## View Poll Results: I voted in this poll AND this conjunction is false.

Voters
13. You may not vote on this poll
• True

2 15.38%
• False

5 38.46%
• Other

7 53.85%
Multiple Choice Poll.

# Thread: What is the truth value of this sentence?

1. Originally Posted by Igor_Goldenberg
I think for the problem to be defined the conjunction (in this particular statement) has to be defined.
I don't understand this comment.

2. Originally Posted by Mangafranga
I don't understand this comment.
In logic conjunction is a combination of other statements. You have to specify which statements (preferably finite number of them) are combined in the conjunction.

3. Originally Posted by Igor_Goldenberg
In logic conjunction is a combination of other statements. You have to specify which statements (preferably finite number of them) are combined in the conjunction.
The statements are "I voted in this poll" and "this conjunction is false".

4. Originally Posted by Mangafranga
The statements are "I voted in this poll" and "this conjunction is false".
Conjunction of what?

5. Originally Posted by Igor_Goldenberg
Conjunction of what?
Of those two statements.

6. Call "I voted in this poll" "a", and "this conjunction is false" "b".

Is (a&b) true or false? By the definition of a conjunction, it is true iff both of its conjuncts are true. Let us for the moment say a is true. Then it comes down to b.
If b is true, then one of a or b must be false. Hence if b is true b must also be false (because a is true).
If b is false, both a and b must be true. Hence if b is false it must also be true.

I think your complaint here is of the "what does "this sentence" refer to" type. If you say it refers to itself, then you have "this sentence this sentence...".

7. Originally Posted by Mangafranga
I think your complaint here is of the "what does "this sentence" refer to" type. If you say it refers to itself, then you have "this sentence this sentence...".
Things could also be construed thusly,

"a" = "I voted in this poll"
"b" = "c is false"
"c" = (a&b)

And then you worry, if this is your worry, is that things come out as (a&~(a&~(a&..., or (a&huh?

8. Originally Posted by Mangafranga
Call "I voted in this poll" "a", and "this conjunction is false" "b".

Is (a&b) true or false? By the definition of a conjunction, it is true iff both of its conjuncts are true. Let us for the moment say a is true. Then it comes down to b.
If b is true, then one of a or b must be false. Hence if b is true b must also be false (because a is true).
If b is false, both a and b must be true. Hence if b is false it must also be true.

I think your complaint here is of the "what does "this sentence" refer to" type. If you say it refers to itself, then you have "this sentence this sentence...".
That's what I was getting to:
It is a combination of infinitive number of statements.

9. Originally Posted by Jono
I'm not sure why Buridan's Sophisms ch. 8 all about liar paradoxes should be called "informal".
Speaking of Buridan, his idea of impetus was also a fore-runner of Galileo's principle of inertia, in turn the fore-runner of Newton's First Law of Motion:

Also, since the Bible does not state that appropriate intelligences move the celestial bodies, it could be said that it does not appear necessary to posit intelligences of this kind, because it would be answered that God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them He impressed in them impetuses which moved them without His having to move them any more except by the method of general influence whereby He concurs as a co-agent in all things which take place; 'for thus on the seventh day He rested for all work …' [Gen. 2:2] And these impetuses which He impressed in the celestial bodies were not decreased nor corrupted afterwards, because there was not inclination of the celestial bodies for movements.

But because of the resistance which results from the weight of the [waterwheel of the] mill, the impetus would continually diminish until the mill ceased to turn. And perhaps, if the mill should last forever without any diminution or change, and there were no other resistance to corrupt the impetus, the mill would move forever because of its perpetual impetus.

10. I don't see how the proposition "I voted in this poll AND this conjunction is false" can be true ... at the time of choosing how to vote, "I voted in this poll" (being past tense) is obviously false, therefore the proposition fails.

11. Originally Posted by Spiny Norman
I don't see how the proposition "I voted in this poll AND this conjunction is false" can be true ... at the time of choosing how to vote, "I voted in this poll" (being past tense) is obviously false, therefore the proposition fails.
Your claim is that at least every vote should be "false". (Unless someone votes with a hydra?) However is the claim also that the proposition per se is always false? Perhaps the real claim is that whatever proposition one votes on is always false. (E.g. Spinny may have voted on "Spinny has already voted at such and such a time", and that doesn't change!) I won't, however, be making a new poll to make the tense (or rather, tenselessness) explicit.

12. Originally Posted by Mangafranga
Unless someone votes with a hydra?
Touche! You might need to define "I" so that it was clear it didn't refer to the bulletin board identity but rather to the 'real person'.

Let V = "I voted in this poll"
Let C = "This conjunction" ... which draws in V again.

So the proposition is that V&C is false. However C=V&C ad infinitum ... but I'm not sure whether to call that "nonsense" or "circular" (or both).

Anyway, I'm going to vote for Other.

13. Originally Posted by Spiny Norman
Let V = "I voted in this poll"
Let C = "This conjunction" ... which draws in V again.

So the proposition is that V&C is false. However C=V&C ad infinitum ... but I'm not sure whether to call that "nonsense" or "circular" (or both).
Igor had a similar worry. And I spelt the worry out similar to you in post 37. If this is the right analysis, it does seem like the sentence doesn't make any sense.

14. ## Doh!

Originally Posted by Mangafranga
Igor had a similar worry. And I spelt the worry out similar to you in post 37. If this is the right analysis, it does seem like the sentence doesn't make any sense.
So this is the 44th post about a sentence that does not make any sense! It must be time for me to do something else!

15. You know, we could start analysing Mangafranga's votes ... he voted for True and False ... ... that would keep us going for another 20-30 posts easily I reckon.