the natural sciences. and this approach is very much the approach of the bourgeoisie, this Newtonian rationalism was at the heart of emancipation from feudalism and the triumph of the reduction of human interaction to one of exchange value.

    instead, things have meaning due to the relationships between them, and these relationships which give something its qualities do not physically exist, so therefore you can't understand something by simply observing it empirically. for example, a planetary system oeprates through a set of relationships between planets and stars, which give a meaning to those things which surpasses anything you can extrapolate by just taking them all as individual building blocks and coming up with a "sum of the parts".

    For example a proletarian is a proletarian, and granted his historical role, due to his relationship with other people and with the means of production - an abstract concept when we think of it as a whole. When a proletarian fights against a capitalist, it's the relationship between them which causes this and which gives this fight its meaning and historical significance, and which causes the two camps to behave in a way which can't be explained by looking at both of them individually and then analysing them together as the result of a simple interaction ebtween those two building blocks.

    The relationship between them in itself has meaning, this is an abstraction, but it's the key to understanding what's really going on.
    Lenin’s internationalism is by no means a form of reconciliation of Nationalism and Internationalism in words but a form of international revolutionary action. The territory of the earth inhabited by so-called civilized man is looked upon as a coherent field of combat on which the separate peoples and classes wage gigantic warfare against each other. No single question of importance can be forced into a national frame.

    Leon Trotsky

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