[Inquiry] Kaina Stoicheia -- Discussion

[Jon Awbrey]

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KS.  Discussion Note 1

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SL = Søren Lund

Re: KS-COM 11.  http://stderr.org/pipermail/inquiry/2005-November/003269.html
In: KS-COM.     http://stderr.org/pipermail/inquiry/2005-November/thread.html#3263

Soren, Peirce List,

Recall that we are working in the context of Peirce's theory of sign relations,
where a proposition is a type of symbol, a symbol is a type of sign, a sign is
defined by its participation in a specified role of a particular sign relation,
and a sign relation in general is defined as a 3-adic relation that satisfies
a particular definition, for instance, this one:

| A sign is something, A, which brings something, B,
| its interpretant sign determined or created by it,
| into the same sort of correspondence with something,
| C, its object, as that in which itself stands to C.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54 (1902).
|
| C.S. Peirce, [Application to the Carnegie Institution], L 75, pp. 13-73 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by Charles S. Peirce,
| Volume 4, Mathematical Philosophy', Mouton, The Hague, 1976.  Available here:
| Arisbe Website, http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm

You give us an able summary of a host of classical and modern aporias
that affect various attempts to say what a proposition is, but all of
those stagmas, so far as I can tell, appear to arise from the attempt
to form a particular order of "wholly useless abstractions" (WUA'a).
Given the obvious utility of many abstractions, that leaves us the
task of saying what exactly pushes an abstraction over the edge
of use.  This can be difficult to diagnose, but it's easier to
diagnose than it is to identify the underlying causes thereof.

One factor that strikes me at present is the fact that some
abstractions are "absolutized" or "decontextualized" past
the point of usefulness, and the inclination to do that
appears to arise from a habit of "essentializing" that
may indeed be innate to our evolutionary inheritance,
or at least built into our most familiar languages.

Essentialism is the tendency of thought that tends to seek the explanation
of everything in "categories of unstructured things" (COUT's).  In effect,
it tends to think that the end of explanation has been reached once we've
named the monadic predicate that classifies the thing to be explained.

This is such a persistent tendency of the human mind that it can be observed
to influence the thinking even of those who more reflectively might know better --
who might know better from reading Peirce, who might know better from being Peirce --
but it is not overall the thrust of Peirce's efforts in logic and semiotics, which
are indeed partly intended as a remedy for this condition of overweening essentialism.

Jon Awbrey
 
SL: Speaking of the proposition and Peirce's conception of it.
    I think there is good reasons for attacking this curious
    logical unit and even better to abandon it.
 
SL: If "proposition" is not a fancy term for "sentence", what is it?  One suggestion
    is that the proposition is the meaning of the sentence, or at least of the type
    of sentence that grammarians call "declarative".  But this will hardly do, for
    the reasons already pointed out by the author of the 'Dissoi Logoi'.  (The
    author of the ancient text known as the 'Dissoi Logoi' points out that the
    words "I am an initiate" may be uttered both by an initiate and by one who
    is not (W. Kneale and M. Kneale, 'The Development of Logic', rev. ed.,
    Oxford Clarendon, 1984, p. 16).  If this is accepted, it seems that
    we have to conclude either that one and the same form of words may
    be both true and false, or else that what is true or false is not
    the form of words itself.  If the former is the case, it frustrates
    any enterprise of formulating the principles of valid inference on
    the basis of relations between sentences.  If the latter is the case,
    then the metalinguistic terms "true" and "false" cannot properly apply
    to sentences at all, but must be deemed to apply to something else.
    Western logic chose the latter option, and thereby conjured into
    existence what was later called the "proposition".)  That is to say,
    if the grounds for rejecting the sentence are valid (i.e. that the
    same sentence can be uttered on one occasion to express a truth, but
    on another occasion to express a falsehood), then the objection must
    carry over to the meaning of the sentence, unless we are prepared to
    divorce the meaning from the sentence.  But if we do that, we have in
    effect ushered in two even more mysterious metalinguistic entities, i.e.
    sentences without (permanent) meanings, and sentence-meaning that float
    free of their sentences.  It is difficult to see where the explanatory
    gain lies, let alone how the two cohere.
 
SL: Another suggestion is that the proposition is the use
    made of the (declarative) sentence.  Thus if A and B both
    utter the sentence I am an initiate, they may be said to be
    putting it to different uses; viz in one case to claim that A
    is an initiate, and in the other to claim that B is an initiate.
    But this does not get us much further either.  For all that has
    been achieved here is the proposal of an arbitrarily restricted
    employment of the term use.  When we investigate the nature of
    the restriction, the "use" of the sentence turns out to be
    whatever it is that results in something true or false --
    e.g. A's claim or B's claim.  Here one metalinguistic
    term (use) simply hides behind another (claim).
 
SL: Is the "proposition", then, more plausibly regarded as what it is
    that is claimed when a claim is made, asserted when an assertion is
    made, stated when a statement is made, etc.?  But here we start another
    metalinguistic wild goose chase.  For claim, assertion and statement are
    all metalinguistic terms with no better credentials than proposition itself.
    To define the proposition as the "object" or "content" of claims, assertions,
    statements, etc. is simply to substitute one obscurity for another.
 
SL: Why do these and similar attempts to rescue the proposition all come to grief
    in this way?  Because what is being attempted is a metalinguistic impossibility.
    The source of the trouble can be traced back to the original culprit, i.e. the
    sentence, deemed to be unsuitable as the basis for logic.  The trouble is that
    the sentences belong to particular languages (English, Greek, Latin, etc.).
    What the logician seeks to substitute for the sentence is an entity which will
    afford the same scope for identification, reidentification, generalization and
    classification, but independently of the particular languages or words used.
    The trouble is that this cannot be done -- or at least, not within the
    Western metalinguistic framework.  For that framework only allows us
    to identify propositions, statements, assertions, etc. by citing
    some sentence or part of a sentence.  
 
SL: The moment this strategy fails, any formalization of logic collapses.
    In other words, the logician cannot, under pain of undermining the
    whole professional enterprise, claim that there are propositions
    that cannot be unambiguously expressed in words.
 
SL: Herculean efforts to move this obstacle merely show how immovable it is.
    For instance, some theorists have conjured up an entity which is supposed
    to be what there is in common between an English declarative sentence and
    its correct translation into any (or all) other language(s).  This proposal
    is either vacuous or circular.  For then either there are no propositions at
    all or else we are off after another metalinguistic will-o'-the wisp, namely
    the criteria for "correct translation".

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