How to refute this claim against the law of non-contradiction

[Ben_Sinner]

I have another question

I read a blog a few weeks ago by a Catholic.
thirdmillennialtemplar.wordpress.com/2011/11/25/a-weaker-law-of-excluded-middle/

The article stated the following statement could reject the law of non-contradiction without causing a problem.

"Not everything is both true and false"

If that statement is true, then that means the statement’s assumption: there are, at least, some things that can be both true and false: is true

If the statement is false, then everything is both true and false

So either way the law of LNC could be rejected here.

Is there a way to solve this one and show that LNC prevails even through this one. Something seems fishy about this because it is referenced as the Weak Law of Noncontradiction (WLNC).

 

[ccmnxc]

Reading over the blog article, I’m not sure the author is arguing for what you ascribe to him here. Rather, he is arguing that there are some a priori statements to which one must hold if any reasoning is to be successful.
Further, he seems to be referring to the Law of the Excluded Middle rather than the Law of Non-contradiction, which are slightly different. When speaking of the WLEM, the term “Weak” denotes a position which is less strong than the original LEM and thus it conflicts with fewer philosophical positions/presupposition (i.e. it should be easier for more people to accept the WLEM than the LEM because it makes a weaker claim). The same thing is done by some philosophers who defend the Principle of Sufficient Reason (PSR). Some philosophers reject the PSR, so some PSR defenders might appeal to a “Weak” PSR in the hopes that those who reject the original PSR will accept the PSR.

To address your original question anyways, “Not everything is both true and false” is indeed true if you don’t attach any assumptions to it. It can simply mean “There is at least 1 thing that is not both true and false” which does not preclude the notion that “There is nothing that is both true and false in the same way at the same time,” which is the PNC. If you do attach the assumption mentioned such that “Not everything is both true and false” entails that there are some thing which are both true and false, then the actual meaning of the sentence “Not everything is both true and false” changes due to the assumption loaded in, an assumption which we can reject.
Thus, either the PNC is allowed given the first reading, or if we take the second reading, we have to acknowledge that the meaning is different from the first reading given the additional assumption and that since the meaning is different, we are free to reject it without contradiction.

 

[dshix]

I have another question

I read a blog a few weeks ago by a Catholic.
thirdmillennialtemplar.wordpress.com/2011/11/25/a-weaker-law-of-excluded-middle/

The article stated the following statement could reject the law of non-contradiction without causing a problem.

"Not everything is both true and false"

If that statement is true, then that means the statement’s assumption: there are, at least, some things that can be both true and false: is true

If the statement is false, then everything is both true and false

So either way the law of LNC could be rejected here.

Is there a way to solve this one and show that LNC prevails even through this one. Something seems fishy about this because it is referenced as the Weak Law of Noncontradiction (WLNC).

In a logical statement, no inferences should be taken which do not logically follow. In the statement "Not everything is both true and false", it certainly sounds like it infers that SOME things are both true and false, but that inference actually does not logically follow at all.

Certainly, in the English language, the phrasing of the statement sounds like it IS saying that there are some things both true and false, but it doesn’t actually say it, there is no problem here. Thus, the statement is true.

If, however, it was phrased like this: "Some things, but not everything are both true and false" then the statement would be FALSE, because of the principle of non-contradiction.

 

[thinkandmull]

“Not everything is both true and false” means “Some things, but not everything are both true and false”. Something can be both true and false, depending on the sense, like when you say “in a sense that is true”

 

[Rhubarb]

“Not everything is both true and false” means “Some things, but not everything are both true and false”. Something can be both true and false, depending on the sense, like when you say “in a sense that is true”

I hesitate to join in because I don’t know how to handle claims about truth in the logic that I’ve learned.
So
Doesn’t Universal Negation return an existential with a negated quantity? So…

Not (everything) is both true and false] would return **(somethings) are not both true and false] ** which seems like a truism to me.

 

[fisherman_carl]

I would disagree with the premise that

“Not everything is both true and false”

Is logically equivalent to

“there are, at least, some things that can be both true and false:”

we are talking about the way words are being used here. In other words it is a kind of trickery or slight of hand. However if you think about it if it is true that not everything is true and false,it could still be true that nothing is true and false. Because nothing is a possibility of not everything. Therefore,the logical equivalency is false. For instance if I said not everyone is a green monster from the planet of mars this does not necessarily mean that there are green monsters from mars. It could still also be true there are no monsters from mars. it is about the way I am using words in a backhanded way to try and make it sound as if there are green monsters from mars, when there are none.

Otherwise, if you still think it is logically equivalent then I guess I could easily get you to believe in green men from mars.

 

[Marc]

"Not everything is both true and false"

If that statement is true, then that means the statement’s assumption: there are, at least, some things that can be both true and false: is true

If the statement is false, then everything is both true and false

While I’m not up to date on any modern discussion on the Law of Noncontradiction. The ancient treatment by Aristotle has been good enough for me. It might be impossible to prove the law but to refute it would require one to assume it. That paradox is evident in your own reasoning. You use the words true and false in two ways each. You cannot relativize the meanings of true and false and simultaneously weaken the absolute meanings of true and false. If you’re caught up with a real world statement that appears to be both true and false, analyze the statement further and you will certainly find an element with two senses. The very art of demagoguery is to exploit such ambiguities.

 

[dshix]

“Not everything is both true and false” means “Some things, but not everything are both true and false”. Something can be both true and false, depending on the sense, like when you say “in a sense that is true”

Not true.

Saying that “not everything” is both true and false does not logically imply that there is something which is true and false. It implies that colloquially, but not logically.

 

[thinkandmull]

Not true.

Saying that “not everything” is both true and false does not logically imply that there is something which is true and false. It implies that colloquially, but not logically.

You are write, but it could mean that everything is true or false

 

[dshix]

You are write, but it could mean that everything is true or false

Not exactly. The statement “Some things are both true and false” is a false statement.

Therefore, the statement" Not all things are both true and false" is only true insofar as it does not logically imply that some things are both true and false.

It’s a rather weird statement, which is why it is so confusing.