Still Wondering about Contradictions

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Wesrock said:
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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I don’t know. So what if I draw a nice square in the second dimension and draw a circle inside of it that is working off the z axis. When you look at it straight on it’s a square with a line down the center. When you look to the side of it you’d see a circle with a line down the center of it. Thus depending on your perspective when you measured it you could measure a square or a circle. That seems to meet the definition but it utilizes more than one dimension to do so.
 
catholicray said:
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Wesrock:
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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I don’t know. So what if I draw a nice square in the second dimension and draw a circle inside of it that is working off the z axis. When you look at it straight on it’s a square with a line down the center. When you look to the side of it you’d see a circle with a line down the center of it. Thus depending on your perspective when you measured it you could measure a square or a circle. That seems to meet the definition but it utilizes more than one dimension to do so.
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Part of it is a square. Part of it is not. The thing as a whole doesn’t fit the concept of a square.
 
If you could see it in a higher dimension wouldn’t you be looking at a square circle?
 
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I don’t know it sounds fishy to me what you’re saying. Wouldn’t a square circle have those component parts by necessity?
 
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Now, the square circle is an ontological logical impossibility. To go back to the example in your first post, we’re dealing with propositions. While there is a contradiction between the two statements, it isn’t this type of ontological impossibility.
 
catholicray said:
I don’t know it sounds fishy to me what you’re saying. Wouldn’t a square circle have those component parts by necessity?
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No. The object meant by “you can’t have a square circle” is both a square (all its points along four straight sides of equal length with right angles between them) and a circle (all its points equidistant from the center). Again, this is about the logical principles of identity and non-contradiction, and it’s just a simple illustration.
 
It’s like saying I want a shape with 2 parts that is made up of one part. I think it can be done the way I shared, where the whole shape is one single shape one part in the third dimension that we are observing from a higher dimension, that is made up of two parts.
 
Would you prefer if, instead of “you can’t have a square circle” people just always instead said “you can’t have an object existing on a two dimensional euclidean surface in which all its points are equidistant from the center and all its points are also along four straight sides of equal length joined at right angles”? Because, really, that’s just a mouthful and a pain to have to explain out every time when the illustration is normally just understood for what it is.
 
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Hmmmmmmm I’m still not sure I agree though. If we were looking at my three dimensional shape on two dimensions it would be a square with a line segment down the center or visa versa. We couldn’t know what shape the line segment represents.

In this case though we know that the line segment contains more information than meets the eye.
 
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undead_rat said:
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?
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Except that Gen 8:21 says: …nor will I ever again destroy every living creature as I have done."

Jer 25:32-33 says “…Those slain by the Lord on that day shall extend from one end of the earth to the other.”

The widespread death in Jeremiah does not equate to the death of every human person nor of “every living creature,” so there is no strict contradiction there.
 
catholicray said:
Hmmmmmmm I’m still not sure I agree though. If we were looking at my three dimensional shape on two dimensions it would be a square with a line segment down the center or visa versa. We couldn’t know what shape the line segment represents.

In this case though we know that the line segment contains more information than meets the eye.
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But when discussing laws of identity and non-contradiction, we’re not interested in cross-sections, we’re interested in exactly what I outlined.
 
I’ve said my piece on square circles. Persons are free to play semantics and talk about something other than what people actually mean when talking about the PoNC, but really has no bearing on the actual question.
 
Your examples are a problem of semantics. Truth is a property of propositions. So when you make propositions about truth, they get wonky. The same thing happens when you make propositions about existence. (in the latter case, because existence is a quantifier, not a predicate)
 
catholicray said:
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AlNg:
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.
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The liar’s paradox isn’t made up of contradictory statements because each of the statements is indeterminate – they cannot be determined to be either true or false precisely because they have no determinable or stable truth value. The referent for each of the statements revises the other statement which refers to it.

So there cannot be a SELF–contradiction because each statement does not refer to itself, but to its unstable referent that keeps switching from true to false through the logic of the referential path. Each proposition functions much like a two-way switch – technically a three way switch – in electrical wiring. One proposition (or switch) controls the other in such a way as to “switch” the truth value of the other proposition making each an unstable truth proposition in itself. Neither is true nor false in a determinable way.

Self-contradictory statements are not unstable in that way – they CANNOT be true because the very ideas they refer to are logically impossible.
 
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Rhubarb said:
Your examples are a problem of semantics. Truth is a property of propositions. So when you make propositions about truth, they get wonky. The same thing happens when you make propositions about existence. (in the latter case, because existence is a quantifier, not a predicate)
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In mathematical logic perhaps “existence” is said to be a quantifier acting on a predicate
Thus, ∃xPx is read as: "There is an object having property P ".

The existence of that particular object is a fact that is not ascertained through the mathematical or logical statement. It’s existence requires an empirical verification or A PROOF.

Existence, in the case of contingent entities is not part of the “concept” P itself, but existence may logically be an aspect of necessary being(s). Aquinas proposed just that to be the case.

There is a great deal of debate over necessarily existent entities. Various forms of the ontological argument actually propose that God as Necessary Being either exists necessarily or logically cannot exist. This would be precisely because a necessarily existing being that only possibly exists would be a self-contradictory proposition. Ergo, God either exists of necessity or cannot possibly exist.

If there is no logical impediment to the existence of God then the proof would stand as a PROOF, i.e., answering the mathematical requirement that IF the existence of a particular object is a fact that is not ascertained through the mathematical or logical statement alone, establishing it’s existence would require an additional empirical verification or A PROOF that a necessary existent must exist as a logical necessity.

In fact, if God’s existence can be demonstrated using an empirical or cosmological argument (empirical verification) and conversely by the ontological argument as logical proof, then what we have is the same kind of symmetrical demonstration as Newton’s inverse-square force of attraction that conforms to the observed orbit of any of the planets around the Sun as a conic section and the converse that if its orbit is a conic section the planet must be attracted to the central source by an inverse square
law (Cf. David Berlinski, Truth Really Matters)
 
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Rhubarb said:
So when you make propositions about truth, they get wonky.
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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?
 
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