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Attributive Adjectives in Predicate Calculus

by Dembadon
Tags: predicate calculus
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Dembadon
#1
Nov10-11, 12:45 AM
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There was a short philosophical debate in my logic course today regarding attributive adjectives and the issues they present in predicate calculus. The professor brought things back on track before it got carried away, but I would like to get some help understanding a few issues I have that arose from the discussion.

Our professor referenced a book he read while in graduate school, but I forget the name of the author (I think his name started with a B). I will ask him and post it later if anyone needs/wants to see it.

Given the following statement:

There are fake diamonds.

My professor said that we are not allowed to infer the following:

There are diamonds.

My 1st issue: I don't see how one can claim that diamonds are fake without first having seen real diamonds. In other words, if fake is an imitation of another thing, how can you have an imitation of something that doesn't exist?

A fellow student used the following example to attempt to explain why the inference in my example is incorrect by saying, "Stating that fake unicorns exist doesn't mean that unicorns exist." This brought up my second issue: If unicorns are fake to begin with, then what the heck is a "fake unicorn"?
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CompuChip
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Nov10-11, 03:48 AM
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I guess the question is: is a fake x really an x?

If a "fake x" is just a special case of "an x" (as could be argued in the case of diamonds) then the statement is something like "there are tall people, therefore there are people."
If not (as could be argued in the case of the unicorns) the statement is similar to "there are trees, therefore there are airplanes" which is not a tautology.
Ryan_m_b
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Nov10-11, 06:30 AM
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I guess you could argue that X doesn't have to physically exist, it just has to exist at least conceptually. For example;

This is my fake son

I don't have a real son but the concept and possibility are there.

When it comes to what it means to be fake I guess that a fake is something that resembles something else but is different in some fundamental way (usually it is also trying to pass itself off as that something). So providing you have a full description of what makes X X you could also have a description of what a fake X is.

Dembadon
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Nov11-11, 04:09 PM
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Attributive Adjectives in Predicate Calculus

Thanks for the responses. Sorry I've left this kind-of hanging, but I wanted to get the name of the author of the book from my professor so I could post the excerpt he showed us in class. However, today is Veteran's Day and the campus is closed, so I won't be in class again until Monday.

Quote Quote by CompuChip View Post
I guess the question is: is a fake x really an x?

If a "fake x" is just a special case of "an x" (as could be argued in the case of diamonds) then the statement is something like "there are tall people, therefore there are people."
If not (as could be argued in the case of the unicorns) the statement is similar to "there are trees, therefore there are airplanes" which is not a tautology.
My professor said, for the purposes of our class, fake diamonds are not diamonds at all. I'll have to ask him which branch of logic allows us to consider a fake diamond as "a special case of a diamond".

Quote Quote by Ryan_m_b View Post
I guess you could argue that X doesn't have to physically exist, it just has to exist at least conceptually. For example;

This is my fake son

I don't have a real son but the concept and possibility are there.

When it comes to what it means to be fake I guess that a fake is something that resembles something else but is different in some fundamental way (usually it is also trying to pass itself off as that something). So providing you have a full description of what makes X X you could also have a description of what a fake X is.
Those are interesting points for consideration, Ryan. I'll think about them and get back.
LaurieAG
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Nov11-11, 11:54 PM
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Quote Quote by Ryan_m_b View Post
When it comes to what it means to be fake I guess that a fake is something that resembles something else but is different in some fundamental way (usually it is also trying to pass itself off as that something). So providing you have a full description of what makes X X you could also have a description of what a fake X is.
Quote Quote by Dembadon View Post
I'll have to ask him which branch of logic allows us to consider a
fake diamond as "a special case of a diamond".
Yes Ryan and Dembadon, very interesting when you consider questions about the existence of reality and the theoretics that lead to these types of conclusions.

Roger Penrose talked about the Wick rotation during his debate with Stephen Hawking in "The Nature of Space and Time".
This a useful tool in QFT. One replaces t with it by means of a rotation of the time axis. This translates Minkowski space into Euclidean space.
CompuChip
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Nov13-11, 02:12 AM
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Quote Quote by Dembadon View Post
Thanks for the responses. Sorry I've left this kind-of hanging, but I wanted to get the name of the author of the book from my professor so I could post the excerpt he showed us in class. However, today is Veteran's Day and the campus is closed, so I won't be in class again until Monday.
Well, in that case I'd argue as follows:
let D(x) be "x is a diamond" and F(x) "x is fake."

Then if fake diamonds are diamonds, you can express the proposition as
[tex]\left( \exists x: D(x) \wedge F(x) \right) \implies \left( \exists y: F(y) \right)[/tex]
however, you just told me that it should be read as
[tex]\left( \exists x: D(x) \right) \implies \left( \exists y: F(y) \right)[/tex]
which is subtly but crucially different.


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