Tag: proposition

‘Language as representational’ on my mind

Is language representational?  The question might be more carefully phrased as, need all languages be representational languages?

That question has been on my mind a lot.  Wittgenstein’s theories (if you can call them that) regarding language are close to my own, in some important ways.  Having said that, it’s hard to really say what Wittgenstein thought regarding just how, or when, language ought to be considered as a representational system.  I’ll leave that issue aside since my primary concern in this post is only to introduce what I take to be a very insightful presentation on the matters as I see them.

The author of the Nedcricology blog introduces the problems of representationalism in a very simple but intriguing way.

I. The representational interpretation of language:

In his Tractatus Logico-Philosophicus, Wittgenstein claims that all expressions susceptible to the ascription of truth or falsity are propositions. Propositions share the same structure and logic as states of affairs, hence their suitability for one another. Wittgenstein encourages thinking of a proposition as a picture, that we can just as easily communicate in pictoral form – and, of course, events lend themselves to being captured in picutres. Propositions represent various possible states of affairs, and true propositions represent actual states of affairs. We can accurately represent in propositional form whatever actually occurs. And added to that is Wittgenstein’s famous dictum: Whatever can be said, can be said clearly.

A few problems pop up:
a) We don’t always need “clear” pictures; not all pictures are representational or portraits – what about abstract expressionism?

b) Thinking of propositions as pictures does not entail that all meaningful sentences are pictures – what about flipping someone the bird?

c) Besides, how do propositions “match up” with states of affairs anyway?

These three problems suggest that the representational interpretation of language is either somewhat narrow or just downright incorrect. First of all, to capture someone, we (well at least I) don’t merely take portraits of them. I take a variety of pictures, and in fact sometimes even encourage them to take a few of their own pictures with my camera so I can see things from their point of view. Second, many of the ways in which we communicate involve little to no “representation,” such as when I say, “I gotta go!” and run towards the toilet. And finally, whatever connections there are between our more “representational” propositions and the world, they are not metaphysically necessary but are conventionally (and humanely, I might add!) important.

I take the third problem as the most pressing for theorists who support the idea, or rather can’t help but to presume it, that meaningful expressions necessary represent the thing(s) or states of affairs, or objects, they are ‘about’.  On the one hand, it is said that any p is true if it accurately represents the R which it is about; on the other hand, if p represents R, in virtue of what does the ‘representing’ obtain? Is it the relation of p and R, or is it it some property of one or the other only, such that it might be said that p inherently is able to represent R or R-type things?

How about propositions about mathematical entities.  ‘I think it’s a number.’ In what sense does my thought make ‘it’–the thing I am thinking of–a number or in what sense does my thought represent it as a number?  Doesn’t a number represent itself as itself without my thinking about it?  Or is its identity as a number contingent on a thought to express it as such?

Do we learn to use language representationally such that its function as a representional system is somehow more basic to its other possible functions–for instance, as ‘capable of emotive expression’ or ‘as a metaphoric system’ ?  To see how how misplaced this idea is, consider the following exchange:

Billy pointed his finger at the apple and said it look rotten.

OR

Billy: <points finger at the apple> It’s rotten!

OR

Billy says, as he points his finger at the apple, “That’s rotten”

Do all three expressions refer equally to the same state of affairs and if so, just what is that state?  On some level, it might appear that yes, the three expression do equally refer to the same state of affairs–namely, the state of affairs containing the individual Billy, who points to a particular apple and exclaims that it is rotten.

Then again it isn’t clear, is it, that in each case, the order of events is always the same.  For instance, in the third expression, the simultaneity of Billy’s act of saying and his act of pointing is emphasized whereas the matter isn’t completely settled in the first instance.  Does that mean that the first expression is comparatively lacking in descriptive value?

Perhaps the first expression is uttered in a different circumstance than the second.  The second looks as it if it belongs in a play, or in some sort of written dialogue.  The third looks more appropriate to a novel.  The first looks hard to place.  But then maybe they each represent different states of affairs, but if that’s the case, then how could we justifiably say that they mean more or less the same thing?

In any event, please do check out the post on the nedricology blog since it presents the case against ‘language as representational’ in a simple but sophisticated way.

“The case of infinitely many propositions following from a single one”

The case of infinitely many propositions following from a single one

Is it impossible that infinitely many propositions should follow from a single one-in the sense, that is, that we might go on ad infinitum constructing new propositions from a single one according to a rule?[1]

Modal interpretation:

Is the following a valid argument, or rather, is it a possible argument:

◊ (p→q /\ (q→r) /\ (r →s)…n)))

Another interpretation:

◊ (p→(q /\ r /\ s…n))

 

 

In English: “it is possible that p implies q and q implies r and r implies s ad infinitum”

 

Now, the justification for the ‘ad infinitum’ is the idea that each the first proposition, p, is the first in a series of logical implications.

I think an example of this idea might be the following:

  1. In order to move to the door of this room I need to travel the distance between this chair and the exit for this room.
  1. The distance between this chair and the exit is roughly 6 feet.
  1. It is necessary that in order to travel from this chair to the room exit, I must also travel from this chair to half of the distance to the exit, which is roughly 3 feet.
  1. It is necessary that in order to travel from this chair to ‘half of the distance to the exit’, I must also travel to ‘half of the half of the distance to the exit’, which is roughly 1.5 feet.

You get the picture: a single proposition functions as a rule for the infinite regress that follows.

 

Wittgenstein’s response to this language game:

Suppose that we wrote the first thousand propositions of the series in conjunction.  Wouldn’t the sense of this product necessarily approximate more closely to the sense of our first proposition than the product of the first hundred propositions? Wouldn’t we obtain an ever closer approximation to the first proposition the further we extended the product? And wouldn’t that show that it can’t be the case that from one proposition infinitely many others follow, since I can’t understand even the product with 1010 terms?

We imagine, perhaps, that the general proposition is an abbreviated expression of the product.  But what is there in the product to abbreviate? It doesn’t contain anything superfluous?[2]

In a nutshell, Wittgenstein opposes the idea that any proposition p can serve as a rule for an infinite regress (or a series of infinitely many propositions following from p) from that proposition.

The assumption in the line of thought Wittgenstein opposes here is that any proposition p is inherently indeterminate; more carefully constructed, the idea is that it’s always possible to infer q or r or s, for instance, from any p.

For convenience I’ll call this view propositional indeterminism.

The logic of propositional indeterminism

Our idea that a proposition is indeterminate and thus may always be inferred from springs from our idea of language as a calculus.

Consider

P: (10+4)=Q: 14

And

P: (10+4)=Q: 14 or R: (7*2)

And

P: 10+4= Q: 14 or R(7*2) or S(5*2+4)

Let’s translate this into a logical argument.  To make it easier, I treated both addition and multiplication as logical conjunctions.  I also added inferences to make the argument valid.

  1. If p, then q
  2. If q, then (r and s)
  3. If q then (t and u)[3]
  4. If q then (r and s) or (t and u)

Wittgenstein, in effect, is saying that the expression ‘10+4′ is not coextensive with respect to the expression ‘14′.  It is in some circumstances, but not in the context of using their coextensionality as a foundation for an infinite regress. By itself, the proposition which says that ‘if 10+4′ then ‘14′ is a valid construction via the rules of arithmetic.  However, the expression doesn’t also say that “14 and 7 multiplied by 2 are identical”.  That they are identical can be expressed in another proposition, but it is not guaranteed or logically necessitated by the distinct expression that 10+4 also means 14.



[1] Wittgenstein, PG 250

[2] Wittgenstein, PG 250

[3] I realize that treating both multiplication and addition as a logical conjunction is problematic but that it is problematic is not relevant to this discussion