McGrath in sec 4.1 of the SEP article briefly mentions an argument for propositions, I'll give a formulation here.

1) 'yesh balagan b'mita sheli' means the same thing as 'there's chaos in my bed'.

2) There is something 'there's chaos in my bed' and 'yesh balagan b'mita sheli' have in common.

(2) takes the form of an existentially loaded statement. The thing quantified over is supposed to be a proposition-like entity. A common response, says McGrath, is to deny that the inference from (1) to (2) is valid.

Let e be 'there's chaos in my bed', h be 'yesh balagan b'mita sheli' and p be that there's chaos in my bed.

All parties would allow use of a -means the same as- relation R between the sentences such that eRh. The opponents of the argument claim that it's unwarranted to presume yet another relation R' -means- that both bear to another entity (eR'p and hR'p).

I don't think it's such a leap to take that step though. Helping ourselves to resources of second-order logic, let P be a relation such that for a particular a, aPb -> aRb and for all x, xRa -> xPa&aPx.

It's 4 AM so I hope I got the details right. I attempted to define a relation such that a is related to everything that has the same meaning as it, and everything a is related to is also related to each other (an equivalence class).

We can define a second order relation R' such that aR'B iff a is one of B's relata. All these taken together (I hope) imply that for any relation V, aVb -> aR'V&bR'V -> EX(aR'X&bR'X). This is the inference that was being denied in the first place. It was obtainable only by assuming second order quantification and the R' relation. Applied to our particular example, eR'P and hR'P. P is the third thing that both e and h bear a relation to.

So what can we take from this? Well, we can really stick it to the (I'm sure very few) philosophers who are happy with (serious) second order quantification and unhappy with propositions. We also have another candidate for what a proposition is, i.e. the relation that utterances with the same meaning bear to one another. It's shareable, and probably not hard to define a notion of truth and falsity for (maybe sellars could pull a trick or two here, this isn't unlike dot quotes).

It occurs to me that once you take higher order quantification seriously you get a lot of abstracta for free, so perhaps this argument will only convince the choir, so to speak.

## Wednesday, September 10, 2008

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## 1 comment:

I think that Sellars is sort of happy to have abstract entities in our metalanguage. He would go something like this:

1) 'yesh balagan b'mita sheli' means the same thing as 'there's chaos in my bed'.

The 'means' here is a disguised form of the copula. As a first step:

2) 'yesh balagan b'mita sheli' (in Hebrew(?)) means the same as 'there's chaos in my bed' (in English).

(2) can be reformulated as:

3) 'yesh balagan b'mita sheli' (in Hebrew(?)) is a •there's chaos in my bed•

And the same move with respect to English:

4) 'there's chaos in my bed' (in English) is a •there's chaos in my bed•

So of course the two sentences mean the same thing! They are distinct token-classes of the same type. And this type encodes the proposition that there is chaos in my bed, with 'yesh balagan b'mita sheli' doing this encoding in one language, just like 'there's chaos in my bed' does in another.

Is this ok with you Dan? Sellars is a nominalist of sorts, wanting a naturalized ontology, but he tries to keep between traditional nominalism and realism as much as possible.

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