numbers vs. words

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Extrain
 
Reply Mon 3 May, 2010 02:43 pm
@fast,
fast;159649 wrote:
I edited all that out. I wrote it too quick. I just don't think that we should infer that there were red cars in my driveway this morning just because I said that I ate every red car in my driveway this morning.


You would just be saying something silly, then, and didn't really mean it.

But if someone says, "I ate all my pancakes this morning," that would imply there were once pancakes this morning. There are now no longer any pancakes because the person ate them.
 
fast
 
Reply Mon 3 May, 2010 03:22 pm
@Extrain,
Extrain;159651 wrote:
You would just be saying something silly, then, and didn't really mean it.

But if someone says, "I ate all my pancakes this morning," that would imply there were once pancakes this morning. There are now no longer any pancakes because the person ate them.

But, isn't it true that you ate every single pancake on your plate this morning? So what that there were no pancakes on your plate! You still ate everyone that was there (!), so the statement "I ate all my pancakes this morning" doesn't necessarily imply that there were once pancakes on your plate this morning.

Facts vs assertions of facts.
 
Extrain
 
Reply Mon 3 May, 2010 06:25 pm
@fast,
fast;159658 wrote:
But, isn't it true that you ate every single pancake on your plate this morning? So what that there were no pancakes on your plate! You still ate everyone that was there (!), so the statement "I ate all my pancakes this morning" doesn't necessarily imply that there were once pancakes on your plate this morning.

Facts vs assertions of facts.


You are getting truth mixed up with logical validity. If it is true that there were pancakes I ate this morning, then it logically follows that there was something I ate, namely pancakes. Of course, I could be saying something false, or I could really be suffering from a poor memory at the time that I recall this event since I really had cereal instead. But none of these possibilities affect the validity of the inference.

The cat is on the mat.
Therefore, there is something on the mat.

Pancakes were what I ate this morning.
Therefore, there was something I ate this morning--pancakes.

...are logically valid whether or not the premise and conclusion are true.
 
fast
 
Reply Mon 3 May, 2010 07:51 pm
@Extrain,
[QUOTE=Extrain;159724]You are getting truth mixed up with logical validity. If it is true that there were pancakes I ate this morning, then it logically follows that there was something I ate, namely pancakes. Of course, I could be saying something false, or I could really be suffering from a poor memory at the time that I recall this event since I really had cereal instead. But none of these possibilities affect the validity of the inference.

The cat is on the mat.
Therefore, there is something on the mat.

Pancakes were what I ate this morning.
Therefore, there was something I ate this morning--pancakes.

...are logically valid whether or not the premise and conclusion are true.[/QUOTE]
The proposition "there is a cat on the mat" is true if there is in fact a cat on the mat; likewise, the proposition "Kennethamy has a sister" is true if Kennethamy in fact has a sister. I'm okay with that, but what I am not okay with is the idea that you think he's expressing that proposition when he says his sister isn't fictional. You think that he is expressing (in part) the proposition that he has a sister and that his sister isn't fictional.
 
kennethamy
 
Reply Mon 3 May, 2010 08:02 pm
@fast,
fast;159753 wrote:

The proposition "there is a cat on the mat" is true if there is in fact a cat on the mat; likewise, the proposition "Kennethamy has a sister" is true if Kennethamy in fact has a sister. I'm okay with that,


You should not be, since neither is true. What is true is that there is a cat on the mat only if there is a cat on the mat; and kennethamy has a sister only if kennethamy has a sister.
 
fast
 
Reply Mon 3 May, 2010 08:22 pm
@kennethamy,
[QUOTE=kennethamy;159756]You should not be, since neither is true. What is true is that there is a cat on the mat only if there is a cat on the mat; and kennethamy has a sister only if kennethamy has a sister.[/QUOTE]
I started to say if and only if, but I don't understand the necessity of adding "only."

It seems to me that if there is a cat on the mat, then the proposition "a cat is on the mat" is true. I don't deny that "only if" is correct. I'm just not sure why "if" isn't.
 
kennethamy
 
Reply Mon 3 May, 2010 08:27 pm
@fast,
fast;159764 wrote:

I started to say if and only if, but I don't understand the necessity of adding "only."

It seems to me that if there is a cat on the mat, then the proposition "a cat is on the mat" is true. I don't deny that "only if" is correct. I'm just not sure why "if" isn't.


You are right, and I wrong. I misread what you wrote, sorry.
 
Extrain
 
Reply Mon 3 May, 2010 09:45 pm
@kennethamy,
fast;159753 wrote:

The proposition "there is a cat on the mat" is true if there is in fact a cat on the mat; likewise, the proposition "Kennethamy has a sister" is true if Kennethamy in fact has a sister. I'm okay with that,


fast;159764 wrote:

I started to say if and only if, but I don't understand the necessity of adding "only."

It seems to me that if there is a cat on the mat, then the proposition "a cat is on the mat" is true. I don't deny that "only if" is correct. I'm just not sure why "if" isn't.


kennethamy;159765 wrote:
You are right, and I wrong. I misread what you wrote, sorry.


It's both. True propositions are biconditional.

"P" is true if and only if P.

If "the cat is on the mat" is true, then there is, in fact, a cat on the mat.
If there is, in fact, a cat on the mat, then "the cat is on the mat" is true.

fast;159753 wrote:
but what I am not okay with is the idea that you think he's expressing that proposition when he says his sister isn't fictional. You think that he is expressing (in part) the proposition that he has a sister and that his sister isn't fictional.


What does that even mean if it means anything at all?? "Kennethamy's sister is not fictional." Would you please tell what proposition he is expressing? The burden is on you to tell everyone. Quite honestly, I can't formulate that proposition logically at all, since, when I do, I end up admitting Ken's sister exists. No wonder I thought he was implying he had a deceased sister!! If he wasn't implying that, then he was just talking nonsense. This is also nonsense: "Santa Claus is not fictional."

(Ex) Sx and ~Fx.

I really do have a brother. None of my brothers are fictional. When I say,
"My brother is not fictional," I am saying "I have a brother and he is not fictional."

(Ex) Brother(x) and ~Fictional(x)

or

(Ex) ~Fictional(x)

"There is something not fictional."

I can say pointing, "That car is not red," meaning, "there is a car and that car is not red."

(Ex) Car(x) and ~Red(x)

or

(Ex) ~Red(x)

"There is something not red."

---------- Post added 05-03-2010 at 10:42 PM ----------

Why always make a logical mess of things?

If we wanted to deny the truth of "Santa Claus is fictional" or deny the truth of "Santa Claus is not fictional," it is much more sensible to say,

"It is not the case there is a Santa Claus that is fictional,"

~Ex (Sx and Fx)

or, "It is not the case there is a Santa Claus that is not fictional,"

~Ex (Sx and ~Fx)

When we try to negate or assert the predicate "fictional" of Santa Claus, we end up admitting Santa Claus exists, Ex (Sx and ~Fx) or Ex (Sx and Fx). Big problem!
 
kennethamy
 
Reply Tue 4 May, 2010 12:41 am
@Extrain,
Extrain;159781 wrote:
It's both. True propositions are biconditional.

"P" is true if and only if P.

If "the cat is on the mat" is true, then there is, in fact, a cat on the mat.
If there is, in fact, a cat on the mat, then "the cat is on the mat" is true.



What does that even mean if it means anything at all?? "Kennethamy's sister is not fictional." Would you please tell what proposition he is expressing? The burden is on you to tell everyone. Quite honestly, I can't formulate that proposition logically at all, since, when I do, I end up admitting Ken's sister exists. No wonder I thought he was implying he had a deceased sister!! If he wasn't implying that, then he was just talking nonsense. This is also nonsense: "Santa Claus is not fictional."

(Ex) Sx and ~Fx.

I really do have a brother. None of my brothers are fictional. When I say,
"My brother is not fictional," I am saying "I have a brother and he is not fictional."

(Ex) Brother(x) and ~Fictional(x)

or

(Ex) ~Fictional(x)

"There is something not fictional."

I can say pointing, "That car is not red," meaning, "there is a car and that car is not red."

(Ex) Car(x) and ~Red(x)

or

(Ex) ~Red(x)

"There is something not red."

---------- Post added 05-03-2010 at 10:42 PM ----------

Why always make a logical mess of things?

If we wanted to deny the truth of "Santa Claus is fictional" or deny the truth of "Santa Claus is not fictional," it is much more sensible to say,

"It is not the case there is a Santa Claus that is fictional,"

~Ex (Sx and Fx)

or, "It is not the case there is a Santa Claus that is not fictional,"

~Ex (Sx and ~Fx)

When we try to negate or assert the predicate "fictional" of Santa Claus, we end up admitting Santa Claus exists, Ex (Sx and ~Fx) or Ex (Sx and Fx). Big problem!


Doesn't X is not fictional, or X is not a fiction just mean, something is X? E.g. "You don't believe that I have a sister? Let me tell you that Joan is not a fiction!". That is, "Someone is Joan, and Joan is my sister".
 
fast
 
Reply Tue 4 May, 2010 07:19 am
@kennethamy,
[QUOTE=kennethamy;159841]Doesn't X is not fictional, or X is not a fiction just mean, something is X? E.g. "You don't believe that I have a sister? Let me tell you that Joan is not a fiction!". That is, "Someone is Joan, and Joan is my sister".[/QUOTE]This is all my fault.

Earlier in the thread, you said, "My sister does not exist, but she is not fictional." I thought that meant that she had no properties; thence, I came to the conclusion that you have no (nor ever had a) sister.

My apologies.
 
Extrain
 
Reply Tue 4 May, 2010 08:35 am
@fast,
kennethamy;159841 wrote:
Doesn't X is not fictional, or X is not a fiction just mean, something is X? E.g. "You don't believe that I have a sister? Let me tell you that Joan is not a fiction!". That is, "Someone is Joan, and Joan is my sister".


Sure, I guess....I just wish you would have said something earlier about that. If you never had a sister, why would you even say this? Technically, it's false how it is written because it is a conjunction, not a material conditional.
 
kennethamy
 
Reply Tue 4 May, 2010 08:46 am
@fast,
fast;159946 wrote:
This is all my fault.

Earlier in the thread, you said, "My sister does not exist, but she is not fictional." I thought that meant that she had no properties; thence, I came to the conclusion that you have no (nor ever had a) sister.

My apologies.


No need, and you are right, I have no sister. So, therefore, my sister has no properties. That is vacuously true, of course. The way "I ate every vegetable on my plate" is true because there were no vegetables on my plate to begin with.
 
Extrain
 
Reply Tue 4 May, 2010 08:51 am
@kennethamy,
kennethamy;159972 wrote:
No need, and you are right, I have no sister. So, therefore, my sister has no properties. That is vacuously true, of course. The way "I ate every vegetable on my plate" is true because there were no vegetables on my plate to begin with.


That's just as vacuously true as saying,

"If I have a sister, then she is not fictional."

Why didn't you just say this?? It would have saved everyone so much trouble.
 
fast
 
Reply Tue 4 May, 2010 09:25 am
@Extrain,
Extrain;159974 wrote:
That's just as vacuously true as saying,

"If I have a sister, then she is not fictional."

Why didn't you just say this?? It would have saved everyone so much trouble.


Expound on why "Kennethamy's sister is not fictional" implies that Kennethamy has a sister. Does the logical rule you bring up always hold true?

Does "I ate every vegetable on my plate" imply that I once had vegatables on my plate?
 
kennethamy
 
Reply Tue 4 May, 2010 09:29 am
@Extrain,
Extrain;159974 wrote:
That's just as vacuously true as saying,

"If I have a sister, then she is not fictional."

Why didn't you just say this?? It would have saved everyone so much trouble.


I don't think that I quite understand that sentence.
 
fast
 
Reply Tue 4 May, 2010 09:43 am
@kennethamy,
kennethamy;159984 wrote:
I don't think that I quite understand that sentence.

I think he means "non-existent" when he says "fictional."
 
Extrain
 
Reply Tue 4 May, 2010 09:44 am
@fast,
fast;159983 wrote:
Expound on why "Kennethamy's sister is not fictional" implies that Kennethamy has a sister. Does the logical rule you bring up always hold true?


Yes, it does logically imply that: that's why he needs "If I have a sister...." before it to make it true--vacuously true--otherwise, it's false.

fast;159983 wrote:
Does "I ate every vegetable on my plate" imply that I once had vegatables on my plate?


In logic, you learn how to translate natural language sentences into logical form. And natural language can sometimes be ambiguous, too. So...

"I ate every vegetable on my plate" implies

"I ate."

There is something that ate. Ex Eat(x)

And if someone says, "Vegetables were what I ate" this logically implies,

"There is something I ate," namely, vegetables. Ex Vegetables(x)

---------- Post added 05-04-2010 at 09:47 AM ----------

kennethamy;159984 wrote:
I don't think that I quite understand that sentence.


"Kennethamy has a sister" is false. It makes the statement vacuously true under any truth-interpretation of "his sister is not fictional."

So, "If Kennethamy has a sister, then his sister is not fictional" is true.
 
fast
 
Reply Tue 4 May, 2010 09:59 am
@Extrain,
This is so hurting my head.

Scenario 1: the facts: I did not eat.

Proposition1: I ate every vegetable on my plate this morning.
Proposition2: I ate
Proposition3: There were vegetables on my plate.

P1: true
P2: false
P3: Unknown (either true or false)

Scenario 2: the facts: I did eat from my plate. I ate everything on my plate. There never were vegetables on my plate. I ate no vegetables.

Proposition4: I ate every vegetable on my plate this morning.
Proposition5: I ate
Proposition6: There were vegetables on my plate.

P4: true
P5: true
P6: false

I think proposition 4 is true. Kennethamy thinks proposition 4 is true. Does Extrain think proposition 4 is true? You clearly think P1 is false, but that is a different proposition.

If I solve this, I may be able to confirm whether or not you're always (or only sometimes) using "nonexistent" to be the same as "fictional." [don't ask how].
 
kennethamy
 
Reply Tue 4 May, 2010 10:00 am
@Extrain,
Extrain;159988 wrote:
Yes, it does logically imply that: that's why he needs "If I have a sister...." before it to make it true--vacuously true--otherwise, it's false.



In logic, you learn how to translate natural language sentences into logical form. And natural language can sometimes be ambiguous, too. So...

"I ate every vegetable on my plate" implies

"I ate."

There is something that ate. Ex Eat(x)

And if someone says, "Vegetables were what I ate" this logically implies,

"There is something I ate," namely, vegetables. Ex Vegetables(x)

---------- Post added 05-04-2010 at 09:47 AM ----------



"Kennethamy has a sister" is false. It makes the statement vacuously true under any truth-interpretation of "his sister is not fictional."

So, "If Kennethamy has a sister, then his sister is not fictional" is true.


I ate every vegetable on my plate does not imply that something was a vegetable on my plate, although it certainly suggests it. All the things I ate were vegetables does not have existential import any more than any universal proposition does. Universal propositions do not have, but particular propositions do have, existential import under the modern (Boolean) understanding of predicate logic. But I don't believe we are really disagreeing. The logical form of a universal proposition is hypothetical, so we agree. No real dispute between us.
 
Extrain
 
Reply Tue 4 May, 2010 10:21 am
@kennethamy,
kennethamy;159999 wrote:
I ate every vegetable on my plate does not imply that something was a vegetable on my plate, although it certainly suggests it. All the things I ate were vegetables does not have existential import any more than any universal proposition does. Universal propositions do not have, but particular propositions do have, existential import under the modern (Boolean) understanding of predicate logic. But I don't believe we are really disagreeing. The logical form of a universal proposition is hypothetical, so we agree. No real dispute between us.


But "I ate every vegetable on my plate" is not a universal generalization. If we really wanted to translate that strictly into logical form, it looks something like this..."Eating" is a relation

EyAx Eating (y,x)

Which says, "Someone eats everything"

And what someone ate, are every one of his pancakes. So,

Ey [Someone(y) and Ax (pancakes (x) --> Eat (y,x))]

This says someone ate all pancakes....so, the scope of (Ax) has to be restricted to the 1, 2, or 3, pancakes that he ate, and not all the pancakes in the world. I would have to think how to translate that more accurately since (Ax) takes on a distributive reading and so you have to specify each pancake someone ate by using the identity relation.

---------- Post added 05-04-2010 at 10:37 AM ----------

fast;159998 wrote:
This is so hurting my head.

Scenario 1: the facts: I did not eat.

Proposition1: I ate every vegetable on my plate this morning.
Proposition2: I ate
Proposition3: There were vegetables on my plate.

P1: true
P2: false
P3: Unknown (either true or false)

Scenario 2: the facts: I did eat from my plate. I ate everything on my plate. There never were vegetables on my plate. I ate no vegetables.

Proposition4: I ate every vegetable on my plate this morning.
Proposition5: I ate
Proposition6: There were vegetables on my plate.

P4: true
P5: true
P6: false

I think proposition 4 is true. Kennethamy thinks proposition 4 is true. Does Extrain think proposition 4 is true? You clearly think P1 is false, but that is a different proposition.

If I solve this, I may be able to confirm whether or not you're always (or only sometimes) using "nonexistent" to be the same as "fictional." [don't ask how].


"Eating" is a relation. And all of us are now discussing quantificational logic. All these sentences can be formulated logically.

If there were no vegetables that you ate, then "I ate all my vegetables this morning" is simply false. There is no other way around it. So I don't see what the problem is.
 
 

 
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