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Predicates

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Predicates
Horace
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Posted 07/24/09 - 05:39 AM:
Subject: Predicates 		quote post
#1
Hello folks, err, hello "people"... I am supposed to look at these expressions and decide which of them are predicates. A. The police suspect that [1] is a murderer. B. It is necessary that [1] = 2. C. It is necessary that [1]= 1. D. She expects to find [1]. E. Prince Charles believes that [1] < 7. F. [1] believes that 4 < 7. G. If Prince Charles believes that [1] < 7, then 2+2=4. H. It is contingent that [1] is the murderer. I. Tom has never met [1]. J. The Pope gave his blessing to [1]. My first impressions were that A, C, D, I and J were predicates with B, E, F, G, H as not predicates, but I am not so sure about A and D anymore. Does anyone have any tips for helping me discern??? Thanks in advance.
Horace
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Posted 07/25/09 - 08:02 AM:
quote post
#2
Is there any more information I can provide, or should I just reformat these questions (not sure why they turned out this way):

A. The police suspect that [1] is a murderer.
B. It is necessary that [1] = 2.
C. It is necessary that [1]= 1.
D. She expects to find [1].
E. Prince Charles believes that [1] < 7.
F. [1] believes that 4 < 7.
G. If Prince Charles believes that [1] < 7, then 2+2=4.
H. It is contingent that [1] is the murderer.
I. Tom has never met [1].
J. The Pope gave his blessing to [1].

My first impressions were that A, C, D, I and J were predicates with B, E, F, G, H as not predicates, but I am not so sure about A and D anymore.
chadlee
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Posted 07/25/09 - 02:48 PM:
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#3
So, the object of the exercise is to indicate whether or not "[1]" is a predicate in each of the sentences?

It would be helpful to see the full chapter and context in which this exercise is presented. Do you have that information?
aufbau87
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Posted 07/25/09 - 03:25 PM:
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#4
Horace wrote:
Hello folks, err, hello "people"... I am supposed to look at these expressions and decide which of them are predicates. A. The police suspect that [1] is a murderer. B. It is necessary that [1] = 2. C. It is necessary that [1]= 1. D. She expects to find [1]. E. Prince Charles believes that [1] < 7. F. [1] believes that 4 < 7. G. If Prince Charles believes that [1] < 7, then 2+2=4. H. It is contingent that [1] is the murderer. I. Tom has never met [1]. J. The Pope gave his blessing to [1]. My first impressions were that A, C, D, I and J were predicates with B, E, F, G, H as not predicates, but I am not so sure about A and D anymore. Does anyone have any tips for helping me discern??? Thanks in advance.


The instructions you gave don't make sense. [1] in each one is an object. Are we supposed to find the predicates in each one? Moreover, does the resource that this exercise come from only admit as predicates EXTENSIONAL ones (i.e. ones not embedded in referentially opaque contexts, e.g. 'believes that')? Also, does it include what are called functors, e.g. '<' or 'is greater than'? All that info would be helpful!
Kamerynn
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Posted 07/25/09 - 04:49 PM:
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#5

A. The police suspect that [1] is a murderer.

M[1] = "1 is a murderer" In this case, M would be the predicate. We could define another predicate: Sxy = x suspects y. We could write A as: S(p(M[1])). P (police) suspects that [1] is a murderer. In this, the predicates would be "S" and "M."


Horace wrote:
My first impressions were that A, C, D, I and J were predicates with B, E, F, G, H as not predicates, but I am not so sure about A and D anymore.


None of A through J are, themselves, predicates. Either your professor has no idea what a predicate is, or you're completely misconstruing/misrepresenting his instructions.
When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong.
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Horace
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Posted 07/25/09 - 05:41 PM:
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#6
So my understanding is this: A predicate is a functiont hat when invoked, returns a truth table.

For #1 we have the expression: "The police suspect that [1] is a murderer."

We can put whatever designator we want in to stand as [1], and in my estimation gramatically the predicate would be something like "[1] is a murderer" but logically, I don't think we could get a truth table out of this, becuase the truth value of the "predicate" will have no bearing on whether the police suspect who or whatever "1" is...

As a result, though I first though 1 would be a predicate, I now lean towards it not being. In contrast 10 would be a predicate...

I might not be right, but in my mind its simplified for me...

But I could use some affirmation or correection...
chadlee
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Posted 07/26/09 - 02:32 PM:
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#7
Horace wrote:
So my understanding is this: A predicate is a functiont hat when invoked, returns a truth table.

Ah, so it seems that you're studying not merely the identification of predicates, but some sort of truth function of predicates. See, this is why many of us are puzzled when you just say "are these predicates", when what you really mean is "are these predicates truth functional". Again, it would really help to know which chapter this material comes from. Is it from a chapter about truth functors? Or just tell us exactly the source of the material.

Edit: After some web research, I've noticed that the terminology of sentence functors vs truth functors is largely attributable to Wilfrid Hodges. His approach is so unique that some refer to his language of logic as "Hodgise".

But I'm still not sure what Hodges is up to in this exercise. Normally, predicate logic dosen't involve truth tables but rather interpretations. So, to define a predicate as "a function that when invoked, returns a truth table" seems strange. Anyway, the OP needs to provide much more background information when posting questions like this.

Edited by chadlee on 07/26/09 - 03:25 PM
Horace
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Posted 07/26/09 - 07:31 PM:
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#8
Ok. Let's take the sentence "Brutus killed Ceasar."

"Brutus" is the subject, "killed Ceasar" is the predicate.

When Brutus is the subject, we might say that the predicate is "true" or Brutus, or that Brutus "satisfies" the predicate.

Let's make the predicate as that which is left over when we delete the proper name "Brutus" from our sentence.

We get "x killed Brutus."

Nothing in principle prevents us from delete Ceasar instead from our original "Brutus killed Ceasar" which would give us the predicate "Brutus killed" rendering our sentence "Brutus killed x."

We might even delete both Brutus and Ceasar leaving our remainder "killed" as the predicate and "x killed y" as our sentence. In this sort of two-placed predicate we will find certain ordered pairs satisfying the predicate (Brutus, Ceasar; Ruby, Oswald; Earl Jones, MLK...).

We might offer the following statement: Given any sentence containing one or more proper names and/or definite descriptions, the result of deleting one or more of these is a predicate.

Take emaple "I" in the questions I am working through:

Tom has never met [1].

Could not Tom be justifiably deleted rendering the sentence "x has never met y" leaving "has never met" as the predicate, or more simply as it is in the example could not "Tom has never met" be the predicate, or suppose the identity of [1] were known. Let's say it's Stephen Harper, and Tom's identity was not known. "has never met would then become the predicate...

With this in mind, "I" does render a predicate.
despinozist
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Posted 07/28/09 - 12:02 PM:
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#9
One major problem here is a lack of precision and clarity. A-J are each of them complex things. But one thing we cannot say of A-J as wholes is that they are predicates. A sentence contains one or more predicates, logical or grammatical, but it cannot itself be a predicate.

So initially, we have a very rocky start. The common trait of all these sentences is that the subject-variable is undisclosed (it's given the label "[1]"). Additionally, there is a predicate present, one- or two- place, within in every statement.

A. The police suspect that [1] is a murderer.

Sp(M[1]) (opaque)

B. It is necessary that [1] = 2.

⟡(=([1], 2)) (opaque)

C. It is necessary that [1]= 1.

⟡(=([1], 1)) (opaque)

D. She expects to find [1].

Es([1]) (non-opaque)

E. Prince Charles believes that [1] < 7.

Bc(<([1], 7)) (opaque)

F. [1] believes that 4 < 7.

B[1](<(4, 7)) (opaque)

G. If Prince Charles believes that [1] < 7, then 2+2=4.

Bc(<([1], 7)) > A (opaque)

H. It is contingent that [1] is the murderer.

C(M[1]) (opaque)

I. Tom has never met [1].

M(t, [1]) (non-opaque)

J. The Pope gave his blessing to [1].

B(p, [1]) (non-opaque)

1. Now, do you want us to identify the predicates in opaque contexts and the ones in non-opaque contexts? If so, I have done this above.

2. If you're asking which of the components of the statements are predicates I have done this above.

3. Capital letters and arithmetical symbols inside opaque contexts are predicates; the outermost capital letters of opaque contexts are intensional predicates.

4. Capital letters in non-opaque contexts are predicates.

Generally, again, they all have predicates, but are not themselves predicates. I don't see the point of the "[1]"s, if my interpretation of your homework is right. Some of these predicates pick out properties, others relations, and still more, generally, opaque contexts. Intensional predicates invoke opaque contexts which contain predicates (one- or two-place).

Edited by despinozist on 07/28/09 - 12:26 PM
I'll show you differences.
despinozist
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Posted 07/28/09 - 12:16 PM:
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#10
Let's be clear here: Sentences contain predicates. Sentences cannot themselves be predicates. You're essentially getting your language mixed up by saying:

"...the result of deleting one or more of these is a predicate."

and, in contradiction to this you say:

"...renders a predicate."

You cannot have both. A sentence cannot both be a predicate and render a predicate. And really, a sentence is neither a predicate nor does it render one. One renders a predicate in virtue of doing certain things to a sentence, as you've perfectly outlined for us. In your example of "I," you rendered a predicate in virtue of showing us the logical form of a well-formed formula. But again, "x is y" is not a predicate. It contains a predicate, one which you render or illustrate to us by picking out the logico-grammatical construction "is y."

"x is y" is a well-formed formula. Using variables doesn't make a sentence into a predicate. Using variables in place of particulars makes a sentence more general, not a predicate.

"is y" is a predicate; but really, only "y" is the predicate whereas "is" is a tense operator. "is y" is a predicate phrase.

The result of switching out a particular entity with a variable is not a predicate. The result is a well-formed formula. The WFF could be converted into a sentence, say, in English, which would contain a predicate.

1. "x killed y," or "Kxy" is not a predicate; it is a well-formed formula which contains the predicate "killed" that picks out a relation. We call the linguistic representation of relations, in English, "two-place predicates."

2. "s is tall," or "Ts" is not a predicate; it is a well-formed formula which contains the predicate "is tall" that picks out a contingent property of "s." We call the linguistic representations of properties, in English, "predicates."

Edited by despinozist on 07/28/09 - 12:48 PM
I'll show you differences.
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