Friday 25 December 2009

Thought for the Christmas day



How do you love Jesus? Would your love survive if you realised that Jesus can do nothing for you? Would you still love him if you learned that Jesus was no God, but an ordinary man like you and me? Mine would. Because his life shows that you can never tell, if your life ultimately proves to be a success or a failure. Jesus was a failed prophet, died a terrible and shameful death, condemned by both the Romans and the Jews. His pupils fled and he had only criminals for company. He sighed: "God, why have you forsaken me?".

Yet he was a founder of a world religion (the spadework was done by his pupils, but he was the inspiration), though he never lived to know it. His example shows that, however successful or however unfortunate we are, we will never be able to know enough to judge our lives. So let's keep our heads up and never cease to smile. And let us be merry as in

Merry Christmas

Marco

Thursday 17 December 2009

Why Tarski cannot handle propositions? Because there are infinitely many primitive of them




Intensional sentences such as:

(1) Georgio believes that Rome is a beautiful city

are sentences whose truth or falsity (i.e. logical) value depends not only the denotation their constituent parts, but on something else, like in the example above: the content of the sentence “Rome is a beautiful city” and (probably) on how Georgio understands this sentence (or its translation or synonym).

From a certain angle there seems to be no intensionality paradox. Sentence (1) is true if Georgio believes that Rome is a beautiful city. Why should the truth of (1) depend on whether the sentence

(2) Rome is a beautiful city
true or false

[Here we can immediately see the relationship between the intensional sentences and intentional objects, the contents of thoughts. The inexistence of the unicorn does not make my thinking of it any less true. The existence of a turbojet does not make my thinking of it true, if I do not realise its existence]

But of course there is a problem. You simply cannot write a Tarski-style definition for each belief sentence like the one

(3) The sentence “Georgio believes that Rome is a beautiful city is true” if and only if Georgio believes that Rome is a beautiful city is true

The reason is that one would have to write infinitely many of such definitions. This is due to the fact that there are recursively infinitely many sentences like:

(1) „Rome is a beautiful city”
(2) „the city in which there lives his only uncle is a beautiful city”
(3) „the city in which there lives the only uncle of his uncle is a beautiful city”
(4) „the city in which there lives the only uncle of his uncle’s uncle is a beautiful city”
(5) „the city in which there lives the only uncle of his uncle’s uncle’s uncle is a beautiful city”


The subjects of these sentences are coreferential with Rome

And now comes the important part. These sentences may be generated recursively. We may even understand them recursively from bottom up. For instance:

(6) the city in which there lives his only uncle

can be understood in such a way

But as far as truth conditional semantics goes, phrases like (6) are absolutely non-compositional, vocabulary items. We must take them as whole. And you cannot formally write a grammar or truth conditional semantics which has an infinite vocabulary, an infinite number of building blocks.

That the vocabulary (in terms of referential semantics) is indeed can easily be seen if we replace the relevant descriptions with coreferential proper names

(7) Rome is a beautiful city”
(8) „the city in which there lives Silvio Berlusconi is a beautiful city”
(9) „the city in which there lives Luca Barbone is a beautiful city”
(10) „the city in which there lives Giordano Bruno is a beautiful city”
(11) „the city in which there lives Giorgio Pier Georgi is a beautiful city”, etc.

We could quickly run out of telephone directory names

These proper names are primitive (non-decomposable) both in syntactic and semantic terms. But from the point of view of intensional semantics the phrases:

(12) “that Rome is a beautiful city”
(13) „that the city in which there lives Silvio Berlusconi is a beautiful city”
(14) „that the city in which there lives Luca Barbone is a beautiful city”
(15) „that the city in which there lives Giordano Bruno is a beautiful city”
(16) „that the city in which there lives Giorgio Pier Georgi is a beautiful city”

are also primitive. Why? Because nothing inside them will help us establish the truth of sentences like:

(17) “Georgio thinks that Rome is a beautiful city”
(18) „Georgio thinks that the city in which there lives Silvio Berlusconi is a beautiful city”
(19) „Georgio thinks that the city in which there lives Luca Barbone is a beautiful city”
(20) „Georgio thinks that the city in which there lives Giordano Bruno is a beautiful city”
(21) „Georgio thinks that the city in which there lives Giorgio Pier Georgi is a beautiful city”, etc.


So this is the real problem of intensional sentences. The truth-conditional semantics of intensional sentences is not formalisable. Why? Because the formalisation would need to use an infinite number of definitions, an infinite list of them. This again is because what counts as a recursive phrase inside a complement sentence, would need be reanalised as primitive, non-analysable element in intensional semantics.

Wednesday 9 December 2009

Suicidal mission


However you solve the details of the intensionality problem, it is quite clear that you will not find a general substitution principle which would be truth preserving in the context of „I believe, etc. Whether the Morning Star and the Evening Star are substitutable depends on nothing else, but whether they are “the same thing” for the subject of the sentence. It does not depend on any “fact” facts, but on whether man-in-the-street, educated or not, treats them as the same thing. This is not a very comforting conclusion, if you want to build a general truth-conditional semantics.

A similar conclusion seems to stem from the discussion (which I am trying to study now) on the slingshot argument. In his review of Steven Neal’s Facing the Facts John McFarlane writes: “The slingshot is not a single argument, but a family of arguments designed to show that the intentional entities (facts, state of affairs, propositions) must be individuated either so finely or so crudely that they can do no useful work”. Hopefully, one day I will fully comprehend the slingshot argument and give it a clear presentation on this blog. Just give me some time. At the moment I can just say that parts of McFarlane’s sentence could be taken as part of my the conclusion of my own discussion in previous notes.

Given these difficulties, I wonder what people are even thinking of doing, when they try to build semantics upon the concept facts, situations, rather than things and relations. When are two situations identical? Are the two situations

“The astronomer sees the Morning Star”
“The astronomer sees the Evening Star”

identical?

There are so many problems with extensional phenomena that basing your philosophy of language on intensional entities seems a suicidal mission. But I know that some practitioners of situational semantics are not suicidal. I will need to talk to them.

Marco