Monday, February 20, 2012

Explaining 'the morning star'

Belete suggests here that the ‘Morning star’ example in the SEP article on intensional logic is not very well explained.
I’m not seeing that, but let me explain the it in my own terms, here. Assume you do not know much about astronomy, but you know how to identify the “morning star”, namely as the heavenly body that is visible in the East in the morning, and you also know how to identify the “evening star”, namely the heavenly body that is visible in West in the evening. Then you may assume these are different objects, and so, if I tell that the morning star is in fact the same object as the evening star, I have given you some useful information. I could go on to tell you that it is not a star at all, but a planet, in fact the planet Venus, which rises and sets with the sun because it is much closer to the sun than we are. But that is not relevant here. The point is that the sentence “the morning star is the evening star” is informative, it tells you something you could not have worked out from the meaning of the terms alone. By contrast “the morning star is the morning star” gives you no information at all. Given that you know what the morning star is, it is simply an expression of the principle of identity, A = A for all A, which presumably you knew, or would have assumed, already. Thus ‘the morning star’ and ‘the evening star’ have different informational content.

Summarising:
(1) The sentence “the morning star is the evening star” has informational content.
(2) The sentence “the morning star is the morning star” does not have informational content.
(3) Therefore, the term “the morning star” does not have the same informational content as “the evening star”.
What’s wrong with that? We might want to make a few extra assumptions to make it logically watertight. For example, to add the assumption that if all the component parts of two sentences have the same informational content, then the sentences themselves have the same informational content (the compositionality principle). But I don’t see what’s desperately wrong with it as it stands.

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9 Comments:

Blogger Belette said...

You're assuming that all objects have names that never change over time. If "the morning star" actually means "the planet Venus, when in portion X of its orbit wrt Earth"; and "the evening star" means "when in portion Y"; then MS = ES is wrong.

3:06 pm  
Blogger Edward Ockham said...

>>If "the morning star" actually means "the planet Venus, when in portion X of its orbit wrt Earth"; and "the evening star" means "when in portion Y"; then MS = ES is wrong.
<<

It doesn't mean that, of course. It means, the bright shiny thingy that you can see in the morning, or in the evening, respectively.

By 'names that never change over time' you mean 'whose meaning never change over time' yes?

9:03 pm  
Blogger Belette said...

> It means, the bright shiny thingy that you can see in the morning, or in the evening, respectively.

Of course. But what we know is that this is equivalent to "Venus, at certain positions in its orbit". So no, MS != ES. Unless you're inventing a new rule, that a nearly-given collection-of-atoms must have a time-invariant name.

> whose meaning never change over time

I might, but I'm not sure what you mean by meaning :-)

9:50 pm  
Blogger Edward Ockham said...

>>Of course. But what we know is that this is equivalent to "Venus, at certain positions in its orbit". So no, MS != ES. Unless you're inventing a new rule, that a nearly-given collection-of-atoms must have a time-invariant name.
<<

You fail to understand. It is not equivalent to 'Venus, at certain positions in its orbit'. For the sentence 'the morning star = Venus, at certain positions in its orbit' is informative. Ergo etc.

9:58 pm  
Blogger Anthony said...

>> The point is that the sentence "the morning star is the evening star" is informative

Shouldn't this say that it might be informative? If I already know that the morning star is the evening star, then there's nothing informative about it at all.

12:03 am  
Blogger Anthony said...

This comment has been removed by the author.

12:18 am  
Blogger Edward Ockham said...

>>If I already know that the morning star is the evening star, then there's nothing informative about it at all.
>>

So 'the earth is not flat' is not informative, contains no information, because everyone (or nearly everyone) knows this? Thus the informational content, the information contained in a discourse, is relative to whether a person already has the information?

In that case, all informational content is relative, and therefore it is meaningful to talk about the information "contained" in a discourse. Interesting idea.

8:36 am  
Blogger David Brightly said...

Ed, like the Maverick, I worry about your summary formulation. You seem perilously close to suggesting that information content is some additive function over sentence components. Using |x| to denote information_content(x), the argument seems to be that

|MS=ES| > |MS=MS|
=> |MS| + |=| + |ES| > |MS| + |=| + |MS|
=> |ES| > |MS|

But by symmetry this can't be right. Why do we need this theoretical concept 'information content'? Bill makes it worse by introducing a whole farrago of theoretical concepts. Why not simply say that MS=MS and MS=ES have distinct logical consequences. The former has none whereas the latter has many---one fewer space missions to nearby celestial bodies, say, or a reduced budget for temples if these objects are deemed worthy of worship. Isn't this what we are trying to get at with the 'information content' idea?

4:16 pm  
Blogger Anthony said...

>> In that case, all informational content is relative, and therefore it is meaningful to talk about the information "contained" in a discourse.

I assume you mean not meaningful?

I would define "informative" as "providing information". I didn't think of it as "containing information".

In any case, I think what is necessary before one can talk about information contained in and/or provided by a discourse, is context. This is a recurring theme, but I still do not accept what I see as an attempt to separate sentences or paragraphs or even entire texts, from context.

If my 5-year-old said to me tomorrow morning "the morning star is the evening star", that sentence would have provided quite a bit of information. Even more after the ensuing conversation we would have, which would include me saying something like "Wow, where did you learn that?"

Granted, this might be related to another recurring theme, which is what I see as the difference between propositions and sentences. If we're talking about the proposition that the morning star is the evening star, that's a whole different thing from the sentence "the morning star is the evening star".

12:27 am  

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