[Wittrs] [quickphilosophy] Re: 1.21 Continued

  • From: wittrsl@xxxxxxxxxxxxx
  • To: quickphilosophy@xxxxxxxxxxxxxxx
  • Date: Wed, 21 Jul 2010 15:17:28 -0000

I was a little reluctant to shoot ahead to these issues, but what the
hell.  There's a very good discussion of what W had in mind with respect
to the limits of what can be said and what his reasons were in James
Griffin's excellent book "Wittgenstein's Logical Atomism."  Here are
some excerpts:

The Theory of types...seemed to lead to two incompatible states of
affairs.  First, it required that the hierarchical order of types be
strictly observed; a type of order n, according to the theory, should
have as arguments only types of order n-1 and should be an argument for
only types of order n+1.  Now several functions are, on this standard
ambiguous as to type: functions, namely, which can take arguments of
several or all different orders.  Such functions, because they do not
hehave as the Theory of Types requires, are improper; they can lead to
contradiction and paradox; and what one tries to say with them, if there
is any sense to it at all, must be expressed in a different way....Then,
secondly, the Theory of Types made words like 'thing', 'property',
'relation', 'fact', 'type'', &c., important in logical vocabulary.  So
the incompatibility is between on the one hand, the theory's restriction
on the behaviour of functions and, on the other, the vocabulary which
the theory itself makes important.  The items in the vocabulary do not
themselves meet the requirement.  'Type', for example, can take an
argumt of any order; 'function' can take an argument of any order except
the first; &c.  Each is typically ambiguous.  However, W did not think
that this incompatibility called for revision in the Theory of Types. 
He thought, as we see in the Notes Dictated to Moore, that, much to the
contrary, it shows a theory of types to be altogether impossible.  To
SAY something like 'M is a thing' uses the typically ambiguous word
'thing'.  To SAY that there are types or that a function can have as an
argument only a type of an immediately lower order makes use of the
typically ambiguous words 'type', 'function', and 'argument'.  And these
statements are what would make up a theory of types.  But this does not
leave logic in a difficult position, W says, because even were a theory
of types possible, it is unnecessary:

"Even if there WERE propositions of the form 'M is is a thing', they
would be superfluous (tautologous) because what this tries to say is
something which is already SEEN when you see 'M'." [Notes Dictated to
Moore, 108.29-31]

So, a theory of types is both impossible and superfluous.  First, what
it tries to say cannot be said; second, what it tries to say is already
SHOWN by the symbolism.  In order to say about a certain sysmbol what
the Theory of Types wants to say, one would first have to know what the
symbol is, and in knowing this one would SEE the type....

"That M is a THING can't be SAID; it is nonsense: but SOMETHING is SHOWN
by the symbol 'M'."

"...that a proposition is a subject-predicate proposition can't be said:
but it is SHOWN by the symbol."

"Every REAL proposition SHOWS something, besides what it says, about the
Universe: or, if it has no sense, it can't be used; and if it has a
sense, it mirrors some logical property of the Universe." [NM  107-109]

...Just as only certain types of elements in the world can fit together
to make a fact, so only certain types of symbols can combine to make
propositions.  In this sense, propositions SHOW (mirror) the logical
properties of the world....W says that a language which did not mirror
these properties, i.e an illogical language, would be one in which "you
could put an EVENT into a hole."

[All from Griffin, at 18-20]

One other related point made nicely by Griffin brings us back to the
point we discussed earlier about whether, according to W in TLP
propositions are themselves facts:

A substantive's role in a sentence is to represent; a substantive is, as
it were, the deputy in a proposition for an object in the world.  A
function is quite different.  For example, the 'R' in 'aRb' differs from
'a' and 'b' in that it is not what symbolizes; what symbolizes is that
it comes between the 'a' and the 'b'.  That is, what symbolizes in 'aRb'
are (i) the sign 'a', (ii) the sign 'b', and (iii) the FACT that 'R'
comes between 'a and 'b'.  Propositions must themselves be facts, the
facts that their constituents have a particular arrangement.  Thus, the
function-part of a prop is a fact, while a name is not.  Also it is by
makign a certain thing the case in a proposition sign that I say that a
certain thing is the case in the world.  Thus while names stand for
objects, arrangements of names say something about them; names
represent, functions assert.  [Griffin, at 16]

Some time prior to TLP, W put this as follows:

"Propositions, which are symbols having reference to facts, are
themselves facts (that the inkpis on this table may express tha I sit in
this chair)."  [Notes on Logic II, 11-13]

Anyhow, W's take on the realism-idealism controversy will turn out to
be, I think, that general statements about EVERYTHING simply can't make
sense.  One can show maybe, but not say.


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