[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 16

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JA = Jon Awbrey
JR = Joe Ransdell

Re: FOLG-DIS 9.  http://stderr.org/pipermail/inquiry/2005-October/003148.html
In: FOLG-DIS.    http://stderr.org/pipermail/inquiry/2005-October/thread.html#3135

Joe, Peirce List,

I will record your whole message below, so that I can find it
again later in the various archives, as it may take some time
to work through it all, and I still have many leaves to rake
in real life.

JA: The question is simply one of whether there exist symbols that do not
    involve icons and indices.  Here, we have Peirce's testimony in one place
    that he thinks there are such things, and what he thinks a likely sample of
    them are, and in other places we have him seeming to say something different.

JR: Yes, that is the question, Jon.  You are presumably referring
    to the same passage that initiated this dispute to start with
    several months and I have already pointed out (in our earlier
    discussion) that your interpretation of what he means by a
    "pure symbol" in that place is not supported by the context
    immediately following it, and this is, as far as I know, the
    only place in his writings where he even seems to be stating
    such a view as you suppose him to hold (namely, the view that
    there are pure symbols, meaning by that symbols which do not
    involve icons or indices in performing their function as
    symbols), whereas there are many, MANY places where he
    is clearly saying something to the contrary of that
    in explaining what symbols are.

Okay, so we have read the same passages, and even if a census of what
shows up in the CP is hardly definitive or final, it's clear that we
weight the various items of the present sample somewhat differently,
and also that we have different senses of what constitutes a proper
context for interpreting Peirce's statements.  You tried out several
different ways of explaining away what Peirce said about "and", "or",
"of", etc. being pure symbols, and I did not find your explanations
satisfactory, most importantly on the grounds that they conflict with
many explicit principles that we find throughout Peirce's approach to
logic, in particular, his treatment of logical symbols as denotative
symbols in their own right, definitely not "syncategorematic" signs,
and also with the specific ways that he makes use of second intentions
in his logic of relatives.

Looking back over the many discussions that we have had since last Spring,
there are a couple of issues that rise to more salient notice than they did
at first sight.  The tougher issue seems to be certain differences as to what
exactly constitutes a "theory", in particular, a theory of signs, in other words,
a "semiotics", that can step up to the challenge of becoming a bona fide science.
Although I did call attention to this issue right up front, I will put off further
discussion of it until another time.  What I hope will be an easier difficulty to
clear up, or at the very least to circumscribe, appears to turn on the vaguities
of the word "involve" that's involved in the bedeviled examples.  So I'll take
a moment to clear my head, and try to treat the trickiness of that, next time.

Jon Awbrey

JR wrote:

> Yes, that is the question, Jon. You are presumably referring to the same 
> passage that initiated this dispute to start with several months and I have 
> already pointed out (in our earlier discussion) that your interpretation of 
> what he means by a "pure symbol" in that place is not supported by the 
> context immediately following it, and this is, as far as I know, the only 
> place in his writings where he even seems to be stating such a view as you 
> suppose him to hold (namely, the view that there are pure symbols, meaning 
> by that symbols which do not involve icons or indices in performing their 
> function as symbols), whereas there are many, MANY places where he is 
> clearly saying something to the contrary of that in explaining what symbols 
> are.
>      We can return to that again later, but what I want to do immediately is 
> to point out that he is quite explicit about the essential involvement of 
> icons and indices in the functioning of symbols in the Kaina Stoicheia or 
> New Elements paper (MS 517) of 1904, which is a paper which you rely upon 
> heavily in the present discussion, particularly as regards the concept of 
> the _tabula rasa_ as an explicating conception of the functioning or working 
> of the symbol. But leaving aside this particular issue for the moment --  
> which has to do with the nature of the sheet of assertion construed as a 
> symbol -- let us turn first to the following passage from part 4 of the New 
> Elements, pp. 317f (in volume 2 of The Essential Peirce). Peirce is at this 
> point in this paper attempting to explain the sense in which it is only 
> "accidental" that a given symbol has the signification it has (i.e. 
> explaining that and why the symbol is "unmotivated" or "arbitrary", as the 
> point is sometimes put). It is a long quote which I will interrupt several 
> times with comments:
> 
> ===========QUOTE PEIRCE============
> It will be well here to interpose a remark as to the identity of a symbol. A 
> sign has its being in its adaptation to fulfill a function. A symbol is 
> adapted to fulfill the function of a sign simply by the fact that it does 
> fulfill it; that is, that it is so understood. It is, therefore, what it is 
> understood to be. Hence, if two symbols are used, without regard to any 
> differences between them, they are replicas of the same symbol. If the 
> difference is looked upon as merely grammatical (as with _he_ or _him_) or 
> as merely rhetorical (as with _money_ and _spondesime_), or as otherwise 
> insignificant, then logically they are replicas of one symbol.
> [INTERRUPT QUOTE]
> 
> COMMENT 1: Notice how Peirce himself uses the word "function", namely, to 
> refer to what the symbol is supposed to do AS a symbol. That is how I use 
> the word "function", too. Contrast this with the notion of "function" which 
> you are using, as you explain in a recent message: "For my part, the 
> "function" of a symbol means its "role" as a sign in an elementary sign 
> triple of the form <object, sign, interp> and the membership of this triple 
> in a bona fide sign relation, that is, a set of such triples." If I didn't 
> know better I would think you are joking! But if that is the formalist's 
> idea of what a function is, so be it.
> 
> COMMENT 2: Note also that the identity of symbol is constituted by its 
> interpretant, with what it is represented to be in its interpretant. He then 
> goes on to say, in effect, that two synonyms (e.g. "money" and "spondesime") 
> are the same symbol. Symbols thus are not linguistic entities and, indeed, 
> need not be linguistic in type in order to be symbols. Semiotic is not 
> philosophy of language. What gives any particular symbol its identity as a 
> symbol is what it is represented to be in its interpretant. (This assumes 
> that what is purportedly its interpretant really is such and is not the 
> content of a misinterpretation of the replica of the symbol.) The 
> interpretation of a symbol is not, therefore, a matter of mere translation 
> into a further symbol in the way that a word can be translated, using a 
> dictionary definition. What is the proper interpretant of a symbol like, 
> then? Peirce then goes on to explain this by explaining what a symbol as 
> such SIGNIFIES.
> 
> [CONTINUE PEIRCE QUOTE]================
> Hardly any symbol directly signifies the characters it signifies; for 
> whatever it signifies it signifies by its power of determining another sign 
> signifying the same character.
> [INTERRUPT QUOTE]
> 
> COMMENT 3: Note that in what follows he is distinguishing between what a 
> sign directly signifies and what it indirectly signifies. Icons are said to 
> directly signify, meaning that they present immediately, in themselves, what 
> they signify. To ascertain what an icon signifies -- which is a character --  
> one inspects the icon itself, which contains it, that is, IS it, at least in 
> part. A symbol does not, as such, do this. In order to ascertain what a 
> symbol signifies one must inspect something which is functioning as an icon 
> with which the symbol is arbitrarily associated. That is, the symbol 
> indirectly signifies a character and does this by determining (arbitrarily) 
> a sign which directly signifies that character, i.e. by determining an icon 
> to be directly representative of what the icon presents in itself.
>      A problem is apparently presented, though, by the case of the 
> onomatopoetic symbol, which is the case where the character-bearing icon is 
> present in the symbol replica, and this can be a matter of more or less. But 
> Peirce holds that even in the case of an onomatopoetic symbol the fact that 
> the character is iconized by the symbol REPLICA does not imply that the 
> symbol directly signifies that character. In what follows Peirce is -- in 
> part at least -- concerned to insist that although onomatopoesis must be 
> recognized it is not to be misunderstood as a case of direct signification: 
> the signification of the symbol is always logically indirect, via an 
> interpretant sign. Unlike the case with icons and indices, one must always 
> look to the interpretant for that which gives the particular symbol its 
> distinctive identity. But there appears to be a conflict of this with what 
> he is saying about the onomatopoetic symbol, where one finds the 
> signification in the symbol itself, and so Peirce is trying to explain why 
> that is not the contradiction in his theory which it at first appears to be, 
> which he does -- I will put it crudely -- by saying that one is still 
> looking to the interpretant as such rather than to the symbol as such when 
> one considers the onomatopoetic sign, but it just happens de facto that the 
> sign is in such cases functioning both as symbol replica and as an icon 
> signifying directly the character signified by the symbol being replicated. 
> In doing this, Peirce appears to be relying upon the idea of the limit case 
> and perhaps also the idea of asymptotic approximation, though if so the 
> latter is only implicit in what he is saying.
> 
> [CONTINUING PEIRCE QUOTE]============
> If I write of the "sound of sawing," the reader will probably do little more 
> than glance sufficiently at the words to assure himself that he could 
> imagine the sound referred to if he chose to do so. If, however, what I 
> proceed to say about that sound instigates him to do more, a sort of 
> auditory composite will arise in his imagination of different occasions when 
> he has been near a saw; and this will serve as an icon of the signification 
> of the phrase "sound of a saw". If I had used, instead of that phrase, the 
> word "buzz," although this would have been less precise, yet, owing to the 
> sound of the word being itself a sort of buzz, it would have more directly 
> called up an iconic interpretation. Thus some symbols are far superior to 
> others in point of directness of signification.
> [INTERRUPT QUOTE]
> 
> COMMENT 4: Thus the word "buzz" is sort of mildly onomatopoetic, which he 
> describes by saying that it is "more direct". Directness is thus a matter of 
> degrees, as is onomatopoesis.
> 
> [CONTINUE PEIRCE QUOTE]============
> This is true not only of outward symbols but also of general ideas.
> [INTERRUPT QUOTE]
> 
> COMMENT 5:
> Peirce now switches from discussion of the case of onomatopoetic public 
> symbols -- words publicly inscribed or publicly spoken -- to the case of 
> symbols which are "inward": symbols occurring in the "inner world", as he 
> sometimes expresses it. Thought occurs both in the "outer world" and the 
> "inner world", but he never, so far as I am aware, speaks of thought as it 
> occurs inwardly as being private. Thus in equating outward thought with 
> publicly available thought, as I am implicitly doing here, I may be mistaken 
> since he might want to say that even inward thought is public. But if so he 
> would have to admit that it is not "directly" public (in the sense of 
> "direct" he is using here) but only indirectly so, in that it is obtainable 
> for purposes of identification of it only by inference from behavior. It 
> seems best to me, then, just to say that although an inward (not publicly 
> expressed) thought is not public, it must be assumed that it is capable of 
> being made public. In any case, I will treat inward or inner thought as not 
> immediately available publicly and characterize it here as "unexpressed 
> thought", without intending to imply that it is not public, though with the 
> understanding that it is to be regarded as publicly available only on the 
> basis of an inference from public evidence.
>      Now I have myself, in the past, laid strong stress on the claim that 
> what Peirce initially and always primarily meant by "all thought is in 
> signs" is precisely that thought is publicly available, and that this was of 
> fundamental importance to him because he wanted to establish logic as a 
> science -- to bring that about was, from beginning to end, his abiding 
> aim -- and this required that thought be publicly available. What I had not 
> paid attention to, though -- and I am not aware that anyone else has either, 
> but if I am mistaken about this I hope someone will correct me -- is that he 
> was also much concerned, though perhaps less fundamentally, with 
> establishing that inner thought, thought not immediately available to 
> others, also be taken duly into account. I now understand this to mean that 
> he thought that inner thought is indeed publicly available in principle --  
> if only by inference, but publicly available nonetheless -- but that it 
> should be understood that inner thought is often seemingly very unlike 
> thought which is directly available publicly. I now believe that he not only 
> thought this but thought it to be of great importance to recognize that 
> there is usually -- not necessarily but usually -- a great difference 
> between externally expressed and internal thinking because his reflection 
> upon his own thinking convinced him that in order to think effectively about 
> difficult matters unexpressed thought has to be importantly different, 
> perhaps not always but at least usually so when it is truly effective, and 
> this should be recognized in order to encourage the development of truly 
> effective and powerful thinking.
>      That is, it is necessary for THIS purpose to minimize the word-like 
> character of the symbolic aspect of thinking and make use in practice 
> instead of what may well be idiosyncratic and highly personal symbols the 
> character of which may well be all but impossible for the individual to 
> identify in his or her own thinking. In fact, he attributes the 
> communicational difficulties he has in writing or speaking to others to the 
> enormous difficulty he has found in moving from his own most important 
> discoveries to the communication of his findings to others. Thus he says, in 
> the introductory segment of one of the drafts of MS L75 (the Carnegie 
> application of 1902), that by the time of his greatest discoveries he had 
> "reached a mode of thought so remote from that of the ordinary man, that I 
> was unable to communicate with him. Another great labor was required in 
> breaking a path by which to lead him from his position to my own. I had 
> become entirely unaccustomed to the use of ordinary language to express my 
> own logical ideas to myself. I was obliged to make a regular study of 
> ordinary ideas and language, in order to convey any hint of my real meaning. 
> I found that I had a difficult art to acquire. The clear expression of my 
> thoughts is still most difficult to me. How awkward I am at it, this very 
> statement will in some measure show."
>      Now, the point that is immediately relevant here is that he is 
> especially concerned in what follows in the interrupted quote -- as he is 
> elsewhere as well, I believe, though that concern has gone unnoticed by me 
> until recently -- he is much concerned, I say, to explain how it is that 
> inner or unexpressed thought and thought as it occurs in publicly available 
> form can be regarded as equivalent for logical purposes even though the 
> apparent character of such thought is very different in the two kinds of 
> manifestations. That this is what he is concerned about is indicated when he 
> says below that "It is clear that this feeling functions as a symbol. To 
> call it an _icon_ of the past idea would be preposterous." The feeling he is 
> referring to is a feeling of similarity which he is invoking as being a part 
> of the process of an inner thought. He is arguing that although it may seem 
> as if no symbol is involved in a certain thought process, a certain feeling 
> which we supposedly must recognize as being involved in such a process is 
> itself a symbol. In the experience of a certain kind of recognition it may 
> seem as if there is no difference at all, no distinction to be drawn, 
> between the character being recognized, the icon presenting that character 
> directly (which IS that character as felt). and the feeling that this 
> character is similar to the character of something not in the present 
> experience which one is trying to match. Yet all of these factors must be 
> understood to be involved if one is to understand what is happening when 
> that sort of character recognition occurs: there is a feeling which is at 
> once the icon AND the character iconized (perhaps to a limited extent), AND 
> there is the character of being similar, which is, in the experience, all 
> but indistinguishable from the character being iconized; AND that feeling is 
> ALSO functioning as an onomatopoetic symbol of what is being iconized.
>      In the passage from which the interrupted quotation is taken he 
> discusses this problem in much more length in connection with the indexical 
> value of the inner thought, too, but I have omitted that part of it from 
> quotation here.
> 
> [CONTINUE PEIRCE QUOTE]==========
> When a person remembers something, as for example in trying in a shop to 
> select a ribbon whose color shall match that of an article left at home, he 
> knows that his idea is a memory and not an imagination by a certain feeling 
> of having had the idea before, which he will not be very unlikely to find 
> has been somewhat deceptive. It is a sort of sense of similarity between the 
> present and the past. Even if he had the two colors before his eyes, he 
> could only know them to be similar by a peculiar feeling of similarity; 
> because as two sensations they are different. But in the case supposed, it 
> is not the mere general feeling of similarity which is required but that 
> peculiar variety of it which arises when a present idea is pronounced to be 
> similar to one not now in the mind at all, but formerly in the mind. It is 
> clear that this feeling functions as a symbol. To call it an _icon_ of the 
> past idea would be preposterous. For instead of the present idea being 
> serviceable as a substitute for the past idea by virtue of being similar to 
> it, it is on the contrary only known to be similar to it by means of this 
> feeling that it is so. Neither will it answer to call it an index. (pp. 
> 317f) [EDITORIAL NOTE: I omit at this point Peirce's further elaboration on 
> the feeling of similarity as a symboI, as well as the ensuing discussion of 
> the feeling as an index.] My principal object in drawing attention to this 
> symbol of similarity is to show that the significations of symbols have 
> various grades of directness up to the limit of being themselves their own 
> significations. An icon is significant with absolute directness of a 
> character which it embodies; and every symbol refers more or less indirectly 
> to an icon. (p. 320)
> ==========END PEIRCE QUOTE============
> 
> Note that last sentence, Jon. EVERY symbol refers more or less indirectly to 
> an icon. And there is more in that paper as well that makes it clear that 
> symbolism cannot do what it is its special job or function to do without 
> pressing into service, as it were, something functioning iconically and 
> something functioning indexically. Yet you take no account of this in your 
> interpretation of what he is talking about when he talks about the tabula 
> rasa in the later part of the New Elements paper, much less in your 
> continuing claim that some symbols have nothing to do with icons or
> indices.
> 
> Joe Ransdell

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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