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Predicate logic translation - help needed

Malac
Posts: 3
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9/20/2012 6:40:31 PM
Posted: 4 years ago
I hope this is the right spot for this. I've requested for info from someone who's been helpful in the past, but bring it here for further support.

My issue in predicate logic is concerned with English - translation. I understand that when translating occurs, an individual is ascribed a predicate, the former denoted by an individual constant and the latter by a predicate constant. I also am aware to an "extent", the usage of variables that represent individuals in the monadic aspect. However, specifically, my problem lies with general sentences and how variables are assigned to expressions that subsequently fit into polyadic relational predicates (2 place, etc.) What exactly does it mean for a general sentence (a sentence not denoting a subject with a singular term) to say something about a quantity of something, and to what scope is that quantity extended, in terms of the English sentence saying so?

EX 1: "Dave is good" could be translated as "Gd". I know this.

EX 2: All men are good" could be translated as "(x)(Mx-->Gx)". I know this too, and looking at "men" as a class of individuals, I understand that the quantifier in relation to men is mentioning every individual within it.

--HERE'S THE PROBLEM--

EX 3:

a) "All women admire cats"

and

b) "All women love to dance"

3.a How are both general subjects "women" and "cats" different than if we used instead "Melissa" and "Mr. Pebbles"? Are we using the universal quantifier in the general sentence to state that "all of something" RELATES TO "all of something?" And is the term "cats" implicitly universal VS if we had instead added "some" cats? Also, when relating a subject to something else, does it necessary have to be a SET or CLASS OF INDIVIDUALS? Such as (x) RELATION(class,class). If so, how is this SET distinguished when using class terms not as obvious such as the aforementioned? (<-more about this below)

3.b. My confusion lies in how to pick out whether "love to" is a 2_place predicate or not. I'm not even sure if "dance" can be an entity to be used IF "love to" is by itself relational, as they may be dependent on each other to be only a monadic predicate, and I can't imagine "dance" itself representing individuals.
Polaris
Posts: 1,120
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9/21/2012 12:34:29 AM
Posted: 4 years ago
At 9/20/2012 6:40:31 PM, Malac wrote:
I hope this is the right spot for this. I've requested for info from someone who's been helpful in the past, but bring it here for further support.



--HERE'S THE PROBLEM--

EX 3:

a) "All women admire cats"

and

b) "All women love to dance"

3.a How are both general subjects "women" and "cats" different than if we used instead "Melissa" and "Mr. Pebbles"? [/quote]

You would have to represent "Mr. Pebbles" differently than "cats".

Are we using the universal quantifier in the general sentence to state that "all of something" RELATES TO "all of something?" And is the term "cats" implicitly universal VS if we had instead added "some" cats?

If I recall correctly from my Logic course (it's been awhile), unless it's specified as being "all", then we assume that it is only "some".

Also, when relating a subject to something else, does it necessary have to be a SET or CLASS OF INDIVIDUALS?

It depends on what you're doing. If categorical syllogisms, yes. Otherwise, no.

3.b. My confusion lies in how to pick out whether "love to" is a 2_place predicate or not. I'm not even sure if "dance" can be an entity to be used IF "love to" is by itself relational, as they may be dependent on each other to be only a monadic predicate, and I can't imagine "dance" itself representing individuals.

One good way to distinguish this is to change actions into entities performing actions. For example:

"All frogs jump" you can modify this to "All frogs are things that jump"

or in your case:

"All women are people who like to dance"
"All women are people who admire cats"

This will make it easier to identify the Subjects and predicates. Hopefully this helps.
Polaris
Posts: 1,120
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9/21/2012 12:41:31 AM
Posted: 4 years ago
I forgot to mention that you can also turn an individual entity into a category by adding the phrase "all thing identical to..." in front of it. For instance if you wanted to turn Mr.Pebbles into a category you could say:

"All things identical to Mr.Pebbles are cats"

And since only one thing is identical to Mr.Pebbles it is both a category and an individual entity. This should help when you're doing categorical syllogisms.
Malac
Posts: 3
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9/21/2012 5:56:27 PM
Posted: 4 years ago
At 9/21/2012 12:41:31 AM, Polaris wrote:
I forgot to mention that you can also turn an individual entity into a category by adding the phrase "all thing identical to..." in front of it. For instance if you wanted to turn Mr.Pebbles into a category you could say:

"All things identical to Mr.Pebbles are cats"

And since only one thing is identical to Mr.Pebbles it is both a category and an individual entity. This should help when you're doing categorical syllogisms.

Thanks man. Using this info and other, I managed to mostly "figure" out my confusion ha.