False Paradox?
Is the following paradox an actual paradox?
Or is there an answer?

Is it a real paradox?
Yes.

swstephe, Fallen Hawthorn, BalanceofEquilibrium
3 100%
No, because the sentence is false.

0 0%
No, because the sentence true.

0 0%
3 votes

False Paradox?
philosophydreams
Newbie

Usergroup: Members
Joined: Mar 09, 2012

Total Topics: 1
Total Posts: 2
#1 - Quote - Permalink
Posted Mar 9, 2012 - 7:18 PM:
Subject: False Paradox?
Context:
Imagine I draw a box, and within that box I write the following sentence:

"All sentences in this box are false."

Question:
Does the sentence above represent an actual paradox?
At first glance, one would assume it to be a paradox.
If all sentences in the box are false, and that sentence is inside the box, then that sentence would be false. But that would mean all sentences in the box are true when we already established it was false...

I believe that this is in fact a "false paradox", meaning it only appears to contradict itself.

My reason:
i'll try my best to explain my thinking.
I think that if the sentence can safely be said to be false, just false, and it wouldn't contradict itself. The sentence cannot be true, so we must test to see if it is false.
IF the sentence were false, that would NOT mean that ALL sentences in the box were TRUE.
We are left with one other option, and that is, ALL sentences in the box are Either true or either false.

If it is true, then it is false.
If is is not true, then it is false.

Sorry for the poor explanation.

Please share your ideas



Edited by philosophydreams on Mar 9, 2012 - 7:27 PM
Sapere Aude
Ecce Homo
Avatar

Usergroup: Members
Joined: Mar 05, 2012
Location: Lasciate ogne speranza, voi ch'intrate

Total Topics: 6
Total Posts: 305
#2 - Quote - Permalink
Posted Mar 9, 2012 - 7:31 PM:

philosophydreams wrote:
We are left with one other option, and that is, ALL sentences in the box are Either true or either false.


Reword the last part to: "All sentences in the box are either true or false." and yes you've provided an acceptable solution. If the sentence is false we can accept that all sentences in the box are either true or false but not that all sentences in the box are true. But I think the paradox was escaped by making the original statement a universal, viz. with "All". Try your solution on "This sentence is false."
philosophydreams
Newbie

Usergroup: Members
Joined: Mar 09, 2012

Total Topics: 1
Total Posts: 2
#3 - Quote - Permalink
Posted Mar 9, 2012 - 8:38 PM:

but if the sentence "all sentences in this box are false" is the only sentence in the box, isn't that equivalent to "this sentence is false"?
Or is my 'escape' correct?
swstephe
PF Addict
Avatar

Usergroup: Moderators
Joined: Apr 20, 2006
Location: San Jose, California

Total Topics: 39
Total Posts: 1432
#4 - Quote - Permalink
Posted Mar 9, 2012 - 9:21 PM:

A "paradox" is something that only looks like a logical contradiction. That looks like a logical contradiction, so it is a paradox. It isn't actually a logical contradiction, as there are several solutions. My favorites involve separating what the words are saying from the truth they are expressing.
Sapere Aude
Ecce Homo
Avatar

Usergroup: Members
Joined: Mar 05, 2012
Location: Lasciate ogne speranza, voi ch'intrate

Total Topics: 6
Total Posts: 305
#5 - Quote - Permalink
Posted Mar 10, 2012 - 12:49 AM:

philosophydreams wrote:
but if the sentence "all sentences in this box are false" is the only sentence in the box, isn't that equivalent to "this sentence is false"?
Or is my 'escape' correct?


They are not equivalent because one is a singular the other a universal proposition, i.e. the latter includes other cases than the singular case of "This sentence is false." Oftentimes, this quantitative distinction is irrelevant but this time the difference is exactly what allows your escape to work. So "All sentences in this box are false" fails to be a contradiction or a real paradox (except on the surface).

Consider:
A = "This sentence is false."
1. If false, then the sentence is false and therefore true. So A is true and false.
2. If true, then the sentence is false but then we return to 1 because the sentence is false.

The loop is inescapable as long as truth value is assigned to the sentence and the law of bivalence is followed.
Try your exact method on "This sentence is false."
angslan
Malevolent AI
Avatar

Usergroup: Sponsors
Joined: Jan 31, 2011

Total Topics: 56
Total Posts: 3926
#6 - Quote - Permalink
Posted Mar 10, 2012 - 3:04 AM:

Do the sentences reference anything with a truth-value? What if I draw a box and say, "This box is false". What does that mean?
psychotick
Dazed and confused
Avatar

Usergroup: Sponsors
Joined: Oct 05, 2009

Total Topics: 16
Total Posts: 1465
#7 - Quote - Permalink
Posted Mar 10, 2012 - 5:58 AM:

Hi,

I think it's a logical loop. Consider if the sentence were the only sentence in the box. So the sentence says it's false. Now we have two options. The sentence either is false or it isn't. If it is false, then that means that not all sentences in the box are false, and since it's the only sentence in the box, then it must be true. But if it's true, then it must be false, since the truthful sentence says its false.

But now we come to the other option, that the sentence is true. If the sentence is true, then as one of the sentences in the box, or the only one, then it must be true that the sentence is false. So the sentence is false. But if the sentence is false then it must be true.

You just run around endlessly in circles, with each determination of the sentence as true, making the sentence false, and each determination of the sentence as false, making it true.

Cheers, Greg.
jedaisoul
exponent of reason

Usergroup: Sponsors
Joined: Aug 14, 2008
Location: UK

Total Topics: 124
Total Posts: 3708
#8 - Quote - Permalink
Posted Mar 10, 2012 - 9:01 AM:

1. (deleted in error)

2. The statement cannot be true, because that would be self-contradictory.

3. If the statement is the only one in the box, then it triggers an infinite regress. However there is nothing in the scenario to require that to be the case.

4. The falsity of this statement does not necessitate that all statements in the box are true, only that at least one is true.


Edited by jedaisoul on Mar 10, 2012 - 7:06 PM
Mr. Natural
Old Mystic Madcap
Avatar

Usergroup: Members
Joined: Jan 09, 2012
Location: Florida: America's Biggest Ponzi Scheme

Total Topics: 4
Total Posts: 232
#9 - Quote - Permalink
Posted Mar 10, 2012 - 9:16 AM:

philosophydreams wrote:
Context:
Imagine I draw a box, and within that box I write the following sentence:

"All sentences in this box are false."


Why would you do that?
Legion
Unmoderated Member
Avatar

Usergroup: Unmoderated Member
Joined: Apr 25, 2008
Location: somewhere in between

Total Topics: 79
Total Posts: 2107
#10 - Quote - Permalink
Posted Mar 10, 2012 - 9:31 AM:

Oh man, I want to understand this. What if we re-write it in more formal terms?

S1: Every S in a B is false.
S2: S1 is in a B.

Is that a valid re-write?

How might this differ from...

S: S is false
locked
Download thread as
  • 80/5
  • 1
  • 2
  • 3
  • 4
  • 5



This thread is closed, so you cannot post a reply.