Still Wondering about Contradictions

[Rhubarb]

Rhubarb:

So when you make propositions about truth, they get wonky.

Isn’t that proposition, itself, a proposition about the truth of propositions, and therefore “about truth?”

Perhaps your thinking about propositions is what is “wonky” rather than all propositions ever made about truth?

Let me clarify. Propositions such as “X is true/not true” are wonky. That’s what I meant by “propositions about truth”

 

[HarryStotle]

HarryStotle:

Rhubarb:

So when you make propositions about truth, they get wonky.

Isn’t that proposition, itself, a proposition about the truth of propositions, and therefore “about truth?”

Perhaps your thinking about propositions is what is “wonky” rather than all propositions ever made about truth?

Let me clarify. Propositions such as “X is true/not true” are wonky. That’s what I meant by “propositions about truth”

Some such propositions might be, but you seem to be insisting that all propositions of the form “X is true/not true” are wonky – whatever that means. That is quite the claim.

Let X = “The proposition ‘Water is clear.’”
X is true.
Is the proposition “X is true,” wonky in all cases?

 

[Rhubarb]

I can’t tell if you’re genuinely concerned with this or if you’re just trying to score pedantic points. Either way, that wasn’t what I meant either. So I’ll clarify again.

Analyzing propositions that use “true” or “truth” or such things as predicates in arguments of formal logic can get wonky. Much in the same way using existence as a predicate can make things wonky.

You should look up the principle of charity as it pertains to philosophy. This isn’t the political forum.

 

[undead_rat]

Some survived the Deluge.

But, assuming that this is an apparent contradiction, what is the solution? I believe that there is one.

 

[AlNg]

The liar’s paradox isn’t made up of contradictory statements

Taken as a whole, it is equivalent to a contradictory statement:
I am telling the truth and I am not telling the truth.

 

[AlNg]

Is your position based on the law of non-contradiction?

Is that principle demonstrably true?

I don’t know. What i do know is that your “paradox” and the liars “paradox” are not paradoxes. They are contradictions as I already explained. I cannot make sense of a contradiction.

 

[catholicray]

Well I found my “contradiction” listed under “paradox” in an old logic book I once read. Information is evolving.

Still, it would seem that we can not logically conclude the it is “true” that contradictions do not “exist” at this time. Whether or not we can make sense of them is besides the point. Or am I missing something?

 

[catholicray]

It seems like the way we deal with contradictions is to set the value of contradictions to false by default.

I suppose I wonder if the value of a contradiction is merely the product of man and our systems or actually factual about reality.

 

[po18guy]

Kinda like insisting that there is no truth - except that the statement itself purports to be true.

 

[catholicray]

Yes exactly. My thinking is that perhaps there is some way to accurately measure the truth value of contradictions. The one you’re highlighting suggests that truth is established absolutely. Maybe the problem is that we are dealing with absolutes that can not fit within our systems of logic.

 

[HarryStotle]

I can’t tell if you’re genuinely concerned with this or if you’re just trying to score pedantic points. Either way, that wasn’t what I meant either. So I’ll clarify again.

Analyzing propositions that use “true” or “truth” or such things as predicates in arguments of formal logic can get wonky. Much in the same way using existence as a predicate can make things wonky.

You should look up the principle of charity as it pertains to philosophy. This isn’t the political forum.

The principle of charity would suggest that you not turn a philosophical discussion into a political one purely on the basis of your own apprehensions. Nothing in my posts have even come near to making this discussion political.

Let’s be clear here…

Using existence as a predicate isn’t “wonky.”

Giraffes exist. Aliens may not exist. Antarctica exists as a continent in the Southern Ocean. One of my cats no longer exists. Dinosaurs existed millions of years ago. Which of those statements is “wonky?”

Most propositions that use existence as a predicate are straightforward and largely easily refuted or are self-evident and not “wonky.”

Likewise, to make a claim that some proposition is true or false isn’t “wonky,” but either refutable, self-evident, or significant but in dispute or contentious.

I have no idea what you mean by “wonky” nor have you made a case that “propositions that use ‘true’ or ‘truth’ or such things as predicates” can be characterized as “wonky.”

Perhaps some examples might get your point across better?

It just appears to me that you are attempting to frame the philosophical discussion regarding what is true or what simply is (as in exists) according to some post-modern notion that truth and existence claims just cannot be made.

I have to disagree for the simple reason that if those two kinds of propositions are out of bounds because they are “wonky” we may as well pack up any notion that we can know or talk about anything at all in any meaningful sense – which appears to be the direction you are heading.

 

[HarryStotle]

HarryStotle:

The liar’s paradox isn’t made up of contradictory statements

Taken as a whole, it is equivalent to a contradictory statement:
I am telling the truth and I am not telling the truth.

Well, no, the statements aren’t contradictory because neither is attempting to make an actual truth claim.

Which of the statements is to be taken seriously as an actual truth claim?

Neither.

Also, by definition a contradiction is

2a : a proposition, statement, or phrase that asserts or implies both the truth and falsity of something… both parts of a contradiction cannot possibly be true …— Thomas Hobbes

b : a statement or phrase whose parts contradict each other; a round square is a contradiction in terms

So…

1. The liar’s paradox isn’t “a contradictory statement” because it isn’t one statement.
2. There is not an actual truth claim being made by either statement because the truth value of each statement is indeterminate and intentionally unstable by the fact that the truth value of each statement is with reference to the other by design.
3. The virtual claim made by the liar isn’t, “I am telling the truth and I am not telling the truth.” It is simply a puzzle left to the reader to work out the possible truth involved, if any. There is no actual truth claim made by the ‘liar,’ because the ‘liar’ is simply asking by implication, “Am I telling the truth here at all?” There is no way of determining that, by the very intention of the “liar” wrapped in the referential illogic. That isn’t a contradiction because no truth claim is being made at all, not even implied.

 

[AlNg]

Or am I missing something?

Perhaps there is a consistency axiom of logic which requires that you cannot have both the statement p and its negation Not p true at the same time. They must be mutually exclusive in a consistent logical system. Whether or not you can prove that this rule can be derived from a system of logical reasoning, i don’t know because of the second incompleteness theorem of Godel, which apparently rules this out under certain restricted conditions.

 

[HarryStotle]

Yes exactly. My thinking is that perhaps there is some way to accurately measure the truth value of contradictions. The one you’re highlighting suggests that truth is established absolutely. Maybe the problem is that we are dealing with absolutes that can not fit within our systems of logic.

“To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true.”
~ Aristotle, Metaphysics 1011b25

Correspondence Theory of Truth.

 

[AlNg]

The liar’s paradox isn’t “a contradictory statement” because it isn’t one statement.

I have to disagree because as I have shown above when it is taken as a whole with its logical consequences it does involve a contradictory statement.
I am lying now.
So if you are lying when you say you are lying, then you are telling the truth.
So what you have is a contradiction:
I am lying and I am not lying.
It comes down to the fact that you are asserting
I am lying is true AND I am not lying is true.
P and Not P are both true, i.e., a contradiction.

 

[HarryStotle]

Whether or not you can prove that this rule can be derived from a system of logical reasoning…

You have to assume that rule in order to derive a system of logical reasoning.

You cannot have a system of logical reasoning without the rule, so it wouldn’t make sense to even try to derive it from logical reasoning because logical reasoning assumes the rule as one of its grounding or foundational principles.

 

[AlNg]

You cannot have a system of logical reasoning without the rule,

Not exactly:
Gödel’s second incompleteness theorem states that in a system which is free of contradictions , this absence of contradictions is neither provable nor refutable. If we would find a contradiction , then we would have refuted the absence of contradictions . Gödel’s theorem states that this is impossible.

 

[HarryStotle]

HarryStotle:

The liar’s paradox isn’t “a contradictory statement” because it isn’t one statement.

I have to disagree because as I have shown above when it is taken as a whole with its logical consequences it does involve a contradictory statement.
I am lying now.
So if you are lying when you say you are lying, then you are telling the truth.
So what you have is a contradiction:
I am lying and I am not lying.
It comes down to the fact that you are asserting
I am lying is true AND I am not lying is true.

Taken “as a whole,” it isn’t “a statement,” it is two statements.

The logical consequences aren’t a contradiction because the logical consequences are indeterminate. The logical consequences (truth value) of the first statement is entirely dependent upon the logical consequences (truth value) of the second, which in turn references back to the first. Endless loop without determinable logical consequence (truth value), therefore NO contradiction because NO logical consequences are there to be had.

 

[AlNg]

Taken “as a whole,” it isn’t “a statement,” it is two statements.

I disagree. It may be a compound statement, but it is still a declarative sentence, which qualifies it as a statement.
Here is an example of two statements:
I am lying. (period)
I am not lying. (period)
Here is an example of one statement:
I am lying and I am not lying. (period)
It really doesn’t matter much, because in either case you have a contradiction. And whether you want to repeat this contradiction in an infinite loop or not, it is still a simple contradiction. You are asserting that both p and Not p are true.

 

[HarryStotle]

HarryStotle:

You cannot have a system of logical reasoning without the rule,

Not exactly:
Gödel’s second incompleteness theorem states that in a system which is free of contradictions , this absence of contradictions is neither provable nor refutable. If we would find a contradiction , then we would have refuted the absence of contradictions . Gödel’s theorem states that this is impossible.

That may be precisely why the law of non-contradiction is assumed rather than either provable or refutable.

Why would there be any need to prove or refute a law that is presumed by the very system in use in the first instance?

The need to prove or refute it would simply be an acknowledgement that the system of logic being used is, itself, worthless as a logical system since it permits illogical propositions from the get go.

What good would an illogical system of logic be? A logical system that permits illogical claims would be baseless.