November 4, 2010


ME + me: More comments on Wittgenstein + site news

I continue being not well, and otherwise also as before, so I cannot do much.
However, now and then I can do a little more.

1. More comments on Wittgenstein
2. Some site news

1. More comments on Wittgenstein

Being a philosopher, I felt inspired to take up my edition and notes on Wittgenstein's Tractatus (Logico-Philosophicus). '

The links just given are to the Wikipedia; and this is The beginning of my translation and comments, with here the complete text of the Tractatus, and here my Wittgenstein-index.

Today there is more of the same - and I should start by remarking as of today it is all done in a new directory for the Tractatus, which means that all the links to the Tractatus with my comments differ from what they were until today.

I have now uploaded the beginning of the new version for the theses starting with 3 and also some more summaries to the theses starting with 2. For those who are interested, here is my summary for 2.1.., as it happens on a subject that

In 2.1.. W. presents his picture theory of meaning, as it became known.

It is based on a sound intuition, namely that human beings try to understand how things are by trying to imagine what they, their causes or antecedents, and their effects or consequences really are.

W.'s presentation of it is unclear, and also mistaken: He seems to confuse, at least for the most part, language and ideas (images, fantasies), and also true ideas (images, fantasies) and the real situations these represent, while his picture theory of meaning, rather oddly, seems to presuppose that language is hieroglyphic or ideographic rather than alphabetic and symbolic.

In a hieroglyphic or ideographic language, the written form does not represent sounds of speech by arbitrary letters and words composed of these, which in turn, to be understood, must evoke an idea of what is meant, but instead consists of stylized pictures of things and situations that represent.

A hieroglyphic or ideographic language thus is closer to how the human mind represents, in the sense that (some, not al) ideas are in some ways rather like hieroglyphs or ideograms for whatever they stand for, than is an alphabetic language, but an alphabetic language, with letters and words representing sounds of speech rather than things meant by speech, is much easier to learn, to write and to use.

The picture theory of meaning is one of the main ideas of the Tractatus, and it is clearly mistaken - and incidentally also shows how confused e.g. Russell and Wittgenstein must have been about the relations of language and symbolism to reality, having both believed at least for some years this fundamentally confused and hieroglyphic theory of symbolic representation makes sense, and is an adequate foundation on the basis of which one can explain language, logic, and mathematics.

Here are some points from my notes, with the sources linked in.

A. (2.1) On the term "picture":

The German term I have translated as "image" is "Bild". Other translators of the Tractatus have translated "Bild" as "picture" (which gave rise to phrases like "Wittgenstein's picture theory of meaning").

I prefer "image" for three reasons over "picture".

First, there is a close parallel between "image" in the sense of "picture" and "image" in the sense of "set associated by a function" in mathematics. This is also the case in German, where one speaks of "das Bild einer Funktion" where in English one speaks of "the image of a function", and W. certainly knew this.

Second, it seems closer to W.'s intended epistemological use of the term "Bild". W.'s basic leading idea here comes, directly or indirectly, from Hertz, and it is that we know the world by making a mental model of it, rather like we know the lay of the land if we have a mental or paper map of it, and like we may know what to expect about the behaviour of a real airplane in turbulence if we have investigated model airplanes in wind tunnels.

Thus, we know the world by imagining a model for it, which is correct to the extent that the model is an image (in the mathematical sense) of the world, and, at least in part, conversely.

And the reader should note that Hertz's theory of representation, first stated in 1899 in Heinrich Hertz's posthumous "Principles of Mechanics" in fact both inspired Wittgenstein's theory and is much clearer and more sensible, for Hertz clearly stated that we know the world by making a mental model of it, rather like we know the lay of the land if we have a mental or paper map of it, which seems quite correct, but not in a pictorial or hieroglyphic way, except in some simple cases.

B. (2.1) On representing and maps

It is important to realize that being an image tends to be a matter of degree just as maps are more or less detailed and have more or less accuracy, but that on the other hand to be able to be an image, model or map of something at all there must be some correspondence between the elements, properties and relations of the things making up the image, model or map, and the things, properties and relations it stands for.

Here are some useful points about maps:

Map: Representation of some features and relations in some territory; in mathematics: function with specified domain and range. A.k.a. mapping.

The ideas of a map and the closely related mapping are very fundamental, and are somehow involved in much or all of human cognition and understanding - which after all is based on the making of mental maps or models of things.

The first definition that is given is from the use of "map" in cartography and the second from mathematics, but both are related, and mappings can be seen as mathematical abstractions from maps.

1. maps: It is important to understand that one of the important points of maps (that also applies to mappings) is that they leave out - abstract from, do not depict - many things that are in the territory (or set) it represents. More generally, the following points about maps are important:

  • the map is usually not the territory (even if it is part of it) \
  • the map does usually not represent all of the territory but only certain kinds of things occurring in the territory, in certain kinds of relations
  • the map usually contains legenda and other instructions to interpret it
  • the map usually contains a lot of what is effectively interpunction

  • maps are on carriers (paper, screen, rock, sand)
  • the map embodies one of several different possible ways of representing the things it does
  • the map usually is partial, incomplete and dated - and
  • having a map is usually better than having no map at all to understand the territory the map is about (supposing the map represents some truth)
  • maps may represent non-existing territories and include guesses and declarations to the effect "this is uncharted territory"

It may be well to add some brief comments and explanations to these points

Maps and territories: In the case of paper maps, the general point of having a map is that it charts aspects of some territory (which can be seen as a set of things with properties in relations, but that is not relevant in the present context).

Thus, generally a map only represents certain aspects of the territory it charts, and usually contains helpful material on the map to assist a user to relate it properly to what it charts.

And maps may be partially mistaken or may be outdated and still be helpful to find one's way around the territory it charts, while it also is often helpful if the map explicitly shows what is guessed or unknown in it.

2. mappings: In mathematics, the usage of the terms "map" and "function" is not precisely regulated, but one useful way to relate them and keep them apart is to stipulate that a function is a set of pairs of which each first member is paired to just one second member, and a map is a function of which also the sets from which the first and second members are selected are specified. (These sets are known respectively as domain and range, or source and target. See: Function.)

Note that for both functions and maps the rule or rules by which the first members in the pairs in the functions and maps need not be known or, if it is known, need not be explicitly given. Of course, if such a rule is known it may be very useful and all that may need to be listed to describe the function or map.

Here are some useful notations and definitions, that presume to some extent standard set theory. It is assumed that the relations, functions and maps spoken of are binary or two-termed (which is no principal restriction, since a relation involving n terms can be seen as pair of n-1 terms and the n-term). In what follows "e" = "is a member of":

A relation R is a set of pairs.
A function f is a relation such that
   (x)(y)(z)((x,y) e f & (x,z) e f --> y=z).
A map m is a function f such that
   (EA)(EB)(x)(y)((x,y) e f --> xeA & yeB).
That m is a map from A to B is also written as:
   "m : A |-> B" which is in words: "m maps A to B".

There are several ways in which such mappings can hold, and I state some with the usual wordings:

m is a partial map of A to B:
   m : A |-> B and not all xeA are mapped to some yeB.
m is a full map of A to B:
    m is a map of A to B and not partial.
m is a map of A into B:
   m : A |-> B and not all yeB are mapped to some xeA.
m is a map of A onto B:
   m : A |-> B and not into. 

One reason to have partial maps (and functions: the same terminology given for maps holds for functions) is that there may well be exceptional cases for some items in A. Thus, if m maps numbers to numbers using 1/n the case n=0 must be excluded.

C. (2.1) On human experience

In a sound and intuitive sense our experience falls apart into the three fields of perception, memory and imagination: We sense our environments and our bodies; we remember what happened to us and in the world we sensed; and we imagine what has happened, happens or might happen, essentially by altering some of our memories in certain ways and for certain reasons, and proposing the altered memories as possible models for certain facts and events.

In each of these cases we design a mental model of something real or unreal; in each of these case we assume again a correspondence between the model and whatever it is a model of; and in each of these cases the correspondence is plausibly explained as a homomorphism between model and modeled. (This means that the two things have a similar structure in mathematical terms.)

The best exemplification of this are a map and its territory (i.e. whatever the map is a map of) and important things to keep in mind are that the territory may be far more complicated than its map (in practice it is, for else there is little point to having a map), and that maps are adequate by reference both to purposes and to territory: A map is adequate for a given purpose if it corresponds sufficiently well to its territory to enable its users to realize their purpose when in the territory.

Incidentally, it should be noted that by far the greatest part of what human beings think of is imaginary, and not known to be true by them, basically because it consists of guesses and generalizations rather than precisely remembered experiences.

D. (2.11) Logical space and domains

It seems that by "logical space" W. meant something like domain or universe of discourse, but he is not very clear, and what he does say seems to be generalized from truth tables, as in "the logical space involved in "it rains (T) or it is cold (C)" consists of [(R&C) V (R&~C) V (~R&C) V (~R&~C)], that is, a tautology involving all mentioned possibilities in all possible combinations.

What is true apart from what W. meant is that the use of language generally does involve some universe of discourse, that is some supposed reality in which the terms of the language represent or do not represent some thing(s) and the statements of the language represent or do not represent some fact (or event or structure or process) in that supposed reality.

Part of what is involved for logic and mathematics, and to some extent natural language, was later articulated in terms of model theory, which I merely mention but do not treat here, and it should also be mentioned that the same text, statements or terms may be taken to different universes of discourse, that also need not be the real world, but may be an imagined reality known to be not really so (as in "Sherlock Holmes lives in Baker Street, London") or an imagined reality that is, at least as far as one's knowledge goes, hypothetical.

E. (2.12) Images, models and ideas

It is true - in a very Pickwickian sense also - that images often represent or are taken to represent some reality, that may be imaginary or hypothetical, but most human ideas do not represent like images do, which one may take to happen in a pictorial way, but in a more complicated way.

Also, even restricting oneself to images, it should be noted that images may depict impossible situations: Something possible may be an image of something impossible, apparently because to be an image requires being a physical object together with certain principles of representation that jointly produce the image, and impossible images seem to depend on a confusion or identification of some of the properties of the physical object and some of the properties of the thing imagined using the physical objects and the principles of representation.

Thus a number of impossible 3-dimensional objects, like Escher's "Waterfall", have been drawn on basically 2- dimensional paper, using the properties of planes and the rules of perspective.

F. (2.131) Representation, interpretation and reality

An alternative phrase for "principles of representation" is "principles of interpretation", and one important consequence of this is that, whereas it often seems to us that such-and-such "obviously", "evidently" or "naturally" means, represents or stands for so-and-so, in any case of representation the things that do the representing do NOT represent whatever they represent "obviously", "evidently" or "naturally", but by some set of assumptions and conventions that need to be known and cannot be inferred from the representing things. If this is "evident" etc. this is so only because this kind of image is habitually interpreted in this "evident" way.

That is: Nothing represents by itself; whatever represents represents because of certain assumptions and conventions that connect it to whatever it is taken to represent.

This is also the case for perception: Each young animal has to learn to make sense of its sensations and, for example, learn to read, so to speak, distances and speeds from seen sizes and movements of shapes, and to relate the information from one sense, e.g. one's body image, to another, such as sight.

G. (2.41) Representing involves principles of representation

Iin (2.131) I remarked that nothing represents by itself; whatever represents represents because of certain assumptions and conventions that connect it to whatever it is taken to represent. Accordingly, [2.141] at least makes a mistaken suggestion: That one can know that a certain fact X is an image of another fact Y simply by being acquainted with the fact X. This is not so in general, for one normally also at least needs to know the principles of representation that are used to understand what X represents.

It may be so in a handful of particular cases, like mirror-images, realistic pictures, good imitations and so on, and it may be that historically these where the first symbols, but even there assumptions are required, if only to the effect that when two things appear similar in some respect one of these may be used voluntarily and purposively to evoke an idea of the other.

H. (2.141) Signs and symbols

A sign is something that is naturally associated with a thing, like smoke is a sign of fire, and clouds a sign of rain. Accordingly, if one experiences the sign one expects what it is often associated with.

A symbol is something that is conventionally associated with a thing, such that the symbol becomes the sign for the idea of the thing. This seems to require a step beyond signs that no animal except man has made: To understand that one can agree to use any (easily reproducible) act or fact as a conventional sign for anything one wishes to make someone think of.

I. (2.15) Representing is more than a simple morphism

There is nothing like an isomorphism or homomorphism of a picture (usually 2-dimensional) or text and what it represents, and the manner of representation depends always on some human assumptions and usually on many, while these assumptions are rarely adequately summarized. This is also the reason W. missed them.

"The structure of the picture", whatever it may be - a diagram, a picture by Escher, a stylized map of the London Underground, a 2-dimensional photograph of a 3-dimensional object, a trick "photograph" of an impossible object, or whatever - is generally NOT "the structure of what is pictured", but at best a structure that, together with assumptions that are not given with that structure, a key to whatever structure the depicted thing(s) may really have.

(2.151) Even a realist picture, even a tromp d'oeil, are 2 dimensional things representing 3-dimensional things, generally (if not necessarily) embodying some unarticulated rules of perspective.

J. (2.1512) Representing is often of uncertain or unexisting possibilities

One of the things W. mostly misses is that representing is often of uncertain or unexisting or merely fantastic, imaginary or hypothetical possibilities, at least as far the person representing knows.

K. (2. 1514) Representing conventions, legenda etcetera

Rarely the pictorial or representing relationship(s) - whatever W. precisely means (and I fear he didn't mean anything precisely, for then he would have seen it is not so) - is given with the picture, diagram, map, statement or formula. Usually it is unstated and tacit, and in the few cases something like it is given with the picture, as with legenda on a map in cartography, it is quite incomplete.

L. (2.16) Even pictures often represent in a very distorted way

Pictures - look at children's drawings - often are partial and distorted, whether by inability or on purpose, as in a charicature of a politician's face, or as with a picture of an arrow and a pointing finger. Besides, it would seem some pictures, indeed including charicatures, but not limited to these, may be ironical, and depict by distortion or irony - as did Hogarth, for example.

(2.161) What is at best true, and that mostly of "typical" pictures, as e.g. occur in children's books, is that there is a similarity between some aspects of what is depicted and some aspects of what depicts it.

M. (2.17) W.'s "pictorial form" is mostly word magic

W.'s phrase "pictorial form" is a manner of verbal suggestion of what is not so or at least not sufficiently clarified to be presented with rational conviction.

N. (2.171) Even pictures do generally not represent photographically

In almost all ordinary pictures - children's drawings again come to mind - there is no simple isomorphism between picture and depicted, and the relation between picture and things pictured is far more complicated than a simple likeness of the form "circle here so circle there".

O. (2.172) Wittgenstein on pictures and pictorial form is rather contradictory

W. on pictorial form is contradictory and misleading: First, he insists pictures and pictured must be alike, and then he insists in 2.172 that this presumed likeness of pictures and pictured, which exists in simple prototypical cases, as pictures of triangles tend to be triangular and pictures of circles circular "cannot, however, depict its pictorial form".

In fact, this is related to W.'s later doctrine of what cannot be said but only be shown, and this first occurence of it is just inconsistent with what he claimed before about picturorial representation.

P. (2.18) "Logical form" as word magic

W. 's suggestion that a picture represents becausse it has something like "logical form", which it also - in some deeply mysterious sense - is "the form of reality", is cant : At best, it amounts to the far from deep theses that pictures and things depicted tend to look alike, especially in prototypical cases. That this is anything like "logical form" as in the Principia Mathematica is pretensious word magic.

(2.181) is a gross form of this: "A picture whose pictorial form is logical form is called a logical picture" and the same goes for (2.182)

Q. (2.19) That "Logical pictures can depict the world" is mostly cant

For why would the same not be true of illogical or non-logical or any kind of pictures whatsoever?! What is "logical" about a picture that does depict some aspect of the world truly, according to its viewers? Why does it need to be "logical" indeed in any sense, and more specifically in W.' sense of "logical", which is "tautologous" as a rule?

Sofar for that summary of my comments on Wittgenstein's theses starting with "2.1..".

As before, if you can't make much of it, I'm sorry - I can only make it clearer by making it longer, and it may be that you need some knowledge of analytic philosophy and of mathematical logic to follow all or be interested at all.

Have fun with it, or do something else that you like better!                              

2. Some site news

Meanwhile I have corrected some typos in the last Nederlog, and should also add that for the moment my edition of and comments on the Tractatus is in a state of flux - which may explain why some links may not work or some backgrounds may be absent. Also, as I remarked before, the Tractatus + comments are now in a new set of directors called Tractatus.

And, at VERY looooong last - namely after 14 years - I have updated the 5 main indexes  of my site to the effect that it's meta name="Maartensz" and it's content="philosophy, logic, computing, ME, ME/CFS, CVS, Nederlog, Nedernieuws, ME in Amsterdam, Lao Tzu, Aristotle, Machiavelli, Boétie, Rochefoucauld, Descartes, Leibniz, Mandeville, Swift, Hume, Chamfort, Hazlitt, Burckhardt, Mill, Multatuli, Clifford, James, Russell, Wittgenstein, Maarten Maartensz".

This is supposed to spread my renown far and wide over the internet, since searchbots and searchmachines thrive on this.

Well... I have added links to the subjects in the list. Have fun!

P.S. The P.S. of november 2, also on the subject of my edition of and comments on the Tractatus should be clear enough for the moment. Note the Tractatus + comments are now in a new set of directors called Tractatus. It's this that I hope to continue, and eventually to delete the old one.

P.P.S. It may be I have to stop Nederlog for a while. The reason is that I am physically not well at all. I don't know yet, but if there is no Nederlog, now you know the reason.

As to ME/CFS (that I prefer to call ME):

1. Anthony Komaroff

Ten discoveries about the biology of CFS (pdf)

3. Hillary Johnson

The Why

4. Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf)
5. Eleanor Stein

Clinical Guidelines for Psychiatrists (pdf)

6. William Clifford The Ethics of Belief
7. Paul Lutus

Is Psychology a Science?

8. Malcolm Hooper Magical Medicine (pdf)

Short descriptions:

1. Ten reasons why ME/CFS is a real disease by a professor of medicine of Harvard.
2. Long essay by a professor emeritus of medical chemistry about maltreatment of ME.
3. Explanation of what's happening around ME by an investigative journalist.
4. Report to Canadian Government on ME, by many medical experts.
5. Advice to psychiatrist by a psychiatrist who understands ME is an organic disease
6. English mathematical genius on one's responsibilities in the matter of one's beliefs:
   "it is wrong always, everywhere, and for anyone, to believe anything upon
     insufficient evidence
7. A space- and computer-scientist takes a look at psychology.
8. Malcolm Hooper puts things together status 2010.

    "Ah me! alas, pain, pain ever, forever!

No change, no pause, no hope! Yet I endure.
I ask the Earth, have not the mountains felt?
I ask yon Heaven, the all-beholding Sun,
Has it not seen? The Sea, in storm or calm,
Heaven's ever-changing Shadow, spread below,
Have its deaf waves not heard my agony?
Ah me! alas, pain, pain ever, forever!
     - (Shelley, "Prometheus Unbound") 

    "It was from this time that I developed my way of judging the Chinese by dividing them into two kinds: one humane and one not. "
     - (Jung Chang)


See also: ME -Documentation and ME - Resources

Maarten Maartensz

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