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# Do false statements imply contradictions?

Wed 8 Jun, 2011 10:48 am
Many people, college professors included, tell me that false statements do not imply contradictions. They instead babble on about how only necessarily false statements imply contradictions. They tell me statements such as "Babe Ruth is Governor of Massachusetts" does not imply a contradiction, even though it's false. They say a world can be conceived in which "Babe Ruth is Governor of Massachusetts," and that therefore it doesn't imply a contradiction. They will even go on to say that in order to have a contradiction, you must have two statements. Well, I disagree. If a statement is false in a world, then it also implies a contradiction in that world. These people seem to be considering the case where "Babe Ruth is Governor of Massachusetts" is true and not false. They fail to realize that I'm not doing that! I'm considering the case where it's false! When a statement is false, it will imply a contradiction, as the last two rows of a truth table show.

To put it formally:

Consider the truth table for logical implication.

P...........Q.............P->Q
T...........T................T
T...........F................F
F...........T................T
F...........F................T

Notice that for a false statement P, the last two rows of the truth table, both Q and ~Q follow. No matter what Q is, it's truth follows from false statement P, as the third row shows. We can therefore take Q to be "P is true." From here it follows that a false statement P implies it's own truth, as the third row shows.

Do false statements really imply their own truth? Do they really imply contradictions? Are false statements also true?
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djjd62

1
Wed 8 Jun, 2011 10:53 am
@browser32,
i once met a man who claimed that everything was true

he was later found to be lying
JLNobody

1
Wed 8 Jun, 2011 11:07 am
@djjd62,
It seems to me that a logically non-contradictory statement can contradict experience (Babe Ruth is NOT the governor...i.e., it's empirically untrue), or it can contradict another statement (literally it "speaks against" itself), i.e., it's logically invalid). But are all logical contradictions empirically false? Don't we sometimes find contradictions that denote or connote profound truths (I'm thinking of language in poetry and zen paradoxes)?
vikorr

1
Thu 9 Jun, 2011 01:30 am
@JLNobody,
I guess JL, that when one says 'false statements' one may not have had fiction in mind, but rather, lies intended to deceive.
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Ding an Sich

1
Thu 9 Jun, 2011 01:10 pm
@browser32,
browser32 wrote:

Many people, college professors included, tell me that false statements do not imply contradictions. They instead babble on about how only necessarily false statements imply contradictions. They tell me statements such as "Babe Ruth is Governor of Massachusetts" does not imply a contradiction, even though it's false. They say a world can be conceived in which "Babe Ruth is Governor of Massachusetts," and that therefore it doesn't imply a contradiction. They will even go on to say that in order to have a contradiction, you must have two statements. Well, I disagree. If a statement is false in a world, then it also implies a contradiction in that world. These people seem to be considering the case where "Babe Ruth is Governor of Massachusetts" is true and not false. They fail to realize that I'm not doing that! I'm considering the case where it's false! When a statement is false, it will imply a contradiction, as the last two rows of a truth table show.

To put it formally:

Consider the truth table for logical implication.

P...........Q.............P->Q
T...........T................T
T...........F................F
F...........T................T
F...........F................T

Notice that for a false statement P, the last two rows of the truth table, both Q and ~Q follow. No matter what Q is, it's truth follows from false statement P, as the third row shows. We can therefore take Q to be "P is true." From here it follows that a false statement P implies it's own truth, as the third row shows.

Do false statements really imply their own truth? Do they really imply contradictions? Are false statements also true?

False. A false statement that implies a contradiction does not mean that the false statement originally asserted is true. It asserts that the negation of the false statement is true.

But you are somewhat right. A false statement can imply a contradiction, but if it does then the negation of it is true.

Let us take P to mean "Babe Ruth is the governor of Massachusetts".

If P is false in a world w, then the negation of the statement ~P, is true in that world. However, P can be true at other worlds (u,v,x,....n) where its negation is false. So P-><>P. If a statement is necessarily false, then there is no world (or the given domain of worlds) in which that statement is true. So in this case if a necessarily false statement is true at a world w, then there is a contradiction.

Hope this clears things up.
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chai2

1
Thu 9 Jun, 2011 01:35 pm
I was having a hell of a contradiction with Peggy over at the Yahoo chat help desk the night before last.

I still haven't recovered.
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G H

1
Fri 10 Jun, 2011 10:09 am
@browser32,
Quote:
They will even go on to say that in order to have a contradiction, you must have two statements.

Yes, a contradiction involves inconsistency between two or more propositions, in that they either present or lead to opposite claims. Whereas a false statement would be just that: One, with the property of being false. If you really can prove that all processes for determining the latter's property had to consist of or include propositions being paired that were logically incompatible, then a statement's condition of being false would then indeed always imply contradiction having transpired in the underlying woodwork. Good luck with your endeavor....
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Artificial

1
Mon 11 Jul, 2011 07:56 pm
This is one of the situations in which my lack of philosophical knowledge leads me to the scientific form of belief instead.

String theory, more exactly, tells us that (is it true) there are an infinite number of three dimensional universes, expanding over a fourth dimensional area. Therefore in one of these, it is possible that Babe Ruth is governor, thus it is not a contradiction, merely a statement untrue in our own world. Obviously this one's quite farfetched, so let me try my way philosophically.

A false statement does not imply a contradiction, as it is only deemed true or false in your own perception. For instance, a child would perhaps believe that Babe Ruth was governor, and therefore in their mind it would be a truth. You, knowing better, would perceive the same thing as a lie. To question if a false statement implies a contradiction, is to question if a truth is a truth based on one's perception of a thing, or the reality in our world.

Therefore, I consider this a paradox, and I'll get the hell out of here before it blows up.
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Thomas

1
Mon 11 Jul, 2011 08:06 pm
@browser32,
False statements imply contradictions with reality, by whatever test you use to establish reality. But they don't necessarily imply contradictions with other statements, and that's what your professors mean when they say false statements don't imply contradictions.

For example, the statement "Babe Ruth is governor of Massachusetts" contradicts reality, as recorded by the Massachusetts Election Division. But it does not necessarily contradict other statements, especially if you don't make any.

Does that clarify it?
JLNobody

1
Mon 11 Jul, 2011 10:15 pm
@Thomas,
Right. This brings to mind the mistaken notion that all "schizophrenia" is a problem only of multiple personality or "split personality" when in fact it may also pertain to a person's schism, or split, with reality--especially the "reality" shared by his fellows.
0 Replies

cicerone imposter

1
Mon 11 Jul, 2011 10:38 pm
@Thomas,
Best explanation thus far. Thx.
0 Replies

MattDavis

1
Tue 19 Feb, 2013 07:23 pm
@browser32,
You seem to be making the assumption of the excluded middle in True False comparisons.
http://en.wikipedia.org/wiki/Law_of_excluded_middle
You seem to be assuming
that if something is "True" then it is "not False" [ T = ~F ]
and that if something is "False" then it is "not True". [ F = ~ T ]

You are right that this is the assumption in formalized logic and number theory, but with those assumptions you are left with Godel's Incompleteness Theorem
http://en.wikipedia.org/wiki/Incompleteness_theorem
demonstrating that there will still exists paradoxes. There will still be statements which are neither "True" nor "False".
Even assuming the excluded middle, leads to a proof that such a middle must exist.

This is a topic that I have attempted to explore at:
http://able2know.org/topic/207948-1
0 Replies

imans

1
Wed 20 Feb, 2013 02:43 pm
no fallacy on the contrary imply one

when truth is the reference of any and for, then truth cant but exist by else recognition which is the reason of absolute till it become existing too and real but then also free
while that free from absolute reality is what realized itself reality right so that free sense would b right present independant free energy, so never one since only by realizin more and more clearly else so always more free

while fallacy by definition is what is not true, when existence is objective then existence is true, then any is real, so fallacy is like a will of bein existing by creatin a form of itself in usin itself energy freedom to force the will to b the present reality, so fallacy cant b but one whole certainty always more
this what also led to such limited rough creations and god force

by inventin smthg bc u want it u become the mytho more and more for what u must deny everything else while existin faster, but then u must also conceive the thing smaller, this is related to arts ways, meanin to do what u want in one thing

inventions cant b but one thing bc truth is superiority while objective so in concept of free will that is more the dimension of truth too and in facts of inventions forms there cant b but one insistin will as max invention possible

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