Still Wondering about Contradictions

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catholicray

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Are contradictions possible? Before you answer this, if you haven’t done this before, do the following:

Take a blank card/paper and on one side write: “The statement on the other side of this card is false”
On the other side: “The statement on the other side of this card is true”
Examine it for a minute.

Now I know there is something called the Liar’s Paradox which is similar to this. This particular paradox does not seem to be explained by the same methods to the Liar’s Paradox.

Does anyone know of an explanation to solving this particular paradox? It seems to be evidence of an actual contradiction to me.
 
Here is my favorite contradiction. In Genesis 8:21 YHWH promises that He will never again wipe out the human race. (No mention of a deluge is mentioned here.) However, throughout the OT the prophets predict some great disaster which will destroy humanity.

Any kind if natural disaster, such as an asteroid strike, would be an act of God and, therefore, not possible going by Genesis 8:21.
So how is it possible that Jeremiah 25:32-33 will be fulfilled?
 
I would clearly need to get to the philosophy library to give a full explanation but I would begin most likely by writing those examples off as arising because of the use of language.

I would differentiate that from a contradiction like, a square circle, which is obviously impossible.

Philosophy of language is the one area I didn’t study at uni so I can’t really give a more in-depth explanation than that. Semantic contradictions are possible as a trick of the language. But other contradictions just aren’t something you can find in the world.
 
It is contradictory and therefore not true. It is equivalent to saying:
B is false and B is true at the same time. That is a contradiction and is therefore false.
Side A: The statement on side B is false.
OK so B is false.
Side B: The statement on side A is true.
But B is false so the statement on Side A is not true, but it is false.
Since the statement on side A is false, the statement on side B is true.
So you are asserting that the statement on side B is both true and false at the same time. But we know that this cannot hold, since it is a contradiction.
In a roundabout way, all you are saying is that B is both true and false, and/or that A is both true and false. This is known as a simple contradiction.
It is like if I were to invite you to join me for a cup of coffee, and you agree.
And as we go into the coffee shop I say to you:
I will pay for your coffee and
I will not pay for your coffee.
Well, I can say such, but it does not make sense since it is a contradiction.
catholicray said:
Does anyone know of an explanation to solving this particular paradox?
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I would say it is more of a contradiction, not a paradox.
 
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AlNg said:
It is contradictory and therefore not true.
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Is your position based on the law of non-contradiction?

Is that principle demonstrably true?

I only ask because this particular contradiction seems to exist. It also is not refuted by the explanations given for the liars paradox.
Rhubarb said:
I would differentiate that from a contradiction like, a square circle
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What if they have their existence in different dimensions?
 
The words have multiple meanings, and the contradiction only exists because not everyone meaning of “true” and “false” apply. The language lacks strict mathmatical precision, allowing ambiguous statements to be formed. We rely on context to navigate ambiguity.
 
I think you’d be hard-pressed to describe a dimension where an entity exists that meets the definition of a square and a circle at the same time.

Or as we might say, there’s no possible world where a square circle can exist.
 
Well when I think of this now I think of a square which is possible in 2D with a curve off of two points in the third dimension. In the second dimension it is only a square and in the third we’ve introduced curvature.

It’s one of those situations where, because of how much we are exposed to both dimensions we don’t really consider it.

A pyramid for example is made up of triangles and a square and is a perfectly functional shape.
 
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catholicray said:
Well when I think of this now I think of a square which is possible in 2D with a curve off of two points in the third dimension. In the second dimension it is only a square and in the third we’ve introduced curvature.

It’s one of those situations where, because of how much we are exposed to both dimensions we don’t really consider it.

A pyramid for example is made up of triangles and a square and is a perfectly functional shape.
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Yeah… but this isn’t a square circle and is just equivocating, it’s not what people mean when they say one can’t have a square circle.
 
Wesrock said:
Yeah… but this isn’t a square circle and is just equivocating, it’s not what people mean when they say one can’t have a square circle.
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I understand what they mean. I tend to think of it as a square circle and that my privilege of being able to comprehend the 3rd dimension renders its’ significance somewhat meaningless to me. What would a flat lander think about it though?

There are other ways I imagine a square circle even in the 2nd dimension only. The idea of a square circle that you seem to be talking about is meaningless because you can’t imagine it in the first place. If you can’t imagine it’s features how would you even know if you saw one?
 
catholicray said:
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Wesrock:
Yeah… but this isn’t a square circle and is just equivocating, it’s not what people mean when they say one can’t have a square circle.
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I understand what they mean. I tend to think of it as a square circle and that my privilege of being able to comprehend the 3rd dimension renders its’ significance somewhat meaningless to me. What would a flat lander think about it though?

There are other ways I imagine a square circle even in the 2nd dimension only. The idea of a square circle that you seem to be talking about is meaningless because you can’t imagine it in the first place. If you can’t imagine it’s features how would you even know if you saw one?
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It’s a logical impossibility for one closed shape on a two dimensional plane in euclidean space to have all its points equidistant from the center while also having all of its points along four straight sides of equal length with right angles at where all the corners meet.

This isn’t a matter of thinking with higher dimensions, it’s an impossibility.
 
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I think it’s the way your approaching it. What do you mean by one shape? You can draw a square with a circle inside of it where the edges meet. How is this not one shape? You can actually utilize this as a single shape as well. Consider a pipe with a square end for bolting it down. I don’t know it just seems like you’re defining things in such a way as to make the situation impossible.
 
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catholicray said:
I think it’s the way your approaching it. What do you mean by one shape. You can draw a square with a circle inside of it where the edges meet. How is this not one shape? You can actually utilize this as a single shape as well. Consider a pipe with a square end for bolting it down. I don’t know it just seems like you’re defining things in such a way as to make the situation impossible.
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A square with a circle inside of it… You do realize that this means it doesn’t have all its points equidistant from the center, right? It also means it doesn’t have all its points along four straight sides of equal length with right angles where they’re joined. What you’re proposing is neither a square nor a circle. This is exactly what people mean when they say you can’t have a square circle, or a sphere cube, or what have you. To be one is to exclude being the other. It can’t have both identities at once. It’s supposed to be a simple example of identity laws and contradiction logical laws. When people use this example, what I’m saying is what they implicitly mean.
 
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To add, what you’re proposing in all of your examples is not a square and is not a circle, but something else in which a part is a square and a different part is a circle. The thing as a whole is neither. The parts individually are one or the other, not both at once.
 
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Thank you for sharing this conversation with me by the way. I hope I don’t offend you I just want to enjoy a good conversation about this.

So I get what you’re saying to a degree. My opinion however, is that what is implied is something no one can imagine.

I tend to think there are contradictions that have a truth value which are logically possible. There are other contradictions that have a false value and are impossible to even imagine.

Consider the following:

x= there is truth
y= there is not truth

if x= true then y=false
if y= true then y=x because y=true

thus y=false because y=true and we have another perpetual contradiction.

By the way I’ve seen this used by Catholic apologists.
 
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Wesrock said:
To add, what you’re proposing in all of your examples is not a square and is not a circle
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What would you name my 2 dimensional shape as a whole? Giving it some name other than squarecircle seems more like a human construct rather than evidence that it is not a square circle as a whole.
 
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catholicray said:
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Wesrock:
To add, what you’re proposing in all of your examples is not a square and is not a circle
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What would you name my 2 dimensional shape as a whole? Giving it some name other than squarecircle seems more like a human construct rather than evidence that it is not a square circle as a whole.
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It’s not a matter of what we name it. It’s a fact that that would not be the thing we mean when we say the words “square” or “circle”. Words are only symbols or pointers to concepts…
 
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